High-Q photonic crystal cavities in all-semiconductor photonic-crystal heterostructures
HHigh-Q photonic crystal cavities in all-semiconductor photonic-crystal heterostructures
Z. L. Bushell, M. Florescu, ∗ and S. J. Sweeney Advanced Technology Institute and Department of Physics,University of Surrey, Guildford, Surrey, GU2 7XH, UK (Dated: November 13, 2018)Photonic crystal cavities enable the realization of high Q-factor and low mode-volume resonators, with typ-ical architectures consisting of a thin suspended periodically-patterned layer to maximize confinement of lightby strong index guiding. We investigate a heterostructure-based approach comprising a high refractive indexcore and lower refractive index cladding layers. Whilst confinement typically decreases with decreasing indexcontrast between the core and cladding layers, we show that, counter-intuitively, due to the confinement pro-vided by the photonic band structure in the cladding layers, it becomes possible to achieve Q-factors > withonly a small refractive index contrast. This opens up new opportunities for implementing high Q-factor cavitiesin conventional semiconductor heterostructures, with direct applications to the design of electrically-pumpednano-cavity lasers using conventional fabrication approaches. PACS numbers:
The development of low-threshold, compact laser sources ishighly relevant for the implementation of photonic integratedcircuits based on III-V or silicon platforms (or hybrid com-binations), with many applications including high-bandwidthcommunications, sensing and imaging . Photonic crystal(PhC) nanocavities are ideal candidates for such devices dueto their very small mode volume, high Q-factor and stronglight-matter interaction .A number of optically pumped PhC cavity lasers have beendemonstrated, mostly using a two-dimensional lattice of airholes perforating a thin (half-wavelength) semiconductor slabsurrounded above and below by air . The PhC lattice pro-vides light confinement within the plane of the material, whilstthe air-clad membrane design minimizes the out of the planelosses by providing strong index guiding. However, thereare several major drawbacks of this approach including poorthermal conductivity, which has led to di ffi culties in achiev-ing continuous-wave (cw) operation at room temperature, aswell as the high manufacturing cost and complexity. Thereare some examples of PhC cavities bonded to low refrac-tive index substrate layers, such as sapphire or silicon diox-ide, which show decreased thermal resistance but theseare electrically insulating. The use of either air-clad mem-branes and / or insulating substrate layers causes significantdrawbacks in adapting to an electrically pumped design. Re-cent examples have used ion-implantation to create a lateral p-i-n junction which, although successful, make fabricationconsiderably more complex than a standard vertical junctionthat can be grown epitaxially.One approach to overcome these challenges is to incor-porate additional cladding layers above and below the ac-tive region, rather than using a free-standing thin membrane.These cladding layers aid thermal conductivity, structural ro-bustness, and, for doped semiconducting layers, also allowfor electrically pumped designs without the need for ion-implantation. There has been very little previous work in thisarea ; Ref. considered a particular photonic crystal cav-ity design and a few combinations of cladding layers but didnot explore a relevant range of refractive index combinationsactually possible in realistic material systems, most likely due to the anticipated monotonic variation of the quality factorwith refractive index contrast.In this article, we explore di ff erent combinations ofnanocavity designs and material layers using 3-dimensionalfinite di ff erence time domain (FDTD) simulations. We con-sider a multilayer slab structure with the air holes of the PhClattice extended completely through the core and cladding lay-ers, as illustrated in Fig. 1(a). The core layer is 400 nm thickand has a fixed refractive index of 3.4, which corresponds tothat of GaAs in the near-infrared, whilst the refractive index n clad of the 1 µ m thick cladding layers is varied from 1.0 –3.4. Such structures require high aspect ratio etching, as hasalready been demonstrated in the literaure . We considertwo well-established high Q-factor designs: the modified L3 and dispersion adapted (DA) cavities. The DA cavity is ofparticular interest here as it is better equipped to minimizeout-of-plane scattering losses and hence it is less a ff ected byreduced total internal reflection at the upper and lower inter-faces. The L3 design is a conventional photonic crystal cavityarchitecture and is chosen as a baseline for comparison.The photonic crystal consists of a triangular lattice with pe-riod a =
270 nm and radius r = . a . The lattice coversan area of 50 a x 30 a , and the slab material has a finite areaof 52 a x 30 a with the simulation region boundaries lying out-side the slab. The DA cavity is formed from a W1 waveguide,where one complete row of holes is removed, and pairs ofholes along the edge of the waveguide are shifted by the dis-tances given for the h
20 cavity described in Ref. . The L3cavity has 3 missing holes and those at each end of the cav-ity are shifted outwards by dx = . a . The cavity designsand electric-field profiles of the fundamental resonant modein each case are shown in Fig. 1(b) and (c) for the DA and L3cavities, respectively.FDTD simulations of the structures were performed withPML boundary conditions in all three directions , assum-ing 7 µ m of air between photonic-crystal slab and boundary.The resonant modes were identified from the peaks in the fre-quency spectrum E ( ω ), whilst the Q-factor was derived fromthe corresponding exponential time decay of the electric field.Figure 1(d) shows the dependence of the cavity Q-factor on a r X i v : . [ phy s i c s . a pp - ph ] J un n = n clad ) n = n clad )0.4 m GaAs core ( n = 3.4) (a) (b) (c) (e)(d) M ode w a v e l eng t h ( m ) Cladding refractive index, n clad A l x G a - x A s a ll o ys o x i de s e . g . A l O , S i O DA L3 Q - f a c t o r FIG. 1. (a) Vertical cross-section of the slab layer architec-ture. (b),(c) Electric-field profiles of fundamental cavity mode inDA and L3 cavities, respectively. (d) Q-factor and (e) fundamentalmode wavelength of DA (squares) and L3 (triangles) photonic crys-tal nanocavities in 400 nm GaAs ( n = .
