III-nitride photonic cavities

Abstract Owing to their wide direct bandgap tunability, III-nitride (III-N) compound semiconductors have been proven instrumental in the development of blue light-emitting diodes that led to the so-called solid-state lighting revolution and blue laser diodes that are used for optical data storage. Beyond such conventional optoelectronic devices, in this review, we explore the progress made in the past 15 years with this low refractive index material family for the realization of microdisks as well as 2D and 1D photonic crystal (PhC) membrane cavities. Critical aspects related to their design and fabrication are first highlighted. Then, the optical properties of passive PhC structures designed for near-infrared such as their quality factor and their mode volume are addressed. Additional challenges dealing with fabrication pertaining to structures designed for shorter wavelengths, namely the visible to ultraviolet spectral range, are also critically reviewed and analyzed. Various applications ranging from second and third harmonic generation to microlasers and nanolasers are then discussed. Finally, forthcoming challenges and novel fields of application of III-N photonic cavities are commented.


Introduction
In the past 20 years, III-nitride (III-N) compound semiconductors have become part of our daily life, as they are at the heart of the solid-state lighting revolution. Indeed, they lie behind the development of blue to green light-emitting diodes and laser diodes that are ubiquitous devices nowadays [1][2][3]. Beyond such conventional optoelectronic devices, the III-N semiconductor family has already proven to be rather versatile and unique, as it possesses numerous assets for expanding areas of nanophotonics that can otherwise hardly be addressed by a single material family. First, thanks to their wide bandgap (up to ~6.0 eV at 300 K for the strain-free AlN compound [4]), the accessible spectral window for optical resonators made from III-Ns can cover regions going all the way from the ultraviolet (UV)-C region (~210 nm for the shortest accessible wavelength) down to the nearinfrared (NIR) spectral range, including the optical communication wavelength bands, namely from the O-band to the L-band, which cover the 1260-1625 nm range [5]. Being compound semiconductors, these low refractive index dielectric media can be grown using well-established epitaxy techniques such as metalorganic vapor phase epitaxy and molecular beam epitaxy (MBE) to fabricate passive resonators or active ones embedding precisely positioned light-emitting and/or absorbing quantum heterostructures, most commonly quantum wells (QWs) or quantum dots (QDs), whose spectral features can be tuned over a broad range via both alloying and quantum engineering. Sputtering has also proven to be ideally suited for NIR applications relying on lowloss AlN waveguides (WGs) and microring resonators [6] that can exhibit both second-and third-order optical nonlinearities for frequency conversion and frequency comb generation. A second important asset of III-Ns for nanophotonic applications relies on their large oscillator strength and exciton binding energy, which fosters strong light-matter interaction phenomena. This is best exemplified by the report of room temperature polariton lasing in both bulk and multiple QW planar microcavities more than a decade ago [7,8]. The large exciton binding energy of III-Ns has also been recently exploited to demonstrate single-photon emission (SPE) at room temperature from site-controlled GaN/Al(Ga)N QDs embedded in a nanowire [9]. Such features illustrate the potential of III-Ns to bring cavity quantum electrodynamics (CQED) up to ambient temperature, a flourishing research field in which specially designed cavities providing a large quality factor (Q) to effective mode volume (V m ) ratio host precisely positioned SPEs that can potentially be tuned independently to harness quantum optical features at the single photon-single quantum emitter level. In this respect, the recent report of triggered SPE in the telecom range at 300 K from point defects in GaN [10] clearly opens up new opportunities for CQED in this technologically important spectral window. Combined with n-and p-type doping capabilities and even the recent development of tunnel junctions, which hence enable efficient lateral current spreading [11], small footprint electrically driven III-N nanophotonic resonators with embedded single-photon sources for ambient temperature CQED applications truly appear to be within reach. In addition to the above-mentioned aspects, III-N nanocavities recently revealed their potential for investigating coherent light emitters operating at the few-photon level [12][13][14] with foreseeable applications for photonic integrated circuits (PICs) or lab-on-a-chip light sources. Owing to their biocompatibility and their reduced invasiveness, III-N nanoresonators could also offer promising perspectives in the field of optogenetics where cellular activity can be manipulated on-demand by exploiting the sensitivity of engineered proteins to blue and green photons [15].
This wide range of topics demonstrates that III-Ns can serve as a suitable toolbox to propel nanophotonics toward novel frontiers. In this respect, in this review, we will focus on small footprint high m Q V ratio III-N photonic structures of the air-clad type that have experienced a fast growing development in the past 15 years, i.e. since the first reports of microdisks [16] and photonic crystal (PhC) membrane cavities [17] by Evelyn L. Hu et al. For the sake of consistency in the reported properties, we will on purpose restrict ourselves to two geometries, namely mushroom-type microdisk cavities with a diameter of <10 μm as well as 2D and 1D PhC cavities. Those cavities are arguably the most widely studied III-N optical resonators if one excludes planar microcavities and microring resonators that have been the subject of a recent review by Jung and Tang [6]. This review article will articulate around three main sections. First, we will provide a description of the main routes commonly adopted to fabricate III-N microresonators and nanoresonators. This will be followed by a second more substantial section that will be the core of this review and that will focus on the optical properties of the fabricated resonators. Thus, a first subsection will address their linear optical properties among which the physics governing the spectral dependence of Q, which is best illustrated in Figure 1. A second subsection will summarize the recent achievements about optical nonlinearities reported in NIR resonators with an emphasis on the strategies adopted to tailor second-and third-order nonlinear processes in this noncentrosymmetric wide bandgap semiconductor family offering reduced twophoton absorption. A final subsection will review lasing features reported in air-clad III-N microdisks and PhC nanocavities. A third main section will address some forthcoming challenges facing those III-N photonic resonators. It will include pending issues about high spontaneous emission coupling factor (high-β) nanolasers such as light extraction and electrical injection but also the requirements to observe two landmarks of CQED, namely the Purcell effect -which remained elusive thus far in III-N resonators relying on a pure dielectric approach despite numerous claims, and the strong coupling regime at the single photon-single quantum emitter level. Finally, a brief summary about this field of research and an outlook will be given.

Design and fabrication of III-N microresonators and nanoresonators
Before any processing step leading to suspended III-N membranes, care should be taken regarding the WG design whatever the targeted final geometry, namely microdisks or PhCs. Indeed, one of the specificities of III-N epilayers vs. their silicon (Si) or GaAs/InP counterparts originates from the heteroepitaxial nature of the waveguiding layers, as to date there is no existing report of such microphotonic and nanophotonic resonators that were grown on polar freestanding GaN or bulk AlN substrates. Hence, the vast majority of the samples are grown on either c-plane sapphire or Si (111) substrates, which Reprinted with permission from Ref. [18]. Copyright (2017) American Physical Society.
is in line with their use in III-N optoelectronics. Sample growth on other substrates has also been reported, but this is often a choice specific to some research groups.
In particular, this is the case for 6H-SiC (0001) substrates (see, e.g. Ref. [19] but also m-plane GaN [20]) or Si (001) substrates used for the growth of cubic (zinc-blende) epilayers [21], with the latter two containing nonpolar quantum heterostructures. The heteroepitaxial growth of III-N epilayers is obviously known to affect the material quality, which often translates into a high threading dislocation density (TDD), typically ≥10 8 cm −2 . This can not only impair the internal quantum efficiency (IQE) of the embedded heterostructures but also increase the top and bottom WG interface roughness, hence potentially altering the measured Q values of the resonators of interest due to increased scattering losses. Let us note in this respect that thin III-N WG epilayers grown on Si are expected to be much more impacted than those grown on sapphire, owing to their tensile strain nature and the much larger TDD (≥10 10 cm −2 ). A symmetric epilayer along the growth axis would be ideally suited to vertically confine optical modes in the central part of the WG. Although this is clearly not an issue for WG epilayers grown on c-plane sapphire substrates, the same statement does not hold true for GaN WGs grown on Si (111) substrates. Indeed, in this latter case, it is known that the growth of a thin AlN buffer layer, a few tens of nanometer thick, is required to prevent any destructive melt-back etching of the Si surface due to the high reactivity between Ga and Si [22]. III-N WGs can essentially be categorized in two families depending on the targeted studies, namely structures with or without embedded quantum heterostructures. In the absence of any such internal light source, III-N resonators are usually optimized for NIR operation, and in this latter case, the WG thickness is much larger than that of their UV to visible counterparts. For long-wavelength (NIR) applications, this is obviously not problematic by any means to deal with reasonably thick WGs for which the mode order (m) is kept to lowest order, i.e. m = 0. However, at shorter wavelengths, preserving lowest-order operation is not necessarily given for granted, especially in the particular case of GaN WGs grown on Si (111) substrates. This can be understood by the trade-off that is required to simultaneously ensure that (i) only the two most fundamental transverse electric (TE)/transverse magnetic (TM) WG modes are present, (ii) the WG will be thick enough to have a surface roughness that is not impacted by pits, and (iii) the embedded active medium will not be plagued by the AlN/GaN interface, whose too close proximity is known to severely alter the IQE due to the presence of nonradiative defects. Knowing that m = 0 operation requires a WG thickness on the order of eff , 2n λ where λ is the wavelength in surrounding air/vacuum and n eff is the effective refractive index of the WG, a suspended GaN WG intended for the blue spectral range (λ ≈ 450 nm) should have a thickness of <93 nm using n (λ = 450 nm) ~2.44 in place of n eff [23]. We will see that such GaN WGs grown on Si (111) substrates require an overall epilayer thickness on the order of 300 nm, including the AlN buffer layer. It therefore leads to the presence of the four most fundamental TE/TM WG modes, i.e. those having m = 0 and 1, before any epilayer structuring. Following those preliminary considerations, we will now address some design and fabrication/processing aspects specific to each geometry. We shall see that, despite the obvious difference in the final shape between the two types of air-clad III-N photonic resonators, they both share several common processing steps. Let us also note that the progress made in terms of processing of those microphotonic and nanophotonic structures culminates with the recent demonstrations of PICs on Si (111) substrates including either microdisks or PhC cavities coupled to a bus WG intended for either NIR [24] or visible [25] operation ( Figure 2).

