Symmetry Breaking of Counter-Propagating Light in a Nonlinear Resonator

Spontaneous symmetry breaking is a concept of fundamental importance in many areas of physics, underpinning such diverse phenomena as ferromagnetism, superconductivity, superfluidity and the Higgs mechanism. Here we demonstrate nonreciprocity and spontaneous symmetry breaking between counter-propagating light in dielectric microresonators. The symmetry breaking corresponds to a resonance frequency splitting that allows only one of two counter-propagating (but otherwise identical) states of light to circulate in the resonator. Equivalently, this effect can be seen as the collapse of standing waves and transition to travelling waves within the resonator. We present theoretical calculations to show that the symmetry breaking is induced by Kerr-nonlinearity-mediated interaction between the counter-propagating light. Our findings pave the way for a variety of applications including optically controllable circulators and isolators, all-optical switching, nonlinear-enhanced rotation sensing, optical flip-flops for photonic memories as well as exceptionally sensitive power and refractive index sensors

Frequency Comb Assisted Diode Laser Spectroscopy for Measurement of Microcavity Dispersion

While being invented for precision measurement of single atomic transitions, frequency combs have also become a versatile tool for broadband spectroscopy in the last years. In this paper we present a novel and simple approach for broadband spectroscopy, combining the accuracy of an optical fiber-laser-based frequency comb with the ease-of-use of a tunable external cavity diode laser. This scheme enables broadband and fast spectroscopy of microresonator modes and allows for precise measurements of their dispersion, which is an important precondition for broadband optical frequency comb generation that has recently been demonstrated in these devices. Moreover, we find excellent agreement of measured microresonator dispersion with predicted values from finite element simulations and we show that tailoring microresonator dispersion can be achieved by adjusting their geometrical properties

Universal symmetry-breaking dynamics for the Kerr interaction of counterpropagating light in dielectric ring resonators

Spontaneous symmetry breaking is an important concept in many areas of physics. A fundamentally simple symmetry-breaking mechanism in electrodynamics occurs between counterpropagating electromagnetic waves in ring resonators, mediated by the Kerr nonlinearity. The interaction of counterpropagating light in bidirectionally pumped microresonators finds application in the realization of optical nonreciprocity (for optical diodes), studies of PT-symmetric systems, and the generation of counterpropagating solitons. Here, we present comprehensive analytical and dynamical models for the nonlinear Kerr interaction of counterpropagating light in a dielectric ring resonator. In particular, we study discontinuous behavior in the onset of spontaneous symmetry breaking, indicating divergent sensitivity to small external perturbations. These results can be applied to realize, for example, highly sensitive near-field or rotation sensors. We then generalize to a time-dependent model, which predicts different types of dynamical behavior, including oscillatory regimes that could enable Kerr-nonlinearity-driven all-optical oscillators. The physics of our model can be applied to other systems featuring Kerr-type interaction between two distinct modes, such as for light of opposite circular polarization in nonlinear resonators, which are commonly described by coupled Lugiato-Lefever equations

Generalized Theory of Optical Resonator and Waveguide Modes and their Linear and Kerr Nonlinear Coupling

We derive a general theory of linear coupling and Kerr nonlinear coupling between modes of dielectric optical resonators from first principles. The treatment is not specific to a particular geometry or choice of mode basis, and can therefore be used as a foundation for describing any phenomenon resulting from any combination of linear coupling, scattering and Kerr nonlinearity, such as bending and surface roughness losses, geometric backscattering, self- and cross-phase modulation, four-wave mixing, third-harmonic generation and Kerr frequency comb generation. The theory is then applied to a translationally symmetric waveguide in order to calculate the evanescent coupling strength to the modes of a microresonator placed nearby, as well as the Kerr self- and cross-phase modulation terms between the modes of the resonator. This is then used to derive a dimensionless equation describing the symmetry-breaking dynamics of two counterpropagating modes of a loop resonator and prove that cross-phase modulation is exactly twice as strong as self-phase modulation only in the case that the two counterpropagating modes are otherwise identical

Dark solitons in Fabry-Pérot resonators with Kerr media and normal dispersion

The ranges of existence and stability of dark cavity-soliton stationary states in a Fabry-Pérot resonator with a Kerr nonlinear medium and normal dispersion are determined. The Fabry-Pérot configuration introduces nonlocal coupling that shifts the cavity detuning by the round trip average power of the intracavity field. When compared with ring resonators described by the Lugiato-Lefever equation, nonlocal coupling leads to strongly detuned dark cavity solitons that exist over a wide range of detunings. This shift is a consequence of the counterpropagation of intracavity fields inherent to Fabry-Pérot resonators. In contrast with ring resonators, the existence and stability of dark soliton solutions are dependent on the size and number of solitons in the cavity. We investigate the effect of nonlocal coupling of Fabry-Pérot resonators on multiple dark solitons, and we demonstrate long-range interactions and synchronization of temporal oscillations

On-the-fly precision spectroscopy with a dual-modulated tunable diode laser and Hz-level referencing to a cavity

