A Compact model for On-Chip Photonic Frequency Combs Authors: R. Shugayev, P. Bermel Purdue University Collaborators: T. Wang, J. Roychowdhury, A. Weiner Objectives Background / Motivation Background / Motivation • Generate VHDL model of the microring frequency comb generation. • Integrate VHDL model with MEEP • Generate basic functional models for other optical clock system elements • Create a system simulation of optical clock system Savchenkov, A. A., et al. "Stabilization of a Kerr frequency comb Papp, Scott B., et al. "Microresonator frequency comb optical clock." oscillator."Optics letters 38.15 (2013): 2636-2639. Optica1.1 (2014): 10-14. Ferdous, Fahmida, et al. "Spectral line-by-line pulse shaping of on-chip Herr, T., et al. "Universal formation dynamics and noise of Kerr-frequency • Simulate linear properties of photonic resonators microresonator frequency combs." Nature Photonics 5.12 (2011): 770- combs in microresonators." Nature Photonics 6.7 (2012): 480-487. 776. • Optical clocks via stabilization to atomic transition • Ability to generate and tailor • Nontrivial comb formation dynamics • Multiple feedback mechanisms • MAPP optical module will be utilized for system modeling amplitude/phase of the frequency comb through Type I/ Type II comb generation • Realistic device modeling can be implemented (laser, photodiode, Rb cell) 1 2 3 Nonlinear optical device physics Mathematical Description Modeling Challenges What are the special challenges that this device presents in terms Nonlinear four wave mixing energy/momentum 2ωωωpis=+ Δk =0 of modeling? conservation laws. ωωωpis,, pump, idler, signal frequencies l Governing equation for first line generation ωω0 =+FSR Δ ω • Long simulation runs • - Cascaded process that starts with a pump mode and a natural long lived modes Large number of modes of the cavity ( at the noise level ). - Obtained lines provide seeding for consecutive four-wave mixing events • Noise and instability modeling Kippenberg, Tobias J., Ronald Holzwarth, and S. A. Diddams. "Microresonator-based optical frequency combs." Science 332.6029 (2011): - dependent on material and geometric dispersion, temperature. 555-559. Δω - temperature proportional to absorbed power , energy inside the cavity, • Temperature change affecting frequency spacing cavity Q. • Step-by-step four wave mixing process - Dispersion is a combination of material dispersion and geometric dispersion • (different for different mode families) 2D/3D mode profile extraction, modeling • Noise seeding of the signal and idler pair • FSR determined by roundtrip time of the cavity 4 5 6 Approach. CMT+FDTD modeling Approach Results • For detailed discussion of approach and results refer to Shugayev, Roman, and Peter Bermel. "Time-domain simulations of nonlinear interaction in microring resonators using finite-difference and coupled mode techniques." Optics express 22.16 (2014): 19204-19218. • Coupled mode theory + FDTD description of comb generation • Mode profiles entering the equations for overlap integrals • Different mode families have different dispersions/ group velocities • Source has Gaussian profile in both time and space domains within the microring cavity • Normal dispersion modes • Anomalous dispersion modes • For proof of principle 2D profiles have been simulated • Good match in both time and • Good match with some discrepancy (infinite third dimension, 2D photonic crystal/ photonic crystal slab) • Overlap integral and system of differential equations are derived from first principles frequency domain due to spurious excitation of normal • Level of complexity is reduced to a set of coupled nonlinear differential equations • Different family modes although orthonormal can interact through modes nonlinear symmetry breaking 7 8 9 Results Results Status and Plans • Implement VHDL model of the microring resonator frequency • Different group velocities allows to separate different pulses comb. • Integrate with a common waveguide/source architecture using MAPP optical module 2 • Create basic models for elements of the optical clock • Self-phase modulation SPM: aa ii (laser, photodiode, Rb cell, temperature feedback) 2 • Soliton-like behavior is modeled Cross-phase modulation XPM: aa ji • Pulse spreading is suppressed † • Mode 1 family is analyzed • Model stabilized optical frequency comb clock Energy transfer terms: aaa jkl ( per architecture Savchenkov, A. A., et al. "Stabilization of a Kerr • Mismatch is attributed to non-uniform source excitation profile frequency comb oscillator."Optics letters 38.15 (2013): 2636-2639) • Model assumes uniformity of the coupling – non-uniform coupling can be incorporated. • Should not be an issue with a soft excitation 10 11 12.