Microdisks
The mushroom-type microdisk resonator geometry is far simpler than its PhC counterpart. It was first reported at Bell Labs by McCall et al. using the InP/InGaAsP material system [26]. Since then, it has been implemented with many other dielectric platforms. As far as air-clad resonators are concerned, the absence of any suitable wet etching route for Ga-polar III-N epilayers precludes the use of soft processing approaches that have been proven successful with other inorganic semiconductor families [27]. Therefore, after sample growth, the most common method adopted to obtain small footprint III-N microdisks, i.e. small mode volume resonators supporting high-Q whispering gallery modes (WGMs) that are tightly confined within the dielectric slab due to total internal reflection, usually consists of first depositing an SiO 2 layer by plasmaenhanced chemical vapor deposition (PECVD). This layer will subsequently act as a hard mask during the whole process and protect the (Al)GaN surface from any damage that could occur during etching steps and ensure a proper transfer of the resonator pattern. Let us note that this SiO 2 layer is generally removed at the very end of the fabrication process using a buffered hydrofluoric acid solution. It is followed by spin coating of a resist, in recent years mostly dedicated to electron beam lithography (EBL) for improved spatial resolution. It is often baked to minimize any transfer of undesired defects such as sidewall roughness and striation that could incur scattering losses [28]. The most popular choice usually goes for the ZEP520A-positive resist [29], whereas the use of the UV3-positive resist remains more confidential [30]. As will be explained in detail hereafter, another recent alternative choice relies on the use of the negative tone hydrogen silsesquioxane (HSQ) EBL resist. The latter can directly be used as a hard mask [18,31], hence allowing for a single-step pattern transfer that leads to improved fabrication and thus higher Q values and higher device yield over the conventional two-step pattern transfer. After resist development, the pattern is transferred to the various layers using either reactive ion etching (RIE) or inductively coupled plasma (ICP)-RIE.
The subsequent membrane release is then determined by the nature of the host substrate. The processing of sapphire -one of the most chemically inert and hardest available oxides -being ruled out, air-clad III-N resonators fabricated from epilayers grown on this substrate are achieved by lateral etching of a sacrificial underlayer (UL) to release the membrane. The most widely used approach consists of the selective etching of an InGaN/GaN superlattice (SL) using a photoelectrochemical (PEC) method, whereby a suitable light source, a xenon lamp whose short wavelength components (≤360 nm) are filtered out, generates most of the carriers in the sacrificial layer. It was first implemented for the realization of III-N microdisks by Haberer et al. [16]. Another successful approach for the realization of mushroom-type GaN microdisks on sapphire was based on the anodic oxidation of an InAlN UL in a basic NTA:KOH solution, which was subsequently dissolved in a heated nitric acid solution [32]. However, the downside when etching those ULs is the potential formation of defects such as whiskers in PEC etched sacrificial InGaN SL layers [33] or inverted pyramids through the nonuniform oxidation of the InAlN layer [32] that can impair the Q values of WGMs.
For samples grown on Si (111) substrates, III-N epilayers are left untouched and the selective etching of the host substrate is used instead. Although RIE has been used in some occasions to release the epilayer membrane [34], the most common approach relies on chemically selective isotropic etching of Si in a pulsed XeF 2 vapor [35]. This is indeed a very gentle process that leaves III-N epilayers, especially the bottom N-polar face, nearly untouched [36]. One great advantage of air-clad III-N resonators fabricated on Si over sapphire stems from the possibility to achieve large air gaps, in excess of a few micrometers [34], together with a large disk diameter to post diameter ratio, hence enabling an efficient decoupling of the WGMs from the substrate. As an illustration, the scanning electron microscopy (SEM) image of a 4.0 μm GaN microdisk fabricated on Si with a reduced post diameter (~1.2 μm) using the above-mentioned single-step pattern transfer is shown in Figure 3. Such large air gaps also open access to the NIR spectral range, which remains presently unaccessible to epilayers grown on c-plane sapphire, and makes the realization of PICs that could be integrated to the Si photonic platform a tangible perspective. In this respect, regarding III-N microdisks that are part of PICs, the optical coupling of those resonators to the circuits is best ensured via side coupling to a suspended bus WG [25,[38][39][40]. In this latter case, the main challenge to overcome in terms of fabrication deals with the fine tuning of the distance between the microdisk and the WG, which will depend on the targeted applications and the desired figures of merit. Indeed, in this configuration, optical characterization is performed through transmission measurements giving access to the loaded Q values (Q load ) that will not only depend on the intrinsic quality factor Q int of the disks but also on the coupling factor Q c that depicts the effective overlap between the bus WG mode and the WGMs and Q split that originates from the eventual splitting between clockwise (cw) and counterclockwise (ccw) propagating modes whose degeneracy is lifted due to surface imperfections [28,41]. Beyond the critical coupling regime, Q load is seen to increase with increasing gap distance, d gap , between the bus WG and the microdisk due to the exponential increase of Q c . It is done at the expense of the transmission, which corresponds to the undercoupled regime [38]. Supplementary fabrication challenges occur when such a side-coupling scheme is implemented at short wavelengths due to the simultaneous need for (i) sub-100 nm d gap values to reach the critical coupling regime, (ii) etching of the upper part of the bus WG to avoid reabsorption phenomena occurring in the embedded active medium (cf. Figure 2), and (iii) the implementation of a bent bus WG to ensure optimum coupling between the resonator and the WG via an increase of the interaction length that also requires proper tuning of the WG width and the disk radius (R) [25].
Let us briefly note that, beyond the above-mentioned circular microdisk fabrication schemes, more exotic approaches relying on selective area growth on m-plane GaN substrates [42] and lateral overgrowth on ZnO nanowalls grown on patterned graphene films [43] of hexagonal microdisks supporting both WGMs and quasi-WGMs have also been reported.
Finally, the readers more specifically interested in fabrication-related issues pertaining to III-N microdisks shall find more detailed explanations about this topic in two recent review articles: one by Zhang et al. [44] that covers all the disk geometries considered to date and a second one by Ren et al. [45] that focuses on PEC etched microdisk resonators and the role of defects such as unetched whiskers.

