[Paper Review] Competition between Raman and Kerr effects in microresonator comb generation

Yoshitomo Okawachi, Mengjie Yu+6 more|arXiv (Cornell University)|May 4, 2017

Advanced Fiber Laser Technologies3 references3 citations

TL;DR

This paper investigates the competition between Raman and Kerr nonlinearities in crystalline microresonators for frequency comb generation. It shows that tuning the free spectral range (FSR) to position the Raman gain peak between cavity resonances suppresses Raman effects, enabling pure Kerr comb formation; this sets a maximum allowable microresonator size, especially critical in high-Raman materials like diamond.

ABSTRACT

We investigate the effects of Raman and Kerr gain in crystalline microresonators and determine the conditions required to generate modelocked frequency combs. We show theoretically that strong, narrowband Raman gain determines a maximum microresonator size allowable to achieve comb formation. We verify this condition experimentally in diamond and silicon microresonators and show that there exists a competition between Raman and Kerr effects that leads to the existence of two different comb states.

Motivation & Objective

• To understand how strong Raman gain in crystalline microresonators limits the feasibility of Kerr frequency comb generation.
• To identify the conditions under which Raman and Kerr effects compete, leading to distinct comb states.
• To determine the maximum microresonator size that allows for stable modelocked Kerr comb operation despite strong Raman gain.
• To experimentally verify theoretical predictions in diamond and silicon microresonators with controlled FSR and pump detuning.
• To demonstrate that Raman suppression via FSR engineering enables the transition from Raman oscillation to pure Kerr comb states.

Proposed method

• Theoretical modeling of Raman and Kerr gain using Lorentzian spectral profiles: $ g_R(\delta) = g_R / (1 + 4\delta^2 / \Gamma_R^2) $, where $ \delta $ is the detuning from the Raman peak.
• Analytical derivation of the condition for effective Raman gain suppression: $ \delta / \Gamma_R > \sqrt{g_R / g_K} / 2 $, ensuring Raman gain is suppressed relative to parametric (Kerr) gain.
• Numerical simulation of comb generation in diamond and silicon microresonators using FSRs of 787–417 GHz (diamond) and 176–70.7 GHz (silicon), with pump wavelengths at 790 nm and 3100 nm.
• Experimental validation in a silicon microresonator with FSR = 128 GHz, using variable pump-cavity detuning to access both Raman-dominated and Kerr-dominated comb states.
• Time-domain and spectral analysis of simulated and experimental comb dynamics to identify soliton formation, Raman lasing, and non-degenerate FWM processes.
• FSR engineering to position the Raman gain peak between adjacent cavity modes, minimizing interaction with resonant Stokes modes.

Experimental results

Research questions

• RQ1 What is the maximum microresonator size that allows for stable Kerr comb generation in the presence of strong Raman gain?
• RQ2 How does the free spectral range (FSR) influence the competition between Raman and Kerr nonlinearities in crystalline microresonators?
• RQ3 Can Raman oscillation be suppressed to enable pure Kerr comb formation, and under what FSR conditions is this possible?
• RQ4 What role does pump-cavity detuning play in transitioning between Raman-dominated and Kerr-dominated comb states in silicon microresonators?
• RQ5 How do the relative magnitudes of Raman and Kerr gain coefficients ($ g_R $ and $ g_K $) determine the existence of two distinct comb states?

Key findings

• In diamond, with $ g_K = 0.2 $ cm/GW and $ g_R = 26 $ cm/GW at 800 nm, the Raman gain is 130× stronger than Kerr gain, requiring FSR > 70.7 GHz to suppress Raman effects.
• For silicon at 3100 nm, $ g_K \approx 0.03 $ cm/GW and $ g_R \approx 3 $ cm/GW, resulting in comparable Raman and Kerr gains, enabling a transition between Raman and Kerr comb states via detuning.
• Experimental results in a silicon microresonator (FSR = 128 GHz) show two distinct comb states: one with strong Raman lines at 1/9 of the Raman shift (3700 nm), and one without, corresponding to multi-soliton formation.
• Numerical simulations show that at FSR = 129 GHz, increasing pump detuning suppresses Raman oscillation and enables multi-soliton and eventually single-soliton formation.
• The intermediate FSR regime (70.7–176 GHz) in silicon enables coexistence of Raman and Kerr effects, with state transitions dependent on pump detuning and power.
• The maximum microresonator length is constrained by the condition that the Raman gain peak must be detuned from cavity resonances by more than $ \sqrt{g_R / g_K} \cdot \Gamma_R / 2 $, setting a hard limit on device size in high-Raman materials.