The absorption of optical power in high-Q microresonators leads to thermal effects, that strongly affect quantum and nonlinear processes. To take these effects into account, rate equations with effective thermal parameters are commonly used. Despite the convenience and simplicity of this approach, its applicability for a certain range of microresonator parameters may not be accurate enough. In our work, we compared various methods for determination of the effective thermal parameters for different resonator structures: the microring and microtorus resonator. As a result, we propose an original and effective method for determining the effective thermal parameters of microresonators based on thermal mode decomposition that considers various thermal relaxation processes. The proposed method agrees better with both direct numerical simulation and well-known theoretical formulas over the entire range of microresonator parameters, in contrast to the classical approach.
We upgraded the original fabrication method based on melting commercially available ZBLAN (heavy metal fluoride glass) optical fiber to obtain high-quality-factor ZBLAN microspheres with a diameter of 250 to 400 μm. The whispering gallery modes were excited in fabricated microresonators by different coupling elements and the high Q-factors at both 1.55 μm and 2.64 μm were demonstrated. At 1.5 μm the intrinsic Q-factor of (5.4 ± 0.4) · 108 determined by material losses was obtained. For 2.64 μm the quality factor was measured as (1.13 ± 0.22) · 108.
Realization of the coupling of the laser diode to an external reflector may provide efficient suppression of the phase noises and significant stabilization of the laser source. Locking a semiconductor laser to high-quality-factor microresonator was shown to result in a laser linewidth narrowing to sub-Hz level. The straightforward way to get better stabilization and wider locking band is to increase the feedback level. However, most of the theories used to describe the self-injection locking effect assume the weak feedback from the external reflector. Here we develop the more complete theory of the laser -- resonant reflector interaction that allows to describe this effect for the high feedback level as well. We define different possible regimes taking place at different feedback levels (including the so-called external cavity laser regime) and study applicability domains of the previous and proposed models. We show that existing model of the self-injection locking to whispering-gallery mode resonator is a consequence of the considered model in the low-feedback regime. Finally, we check the model in high-feedback limit experimentally and show a good correspondence with the theory.
Generation of coherent frequency combs in optical microresonators at normal GVD is a challenging task. It is well known that they can be generated in the form of the flat-top solitonic pulses, platicons, via controllable mode interaction or modulated pump. However, such methods are rather complicated, requiring either sophisticated mode interactions, complex two-cavity systems or high-frequency modulators. Recent investigations have shown that the self-injection locking effect provides interesting possibilities for frequency comb generation. It has been shown that this effect not only provides laser stabilization due to the resonant backscattering of laser radiation from the high-quality-factor microresonator but also leads to the nontrivial nonlinear dynamics in the same microresonator. First, this has been demonstrated for bright solitons with an ordinary laser diode as a pump source. Recently, it has been shown experimentally that such approach is also applicable for platicon generation and does not require additional equipment. In our work we study this process in detail and identify different generation regimes depending on the combination of the pump power and the backscattering coefficient providing the self-injection locking effect. The range of parameters necessary for the efficient platicon generation is found. We also report a novel mechanism of platicon generation based on the thermal effects inevitable in real-life systems. We show that it is possible if thermal effects are negative (the direction of the thermal shift of the microresonator resonance is opposite to the direction of the nonlinear shift) and the ratio of the thermal relaxation time to photon lifetime is small enough. Different generation regimes are found, and the possibility of the turn-key operation regime is demonstrated.
Self-injection locking (SIL) is an effect of the oscillator frequency stabilization by means of a passive external high-quality cavity enabling frequency filtered coherent optical feedback to the oscillator. It is widely used in various photonic applications, including compact narrow-linewidth lasers and microcomb sources. While basic properties of this effect were studied in many theoretical and experimental works, deeper insight on its physical features and parameter space analysis allows us to build a model that describes its behavior and predicts at least an order of magnitude improvement of the stabilized laser linewidth reduction as compared to the best previous results. We find out a global maximum over all parameters and obtain analytical expression for the optimal stabilization coefficient. Influence of the resonator non-linearity and transition from the SIL to single cavity regime are discussed. Quality factor of the resonator appears to be a key parameter for effective SIL and oscillator stabilisation. Crystalline microresonators demonstrated the highest Q and a prism coupling is a robust method of its excitation, broadly used in applications. We developed and verified experimentally a new method of determining the key parameters of the chosen mode of the microresonator - quality factor and vertical index - based on the measurement of the locking bandwidth as a function of the resonator to prism distance. Unlike other methods it allows for the measurement to be made right in the SIL regime and does not require narrow-line lasers or fast photodetectors. A comparison with the FWHM and ringdown methods demonstrated excellent agreement.
During the last decade generation of frequency combs and different types of dissipative solitons was demonstrated and well-studied in high-Q optical microresonators with Kerr nonlinearity. However, recently, it was shown that it is also possible in microresonators with quadratic nonlinearity. In our work, we studied numerically the generation of coherent frequency combs in quadratically nonlinear microresonators via conventional frequency scan method for both second harmonic generation and downconversion processes. We revealed that under particular conditions it is possible to generate two-color flat-top solitonic pulses, platicons, using pump amplitude modulation or controllable mode interaction approach, if the signs of the group velocity dispersion (GVD) coefficients at interacting harmonics are opposite. For SHG process at each combination of GVD coefficients platicon generation was observed at both positive and negative pump frequency detunings from the linear microresonator resonance. Platicon generation was also demonstrated for the downconversion process. Platicon excitation was observed at positive detunings for the normal GVD at pump frequency and at negative detunings in the opposite case. For both SHG and downconversion processes, for the efficient platicon excitation one needs simultaneous accurate matching of the free spectral ranges at interacting harmonics and resonant eigenfrequencies. Excitation conditions and platicon generation domains were revealed for different generation methods, and properties of generated platicons were studied for various combinations of medium parameters.
Silicon is a widely used material in modern microelectronics and photonics. Extremely low optical losses in near and mid-IR wavelengths made it a promising material for whispering gallery mode (WGM) optical micro-resonators. But, till now its potential was not fully utilized because of the best-obtained quality factor - about 2 x 107 - remained orders of magnitude below the material absorption limit. In this work we experimentally demonstrated a quality factor above 109 for the WGM in millimetres size crystalline silicon resonators. Materials with different residual conductivity were compared. Application of original semi-spherical silicon coupler allowed to obtain up to 35% resonance peaks contrast.
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