1D and 2D PhC membrane cavities
At first sight, the different processing steps described for the fabrication of III-N microdisks can be directly transposed to PhC membrane nanocavities. Historically, the first successful realization of such a structure, a pointdefect L7-type GaN PhC slab nanocavity ( Figure 4) with resonance modes close to 480 nm, was reported by the group of Evelyn L. Hu within the year after their report of mushroom-type GaN microdisks [17]. However, the fabrication task of small footprint PhC nanocavities poses extra challenges owing to the reduced feature size of the constitutive elements of the triangular PhC lattice, namely the lattice constant a and the hole radius r. Indeed, in addition to the introduction of openings near the PhC pattern to ensure proper etching of either the sacrificial layer or the substrate, the etching conditions with the ICP-RIE have to be properly optimized to achieve air holes with smooth and vertical sidewalls in epilayers characterized by a high aspect ratio between the epilayer thickness and the hole diameter (height/width up to ~5). In particular, the need to have sub-100 nm diameter holes in the near-UV-visible range [18] leads to slower etch rates stemming from aspect ratio etching phenomena, namely a slowdown of the transport of reactive ions to the etched surface and neutral byproducts away from the etched surface that is hindered by gas-phase collisions, surface scattering, and surface charging [46]. In practice, the increase in the etch time to obtain a full etching of the holes through the III-N epilayers can lead to an overetching of the external dimensions, in particular for structures grown on Si (111) substrates, and requires the use of a thicker resist/hard mask [18]. This explains why early demonstrations of III-N PhC slab nanocavities were accompanied with a strong deviation of the sidewalls from the vertical and Q values of <1000 [17].
Let us note that, compared to III-N microdisks, a wider variety of fabrication approaches have been reported for III-N PhC slabs. Thus, AlN epilayer structures grown on 6H-SiC (0001) substrates that benefit from a lower TDD than epilayers grown on both c-plane sapphire and Si substrates have been considered, but early attempts to release the membranes by PEC etching led to bent slabs and a degradation of the N-polar bottom AlN slab interface [19], hence explaining why it was later chosen to switch to a layer transfer technique to Si substrates using HSQ as a bonding layer and selective back-etching of the SiC substrate [47]. Such structures are often characterized by hexagonal air holes resulting from crystallographic orientationdependent chemical reactions occurring during the PEC and ICP-RIE steps despite the use of circular hole patterns [19]. At one occasion, a bottom-up approach relying on the pre-patterning by EBL of an Si (111) substrate followed by conformal MBE growth of the III-N epilayer replicating the desired PhC pattern was also reported [48]. Thanks to their more resilient nature against structural and nonradiative defects, passive WG structures intended for NIR operation can be synthesized using low-cost nonepitaxial techniques such as sputtering. Thus, Pernice et al. have fabricated low footprint 1D AlN PhC nanobeam cavities, with Q values up to 146,000, using sputtered-deposited AlN-on-insulator layers with a final sidewall residual surface roughness of <4 nm after wet etching of the underlying buried SiO layer with a buffered oxide etchant [49]. Such AlN nanobeams, whose cavity mode is centered in the C-band, were part of a PIC and could therefore be further characterized by means of a bus WG whose coupling gap was varied in the 200-700 nm range, hence allowing to switch from the overcoupled to the undercoupled regime. Another promising approach for the realization of c-axis-oriented membranes has been reported by Arita et al. The latter relies on the growth of an AlGaN WG layer lying on top of a sacrificial GaN-on-sapphire layer [50]. Test L7 AlGaN PhC slab nanocavities with an embedded InGaN QW medium were successfully obtained after the selective thermal decomposition of the GaN UL at ~1000°C under NH 3 /H 2 ambient conditions that let Al x Ga 1 − x N epilayers nearly untouched compared to GaN for x ≥ 0.1 ( Figure 5). Finally, the fabrication of 1D and 2D PhC nanocavities from nonpolar zinc-blende AlN epilayers grown on 3C-SiC (001) pseudosubstrates has also been reported recently [51,52].
Beyond the above-mentioned aspects, it is worth recalling that, for such defect-type 2D dielectric PhC slab cavities, which exhibit the smallest V m [53,54] among 2D dielectric slab nanophotonic cavity structures -with the lowest value corresponding to the H0 cavity design [55], it was first empirically noticed by Akahane et al. [56] that an appropriate shift of air holes nearby the defect cavity leads to a gentle electric field confinement that is accompanied by a dramatic increase in the measured Q values. It was later shown that, by taking advantage of increasing computing capabilities, an automated optimization scheme of PhC slab point-defect cavities based on a genetic algorithm accounting for both bulk absorption and fabrication disorder realizations enabled an exhaustive exploration of the parameter space to find a global maximum of the Q and/or m Q V value for a given material-cavity design combination [57]. Such an approach relies on the use of a small set of variational parameters, most often the spatial shift of a few holes next to the defect, and a Gaussian disorder model with zero mean and standard deviation σ. This type of approach was first successfully tested on small footprint Si (001) PhC membrane nanocavities exhibiting extremely high m Q V values [58,59], with an experimental Q value (Q exp ) close to 2 × 10 6 being reported in an L3-type cavity [58] and low threshold power optical bistability in a H0 cavity [59], whose cavity mode wavelength was centered in the C-band and L-band, respectively. To verify the suitability of such an automated process based on a genetic algorithm in the framework of III-Ns, GaN PhC slab nanocavities of the L3-type design were computationally optimized and fabricated using lithographic tuning. More precisely, 20 groups ( g i = 1−20 ) of cavities were processed, each one of them differing by a 1 nm step in the nominal hole radius, to account for uncertainty in the etching process [60]. Let us point out that with III-Ns, two sets of variational parameters were necessary for the global design optimization instead of only one in the case of Si PhC nanocavities due to the significantly lower refractive index contrast between this dielectric system and surrounding air. Thus, in addition to the outward shift of the three holes seating next to the defect cavity in the Γ-K direction of the triangular lattice, their radius was also part of the optimization scheme, which led to their shrinkage compared to the remaining holes of the lattice. Beyond the very high average unloaded Q value of 16,900 measured by means of the resonant light scattering technique in these modified L3 nanocavities at the resonant wavelength λ ~ 1.3 μm and a maximum experimental Q value of 22,500, the important outcomes of this approach can essentially be summarized as follows. First, the quantitative agreement between values predicted by first principles simulations, where 100 disorder realizations were simulated for each group g i , and the experimental statistics for both the Q values and the resonant wavelength indicates the effectiveness and the consistency of this optimization method to improve PhC slab nanocavity designs for a given material family. Second, the fact that each group g i is characterized by experimental unloaded Q values in excess of 10,000 highlights the technological maturity gained by small footprint III-N PhC slab nanocavities during the past few years. Such a statement is not only valid for NIR nanocavities but can also be transposed to shorter wavelengths. Indeed, the impact of fabrication disorder was successfully accounted for in the framework of 1D III-N PhC nanobeam cavities designed for the blue spectral range where the use of a single-step pattern transfer process allowed designing structures for which the standard deviation in the hole positioning and the hole diameter was reduced to 1 nm ( Figure 6), i.e. a σ value that matches the technical capabilities of the employed EBL tool [18]. Furthermore, such a progress in the fabrication was accompanied by a high yield of 97%, which was derived from the optical characterization of hundreds of nanocavity structures. Let us note that the quantitative estimate of the various parameters that govern the experimental Q values of III-N microresonators and nanoresonators is precisely the subject of the first part of the next section of this review.

