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.
The calculation of thermal shifts caused by the absorption of laser radiation power is extremely important for describing nonlinear processes in microresonators. One way to calculate thermal frequency shifts is to use equations with effective parameters. In our work we calculated the effective parameters by approximating the numerical solution of 3D heat equation in Si3N4 integrated microresonator pumped by a ”step-like” heating power with the empirical exponent and found that the quality of the approximation depends on the geometric and material parameters of the microresonator. As result we obtained the map of parameters where the commonly used equation describes the direct numerical simulation well and the range of parameters where the applicability of this theory becomes inaccurate. To verify the correctness of our calculations, we compared the frequency shifts calculated using effective parameters with frequency shifts obtained with numerical simulation of eigenfrequencies and eigenmodes problem in a ”hot” deformed microresonator.
Compact microresonator-based frequency comb sources are perspective elements of modern photonic technologies. They attract even more interest after the integrated device was demonstrated. The main disadvantage of the Kerr frequency combs is said to be the comparatively low generation power. However, this problem is not studied quite well. Previous studies concerned its dependence on the microresonator FSR, input power and coupling separately, expecting pump-to-comb efficiencies no more than five percents. Usually it is stated that the threshold power should be reduced to provide lower necessary pump and larger soliton existence range. However, the problem is quite complex as coupling also induce the changes into the loaded quality factor, threshold power and even the number of comb lines. Also more than 20% efficiency was demonstrated recently in the self-injection locking regime. Here we present the more comprehensive analysis of the comb generation efficiency optimization and show the theoretical way to reach the limit of 100%.
We have performed a theoretical study and made an experimental realization of a multi-frequency self-injection locking of an external cavity laser, composed of a gain-chip and an external mirror, to a high-Q-chip-scaled ring microresonator. We use a numerical model based on the rate equation system that accounts for spontaneous emission to describe a semiconductor laser and optical feedback from a high-Q cavity. It allowed us to investigate dynamics of the system and to find out regimes when several locked lines are emerged simultaneously via power redistribution over the frequency domain. Due to the well-known phenomenon of mode competition, the multifrequency regimes appear only when several conditions are met, otherwise only single-frequency locking regimes may occur. The performed experimental investigations have shown that it is possible to achieve such states deterministically if these conditions are fulfilled.
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.
Modified rate-equations model for a multi-mode semiconductor laser locked to the high-Q microresonator taking Bogatov effect into account is developed. The effects of the symmetric and asymmetric mode interactions are shown.
The effect of the self-injection locking (SIL) is well-known for many years in the theory of oscillations, radiophysics and optics and is actively used for the stabilization and spectral purification of the corresponding generators. Last years it has attracted even more attention due to the possibility of using such stabilized lasers as pump sources for the realization of the nonlinear processes in the same microresonators, simultaneously used for laser linewidth reduction. However, existing linear theories of the self-injection locking unable to predict soliton generation because enough value of the pump frequency detuning can not be obtained in the linear regime. The development of full nonlinear theory becomes even more important, since recently generation of the solitonic pulses at normal group velocity dispersion has been demonstrated in the self-injection locking regime
We developed an original model describing the process of the frequency comb generation in the self-injection locking regime and performed numerical simulation of this process. Generation of the dissipative Kerr solitons in the self-injection locking regime at anomalous group velocity dispersion was studied numerically. Different regimes of the soliton excitation depending on the locking phase, backscattering parameter and pump power were identified. It was also proposed and confirmed numerically that self-injection locking may provide an easy way for the generation of the frequency combs at normal group velocity dispersion. Generation of platicons was demonstrated and studied in detail. Parameter range providing platicon excitation was found.
Self-injection locking is an effective tool of laser stabilization, known from the origins of radiophysics. Recently it was shown to be useful for perspective compact sources of optical frequency combs. This, however, implies the nonlinearity and high power inside the microresonator. Recently, we showed, that the account for the nonlinearity in the self-injection locking model substantially changes the system behaviour. However, thermal effects, inevitably arising from the high intracavity power, have not been considered yet. This point is also of great importance as these effects are known to be a serious obstacle for stable dissipative Kerr soliton generation. In this work we develop further the self-injection locking theory and show that thermal nonlinearity also introduce novel and important features. We analyse in detail several possible regimes arising due to thermal and Kerr nonlinearity competition and analyse tuning curves at different signs of thermorefractive coefficient. We confirm our predictions that the locking should help to overcome the temperature drift problem and show that nonlinear frequency shift helps to reach the desired detuning for the soliton comb state inside the locking band.
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.