4) slab surrounded by 1 µ mthick cladding layers as function of cladding refractive index. the cladding refractive index. The same fundamental cavitymodes, shown in Fig. 1(b) and (c), are tracked throughoutand plotted in Fig. 1(e). There is an expected gradual shift tolonger wavelengths as the average refractive index of the sys-tem increases. For the air-clad ( n clad = .
0) case, the DA cav-ity has a very high Q-factor of ∼ , as expected given thatthis was designed to maximize Q in the 400 nm slab . TheL3 cavity shows significantly worse performance with a Q-factor of only ∼ , which is again expected as no attempthas been made to optimize the design for the chosen mate-rial dimensions. As the refractive index of the cladding lay-ers is increased from its air value, the Q-factor of both cavitydesigns initially decreases, in agreement with the decreasedvertical confinement of the mode due to reduced total inter-nal reflection at the core-cladding interfaces. The DA cavitystill performs well, with Q > , when n clad is within therange 1.4 – 1.7 corresponding to typical oxide materials such (a)(c) (d)(b) FIG. 2. Electric-field profiles in XY plane (a,c) and XZ plane,overlaid with line profile through cavity center (b,d) for DA cavitywith n clad = . as Al O . The use of oxide layers is known to improve ther-mal conductivity and structural robustness compared to an air-clad membrane but does not address the challenges related toelectrical injection, since they are highly electrically resistive.As the cladding refractive index is increased further, above2.4, there is an increase in Q-factor for both cavity designs.This reaches a peak value > for the DA cavity when n clad is in the range 3.2 – 3.3. The L3 cavity Q-factor peaks at ∼ when n clad = .
2. These are a remarkable resultssince these values lie within the highlighted range of n forAlGaAs alloys, opening up the possibility to implement high-Q photonic crystal cavities in standard epitaxial semiconduc-tor heterostructures in GaAs / AlGaAs material systems. Wenote, however, that this behavior seems counterintuitive, asone would expect the Q-factor to monotonically degrade asindex guiding is reduced and a greater amount of light is ableto leak into the cladding.To explore the origin of this unexpected behavior we beginby examining the electric-field profiles to establish how thespatial distribution of the mode changes with the refractiveindex of the cladding. Cross sections showing the electric-field profiles of the DA cavity in both horizontal and verticalplanes through the center of the cavity are shown in Fig. 2.The horizontal cross sections in Fig. 2(a),(c) illustrate thatthe mode remains well confined to the cavity region, withminimal change to the mode profile as the cladding index in-creases. The vertical cross sections in Fig. 2(b),(d) show agreater spread of the mode into the cladding as the refractiveindex increases due to the reduced index guiding. The over-laid line profile through the cavity center and its optical con-finement factor are typical of GaAs / AlGaAs waveguides ,indicating that good overlap of the optical mode with the ac-tive region is maintained.Since the peak Q-factor occurs for a small di ff erence be-tween the refractive indices of the core and cladding, we sug-gest that the photonic band gaps of the core and cladding lay-ers may overlap in frequency, such that the photonic band gapof the cladding prevents propagation of the resonant mode andconsequent degradation of the Q-factor. As an initial test ofthis hypothesis, the band structure of a 2D PhC with the samelattice parameters as used in the full structure was computed F r equen cy ( T H z ) Cladding refractive index, n clad W a v e l eng t h ( m ) FIG. 3. Band edges (red & purple circles) and band gap (shadedyellow) of 2D photonic crystal as function of material refractive in-dex. Resonant mode frequencies for DA (squares) and L3 (triangles)cavities in full multilayer slab structures shown for comparison. for each refractive index value. Figure 3 shows the resultingPBG frequency range along with the resonant cavity mode fre-quencies from the FDTD simulations. In the region of n ≥ . . This confining mechanism explains howa high-Q mode is maintained by reducing propagation of thelight away in-plane, even though it is able to spread verticallyinto the cladding due to the low refractive index contrast.This analysis treats the cladding as an infinite 2D slab,which is not the case