Linear optical properties: a preliminary testbed for small footprint resonators
At first sight, one could consider that exploring the linear optical properties of III-N microresonators and nanoresonators as a function of their operating wavelength is a pure tale of photonic disorder. Indeed, for resonators whose Q exp values stand far from the theoretical ones (Q th ), the observed decrease in the Q exp values with decreasing wavelength such as that reported in Figure 1 for III-N PhC slab nanocavities, which span a broad spectral range, is commonly ascribed to the increasing weight of Rayleigh scattering originating from fabrication-induced surface roughness. Within this framework, scattering losses are expected to lead to an overall decrease in Q exp that scales as Q exp ∝ λ 3 [28,61], which is qualitatively verified by III-N PhC slab nanoresonators. However, we shall see that the precise determination of Q exp for a given resonator design by theoretical means is more complex than it may seem. Before unveiling the dominant contributions governing Q exp , let us point out that a proper, i.e. unambiguous, cavity mode identification should be carried out first. Obviously, this task is very much different depending whether we consider microdisks or PhC slab nanocavities. In the former case, we deal with a multimode device where, in the best-case scenario, the free spectral range (FSR) between two successive WGMs of the same radial number is simply given by 2 eff 2 n R λ π in the limit of large azimuthal mode numbers. With III-N microdisks, such a situation can be met provided the slab WG thickness only sustains the most fundamental TE/TM vertical modes, i.e. m = 0, and the post + disk diameters limit the number of radial mode families to <3. Due to the WG geometry, TE and TM modes will exhibit a dominant in-plane far-field radiation mode pattern with a stronger coupling to the far-field for TE modes [28,62]. In addition, we already mentioned that surface imperfections such as surface roughness usually lead to a lift of the degeneracy between cw and ccw propagating modes [28,41]. For short-wavelength operating III-N microdisk resonators with an embedded active medium, it is worth mentioning that experimentally a uniform distribution of WGMs across the entire spontaneous emission spectrum was only observed when using QDs rather than QWs [62]. This type of feature was originally ascribed to light reabsorption occurring at higher energy by InGaN/ GaN QW states. This is a direct manifestation of the Stokes shift at play in these quantum heterostructures [29,32]. A successful illustration of WGM identification was reported by Mexis et al. [62] using edge microphotoluminescence (μPL) collection from 2-μm-diameter thin c-plane AlN microdisk slabs with embedded GaN QDs emitting in the blue spectral range (Figure 7), i.e. a region where the oscillator strength of those big dots, as per III-N standards, is strongly reduced by the large built-in electric field that separates electron and hole wave functions. Hence, it makes this platform practically immune to the above-mentioned reabsorption phenomenon [32,63]. Q exp values up to ~7300 were reported in such microdisk samples [62]. However, as can be understood, such an analysis cannot necessarily be easily performed in samples with slightly different parameters. Thus, it was verified with a set of nominally identical 3-μm-diameter GaN microdisks with a single InGaN/GaN QW medium characterized in the backscattering μPL geometry that exhibit Q exp values of several thousands [37]. In this latter case, the reason why no conclusive correspondence could be reached between 3D finite-difference time-domain (3D-FDTD) calculations and collected μPL spectra is due to the large number of parameters impacting the simulations, namely the large WG thickness multiple vertical nodes and the likely resulting mixture of optical modes without any clear polarization dependence in the backscattered emission spectra, the extreme sensitivity of simulated spectra to the Si post diameter whose large complex refractive index in the blue spectral range leads to strong perturbations of higher order radial modes and lower order azimuthal modes due to their large electric field overlap with the post [37]. Furthermore, the release of the tensile strain at the free microdisk edges leading to a slight upward WG bowing (≤20 nm), as deduced from confocal micro-Raman spectroscopy and finite element simulations, and the Si post asymmetry resulting from the fabrication process were also seen to alter the simulated spectra [64]. Hence, in the vast majority of cases, such a complex combination renders any quantitative identification of WGMs in III-N microdisks rather elusive. Conversely, despite their much larger design complexity compared to their microdisk counterparts, small footprint PhC membrane nanocavities sustain a much smaller number of cavity modes whose identification does not suffer from any such ambiguity. This is well documented in both the NIR and the visible spectral range (see, e.g. Refs. [34,65] and Ref. [18], respectively). In particular, a very good agreement was reported between 3D-FDTD simulations of the optical modes and the vectorial mapping of the local density of states in GaN-based modified L3 PhC nanocavities through Fano imaging [66] performed using a scanning near-field optical microscope (SNOM), which offers deep subwavelength spatial resolution 90 nm 15 Based on a previous analysis, to have a fully quantitative determination of Q exp in PhC slab nanocavities, the latter has to be be decomposed by considering up to six contributions depending on whether we are dealing with a passive or an active resonator. Thus, we get where Q th is related to pure radiation losses such as predicted by 3D-FDTD simulations for an otherwise perfect lossless structure, Q bk corresponds to bulk absorption losses, Q gm corresponds to the optical losses originating from the eventual presence of a gain medium (QWs or QDs), Q fab corresponds to the optical losses induced by fabrication disorder, Q ss corresponds to the optical losses due to surface scattering, and finally Q sa accounts for surface absorption-related optical losses.
As far as the determination of Q th is concerned, the guided-mode expansion (GME) method [67], which was benchmarked against 3D-FDTD simulations, used to be the technique of choice to determine the theoretical Q of a particular design thanks to its fast computational time. GME was combined to the genetic algorithm of the Matlab Global Optimization Toolbox to derive the global maximum when considering the set of relevant variational parameters for a given material platform [57,58]. However, later reports  mostly relied directly on 3D-FDTD simulations thanks to the large increase in computational capabilities [18,31,60]. In any case, the computed Q th values for III-N PhC membrane nanocavities always outperform experimental values [12,13,18,47,[68][69][70][71] even in the case of high-Q NIR 1D-PhC AlN nanobeam cavities ( Figure 9) [49], so that its weight is often discarded when evaluating Q exp . Hence, one of the next contributors to be considered as a major source of loss is bulk absorption loss, whose expression is given by the common relationship eff bk 2 n Q π λα = [72], where α corresponds to the residual absorption coefficient in the WG. Let us note that, in the previous expression, we can explicitly discard the optical losses induced by the gain medium, Q gm , if present. Indeed, the contribution of the latter can be canceled by pumping the PhC membrane or the microdisk near transparency. From there, the internal modal loss occurring in the III-N WG epilayer of interest can be estimated from net modal gain measurements performed with the variable stripe length method before any processing step [18,73].
As mentioned above, it has been shown that Q fab can be reliably estimated by relying on a genetic algorithm accounting for fabrication disorder by considering a Gaussian disorder model whose mean and standard deviation are derived from experimental observations [18,[57][58][59][60]. A thorough quantitative statistical analysis of the impact of fabrication disorder pertaining to shortwavelength III-N PhC nanocavities can be found in the work of Rousseau et al. [18]. At this stage, we can point out that Q exp values have been successfully accounted for at NIR wavelengths when dealing with a statistical set of lithographically tuned small footprint GaN PhC slab nanocavities on the sole basis of absorption losses and fabrication disorder (Figure 10), i.e. 1 where a σ value of 5 nm was considered for modeling disorder due to the use of a two-step pattern transfer process, the contribution of Q th being indeed negligible [60]. In this latter case, quantitative agreement between simulations and experimental results was obtained for a Q bk value of 40,000 corresponding to a residual absorption coefficient of 2.8 cm −1 at λ ~ 1.31 μm using n eff = 2.33. It is fully consistent with the value of 1.8 cm −1 at λ = 1575 nm deduced from power-dependent cavity in-plane transmission measurements done on width-modulated GaN WG cavities by Roland et al. [69]. The potential impact of surface scattering, i.e. losses other than those introduced by fabrication disorder, and that of surface absorption at NIR wavelengths in small footprint III-N PhC nanocavities remains to be shown. We can, however, emphasize that, for suspended III-N PICs and long 1D PhC WGs, scattering losses due to the presence of tethers are a well-established experimental fact that requires an aperiodic positioning of the latter to minimize Bragg resonances and hence transmission losses [24,69,74,75].
One could reasonably argue that probing the signature of both Q ss and Q sa in III-N microresonators and nanoresonators appears as devoid of any sense based on the usual assumptions regarding fabrication-related issues with this material family (see, e.g. Ref. [45]). However, the recent use of a single-step pattern transfer process leading to an EBL resolution-limited σ value of 1 nm, which has only been reported at visible wavelengths with 1D GaN PhC nanobeam cavities thus far [18,37], enabled a sample fabrication quality with Q exp values requiring the determination of the respective weight of these two quantities. This feature was restricted up until now to Si-and GaAs-based microdisks [28,76] and Si-based PhC membrane nanocavities [77]. Thus, Q ss values can be precisely estimated by first extracting the top and bottom surface roughness and waviness of membranes from multiscale atomic force microscopy (AFM) measurements [37]. Such mappings can then serve as inputs to generate the 2D autocorrelation function of height values that leads to the power spectral density function of surface roughness in k-space via the Wiener-Khinchin theorem [78]. The next step consists of generating algorithmically rough and wavy surfaces [79] that serve as input parameters for electromagnetic computations that rely on the volume current method [80], from which ss is deduced [28,81], where U is the amount of energy stored in the resonator and P ss is the power due to surface scattering radiated through a halfsphere enclosing the PhC that is computed along the lines given in Ref. [81]. It appears that the scattering losses due to the surface waviness measured on GaN membranes representative of fabricated 1D GaN PhC nanobeam cavities lead to Q ss values one to two orders of magnitude larger than those experimentally measured ( Figure 11) [18,64]. It is explained by the much smaller overlap of the simulated electric field intensities with the top and bottom surfaces compared to the overlap with the vertical sidewalls whose impact is partially accounted for when computing Q fab [64]. Achieving a precise, and hence quantitative, estimate of the vertical sidewall roughness, in particular inside etched holes, is an experimental challenge in itself. Nonetheless, SEM measurements provide an upper bound on the sidewall root mean square (rms) roughness to a value of ~2 nm, whose impact leads to computed Q ss values for this sole contribution on the order of Q th . It explains why its contribution can be safely neglected. Based on our analysis of Q exp constituents, it appears that surface absorption should account for a significant fraction of the observed losses in the blue spectral range in state-of-the-art GaN PhC membrane nanocavities. Considering the high surface-to-volume ratio of these resonators and the fact that III-Ns exhibit deep, localized surface states within the bulk material bandgap, such a statement is not at odds with the reported observations. More precisely, it is well-known that, in n-and nonintentionally doped (nid) GaN epilayers, the Fermi level is pinned by a high density of intrinsic, unoccupied surface states below the conduction band minimum [82,83]. It results in the formation of a space charge region and upward band bending at the GaN surface in thermal equilibrium. As far as optically active surface states of the most relevant planes are concerned, namely the +cand m-plane GaN surfaces, unoccupied states exist in the range of 2.4-2.9 eV above the valence band maximum [84][85][86]. Thus, Figure 11: Quality factor limited by scattering losses (Q ss ) due to a 4.9 nm rms surface waviness computed by the volume current method for the nanobeam geometry from Ref. [18]. Here, 131 realizations of surface waviness were simulated to construct the histograms of the fundamental longitudinally symmetric (blue) and first-order longitudinally antisymmetric (red) cavity modes supported by the nanobeams [64]. preliminary measurements performed under continuous wave optical pumping at 351 nm in ambient atmosphere on 1D GaN PhC nanobeam cavities revealed an irreversible deposition occurring on the sample surface, whereas no such deposition was observed when similar experiment was done under vacuum [18]. To gain further insights into the potentially harmful role of optically active surface states on Q exp via Q sa , photoinduced gas desorption experiments were carried out in a controlled atmosphere by monitoring the time-dependent evolution of μPL spectra of microdisks at room temperature ( Figure 12A) [37], this latter type of structure having the advantage to exhibit a high number of optical modes. In particular, it was noticed that oxygen desorption induces a strong increase of optical attenuation by m-plane surface state absorption, knowing that the m-plane corresponds to the most critical orientation for the cavity modes supported by the III-N microresonators and nanoresonators under review. In a nutshell, upon oxygen desorption triggered by the photogenerated holes, the Fermi level on the surface gets unpinned, which modifies the surface charge and the width of the space charge region. WGMs redshift and broaden upon UV-induced photodesorption at 300 K with a rate that depends on the UV pump power. When introducing oxygen in the chamber, a near-complete recovery of the spectra is observed showing the reversibility of this process. All those WGM changes (spectral shift and broadening) that strongly rely on the vacuum pressure can be translated into effective changes in the refractive index [37,77] and likely into changes in the surface absorption rate coefficient [28]. In GaN microdisks, changes in the absorption coefficient Δα up to 100 cm −1 , which are limited by the InGaN/GaN QW μPL background emission and which correspond to an upper ΔQ sa value of ~3400 at 450 nm, could be measured [37]. Importantly enough, no qualitative change could be observed in the WGM redshift and broadening upon oxygen desorption between n + -doped and nid GaN microdisk samples [37]. Finally, let us also note that the possible impact of sample heating could be ruled out through a study combining confocal micro-Raman spectroscopy measurements of the peak shift of the GaN A 1 (LO) Raman mode as a function of laser power density and finite element modeling of heat transport in a GaN microdisk. Indeed, an elevation of 30°C at most above room temperature was predicted at the power density used for triggering UV photodesorption of oxygen [37]. It is well below the temperature where either oxygen desorption from GaN surfaces is expected to occur (950°C) [87] or water vapor may be converted to an oxide-like surface layer (200°C) [88].
The key role played by surface states and related surface absorption on the optical properties of III-N microresonators and nanoresonators obviously calls for remedies. Hence, preliminary surface passivation solutions were investigated through both surface treatments and thin-film coatings. Regarding surface treatments, among the various cleaning and passivation techniques that were explored, sample preparation in 49% buffered hydrofluoric acid solution followed by annealing in NH 3 and O 2 at 750°C led to low and high oxygen-content surface, respectively, and hence low and high Q exp values ( Figure 12B) [37]. This allowed to measure for the first time Q values in excess of 10,000 in the blue spectral range from small footprint III-N resonators ( Figure 12C). In addition to the monotonous decrease in Q exp with decreasing wavelength that is likely originating from the increasing weigth of Q bk , Q fab , and Q sa , a high-energy cutoff is observed for GaN microdisk near 2.9 eV ( Figure 12B). It appears that such an energy value does coincide with the theoretically predicted peak in the joint density of optically active surface states for m-plane GaN [83,85] and the pinning of the Fermi level above the valence band maximum measured on GaN nanowires [89]. This energy is larger than that measured on clean and stoichiometric nonpolar GaN(101 ̅ 0) m-plane surfaces freshly cleaved in ultra-high vacuum [86]. It could stem from surface reconstruction and a change in surface chemistry due to nitrogen atom desorption taking place during the dry etching process, hence leading to nonstoichiometric sidewalls (e.g. by introducing nitrogen vacancies) [90,91]. It is akin to what has been reported in Si microdisks after RIE damage [28]. In any case, the sensitivity of surface states and their impact on the optical features may likely be responsible for the observed blueshift by about 50 meV in the cutoff energy after optimized annealing treatment ( Figure 12B, blue vs. red vertical solid lines).
Despite the critical importance of surface treatments, the latter did not lead to any stable, i.e. long-term, protective chemisorption solution thus far. Therefore, the encapsulation provided by a thin-film coating could seem a much better suited approach as a priori we could expect a complete protection of the resonators from their surrounding environment, e.g. by passivating surface states, without introducing any additional losses due to absorption or scattering. However, to reach such a goal, a conformal coating technique is desired to ensure the proper coating of the sidewalls, among which those of tiny holes (r < 50 nm) of PhCs, as well as the undersides of the suspended membranes. Although atomic layer deposition (ALD) is known for its conformal character, low-temperature deposition from organometallic precursors does likely result in a nonnegligible carbon incorporation into the thin films [92]. It would explain the significant Q exp degradation even after subsequent annealing of the ALDcoated resonators (attempts included both HfO 2 and Al 2 O 3 ) in ammonia and oxygen at 750°C. The exact nature of the observed additional losses remains unclear and could be due to either absorption induced by impurities present in the ALD-deposited layer or changes in the GaN surface occurring upon ALD deposition. Attempts based on the PECVD of SiO 2 indicate that this technique is suitable for conformally coating the underside of mushroom-type III-N microdisks but not the interior surface of PhC holes (see Supplementary Material section 1). Thus, SiO 2 -coated 3-μm-diameter GaN microdisks annealed in ammonia and oxygen for 5′ each exhibit similar maximal Q exp values to uncoated microdisks that have experienced the same optimized surface treatment, thereby indicating that this approach does not introduce any additional scattering losses and that the postcoating annealing treatment is amenable to cure surface absorption occurring at the nitride-SiO 2 interface (Supplementary Material Section 1).
Let us emphasize that this extreme sensitivity of III-N resonators to surface effects has already been exploited in a few occasions for different purposes. Thus, Aharonovich et al. reported on the controlled WGM tuning by immersing microdisks in deionized water and performing UV laser irradiation [93]. Using controlled tuning rate, permanent, i.e. irreversible, wavelength tuning with an accuracy on the order of 1 nm was reported at low excitation power, without degrading optical features, which was ascribed to selective in situ oxidation of the studied InGaN/GaN microdisks. Those authors demonstrated later that WGM tuning could reach the equivalent of one FSR and that the mode wavelength tuning rate was linear vs. power density (for a fixed time duration) and time (for a fixed power density) [94]. It was argued as being a promising step toward tailored CQED approaches. Similarly, Kouno et al. showed that high filling factor patterned hexagonal AlGaN microdisk arrays dipped into different solutions could offer an interesting potential for microsensing and 2D microimaging applications through real-time monitoring of the room temperature shift of the PL of WGMs [95]. In addition to these two surface effect signatures reported in liquid solutions, the above-mentioned UV-photoinduced oxygen adsorption and desorption phenomena hint toward the gas sensing potential of small footprint air-clad III-N resonators. In this regard, preliminary experiments carried out on 1D GaN PhC nanobeam cavities indicate the large tuning of fundamental and first-order PhC cavity modes by photoinduced gas adsorption using UV illumination at room temperature (Supplementary Material Section 2). In particular, gases such as O 2 , N 2 , CO 2 , or He exhibit a unique gas tuning curve, which is ascribed to the selectivity of surface states to the chemical species that leads to specific changes in surface absorption. A relative tuning range ∆λ λ on the order of a few percent has been recorded, which exceeds by far the values of >10 −3 reported in air-slot PhC nanocavities [96].
To conclude this subsection, we summarize the main features related to the fabrication and the optical properties of the state-of-the-art III-N photonic cavities listed in this review in Table 1.