Advances in high-resolution laser spectroscopy have enabled many scientific breakthroughs in physics, chemistry, biology and astronomy. Optical frequency combs have pushed measurement limits with ultrahigh-frequency accuracy and fast-measurement speed while tunable diode laser spectroscopy is used in scenarios that require high power and continuous spectral coverage. Despite these advantages of tunable diode laser spectroscopy, it is challenging to precisely determine the instantaneous frequency of the laser because of fluctuations in the scan speed. Here we demonstrate a simple spectroscopy scheme with a frequency modulated diode laser that references the diode laser on-the-fly to a fiber cavity with sub-15 Hz frequency precision over an 11-THz range at a measurement speed of 1 THz/s. This is an improvement of more than two orders of magnitude compared to existing diode laser spectroscopy methods. Our scheme provides precise frequency calibration markers while simultaneously tracking the instantaneous scan speed of the laser. We demonstrate several applications, including dispersion measurement of an ultra-high-Q microresonator and spectroscopy of an HF gas cell, which can be used for absolute frequency referencing of the tunable diode laser. The simplicity, robustness and low costs of this spectroscopy scheme could prove extremely valuable for out-of-the-lab applications like LIDAR, gas spectroscopy and environmental monitoring

Geometry optimization for dark soliton combs in thin multimode silicon nitride microresonators

Silicon nitride (Si3N4) has been well established as an ultralow-loss material for integrated photonics, particularly for the generation of dissipative Kerr soliton frequency combs, enabling various applications for optical metrology, biological imaging, and coherent telecommunications. Typically, bright soliton generation in Si3N4 devices requires thick (>600 nm) films to fulfill the condition of anomalous dispersion at telecom wavelengths. However, thick films of ultralow-loss Si3N4 (>400 nm) often suffer from high internal stress, leading to cracks. As an alternative approach, thin Si3N4 films (<400 nm) provide the advantage of one-step deposition and are widely applied for commercial use. Here, we provide insights into engineering an integrated Si3N4 structure that achieves optimal effective nonlinearity and maintains a compact footprint. A comparative analysis of Si3N4 resonators with varying waveguide thicknesses is conducted and reveals that a 400-nm thin Si3N4 film emerges as a promising solution that strikes a balance among the aforementioned criteria. Based on a commercially available 400-nm Si3N4 film, we experimentally demonstrate the generation of low-noise coherent dark pulses with a repetition rate of 25 GHz in a multimode Si3N4 resonator. The compact spiral-shaped resonator has a footprint of 0.28 mm2 with a high-quality factor of 4 × 106. Our demonstrated dark combs with mode spacings of tens of GHz have applications in microwave photonics, optical spectroscopy, and telecommunication systems

Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides

All-optical signal processing is envisioned as an approach to dramatically decrease power consumption and speed up performance of next-generation optical telecommunications networks. Nonlinear optical effects, such as four-wave mixing (FWM) and parametric gain, have long been explored to realize all-optical functions in glass fibers. An alternative approach is to employ nanoscale engineering of silicon waveguides to enhance the optical nonlinearities by up to five orders of magnitude, enabling integrated chip-scale all-optical signal processing. Previously, strong two-photon absorption (TPA) of the telecom-band pump has been a fundamental and unavoidable obstacle, limiting parametric gain to values on the order of a few dB. Here we demonstrate a silicon nanophotonic optical parametric amplifier exhibiting gain as large as 25.4 dB, by operating the pump in the mid-IR near one-half the band-gap energy (E~0.55eV, lambda~2200nm), at which parasitic TPA-related absorption vanishes. This gain is high enough to compensate all insertion losses, resulting in 13 dB net off-chip amplification. Furthermore, dispersion engineering dramatically increases the gain bandwidth to more than 220 nm, all realized using an ultra-compact 4 mm silicon chip. Beyond its significant relevance to all-optical signal processing, the broadband parametric gain also facilitates the simultaneous generation of multiple on-chip mid-IR sources through cascaded FWM, covering a 500 nm spectral range. Together, these results provide a foundation for the construction of silicon-based room-temperature mid-IR light sources including tunable chip-scale parametric oscillators, optical frequency combs, and supercontinuum generators

Frequency Comb Enhancement via the Self-Crystallization of Vectorial Cavity Solitons

Long-range interactions between dark vectorial temporal cavity solitons are induced by the formation of patterns via spontaneous symmetry breaking of orthogonally polarized fields in ring resonators. Turing patterns of alternating polarizations form between adjacent solitons, pushing them apart so that a random distribution of solitons along the cavity length spontaneously reaches equal equilibrium distances, the soliton crystal, without any mode crossing or external modulation. Enhancement of the frequency comb is achieved through the spontaneous formation of regularly spaced soliton crystals, ‘self-crystallization,’ with greater power and spacing of the spectral lines for increasing soliton numbers. Partial self-crystallization is also achievable in long cavities, allowing one to build crystal sections with controllable numbers of cavity solitons separated by intervals of pattern solutions of, again, controllable length

Spectral extension and synchronization of microcombs in a single microresonator

Broadband optical frequency combs are extremely versatile tools for precision spectroscopy, ultrafast ranging, as channel generators for telecom networks, and for many other metrology applications. Here, we demonstrate that the optical spectrum of a soliton microcomb generated in a microresonator can be extended by bichromatic pumping: one laser with a wavelength in the anomalous dispersion regime of the microresonator generates a bright soliton microcomb while another laser in the normal dispersion regime both compensates the thermal effect of the microresonator and generates a repetition-rate-synchronized second frequency comb. Numerical simulations agree well with experimental results and reveal that a bright optical pulse from the second pump is passively formed in the normal dispersion regime and trapped by the primary soliton. In addition, we demonstrate that a dispersive wave can be generated and influenced by cross-phase-modulation-mediated repetition-rate synchronization of the two combs. The demonstrated technique provides an alternative way to generate broadband microcombs and enables the selective enhancement of optical power in specific parts of a comb spectrum. Broadband frequency combs are a key enabling technology for frequency metrology and spectroscopy. Here, the authors demonstrate that the spectrum of a soliton microcomb can be extended by bichromatic pumping resulting in two combs that synchronize their repetition rate via cross-phase modulation