Ultra-small mode volume, high quality factor photonic crystal microcavities in InP-based lasers and Si membranes

1. Ultra-small mode volume, high quality factor photonic crystal microcavities in InP-based lasers and Si membranes Kartik Srinivasan, Paul E. Barclay, Matthew Borselli, and Prof. Oskar Painter California Institute of Technology PECS-V, March 9, 2004

2. PC microcavities for quantum optics • Interested in strong coupling between a single atom (quantum dot) and single photon (cQED) • Coherent coupling rate must exceed decay rates  g > (k,g) • g ~ (1/Veff)1/2 ; for PC microcavities, Veff ~ (l/n)3g ~ 10-100 GHz for coupling to Cs atom; compare with ~10-20 MHz in current state-of-the-art cQED with free-space Fabry-Perot cavities (McKeever et al., Nature (2003)) • g>k Q ~104 for PC microcavities (compare with 107-108 in Fabry-Perot cavities) • cQED with PC microcavities: low Q, small Veff regime; fast time-scale for coherent interactions • PC microcavities can be designed to have field maximum in either air or dielectric • Interaction with introduced atoms or embedded quantum dots is possible • Next-generation cQED experiments involving integrated atom (qdot)-cavity systems

3. High-Q cavity design • Use symmetry and lattice grading to remove Fourier components that radiate • FDTD predicted Q~105 • Veff ~ 1.2(l/n)3 • Q relatively robust (remains >104) to perturbations in lattice grade, hole size. • Modal frequency a/l~0.245 K. Srinivasan and O. Painter, Optics Express10(15), 670 (July, 2002) K. Srinivasan and O. Painter, PECS-IV

4. PC microcavity lasers – initial demonstration of high-Q • Cavities fabricated in InAsP/InGaAsP multi-quantum well material via e-beam lithography, ICP/RIE etching through SiO2 mask and membrane layers, and HCl/H2O undercut wet etch • Optically pumped (pulsed) at 830 nm • Emission at 1.3 mm collected • Sub-threshold (near material transparency) emission linewidth gives estimate for cold cavity Q

5. Photonic crystal microcavity lasers • Sub-threshold measurements using a broad pump beam (eliminate thermal heating effects) • Measure linewidth at pump power level ~10% below threshold (best estimate of transparency); Q value of 13,000 measured, near measurement limit due to detector resolution and thermal broadening effects • Optimization of pump beam reduces thresholds to as low as 100 mW • Polarization measurements consistent with simulation K. Srinivasan, P.E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, Applied Physics Letters, 83 (15), 1915-1917 (Sept., 2003).

6. Probing PC microcavities with an optical fiber taper • Passive measurement of Q using an external waveguide consisting of a tapered optical fiber with minimum diameter of 1-2 mm • Taper interacts with the cavity when aligned laterally and positioned above and in the near-field of the cavity (Dz ≤1 mm), • Fiber serves as an optical probe of the spectral and spatial properties of the microcavities: can probe both Q and Veff • Fabricate arrays of devices (in Si) with average hole radius (ravg) varying for a fixed lattice spacing (a) • Mode of interest is lowest frequency resonance for a given a

7. Probing PC cavities with fiber tapers

8. Linewidth Measurements • Cavities fabricated in undercut silicon membranes • Linewidth of cavity mode (g) examined as a function of taper position above the PC; can back out an unloaded cavity Q factor • FDTD simulations of structure with appropriate hole sizes predict Q~56,000 and Veff~0.88(l/n)3 K. Srinivasan, P.E. Barclay, M. Borselli, and O. Painter, submitted to Physical Review Letters, Sept. 25, 2003(available at http://arxiv.org/quant-ph/abs/0309190)

9. Mode localization measurements • Measure depth of coupling (for fixed taper height) as a function of taper displacement from center along the central x and y axes of the cavity • Data reveals envelope of cavity field (relatively broad taper field profile prevents measurement of exact cavity near-field) • Compared with simple coupled mode theory analysis incorporating FDTD simulations of cavity field; consistent with predicted Veff~0.9(l/n)3 • PC microcavity thus simultaneously exhibits high Q and ultra-small Veff

10. Robust high-Q microcavities • Cavity design is robust, both in simulation ( Q>20,000) and experiment (Q>13,000) to significant deviations from the nominal design (both in average r/a and the grade in r/a) • Robustness due primarily to two mechanisms: • Use of symmetry to reduce vertical radiation loss – independent of size of lattice holes; ratio of defect hole size to lattice hole size. • Grade in hole radius creates a robust way to mode match between defect region and its exterior. Harmonic potential created by modifications to multiple holes; design less sensitive to fluctuations in size and shape of individual holes. K. Srinivasan, P.E. Barclay, and O. Painter, (available at http://arxiv.org/abs/physics/0312060)

11. Recent progress • Cavity Q as high as 56,000 measured • Fiber tapers used to probe other wavelength-scale cavities (microdisks by M. Borselli, et al.) • More efficient means to source cavity • Direct fiber-based excitation limited to 10-20% coupling; such levels also load the resonator (degrade Q) • Currently focused on integrating with suitably designed PC waveguides, which can be sourced by optical fiber tapers with >97% efficiency (P. Barclay et al., Tu-P41)

12. PC microcavities for cQED • Chip-based strong coupling to atomic species (Cs atom) *Collaboration with B. Lev and Prof. H. Mabuchi, Caltech • Similarly, g~100 GHz exceeds k and g for an InAs quantum dot (1 ns lifetime) • Chip-based strong coupling to chip-based atoms (quantum dots) • Single photon sources (Purcell Factor Fp ~3,500 estimated) †B. Lev, K. Srinivasan, P.E. Barclay, O. Painter, and H. Mabuchi, http://arxiv.org/quant-ph/abs/0309190, (2004)

13. Acknowledgements • Research partially funded by the Powell Foundation • K.S. thanks the Hertz Foundation for its graduate fellowship support