Optical nonlinearities of NIR resonators
Contrary to their linear optical properties and, as we shall see, the demonstration of lasing features, studies focusing on the nonlinear optical properties of small footprint air-clad III-N microresonators and nanoresonators remain relatively scarce and have been mostly reported by the group of Philippe Boucaud et al. using both the microdisk and the PhC platforms [38,39,100,101]. As pointed out by Jung et al. [6,102], beyond the basic features enumerated in the introduction, the ability to fabricate high-quality optical resonators made from GaN or AlN that exhibit both second-order Pockels [χ (2) ] and third-order Kerr [χ (3) ] optical nonlinearities is likely to spark additional interest in this material family for implementing novel optical devices spanning a wide range of wavelengths such as on-chip self-referenced optical frequency combs.
As far as air-clad microdisks are concerned, a first interesting outcome arising from continuous-wave resonant second harmonic generation (SHG) experiments deals with the observation of the mode pattern associated with the harmonic cw and ccw propagating modes originating from the above-mentioned surface imperfections. Indeed, the twice lower diffraction limit at 2ω leads to an increased spatial resolution that allows for a precise spatial profile mapping of the NIR resonant modes at the angular frequency ω with, in particular, the clear discrimination between first-and second-order radial modes, which was further confirmed by a good agreement with FDTD calculations [38]. This was followed by phase-matched continuous-wave SHG occurring in doubly resonant on-chip GaN-on-Si microdisks [39]. Such phase matching was made possible through lithographic tuning of the microdisks, which allowed to design structures where fundamental and second harmonic waves are matched with modes that fulfill the conservation of orbital momentum, i.e. Δl = l SHG -2l pump = 0, where 2l is the number of antinodes in the azimuthal near-field profile. The moderate Q load value around 10,000 in the S-to L-telecommunication bands has proven to be a good tradeoff between the interaction length provided by the straight in-plane WGmicrodisk configuration and the bandwidth of frequency conversion. The strong enhancement of frequency conversion reported experimentally for those phase-matched microdisks was also satisfactorily reproduced by the coupled mode theory using the detuning between the NIR pump and the second harmonic as adjustable parameter, hence illustrating once more the suitability of lithographic tuning approaches [39]. Furthermore, let us note that, despite their lower nonlinear optical susceptibility compared to their GaAs counterpart ( (2) zzz 20 pm/V χ ∼ [103] vs. 188 pm/V for (2) xyz χ [104]) and the necessity to optimize the coupling scheme between microdisks and WGs to improve the absolute conversion efficiency, high-Q resonators with a high field strength made from AlGaN epilayers offer the advantage to be transparent in the visible and hence to be much less sensitive to undesired nonlinear effects such as optical bistability stemming from two-photon absorption, free-carrier absorption, and thermal instability that are at play, e.g. in the equivalent Si platform [59,70].
When switching to III-N PhC membrane cavities, two main designs can be considered for SHG and third harmonic generation (THG) that essentially differ by their mode volume. On the one hand, Zeng et al. focused on so-called width-modulated WG cavities characterized by a Q exp value in excess of 15,000 in the C-band and L-band and a mode volume that is well above the diffraction limit [100,101]. Such a geometry is well adapted for PICs, as the light is guided in the PhC by adopting a W0.98 WG design. Using a light collection scheme perpendicular to the PhC plane, those authors first reported a quadratic dependence of the integrated SHG signal as a function of incident power at the entrance of the PhC WG with a measured "threshold" input power of 70 μW using continuouswave resonant excitation [100]. An additional signature of the SHG process stemmed from the narrower lineshape of the second harmonic signal, matching a squared Lorentzian fit, compared to the transmission resonance of the cavity [100]. High spatial resolution imaging of the second harmonic signal was found to be in good agreement with the near-field emission pattern calculated via 3D-FDTD simulations, including the proper susceptibility tensor components. The next step with this width-modulated WG cavity geometry was the report of THG in the green spectral range under continuous-wave resonant excitation using the same in-plane excitation perpendicular light collection/high-resolution imaging scheme as for SHG [101]. In the absence of any phase matching, i.e. without the intended design of a resonant cavity mode for the third harmonic signal, the THG power was seen to exhibit a cubic power law dependence on pumping power coupled to the cavity. It was accompanied by a THG signal whose spectral dependence matched the cubic power of the Lorentzian used to fit the fundamental mode. In a way similar to the previous SHG study, a good quantitative agreement was achieved between the measured high spatial resolution images of the polarization-resolved third harmonic radiated patterns and their 3D-FDTD simulated counterparts accounting for the relevant χ (3) tensor components, namely when comparing the symmetry and the in-plane extension of the THG spots that exhibit a width of >300 nm. The reported 5 λ ∼ spatial resolution is argued to be a strong asset of this imaging technique that would be a competitive alternative to the SNOM technique [65], owing to its ease of implementation, the absence of any perturbation of the near-field induced by a tip, and its suitability to even characterize nanophotonic structures with Q exp value in excess of 1 million [ [70]. A peculiar feature of these lithographically tuned samples lies in the optimization of their design for both mode coupling and confinement, each having a set of holes next to the cavity specifically engineered to act as injectors and allow for proper manipulation of outof-plane radiative losses. This led to experimental coupling efficiencies at the fundamental angular frequency that lies between 3% and 19% for L3 cavities and 2% and 15% for H0 cavities, depending on the injector hole radius, in agreement with the targeted values. SHG was observed under resonant continuous-wave excitation as confirmed by the quadratic power dependence of the collected SHG signal upon increasing coupled power and the squared Lorentzian intensity lineshape of the SHG emission as a function of excitation wavelength. A lower bound value of 2.4 × 10 −3 W −1 for the normalized SHG conversion efficiency was measured that compares favorably to values reported in GaN microdisk resonators [39] and larger footprint GaN ring resonators [105]. By adopting a doubly resonant scheme in such PhCs, an SHG conversion efficiency closer to that obtained with state-of-the-art AlN ring resonators is even expected [106]. THG in the green occurred simultaneously to SHG with a power law intensity ratio as a function of input power of 1.4 slightly below the expected 1.5 ratio (Figure 13). This study allowed to conclude that, despite its larger V m value, the L3 cavity Inset, cavity's emission spectrum, displaying SHG and THG at a wavelength of 772.5 and 515 nm, respectively, with the latter scaled for visibility. Reprinted from Ref. [70].
design was better suited than the H0 one for SHG emission for structures with a comparable Q exp value due to the enhanced coupling factor of the former geometry originating from the better overlap between the Gaussian excitation beam and the orientation of the mode field components [70]. Finally, let us point out that all those results clearly illustrate the increasing degree of maturity gained by III-N microresonators and nanoresonators in the past 15 years, as acute nonlinear phenomena can be triggered and probed under continuous-wave resonant excitation while simultaneously allowing for high spatial resolution imaging, which is a fairly unique feature not accessible with the equivalent Si and III-As/III-P platforms.

