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.
Nonlinear wave mixing in optical microresonators new perospects for compact optical frequency combs with many promising applications. We demonstrate simultaneous generation of multiple frequency combs from a single optical microresonator and a single continuous-wave laser. Similar to space-division multiplexing, we generate several dissipative Kerr soliton states – circulating solitonic pulses driven by a continuous-wave laser – in different spatial (or polarization) modes of a MgF2 microresonator. Up to three distinct combs are produced simultaneously, featuring excellent mutual coherence and substantial repetition rate differences, useful for fast acquisition and efficient rejection of soliton intermodulation products. This method could enable the deployment of dual- and triple-comb-based methods to applications where they remained impractical with current technology.
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.
Dissipative Kerr solitons (DKS) generated in optical microresonators have attracted significant attention over recent years in the areas of optical frequency metrology, spectroscopy and coherent communication. DKS allow for fully coherent, high repetition rate broadband optical frequency combs (soliton combs) and provide access to stable ultrashort pulses of tunable duration. The formation process and the dynamics of such dissipative solitons strongly depend on the interplay of high-order nonlinear and thermal properties of the microresonator, and in many aspects significantly deviate from the behavior of solitons in optical fibers. This talk will focus on the fundamental principles of DKS dynamics, and cover the range of various unique phenomena discovered in such systems.
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.
In our experiment we use silicon nitride waveguides embedded in silicon dioxide on a silicon chip. The cross section of the waveguide is approximately 1.8µm width by 0.8µm height and the ring resonator has a radius of 120µm. This resonator is coupled to a bus waveguide that is used to couple the continuous wave pump light into the resonator and the light from the resonator out again. The pump laser is an amplified diode laser which provides around 2W of pump power in the bus waveguide on the photonic chip. If the pump light is in resonance with one of the resonances of the resonator we can generate a frequency comb from the pump light via the Kerr nonlinearity of the material. The spacing in between the lines of the frequency comb is close to the free spectral range of the resonator, which is 190 GHz for the resonator used. By tuning the pump laser through the resonance and modulating the power of the pump light we can achieve a stable state with a pulsed-shape waveform circulating inside the microresonator. These states are known as dissipative Kerr soliton states and they are solutions to the Lugiato-Lefever equation, which describes the nonlinear physics of the system. So far they had been experimentally demonstrated in fiber-ring cavities as well as crystalline microresonators. The main benefits of these states for Kerr frequency combs is that they allow for low-noise but broadband frequency combs with low modulation in the spectrum. In our case we report a 3-dB bandwidth of 10THz which is equivalent to sub-30fs pulses inside the resonator. Because of the chosen geometry of the waveguide cross section we also observe an effect which is caused by higher-order dispersion. Higher-order dispersion are terms that describe the dispersion beyond the quadratic group velocity dispersion. In order for dissipative Kerr solitons to form, anomalous group velocity dispersion is required. If higher-order terms are present as well, the soliton can still exist but additional dynamics come into play resulting in so called soliton Cherenkov radiation or a dispersive wave. In our measured spectrum this feature can be easily identified as a local maximum offset from the pump wavelength. In the time domain the soliton Cherenkov radiation manifests itself as an oscillating tail that is attached to the soliton pulse inside the microresonator. Using simulated values for the dispersion and coupled-mode equations to numerically simulate the physics inside the microresonator we can achieve a very good agreement between the experimentally observed and the simulated spectrum. In order to demonstrate that our frequency comb can be used for metrological applications we implement a full stabilization of the frequency comb and achieve a relative stability of 1e-15. Additionally we use the large bandwidth of 2/3 of an octave to implement a 2f-3f-scheme in order to monitor the carrier envelope offset of the frequency comb in a self-referenced manner.
In summary we have observed for the first time a soliton-based, broadband frequency comb in integrated microresonators. These frequency combs are perfectly suited for spectroscopy and data communication applications.
In several applications of optical whispering-gallery resonators, in particular for Kerr frequency comb generation,
a possibility to calculate accurately the eigenfrequencies and geometry dependent dispersion is an important prerequisite
for device optimization. While these calculations with significant time consumption may be performed
numerically, analytical approximation are still quite desirable for theoretical considerations. Spheroidal geometry
can fit the form of most types of whispering gallery resonators that are in use today. We propose and check
numerically new accurate approximations for the frequencies and geometrical dispersion of fundamental and
transversal modes of oblate and prolate spheroids using both the eikonal approximation and WKB analysis. We
also suggest approximations for the distribution of optical fields in a spheroidal resonator.
