RESUMEN
In this work, we propose a method for designing optical devices described by coupled-mode equations. Following a commonly applied optimization strategy, we combine gradient-based optimization algorithms with an adjoint sensitivity analysis of the coupled-mode equations to obtain an optimization scheme that can handle a large number of design parameters. To demonstrate this adjoint-enabled optimization method, we design a silicon-on-insulator Raman wavelength converter. As structure, we consider a waveguide constructed from a series of interconnected and adiabatically-varying linear tapers, and treat the width at each interconnection point, the waveguide length, and the pump-Stokes frequency difference as independent design parameters. Optimizing with respect to these 1603 parameters results in an improvement of more than 10 dB in the conversion efficiency for a waveguide length of 6.28 cm and frequency difference 187 GHz below the Raman shift as compared to a converter designed by the conventional phase-matching design rule and operating at perfect Raman resonance. The increase in conversion efficiency is also accompanied by a more than 7 dB-improvement in the Stokes amplification. Hence, the adjoint-enabled optimization allows us to identify a more efficient method for achieving Raman conversion than conventional phase-matching. We also show that adjoint-enabled optimization significantly improves design robustness. In case of the Raman converter example, this leads to a sensitivity with respect to local variations in waveguide width that is several orders of magnitude smaller for the optimized design than for the phase-matched one.
RESUMEN
We present a generic approach to determine the phase mismatch for any optical nonlinear process. When applying this approach, which is based on the evaluation of local phase changes, to Raman- and Kerr-based four-wave mixing in silicon waveguides, we obtain an expression for the phase mismatch which is more accurate as compared to the conventional definition; and which contains additional contributions due to the dispersion of the four-wave-mixing processes. Furthermore, starting from the general propagation equations for the involved pump, Stokes and anti-Stokes waves, we investigate the impact of this four-wave-mixing dispersion in silicon waveguides and examine how it is influenced by changing the frequency difference between the pump and Stokes input waves. We show by means of numerical simulations that, by detuning this frequency difference slightly away from Raman resonance, the four-wave-mixing conversion efficiency can be more than doubled, but can also lead to a decrease in efficiency of more than 10 dB. We also discuss how the pump-Stokes frequency difference that is optimal for wavelength conversion varies with the length of the silicon waveguides and with their dispersion characteristics. Finally, starting from the newly introduced phase mismatch formula we simplify the set of propagation equations such that they are less computationally intensive to solve while still giving accurate estimates of the optimal pump-Stokes frequency difference and the corresponding wavelength conversion efficiency.