Microlasing and nanolasing features in the UV to visible range
The observation of lasing features in dielectric optical resonators is a major landmark in the field of microphotonics and nanophotonics, as it is often considered as a way to validate the fabrication and the quality of such devices. Both the mushroom-type microdisk [26] and the PhC membrane cavity [107] geometries proved to be suitable to sustain lasing in small footprint dielectric systems. Similar features have been reported in the III-N material platform, although to date the demonstration of lasing in III-N PhC membrane nanocavities remains limited to the sole 1D PhC nanobeam geometry [12][13][14].
If one focuses first on microdisks, lasing has been initially reported by Haberer et al. in PEC-etched GaN microdisk structures using InGaN/GaN multiple QWs as gain medium under pulsed excitation that exhibits a reasonably high Q exp value of ~4600 at transparency [16]. The large peak power density required to get lasing did not allow for a systematic study of these devices in the stimulated emission regime. It was partly ascribed to the low thermal dissipation rate associated with the air-clad geometry and the subsequent degradation of the gain region as well as scattering losses due to the nonnegligible sidewall roughness. Another recognized potential drawback with the microdisk geometry originates from the small FSR between WGMs, which leads to mode competition over the gain band that typically covers an optical bandwidth between 10 and 20 nm in the blue spectral range [108] and hence an expected reduced β value in such devices. Nonetheless, the same group was the first to report lasing under room temperature continuous-wave optical pumping using a HeCd laser with a threshold power density ~300 W cm −2 [29]. This was attributed to improved processing that relied on EBL instead of conventional UV photolithography and the use of SiO 2 as a hard mask and a reduced microdisk diameter (1.2 vs. 3.5 μm in Ref. [16]) and hence a resulting smaller number of WGMs and a larger β value. Lasing was also linked to second-order radial modes, whose presence was made possible thanks to a small post diameter, which are less sensitive to sidewall roughness and ion damage occurring during the RIE step. Beyond those studies, Tabataba-Vakili et al. pointed out that the use of a bus WG is amenable with single-mode lasing operation, which would have to do with WGM selection taking place at the level of the whole PIC structure that involves a microdisk, a bus WG, and tethers [25], although those authors recently reported on two-mode lasing under pulsed excitation with such a PIC geometry [40].
One of the most systematic studies about the lasing characteristics of air-clad III-N microdisks was conducted by Sellés et al. on both AlN and GaN microdisks spanning a wide range of wavelengths, namely from the deep UV (275 nm) to the blue spectral range (470 nm), under pulsed optical excitation [30,109]. Depending on the targeted emission wavelength, the gain medium consisted of either binary GaN/AlN MQWs or InGaN/GaN MQWs. It was shown that, in the UV range, GaN/AlN QWs are better suited than their QD counterparts due to the detrimental role played by the excited states of large GaN dots that suppress the gain provided by small dots due to their strong absorption in the corresponding spectral range. This feature emanates from the large QD size distribution observed with GaN/ AlN QDs that is not seen in the InAs/GaAs platform [30].
Spectroscopic studies indicate that GaN/AlN QWs are characterized by a narrower emission linewidth than GaN/AlN QDs and hence a smaller Stokes shift, which makes them a more suitable gain medium at those critical wavelengths that can exhibit an IQE of several tens of percent. Additionally, mode competition arising from the disk geometry (WG thickness and disk diameter) was invoked to explain the measured β factor of ~4 × 10 −4 that also accounted for the IQE of the gain medium. The asymmetric lineshape of the lasing mode was ascribed to the pulsed excitation scheme that could be responsible for transients originating from either density-dependent or heating effects. The observed redshift of the lasing modes upon increasing pumping power above threshold was linked to photochemical effects such as those pointed out by Aharonovich et al. [93], but it is also likely reminiscent of the changes in the spectral signature of WGMs reported by Rousseau et al. [37], where the critical role played by surface states was highlighted, especially at room temperature when using short pumping wavelengths. Sellés et al. also pointed out that provided Q exp values in excess of 1000 are measured, the lasing threshold fluence did not depend on the disk diameter at a given lasing wavelength [109]. Similarly, the carrier density at threshold (n thr ) was estimated to be nearly lasing wavelength independent for a given gain medium quality provided the quantum-confined Stark effect characteristic of c-plane-oriented quantum heterostructures does not play any prominent role [109].
Room temperature lasing under continuous-wave optical pumping was also reported in the green spectral range, at λ = 514 nm, in ~1 μm diameter GaN microdisks with embedded InGaN/GaN MQWs with a threshold power density of ~1 kW cm −2 [110]. By analyzing the input-output (I-O) curve using standard laser rate equations [111], a relatively high-β value for this geometry of 0.043 was extracted. It is likely due to the small number of WGMs overlapping with the optical gain bandwidth. Let us note that β values in excess of 0.1 have been reported in microdisks with a diameter in excess of 2 μm [99,112], whose exact origin remains relatively unclear knowing the small FSR of these devices and hence the large number of competing modes. In any case, as will be recalled hereafter, connecting the high-β values deduced from a laser rate equation analysis of I-O curves to a Purcell factor (F P ) in excess of unity for conventional dielectric resonators such as those considered in this review, which exhibit room temperature lasing, is a misconception.
Besides QWs, InGaN QDs and so-called InGaN fragmented QWs have also been used as active gain medium leading to room temperature pulsed lasing in air-clad c-plane III-N microdisks [97,113]. In particular, it was highlighted that lasing occurring in these samples was ultimately the result of a tradeoff between the carrier capture efficiency, which is related to the areal density of the active medium, and the radiative emission efficiency of the latter. It is usually characterized by a high IQE even at room temperature due to strong spatial localization of the carriers. It is noteworthy that, despite an expected lower n thr value in QD lasers [114], continuous-wave lasing occurring in III-N QD microdisks remains to be shown.
High-β lasing is a well-known feature of small footprint nanolasers such as high resonators sustaining a reduced number of cavity modes. In particular, in the past decade or so, PhC membrane nanocavities proved to be ideally suited to investigate the lasing transition in devices where neither a sharp increase in the intensity nor a clear linewidth narrowing in the emission spectrum is observed [115,116]. In such a situation, basing an analysis on the sole conventional laser rate equations [111] becomes problematic due to the efficient coupling of spontaneous photon emission to the nanocavity mode, hence explaining the terminology highβ nanolaser, which is a source of noise in those devices that operate with a small average number of photons stored in the cavity mode (roughly between one and a few hundreds) [117]. Therefore, to obtain additional insights into the emission properties of high-β nanolasers, one is usually led to assess the threshold based on the statistical nature of the emitted light [115]. In other words, the evolution of the second-order intensity autocorrelation function at zero-time delay, i.e. g (2) (0), must be monitored as a function of input power density. When β is high, this quantity exhibits a transition from thermal or bunched photon statistics (i.e. chaotic photon emission), for which bunches of photons are emitted as a function of timein which case g (2) (0) > 1 -to coherent or random photon statistics, for which photons are randomly emitted as a function of time, i.e. g (2) (0) = 1. Remarkably, the larger the β value is, the smoother is the lasing transition and hence the less defined is the threshold [118].
In the specific framework of III-N PhC membrane cavities, to date, lasing has only been reported in structures having the 1D PhC nanobeam cavity geometry, with all of them showing high-β lasing features [12][13][14]. Thus, Niu et al. have demonstrated room temperature lasing under pulsed optical pumping at ~450 nm with a threshold fluence down to 9.1 μJ cm −2 in GaN PhC nanobeam cavities with a Q exp value ranging between 1300 and 1900, which rely on three fragmented InGaN/GaN QWs as gain medium. Using laser rate equations, these authors derived a β value of 0.94 for their structures. In Refs. [12,14], the authors have reported a systematic study of the lasing transition occurring in the 445-460 nm range under room temperature continuous-wave optical pumping in GaN PhC nanobeam cavities with a single InGaN QW gain medium exhibiting a Q exp value in excess of 2000 at transparency. To go beyond a rate equation analysis, which led to β values in excess of 0.7 at 300 K in those structures ( Figure 14A and D), and in the absence of any obvious linewidth narrowing upon increasing input power density that is usually synonymous of onset of lasing ( Figure 14B and E), a quantum optical characterization, coupled to microscopic laser modeling for the interaction between the 2D QW gain medium and the fundamental cavity mode, was conducted both at room temperature ( Figure  14C and F) and at cryogenic ones [14]. Power-dependent g (2) (0) measurements performed with a Hanbury-Brown and Twiss (HBT) interferometer show a progressive transition from thermal emission to the Poisson (coherent) limit ( Figure 14C) as reported previously in Refs. [115,118] for L3-type GaAs PhC nanocavities containing InAs QDs characterized at cryogenic temperatures. One very important outcome of such power-dependent g (2) (0) measurements led on nanolasers with an extended gain medium like QWs is that the input power density at which the g (2) (0) function starts to exhibit a progressive decrease toward unity, which is associated with the coherent emission threshold region, i.e. that where stimulated emission takes over spontaneous emission, does not coincide with the intensity threshold position such as that deduced from laser rate equation analyses ( Figure 15A and B) [119]. The difference between those two thresholds is all the more important that β gets closer to one. It may very well explain the large difference Note that the intracavity photon number is higher for the lasing nanobeam, which allows building up a coherent photon population. (B and E) Resonance peak wavelength (green) and linewidth (FWHM; black). Above 10 kW cm −2 , the development of resonance wavelength and emission linewidth is dominated by heating of the cavity region. The lasing structure in (B) exhibits a slight decrease in linewidth around P ≈ 5 kW cm −2 . (C and F) Second-order autocorrelation function at zero time delay as obtained from experiment (data points) and theory. Proof of the transition to coherent emission (shaded excitation range) is provided by the power dependence of the deconvolved second-order autocorrelation data, showing a clear trend toward the Poisson limit (g (2) (0) = 1) with increasing excitation power density. In contrast, the power dependence in (F) reveals a constant g (2) (0) ≤ 1.2. The evolution of the photon statistics is well reproduced by the microscopic theory (ideal, solid line; convolved, dashed line) when taking into account the calculated coherence time and the convolution with the temporal resolution (~225 ps) of the HBT setup. Error bars in (C and F) indicate the standard deviation obtained from fitting the recorded histograms that mirror g (2) (τ). Reprinted from Ref. [14].
in the quoted threshold power densities reported in Refs. [12] and [14], with values that roughly differ by one order of magnitude, for the very same 1D GaN PhC nanobeam structures. The evolution of the g (2) (0) function as a function of input power density is accompanied by an increase in coherence time from ~1 to ~800 ps across the lasing transition region based on the above-mentioned microscopic laser modeling [14]. Another relevant aspect of this study is related to the fact that for high-β nanolasers operating under realistic device conditions, i.e. for which nonradiative recombinations cannot be ignored, the estimated mean intracavity photon number at the coherent emission threshold is larger than 1, as what really matters is the imbalance between photons of stimulated and spontaneous origin ( Figure 14A).
Finally, let us note that temperature-dependent I-O curves measured on those 1D GaN PhC nanobeam cavity lasers reveal a complex interplay between the 0D and 2D nature of the InGaN/GaN QW gain medium. Such a signature manifests itself through a thresholdless I-O curve measured at ~160 K despite an extracted β value less than unity. It can be related to a progressive quenching of nonradiative loss channels with decreasing temperatures.
However, the observed inversed S-shaped I-O curves at lower temperatures was ascribed to the contribution of localized (0D) states typical of InGaN/GaN QWs that would contribute to the gain in the low excitation regime [14]. As at room temperature, at those cryogenic temperatures the only way to prove that a transition toward Poissonian emission statistics effectively takes place consists of monitoring the evolution of the g (2) (0) function as a function of input power density, hence showing that quantum-optical investigations are critical to demonstrate lasing in the β → 1 regime.