Using quasiclassical approach rather precise analytical approximations for the eigenfrequencies of whispering
gallery modes in convex axisymmetric bodies may be found. We use the eikonal method to analyze the limits
of precision of this approach using as a practical example spheroidal dielectric cavity. The series obtained for
the calculation of eigenfrequency is compared with the known series for dielectric sphere and numerical
calculations.
Quasiclassical approach and geometric optics allow to describe rather
accurately whispering gallery modes in convex axisymmetric bodies. Using this approach we obtain practical formulas for the calculation of eigenfrequencies and radiative Q-factors in dielectrical spheroid and compare them with the known solutions for the particular cases and with numerical calculations. We show how geometrical interpretation allows expansion of the method on arbitrary shaped axisymmetric bodies.
Properties of whispering gallery modes in microresonators of different types proposed lately may be analyzed with the help of introducing equivalent spheroid. We describe and compare two methods of approximate calculation of scalar field equation in such spheroid.
Thermal nonlinearity can produce oscillatory instability in
optical microspheres. We analyze theoretically the conditions of
observations of this regime and demonstrate it experimentally. The
observed curves are well compared with results of numerical
modelling. In pure fused silica with low absorption thermal
oscillations are suppressed due to concurrency with Kerr
nonlinearity. We also describe for the first time experimentally
observed slow and irreversible thermooptical processes in
microspheres.
We present the results of measurements of thermal fluctuations in microspheres. Experimental noise spectra are in good agreement with the theoretical model of recently predicted thermorefractive noise.
Thermodynamical fluctuations of temperature in microspheres transform to fluctuations of its resonance frequencies due to coefficient of thermal refraction. These fluctuations produce additional phase and amplitude noise in the output of the cavity. The implications of this noise for laser stabilization and other applications are discussed. Experimental conditions for the direct observation of this new effect are given.
We present a detailed analysis of the effect of volumetric and surface inhomogeneities as a source of quality-factor limitation and intracavity resonant backscattering in optical microsphere cavities of fused silica. Intrinsic scattering in microspheres is shown to be significantly inhibited as compared to standard Rayleigh scattering in the bulk material. This reassessment of fundamental losses indicates that Q-factors substantially exceeding the previously expected limit of approximately 1011 can be obtained in microspheres, as soon as surface hydration is prevented. The intracavity backscattering is analyzed as a source of whispering-gallery mode splitting and resonant optical feedback in presence of a mode-matched travelling- wave coupler.
A general model is presented for coupling of high-Q whispering-gallery modes in optical microsphere resonators with coupler devices possessing discrete and continuous spectrum of propagating modes. By contrast to Fabry-Perot resonators, in microspheres independent high intrinsic quality-factor and controllable parameters of coupling via evanescent field offer variety of regimes earlier available in RF devices. Latest results on realization of material- limited Q approximately 1010 in microspheres in the visible and near-infrared band and preservation of very-high Q in surface-hydration-preventing environment are presented.
We demonstrate the quality factor Q equals (0.8 plus or minus 0.1) multiplied by 1010 of whispering-gallery modes in fused silica microspheres at 633 nm, close to the limit determined by fundamental material attenuation. The lifetime of ultimate Q is limited by adsorption of atmospheric water. Optical effects of adsorption are investigated and conditions for fabrication of long-lifetime microspheres are clarified.
Quality factor 2.5 X 109 at the wavelength (lambda) equals 0.63 micrometers is reported in approximately 100 micrometers spherical resonators of fused silica with whispering-gallery modes (equivalent finesse F equals 2.5 X 106). Quality-factor 3 X 107 and effective thermal tunability of modes (up to 0.1%) is demonstrated in whispering-gallery microresonators of optical glass. Dispersive bistability and other nonlinear effects are observed at the level of input power about tens of microwatts. Nonlinear properties of optical whispering-gallery modes are investigated by mode cross-modulation technique. Prospects of applications in linear signal processing and quantum-nondemolition measurements are outlined.
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