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Modal-reflectivity enhancement by geometry tuning in Photonic Crystal microcavities

C. Sauvan, G. Lecamp, P. Lalanne, and J.P. Hugonin

Open Access Open Access

Abstract

When a guided wave is impinging onto a Photonic Crystal (PC) mirror, a fraction of the light is not reflected back and is radiated into the claddings. We present a theoretical and numerical study of this radiation problem for several three-dimensional mirror geometries which are important for light confinement in micropillars, air-bridge microcavities and two-dimensional PC microcavities. The cause of the radiation is shown to be a mode-profile mismatch. Additionally, design tools for reducing this mismatch by tuning the mirror geometry are derived. These tools are validated by numerical results performed with a three-dimensional Fourier modal method. Several engineered mirror geometries which lower the radiation loss by several orders of magnitude are designed.

©2005 Optical Society of America

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Figures (7)
Fig. 1.
Fig. 1. Optical microcavities considered in this work. (a) Air-bridge microcavity. (b) Micropillar. (c) Single defect PC microcavity in a semiconductor membrane (top view).

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Fig. 2.
Fig. 2. Modal reflectivity and transverse mode-profile mismatch. (a) Modal reflectivity spectrum for the air-bridge mirror (a=420 nm and d=230 nm). Solid red curve: computational data using exact electromagnetic theory. Blue circles: square of the overlap integral η2. The vertical dashed lines indicate the band edges. (b)–(f) Comparison between the y-component of the transverse magnetic field of the fundamental air-bridge mode H 1 (bottom) and that of the half-Bloch wave H T (top) for several wavelengths covering the whole bandgap. White solid lines indicate the semiconductor-air boundaries of the air-bridge. The transverse H T field is calculated in a symmetry plane shown as vertical dashed lines in the left-hand side of Fig. 3.

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Fig. 3.
Fig. 3. Illustration of geometry tuning for tapering. Two segments of length a’ and a” are inserted between the PC mirror and the air-bridge.

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Fig. 4.
Fig. 4. Relevant quantities for the evanescent Bloch mode associated to three segments with different hole diameters, d=230, 170 and 100 nm, for λ=1.5 µm. (a) 1-η as a function of the segment period. (b) Real part of the effective index neff of the Bloch mode of the segments. The curves for d=230 and 170 nm are down shifted by 0.07 and 0.03, respectively, for the sake of clarity [otherwise, Real(neff)=λ/(2a)]. The horizontal dashed line represents the effective index of the fundamental air-bridge guided mode. The vertical arrow labelled A indicates the location associated to the mirror with a 420-nm period. The vertical arrows labelled B and C indicate the location associated to the segments used in Section 4.2 to reduce the losses.

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Fig. 5.
Fig. 5. Effect of hole shifting on the modal reflectivity of 1D and 2D PC mirrors. (a) 2D PC configuration. (b) Related air-bridge configuration. (c) and (d) Modal reflectivities R1 and R2 for λ=1.54 µm as a function of the normalized hole shift s/a. (e) and (f) Corresponding modal reflectivity spectra. The solid and dashed curves are obtained for s=0 and s=0.18a, respectively.

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Fig. 6.
Fig. 6. Single-segment tapers for micropillar Bragg reflectors. (a) Reflector geometry (a=d 1+d 2=228 nm). Dark and light regions correspond to GaAs and AlOx materials. (b) Modal reflectivity as a function of the normalized thicknesses x1/a and x2/a of the first GaAs and AlOx layers for λ=0.95 µm. Points A and B correspond to geometries with periodic and optimized mirrors, respectively.

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Fig. 7.
Fig. 7. Radiation loss spectra L=1-R for air-bridge mirrors with two-segment tapers. Red bold curve: hand-driven design for segments defined by (a’, d)=(320, 170) nm, and (a”, d)=(280, 100) nm. Blue thin curve: optimized design for segments defined by (a’, d)=(240, 210) nm, and (a”, d)=(414, 100) nm. The dashed curve corresponds to the modal reflectivity of the periodic mirror and the vertical dotted lines indicate the band edge.

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Equations (1)

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η = ℜe { [ ∬ dxdy ( E 1 × H T * ) e z ∬ dxdy ( E T × H 1 * ) e z ] ⁄ [ ∬ dxdy ( E T × H T * ) e z ] } ℜe { ∬ dxdy ( E 1 × H 1 * ) e z }
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