Forthcoming challenges and novel fields of application
The previous sections showed that the field of III-N microresonators and nanoresonators evolved at a fast pace in the past few years, and as such, it will most likely be confronted to novel challenges. Hereafter, we have chosen to highlight some topics that are commonly addressed when dealing with dielectric resonators with embedded quantum nanostructures. We have also identified some emerging fields of application that are by no means exhaustive but rather illustrative of the potential of those optical resonators.

Vertical light extraction
The first relevant topic deals with light extraction from III-N resonators. Indeed, light emission mostly occurs within the membrane plane, which can require some specific experimental configurations to implement an efficient light collection scheme especially for experiments that are conducted at cryogenic temperatures. In this regard, it is worth mentioning that in-plane light collection through tapered optical fibers is not, to say the least, a well-established approach in the UV to blue spectral range for some obvious geometrical reasons. In fact, there is often the need to extract the light vertically, i.e. perpendicularly to the membrane plane. Thus, some recent demonstrations of III-N PICs relied on the use of grating outcouplers positioned at the extremity of bus WGs to ensure efficient vertical extraction of guided light with simulated outcoupling efficiencies of 3%-7% in the 400-420 nm spectral range for GaN-based structures on the one hand [25] and measured values up to 9% at 380 nm for AlN ones on the other [120]. A promising strategy to increase those numbers would consist of engineering grating outcouplers based on the inverse design technique that recently proved to be extremely powerful for improving the overall performance of integrated photonic components [121,122]. For small footprint 2D PhCs, it was recently shown that holes next to the cavity can be precisely tailored to promote vertical light emission [70,123]. It consists of doubling the periodicity of those holes, which play the role of an extractor structure, compared to that of the PhC lattice to fold back the Fourier components of the electric field inside the light cone. A somewhat similar strategy has been proposed by Rousseau et al., which consists of forming a sidewall Bragg cross-grating in 1D GaN PhC nanobeam cavities operating in the blue spectral range that subsequently acts as vertical far-field coupler ( Figure 16A) [31]. Using 3D-FDTD simulations, an increase in the vertical light extraction by up to three orders of magnitude was predicted compared to straight sidewalls, i.e. unmodified, ideal nanobeam cavities. An experimental investigation focusing on the evolution of the Q exp value and the far-field intensity as a function of the cross-grating coupler amplitude revealed that the average quality factor remains unaffected by the sidewall modulation while exhibiting up to a ninefold average increase in integrated far-field emission intensity, due to partial back-folding of the mode profile to k = 0 induced by the subharmonic sidewall modulation, compared to unmodulated nanobeam structures ( Figure 16B) [31]. Such a geometry should prove extremely beneficial in photon counting experiments requiring long integration times, and hence a high signal-to-noise ratio, such as the above-mentioned second-order intensity autocorrelation function measurements. Let us note that, contrary to their PhC counterparts, there is presently a lack of similar strategy for isolated small footprint III-N microdisks operating in the UV to visible range likely because a solution such as that implemented in the far-infrared to promote vertical light emission from WGMs in microdisks [124] could hardly be adapted to short wavelengths.

Electrical injection
Next to vertical light extraction, electrical injection is an obvious topic of wide interest to promote the eventual adoption of III-N PICs or the merger of III-N resonators, e.g. with Si photonics. As far as the two geometries considered in this review are concerned, a few demonstrations have been reported with the microdisk structure but most of the time on devices with a significantly larger footprint than the structures we are focusing on (diameter >> 10 μm vs. <10 μm here) and with a design that is not necessarily of the air-clad type. Among them, we can cite the case of spiral-shaped GaN-based microdisk lasers grown on c-plane sapphire susbtrate having a radius in excess of 50 μm and sandwich-like InGaN microring lasers grown on Si substrate with an external radius of 20 μm that both exhibit room temperature lasing under pulsed currentinjection conditions [125,126]. The geometry the closest to the structures of interest for this work has been reported by Tabataba-Vakili et al., who showed electroluminescence from wide GaN microrings that are part of a PIC [127]. In each case [125][126][127], the authors did not observe any WGMs below threshold, which was tentatively ascribed to the small FSR in these large diameter microdisk devices and the resulting strong competition between the different families of modes. Unlike their microdisk counterparts, electroluminescence has not been demonstrated in III-N PhC membranes yet, which is likely related to the stringent requirements in terms of mode volume and efficient lateral injection of carriers in such structures. Let us note that, in PhC membranes made from III-V semiconductors, electrical injection in 2D PhC lasers relied on either a lateral p-n junction obtained via ion implantation and/ or impurity diffusion [128,129], which remains a challenging strategy to implement in the III-N platform, or a more conventional vertical p-n junction design [130]. 1D InPbased PhC nanobeam cavity LDs have also been reported that relied on either the use of central posts enabling hole injection, hence circumventing issues due to the short diffusion length of the latter [131], or a complex heterogeneous integration to an Si-WG circuitry [132]. As mentioned earlier, the dual constraint, which consists of keeping a thin enough WG to have fewer cavity modes competing against each other while ensuring efficient hole injection, will likely call in favor of the use of a buried tunnel junction [11] in forthcoming electrically driven III-N PhC membrane cavities. In this respect, one could envision, for example, 1D PhC nanobeam cavities with support pads covered by a top metal electrode allowing for efficient lateral electron injection and hence hole generation in the cavity region. It would avoid the detrimental use of p-type GaN contacts whose contact resistance is quite high, typically in the 10 4 Ω cm 2 range [11], and for which the layer resistivity remains on the order of a few tenths of Ω cm in good quality GaN [133], and likely much more for thin GaN WGs grown on Si. Another benefit from buried tunnel junctions deals with the expected decrease in the WG losses due to the lower residual absorption losses that are known to be mostly due to the p-type doped region in GaN-based edge emitting laser diodes [134,135].

