Multiply resonant high quality photonic crystal nanocavities
MMultiply resonant high quality photonic crystal nanocavities
Kelley Rivoire ∗ , Sonia Buckley, and Jelena Vuˇckovi´c ∗ E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305-4088
We propose and experimentally demonstrate a photonic crystal nanocavity with multiple reso-nances that can be tuned nearly independently. The design is composed of two orthogonal inter-secting nanobeam cavities. Experimentally, we measure cavity quality factors of 6,600 and 1000for resonances separated by 382 nm; we measure a maximum separation between resonances of 506nm. These structures are promising for enhancing efficiency in nonlinear optical processes such assum/difference frequency and stimulated Raman scattering.
Photonic band gap nanocavities confine light into subwavelength volumes with high quality factor, and have beenused to build ultracompact optoelectronic devices such as lasers[1] and modulators[2], as well as to study fundamentalphysics such as cavity quantum electrodynamics[3, 4]. State of the art photonic crystal nanocavity designs[5–8] canbe optimized to generate quality factors exceeding one million for a single cavity resonance. For nonlinear opticalinteractions such as frequency conversion or stimulated Raman scattering, however, it is desirable to have multiplyresonant nanostructures[9] with arbitrary frequency separation and with good spatial field overlap. While manynanocavity designs have multiple resonant modes within a single photonic band gap, it is difficult to independentlycontrol their frequencies; moreover, field patterns of different resonances typically have minimal spatial overlap, andthe absolute frequency separation between resonances is limited by the size of the photonic bandgap. Photoniccrystals and quasicrystals[10] can have multiple photonic band gaps, but the size of the higher order band gapsgreatly diminishes for finite thickness structures; in addition, in such planar structures, higher order band gaps arelocated above the light line, implying that the resonances at those frequencies would also have low Q factors, resultingfrom the lack of total-internal reflection confinement. Band gaps for different polarizations (e.g. transverse magneticand transverse electric) have also been proposed[11–13] to generate additional resonant modes; however, it is difficultto independently tune the frequencies, and the proposed designs require relatively thick membranes which are moredifficult to fabricate. Here, we propose and experimentally demonstrate a crossed nanobeam photonic crystal cavitydesign that allows at least two individually tunable resonances with a frequency separation larger than the size of thephotonic bandgap in a single nanobeam.The proposed multiply resonant structure is shown in Fig. 1a, 1b. The basic element of the design is the nanobeam[6,7, 14–17], a 1D periodic photonic crystal waveguide clad in the other two directions by air. Our design uses twoorthogonal intersecting beams to achieve lithographically tunable resonances at multiple frequencies. A cavity isformed in each beam by introducing a central region with no holes (cavity length l ) and tapering the lattice constantand hole size near the cavity region[7, 16]. In each beam, confinement along the periodic direction is provided bydistributed Bragg reflection; confinement out of plane is provided by total internal reflection. Confinement in thein-plane direction orthogonal to the beam axis is provided by total internal reflection, and in the case of beamswith overlapping photonic band gaps, also by distributed Bragg reflection (as in structures designed for minimizingcrosstalk in waveguide intersections [18]). This structure allows nearly independent tuning of each resonant frequencyby tuning the parameters (e.g. width, lattice constant, cavity length) of each beam. Additionally, the structurehas natural channels for coupling through each beam to an access waveguide at each wavelength[19]. To optimizethe design, parameters of cavity length, lattice constant ( a ), number of taper periods N , distance between holesin the taper region ( a i , i = 1 , , ...N ), hole size in the taper region ( d i , i = 1 , , ..., N ), and beam width ( w ) werevaried in each beam. Fig. 1c shows the 3D finite difference time domain (FDTD)-simulated E y field pattern for aresonance at 1.55 µ m, with mode volume 0.35( λ/n ) where n is the refractive index, and Q=19000, limited by lossin the vertical direction. Fig. 1d shows the field pattern of E x for a resonance primarily localized by the verticalbeam with wavelength 1.1 µ m (also limited by vertical loss) and mode volume 0 . λ/n ) . The shorter wavelengthmode likely has a lower quality factor in part due to its narrower width than the horizontal beam and partly dueto FDTD discretization error (12 points per period). Decreasing the vertical lattice constant further (10 points perlattice period) leads to resonances with separation of 574 nm (1550 nm and 976 nm).Because a real structure has a fixed membrane thickness, decreasing the periodicity in one beam relative to theother leads to larger relative thickness t/a , redshifting the wavelengths of the bands; therefore achieving resonanceswith relative frequency f /f requires superlinear scaling of the feature size, e.g. a /a > f /f , as shown in Fig. 2a(there is a second less important contribution because refractive index increases for higher frequencies, from 3.37 to ∗ Electronic address: [email protected] a r X i v : . [ phy s i c s . op ti c s ] J un F OM = Q Q / √ V V in Fig. 2d (right axis), which is seen to depend primarily on Q (as mentionedpreviously, for large horizontal beamwidths, the quality factor of the higher frequency mode is limited by diffractioninto the orthogonal beam).For nonlinear frequency conversion applications, it is important for cavity field patterns to have large spatial overlap.Defining the nonlinear overlap, normalized to 1, as[12] γ ≡ (cid:15) NL (cid:82) NL dV (cid:80) i,j,i (cid:54) = j E ,i E ,j (cid:113)(cid:82) dV (cid:15) | E | (cid:113)(cid:82) dV (cid:15) | E | (1)where N L indicates nonlinear material only, we calculate γ =0.02 for the structures shown in Fig. 1. This numbercould be increased to 0.07 by decreasing the number of taper periods from 5 to 3 to further localize the field to thecentral region; however, the quality factors are reduced to 1440 and 1077 respectively, although this could likely beincreased by reoptimization of other parameters.A scanning electron microscope (SEM) image of a fabricated structure is shown in Fig. 3a. The structures aredefined by e-beam lithography and dry etching, as well as wet etching of a sacrificial AlGaAs layer underneaththe 164 nm thick GaAs membrane. To compare the experimental structure with the proposed design, we simulatethe fabricated structure by converting the SEM image to the binary refractive indices of air and GaAs[21]. Thethresholded SEM image used for simulation is shown in Fig. 3b. Figs. 3c, 3d show the simulated electric field for thetwo resonances of the fabricated structure, with expected resonances at 1477 nm (Q=4100) and 1043 nm (Q=540).Finally, we experimentally characterize our design by performing a reflectivity measurement in the cross-polarizedconfiguration[22] (Figs. 3e, 3f) using light from a tungsten halogen lamp which is linearly polarized using a GlanThompson polarizer and polarizing beamsplitter. The cavity is oriented at 45 degrees to both the polarization of theincident light and orthogonal polarization used for measurement. We measure quality factors of 6600 at 1482.7 nm and1000 at 1101 nm. Differences between simulation of fabricated structures and experimentally measured resonancesare most likely due to computational error in binary thresholding of the refractive index. 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(c) Field pattern of E y for cavity mode localized byhorizontal beam. Parameters are: a h,N =453 nm, a v,N =272 nm, d hx, /d hx,N = d hy, /d hy,N =0.5, a h, /a h,N = a v, /a v,N =0.7, l h /a h,N = 1 . l v /a v,N =0.83, w h /a h,N =1.65, w v /a v,N =1.8, d hy,N /w h = d vx,N /w v =0.7, d hx,N /a h = d vy,N /a v,N =0.5, refractiveindex n = 3 .
37, with slab thickness t/a h,N =0.35, N =5, and 6 mirror periods for both beams. Resonant wavelength is 1.55 µ m with Q=19,000 and V=0.35( λ/n ) . (d) Field pattern of E x for cavity localized by vertical beam. n = 3 .
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