within the actual system. The claddinglayers have a finite thickness and are also in an asymmetricarrangement due to the presence of the core layer at one in-terface and air at the other. It is known that there is still apseudo-gap e ff ect in optically thick PhC slabs, where cav-ity modes have only minimal coupling to the extended Blochmodes, that can lead to high-Q resonant states . This e ff ectcan be further enhanced in slabs with reflective (e.g. metal-lic or semiconductor / air) boundaries in the horizontal plane,due to alterations of the density of Bloch modes in momen-tum space . The structures investigated here fulfil both ofthese criteria, being both optically thick and having a finite FIG. 4. Directional Q-factors of DA cavity, showing contributionsfrom losses through surfaces of (a) core layer only and (b) wholemultilayer structure, as illustrated in inset. horizontal extent with semiconductor / air interfaces within thesimulation region. It is therefore expected that a similar ef-fect occurs in this case and the argument of minimal propaga-tion through the cladding would hold. To demonstrate this weundertook further analysis of the FDTD simulation results toinvestigate this hypothesis.The relative contributions to losses from the DA cavity aredetermined by monitoring the power flow through various sur-faces surrounding the cavity. The power flow is obtained fromthe FDTD simulation by integrating the time-averaged Poynt-ing vector across the surface of interest. This is converted tothe directional Q-factor as described in Ref. . In Fig. 4(a)we first consider the loss from the core layer only and breakit down into two components: the out-of-plane loss verticallyinto the cladding layers and the in-plane loss through the pho-tonic crystal lattice. The lowest Q-factor and therefore dom-inant contribution to loss is in the out-of-plane direction andincreases as n clad increases due to the decreased index guid-ing. There is a small increase in this out-of-plane Q-factor inthe region of n clad ≥ . n clad = . − . ff ects in the claddingare reducing propagation of the resonant mode and are thereby k y ( π / a ) (a) −1−0.500.51 (b) k y ( π / a ) k x (2 π /a ) (c) −1 −0.5 0 0.5 1−1−0.500.51 k x (2 π /a ) (d) −1 −0.5 0 0.5 1 FIG. 5. Spectra of the Fourier components of the electric-field dis-tribution for the DA cavity mode within the cladding layer, with n clad = k = ω c indicatedwith dashed white line.TABLE I. Fraction of Fourier transform (FT) components fallingwithin light cone for spectra shown in Fig. 5. n clad Q in − plane Q out − of − plane FT in light cone (%)1.2 3.5x10 increasing the Q-factor.We also analyzed the spatially Fourier transformed in-planeelectric-fields. Only Fourier components lying with the lightcircle defined by k <ω c can radiate into the far field, so com-paring the Fourier spectra can give information about lossfrom the modes . Additionally, if components overlap in mo-mentum space with the extended Bloch modes of the cladding,the cavity mode is able to couple to those extended modesand propagate away. As it is the behavior of the mode once itspreads to the cladding that is of interest, Fourier transformsare taken of the electric-field profile within the cladding, closeto the core-cladding interfaces. Examples of the Fourier spec-tra for di ff erent values of n clad are shown in Figs. 5(a)-(d). It can be seen that in the high-Q cases of n clad = . n clad = . n clad = . n clad = . − . ff ects in the cladding, with minimal coupling of the cavitymode to extended modes reducing propagation of light awayfrom the cavity.In summary, our study demonstrates that it is possible tomaintain Q-factors ∼ with cladding layers correspondingto typical oxide materials and, more importantly, > withcladding layers corresponding to typical semiconductors suchas AlGaAs alloys, each surrounding a GaAs ( n = n clad = . − . ff ects in the cladding layers. Thesee ff ects prevent propagation of the light in-plane through thecladding, despite the fact that the index guiding responsiblefor the vertical confinement of the light to the core layer isreduced. This counterintuitive behavior can be exploited todesign PhC nanocavities in low refractive index contrast mul-tilayer slabs, for example in standard GaAs / AlGaAs semicon-ductor heterostructures. This opens up a new design possibil-ity for nanocavity lasers with improved properties and ease ofmanufacture compared to existing air-clad membrane designs.