CQED with III-N photonic cavities
Another aspect of relevant interest when using high m Q V ratio dielectric resonators, such as those considered in this work, which requires some clarification in view of forthcoming studies about high-β lasing and CQED studies, deals with the improper univocal link often made between a high spontaneous emission coupling factor and the enhancement of the spontaneous emission rate via the Purcell effect especially when leading room temperature studies. First of all, let us recall that a high-β value can be obtained in dielectric nanolasers without involving an F P value in excess of unity in situations where the FSR is on the order of or larger than the optical gain bandwidth, in which case values of β > 0.1 are only stemming from a pure geometrical origin [111]. This is the case, for example, in 1D PhC nanobeams that sustain a very small number of optical modes, typically ≤2, in which efficient spontaneous photon emission funneling into the lasing mode takes place [12,14,116]. The reason why F P < 1 has to do with the fact that, at room temperature, high-β dielectric resonators operate in the broad emitter regime, i.e. Δω em >> Δω cav , where Δω em is the emitter linewidth, be it an inhomogeneously broadened light source like InGaN QWs or a homogeneously broadened single QD, and Δω cav is the cavity mode linewidth. In such a case, the original expression of F P derived for the situation where a cavity mode is on resonance with a two-level system, located at the maximum of the electric field in the cavity, whose dipole is aligned with the polarization of this cavity mode, given by [136] 3 cav cav 2 3 where λ cav is the cavity mode wavelength and Q cav is the quality factor of the cavity mode, has to be modified into a generalized F P (F P,gen ) (see, e.g. Refs. [137,138] and references therein). We therefore have where eff c av em is the effective quality factor that also depends on the emitter quality factor given by cav em em where ω cav is the angular frequency of the cavity mode.
Following this clarification, we can point out that the recent progress made with the fabrication of 1D GaN PhC nanobeam cavities for which Q exp values of ~8000 have been reported ( Figure 17A) should allow to explore the mechanisms of coherent emission in nanolasers with extended gain media such as InGaN QWs from a situation where the β value has little impact on the pump rate at the coherence threshold (P coh ), corresponding, for example, to a Q exp value of ~2000 (cf. the vertical solid line in Figure 17B that illustrates the samples studied in Refs. [12,14]), to a regime akin to that observed with a small number of emitters like QDs where P coh varies by several orders of magnitude for β ∈ 0.1-1 ( Figure 17B) [119]. In particular, we should expect an alteration of β when switching from unmodulated nanobeam structures to structures incorporating a sidewall cross-grating coupler without modifying the Q exp value [31]. Such a feature would not be easily accessible at room temperature with other platforms, but it would require an efficient passivation of surface states possibly through a combination of atomic layer etching, which has already been successfully applied to the case of Si [139] and InGaAs [140] materials, to clean the exposed surface after processing and ALD using appropriately chosen precursors to encapsulate the 1D PhC nanobeams. Note that such studies could be led at cryogenic temperatures before their investigation at 300 K. In addition to the enhancement of the spontaneous emission rate due to the Purcell  is the vacuum field amplitude, ħ is the reduced Planck constant, ε 0 is the permittivity of free space, and γ and κ are the homogeneous decay rates of the quantum emitter and the cavity mode, respectively. When following the steps described in Ref. [142] in the situation where γ is dominated by the Purcell effect (i.e. γ ≈ F P γ em , where γ em is the radiative decay rate of the bare emitter), we can show, after some straightforward calculations, that Q exp should verify the following inequality: where we considered a representative mode volume keeping in mind that here ω em = ω cav . Hence, assuming a reasonable radiative emitter lifetime of 1 ns at γ = 450 nm, we then obtain Q exp > 7400, a value that is clearly within reach for 1D GaN PhC nanobeam cavities ( Figure 17A). Let us point out that the significantly larger Q exp values reported in the NIR, e.g. with 1D AlN PhC nanobeam cavities [49], could potentially allow for strong coupling observations with appropriate point-defect-like quantum emitters operating in this spectral range. For the sake of clarity, the challenges of relevant interest when dealing with III-N photonic cavities discussed in the previous subsections are listed in Table 2.

Emerging applications
Beyond the above-mentioned subjects, other emerging areas would certainly be worth being applied to the present III-N membrane resonators. One such example is that of so-called two-laser Raman thermometry, which can probe both thermal conductivity and thermal field mapping in a contactless, and hence in a nondestructive, manner [145,146]. In such an experiment, a high-power fixed laser is used as a heat source, whereas a second low-power laser scans the sample to probe the local temperature by precisely monitoring the spectral position of a known Raman active mode. Using a 488 nm probe laser, a spatial resolution reaching 300 nm together with a high-temperature accuracy, down to ±2 K, was reported [145]. As an illustration of the potential of this technique, using conventional one-beam Raman experiment, Jagsch et al. showed by following the redshift of the polar A 1 (LO) phonon peak as temperature sensor that the increasing cavity mode linewidth broadening reported at room temperature with increasing pumping power density in high-β 1D GaN PhC nanobeam cavity lasers originated from a temperature increase of the cavity by about 50-80 K in the high excitation range [14]. With the two-laser Raman thermometry technique, it would become possible to determine the profile of the thermal field decay, e.g. distinguish the diffusive limit when the membrane experiences a small temperature gradient, which is characterized by a ln(d) dependence of the temperature with increasing distance d from the excitation spot, from an exponential decay in the case of large temperature gradients [145]. The impact of geometrical parameters such as holes on the thermal field decay could be clearly quantified. It would certainly prove extremely beneficial to optimize large surface-to-volume ratio III-N nanophotonic devices for their subsequent integration to more advanced PICs. Furthermore, multicausal origins to linewidth broadening phenomena (photodesorption, etc.) could be better understood if the specific impact of temperature could be clearly isolated.
Another field with a significant potential deals with piezo-acousto-optic experiments carried out with high-Q 1D AlN PhC nanobeam cavities that have been engineered in both photonic and acoustic domains [147,148]. By taking advantage of the piezoelectric properties of III-N semiconductors, the acousto-optic modulation of those nanocavities was reported in the GHz frequency range with a mechanical frequency of 3.18 GHz being achieved in a structure having a C-band optical Q int value of 120,000 and a mechanical Q (Q mech ) in excess of 10,000 at 2.5 K (>3000 at 300 K) on the one hand [147] and a modulation up to a frequency of 19 GHz, corresponding to the microwave K band, in a nanobeam device characterized by a nearly equivalent C-band optical Q int value of 110,000 on the other hand [148]. One of the challenges when designing such structures consists of obtaining simultaneously a photonic bandgap and an acoustic quasi-bandgap with high-Q values, hence requiring precise structure engineering. In particular, it was pointed out that undesired mechanical deformation such as buckling in uniaxially strained nanobeams should be avoided via an appropriate design of the support pads to release the accumulated stress along the suspended PhC structure [147]. In the same vein, the membrane thickness will ultimately determine the resonance frequency when targeting very high microwave frequencies, the thinner it is, the higher is the frequency [148]. The exploitation of such optomechanical nanoresonators is still in its infancy, but they may prove instrumental for both fundamental and applied studies with topics including, but obviously not restricted to, nonreciprocal and break time-reversal symmetry studies in photonic systems [149] and coherent signal processing, opto-acoustic oscillators, and mechanical sensors, respectively [147]. In this respect, let us note that Bochmann et al. have achieved electromechanically induced optical transparency stemming from coherent interactions between microwave, mechanical, and optical modes using a suspended high-Q 1D AlN optomechanical crystal with Al electrodes and an AlN photonic circuit ( Figure 18) [150]. Their AlN nanobeam photonic structure features an optical Q int value of 130,000 in the C-band and a Q mech value of 2500 at room temperature at the resonance frequency ω m /2π = 4.24 GHz, which matches the operating frequency of superconducting quantum bits (qubits). Such on-chip demonstration could therefore enable coherent quantum state transfer from the microwave to the optical spectral range while offering long-range quantum network capabilities in novel superconducting qubit circuit architectures. Because of its likely more long-term development, we briefly mention the potential of III-N resonators for the field of optogenetics [15]. First, let us point out that 1D GaAs nanobeam cavities with embedded QDs have already been successfully used to probe in vitro proteins inside single cells, hence indicating that this type of nanophotonic devices offers possibilities to explore cell biology with novel insights [151]. In this regard, the reduced cytoxicity of III-N and the ability to engineer III-N nanophotonic structures emitting in the near-UV to green spectral range make this system a very appealing platform for optogenetic studies with minimal invasiveness compared to solutions currently implemented, e.g. for optogenetic stimulation experiments [152]. Among the future directions identified to improve existing optical neural interfaces, the miniaturization of existing light sources enabling the optical stimulation with single-cell resolution in freely behaving mammals is of high interest [153]. A major asset of such low footprint light sources would be the possibility to address individual cells with an unprecedented spatial control, hence allowing for more selective optogenetic activation and silencing experiments. Despite their reduced light output power, those devices would most certainly be ideally suited for the readout and control of bistable step-function channelrhodopsin derivatives that offer a light sensitivity increased by orders of magnitude to expressing cells [154]. With the ongoing downsizing of wireless optical-neural interfaces for light delivery to brain tissue in freely moving mammals, nearly lifelong in vivo experiments could be carried out, hence allowing an unprecedented monitoring of the neural activity as a function of the aging status of the brain. In particular, the use of parallelized nanophotonic structures emitting at different wavelengths that would target proteins made sensitive to different colors would most certainly open new pathways to unravel the complex processes taking place in living cells.

Conclusion
Through this review, we have demonstrated that, thanks to their fast growing technological maturity, small footprint III-N membrane resonators can nowadays exhibit optical quality factors mostly limited by surface absorption in the visible range and residual bulk absorption in the NIR, a general feature that was most certainly considered as out of reach when the first heteroepitaxial structures of this type were realized 15 years ago. This has been made possible thanks to the combination of a genetic algorithm automated process and the progress made in terms of sample processing, e.g. via the introduction of a singlestep pattern transfer. The broad spectral tuning range and the possibility to fabricate both active and passive devices with this material platform allow to explore a breadth of applications. The demonstration of room temperature blue lasing under continuous-wave optical pumping in both GaN microdisks and 1D GaN PhC nanobeam cavities and the recent advent of PICs open promising pathways for the realization of a novel generation of compact devices operating under electrical injection. Beyond structures exhibiting larger SHG and THG conversion efficiencies, we pointed out that foreseeable demonstrations within the next few years could include the report of the Purcell effect at cryogenic temperature using suitably positioned quantum emitters and potentially the strong coupling regime as well. High-β III-N nanolasers also promise to be an exciting platform to unravel the complexity of photon statistic properties when those sources are subjected to unconventional excitation regimes.

Supplementary Material
See supplementary material for additional information on (Section 1) thin SiO 2 film coating of air-clad III-N microdisks and PhC nanocavities and (Section 2) gas tuning of PhC nanobeam cavities.