Spectrum and Dynamics of Optical Frequency Combs Generated with Monolithic Whispering Gallery Mode Resonators

Abstract

Optical frequency comb generation in whispering gallery mode resonators has been demonstrated in several experiments. The spectra of the combs exhibit a wide variety of complex profiles that are not fully understood. We report a detailed study on frequency comb generation in whispering gallery mode resonators including a complete stability analysis and numerical simulations. We show that the interaction of dispersion and nonlinearity is the key in determining the stability of the comb, the complex characteristics of its spectral profile, and its frequency span. The results will be important for understanding the essential physical processes leading to efficient comb generation.

Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator

“…The same approach was taken in the description of the original RNGH instability [10][11][12][13][14]; the underlying assumption is that the cavity modes are densely spaced, so that a pair of sidebands that satisfies the instability condition for the gain will always be "close enough" to two cavity modes that satisfy the phase condition. However, the experimental and theoretical developments of the last decade concerning optical parametric oscillation in externally pumped microresonators have shown that the phase condition has a large effect on the oscillation threshold and sideband spacing [55]. In microresonator experiments, the detuning between the external pump frequency and the center frequency of the cold-cavity mode is a degree of of freedom that must be precisely controlled to achieve the lowest possible instability threshold.…”

“…The position-dependent polarization is then inserted as the source term in Maxwell's wave equation. From here, the calculation follows the same steps as the instability analysis done for Kerr microresonators [55], and is detailed in Appendix G. After making the slowly varying envelope approximation and projecting the equation onto each of the orthonormal spatial modes, one finds a first-order differential equation for each sideband amplitude. Unlike the earlier example where we hand picked the phases of the sidebands to study the effect of an AM and FM field, here the AM and FM sideband configurations emerge organically as the two "natural modes" of the system of two sideband equations.…”

“…One approach is to numerically solve the full spatiotemporal Maxwell-Bloch equations [53,54]. To obtain analytical results, we follow a common approximation and decouple the spatial and temporal dependencies [55], writing the field as…”

Frequency Comb Generation in Superconducting Resonators

“…However, the microcavities, typically consisting of toroidal silica structures [10], need to be pumped with high laser powers because of their intrinsically weak χ(3) optical Kerr nonlinearity. In addition, output over much more than a single octave in frequency is difficult to obtain from these structures due to frequency dispersion from material and geometric factors, which make the modes non-equidistant.These Kerr combs continue to be the focus of extensive theoretical analysis to understand the nonlinear dynamics that give rise to their threshold of stability, mechanism of cascade, amplitude of responsiveness, and maximum spectral bandwidth [11][12][13][14][15]. Generation of these combs directly in the 1-20 GHz range would further simplify the instrumentation and potentially elucidate the dynamics involved by making them more accessible to direct measurement.…”

“…These Kerr combs continue to be the focus of extensive theoretical analysis to understand the nonlinear dynamics that give rise to their threshold of stability, mechanism of cascade, amplitude of responsiveness, and maximum spectral bandwidth [11][12][13][14][15]. Generation of these combs directly in the 1-20 GHz range would further simplify the instrumentation and potentially elucidate the dynamics involved by making them more accessible to direct measurement.…”