ACKNOWLEDGMENTS
Z.L.B. gratefully acknowledges support from the Mar-ion Redfearn Scholarship and Advanced Technology Insti-tute Scholarship. We also gratefully acknowledge fund-ing under EPSRC (United Kingdom) grants EP / H005587 / / L02263X / / M008576 /
1) and EP / M027791 /
1. The au-thors confirm that data underlying the findings are availablewithout restriction. Details of the data and how to request ac-cess are available from the University of Surrey publicationsrepository: http: // epubs.surrey.ac.uk / / . ∗ m.fl[email protected] P. Chaisakul , D. Marris-Morini , J. Frigerio , D. Chrastina , M.-S. Rouifed , S. Cecchi , P. Crozat , G. Isella , and L. Vivien , Nat.Photonics , 482 (2014). M. Smit, J. van der Tol, M. Hill, Laser & Photon. Rev. , 1 (2012). S. Kita, K. Nozaki, and T. Baba, Opt. Express , 8174 (2008). H. Abe, M. Narimatsu, T. Watanabe, T. Furumoto, Y. Yokouchi,Y. Nishijima, S. Kita, A. Tomitaka, S. Ota, Y. Takemura, and T.Baba, Opt. Express , 17056 (2015). J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Stein-meyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith,and E. P. Ippen, Nature , 143 (1997). ] O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O Brien, P. D.Dapkus, and I. Kim, Science , 1819 (1999). S. Matsuo, A. Shinya, T. Kakitsuka, K. Nozaki, T. Segawa, T.Sato, Y. Kawaguchi, and M. Notomi, Nat. Photonics , 648(2010). M. Nomura, S. Iwamoto, N. Kumagai, and Y. Arakawa, PhysicaE , 1800 (2008). M. H. Shih, A. Mock, M. Bagheri, N. Suh, S. Farrell, S. Choi, J.D. OBrien, and P. D. Dapkus, Opt. Express , 227 (2007). J.-K. Hwang, H.-Y. Ryu, D.-S. Song, I.-Y. Han, H.-W. Song, H.-K. Park, Y.-H. Lee, and D.-H. Jang, Appl. Phys. Lett. , 2982(2000). B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E.Haller, and J. Vuckovic, Nat. Photonics , 297 (2011). K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H.Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo,Nat. Photonics , 569 (2013). S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, andL. A. Kolodziejski, Guided modes in photonic crystal slabs, Phys.Rev. B , 5751 (1999). H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Braud, and C. Jouanin, Appl. Phys. Lett. , 532(2000). A. Mock and J. D. OBrien, IEEE J. Lightwave Technol. 28, 1042(2010). K. Avary, J. P. Reithmaier, F. Klopf, T. Happ, M. Kamp, and A.Forchel, Microelectron. Eng. , 61 (2002). S.-H. Kim, J. Huang, and A. Scherer, Opt. Lett. , 488 (2012). S. Kita, K. Nozaki, S. Hachuda, H. Watanabe, Y. Saito, S. Otsuka,T. Nakada, Y. Arita, and T. Baba, IEEE J. Sel. Top. Quantum Elec-tron. , 1632 (2011). J. Moosburger, M. Kamp, A. Forchel, R. Ferrini, D. Leuenberger,R. Houdre, S. Anand, and J. Berggren, Nanotechnology , 341(2002). E. Kuramochi, E. Grossman, K. Nozaki, K. Takeda, A. Shinya, H.Taniyama, and M. Notomi, Opt. Lett. , 5780 (2014). S.-H Kim, A. Homyk, S. Walavalkar and A. Scherer, Phys. Rev.B , 245114 (2012). K. Welna , M. Hugues , C. P. Reardon , L. O’Faolain , M. Hop-kinson , and T. F. Krauss , Photonics Nanostruct. Fundam. Appl. , 139 (2013). K. P. Welna, E lectrically Injected Photonic-Crystal Nanocavities,PhD thesis, University of St. Andrews (2011). S. Wu, Y. Cao, S. Tomi, and F. Ishikawa, J. Appl. Phys. ,013107 (2010). M. E. Givens, L. M. Miller and J. J. Coleman, J. Appl. Phys. ,4583 (1992). M. Florescu, S. Torquato, and P.J. Steinhardt, Appl. Phys. Lett. , 201103 (2010). T. Amoah and M. Florescu, Phys. Rev. B91