We analyze in detail a scheme of the comb-calibrated frequency-modulated continuous-wave (FMCW) laser and study the accuracy of the laser frequency measurements. In this scheme the moment when the tunable laser frequency crosses the reference comb lines is obtained by filtering the heterodyne signal between the frequency comb and the tunable laser with a narrow band-pass filter. We show that the accuracy of the measured instantaneous frequency depends on the frequency sweep speed, bandwidth filter parameters and total phase noise of the laser and applied frequency comb. In this work we present the optimal ratio of frequency sweep and filter bandwidth for the given total phase noise and type of narrowband filter providing the highest frequency calibration accuracy.
We developed original model describing the process of frequency comb generation in the self-injection locking regime and performed numerical modelling of this process. Generation of dissipative Kerr solitons in the self-injection locking regime at anomalous GVD was observed and studied numerically. It was proposed that self-injection locking may provide easy way for generation of frequency comb at normal group velocity dispersion. This idea was investigated in detail and platicon generation was demonstrated. Parameter range providing platicon excitation was found.
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.
We introduce a technique capable to produce and control stabilized single-frequency emission with a sub-kHz linewidth and independently soliton comb generation from a multi–frequency regular Fabry-Perot laser diode selfinjection locked to a high-Q optical microresonator. We also observed novel regimes of controllable single, dual, and multiple-frequency generation that may be useful for the creation of narrow-linewidth lasers required for the spectroscopy, LIDARs, and telecommunications. For analysis of the considered effects original theoretical models taking into account self-injection locking effect, mode competition and Bogatov asymmetric mode interaction were developed and numerical modeling was performed.
Kerr frequency combs in optical passive microresonators promise new breakthroughs in photonics. Such combs result from multiple hyper-parametric four-wave mixing processes when reaching a threshold of modulational instability. These combs however have chaotic nature. It was revealed in recent experiments, theoretical and numerical analysis that transition form these chaotic states to highly ordered states associated with dissipative Kerr solitons is possible. In this report we discuss theoretical approaches to analyze these soliton states and reveal methods of reliable transition to single soliton states. Latest experimental results with soliton combs are reported.
The total reflection effect of the weak signal pulse from the high-power reference pulse with another frequency is first
demonstrated in the dispersive nonlinear medium. It is shown that as a result of the binary collision, signal pulse
frequency shift occurs, propagation velocity changes and time delay takes place. The conditions of total internal
reflection from moving inhomogeneity induced by pump pulse in nonlinear medium are found. The expression for the
reflected wave frequency shift is obtained. The possibility of pulse reflection from bright solitons in cubic medium is
considered.
Novel effects for few-cycle pulses propagation in quadratic media with dispersion management are considered. First, the
process of extraordinary wave generation in uniaxial crystal is tightly related with the process of ordinary wave profile
differentiation. Velocity mismatch limits interaction efficiency and leads to splitting of generated waves into two subpulses.
Such effect can be suppressed in the medium with periodic modulation of quadratic nonlinearity or with velocity
mismatch sign modulation. Second, highly interesting effects arise with the third-order dispersion. Dispersive spreading
can be reduced in layered medium with alternating third-order dispersion coefficients. Quadratic photonic crystals with
modulated dispersion coefficients or with managed dispersion are very promising for few-cycle pulse nonlinear optics.
One- and two-wave soliton trapping and propagation dynamics are also studied in such crystals. The analytical theory is
accompanied with the numerical simulation results.
We first study features of optical periodic lattices generated with mismatched cascade three-wave interaction in
quadratically nonlinear media. We elaborate the theory of parametric waveguides arrays induced by two crossing pump
waves together with exited sum wave. As the signal wave spreads due to the diffraction the induced lattice appears and
its transverse dimension increases. Note the parametric periodic grating becomes apparent since launching any signal
beam. It's likely to be the leading peculiarity of cascaded induced lattices. Parametric inhomogeneity depends on wave
vector mismatch sign, and its modulation depth can be controlled by pump beam intensity. We observed a transformation
from the discrete diffraction into the waveguiding of one or several signal beams with the increasing of pump intensity.
The discrete diffraction dynamics dependence on pump intensity, spatial period, and signal beam tilting is analyzed when
one or few central waveguides are exited at the input. At the certain incidence diffractionless propagation of signal beam
takes place. The similar discrete diffraction effects in 2D cascaded lattices with various pump structure geometries have
been studied. The additional degree of freedom gives novel properties to the effect of discrete diffraction.
New effect of mismatched parametric reflection due to noncollinear three-wave interaction in quadratic and cubic medium is studied. Original theory of this phenomenon is developed. Simple expression for the parametric reflection critical angle is found. Theoretical results are confirmed by numerical simulation.
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