Low-noise Optical Frequency Comb Research Articles

Experimental demonstration of a low repetition rate optical frequency comb

Optical frequency combs operating at low repetition rate exhibit high pulse energy for a given average power. Therefore, low repetition rate frequency combs may efficiently drive nonlinear frequency conversion into the mid-infrared or extreme ultraviolet region to extend frequency metrology to such exotic wavelengths. In this work, we have experimentally demonstrated a low-noise optical frequency comb operating at 40 kHz repetition rate using a Yb:KYW mode-locked laser (center wavelength at 1030 nm, repetition rate 40 MHz) and an acousto-optic modulator-based pulse picker. We have stabilized a single comb mode to an ultra-stable continuous wave laser operating at 1033 nm. The integral rms phase noise (in the range 10 Hz - 20 kHz) was measured to be 167.2 mrad.

Noise Measurement and Reduction in Mode-Locked Lasers: Fundamentals for Low-Noise Optical Frequency Combs

After five decades of development, mode-locked lasers have become significant building blocks for many optical systems in scientific research, industry, and biomedicine. Advances in noise measurement and reduction are motivated for both shedding new light on the fundamentals of realizing ultra-low-noise optical frequency combs and their extension to potential applications for standards, metrology, clock comparison, and so on. In this review, the theoretical models of noise in mode-locked lasers are first described. Then, the recent techniques for timing jitter, carrier-envelope phase noise, and comb-line noise measurement and their stabilization are summarized. Finally, the potential of the discussed technology to be fulfilled in novel optical frequency combs, such as electro-optic (EO) modulated combs, microcombs, and quantum cascade laser (QCL) combs, is envisioned.

Soliton bursts and deterministic dissipative Kerr soliton generation in auxiliary-assisted microcavities

Dissipative Kerr solitons in resonant frequency combs offer a promising route for ultrafast mode-locking, precision spectroscopy and time-frequency standards. The dynamics for the dissipative soliton generation, however, are intrinsically intertwined with thermal nonlinearities, limiting the soliton generation parameter map and statistical success probabilities of the solitary state. Here, via use of an auxiliary laser heating approach to suppress thermal dragging dynamics in dissipative soliton comb formation, we demonstrate stable Kerr soliton singlet formation and soliton bursts. First, we access a new soliton existence range with an inverse-sloped Kerr soliton evolution—diminishing soliton energy with increasing pump detuning. Second, we achieve deterministic transitions from Turing-like comb patterns directly into the dissipative Kerr soliton singlet pulse bypassing the chaotic states. This is achieved by avoiding subcomb overlaps at lower pump power, with near-identical singlet soliton comb generation over twenty instances. Third, with the red-detuned pump entrance route enabled, we uncover unique spontaneous soliton bursts in the direct formation of low-noise optical frequency combs from continuum background noise. The burst dynamics are due to the rapid entry and mutual attraction of the pump laser into the cavity mode, aided by the auxiliary laser and matching well with our numerical simulations. Enabled by the auxiliary-assisted frequency comb dynamics, we demonstrate an application of automatic soliton comb recovery and long-term stabilization against strong external perturbations. Our findings hold potential to expand the parameter space for ultrafast nonlinear dynamics and precision optical frequency comb stabilization.

High-detectivity optical heterodyne method for wideband carrier-envelope phase noise analysis of laser oscillators.

Broadband characterization of the carrier-envelope phase (CEP) noise spectral density of free-running mode-locked lasers is essential for advanced low-noise optical frequency comb designs. Here we present a direct method that utilizes an optical heterodyne beat between a pair of repetition-rate-locked mode-locked lasers for CEP noise characterization, without requiring an f-2f interferometer or nonlinear optical conversion steps. A proof-of-principle experiment in a femtosecond Yb-fiber laser achieves CEP noise spectral density characterization with >270 dB dynamic range over a Fourier frequency range from 5mHz to 8MHz. The measurement noise floor is well below 1 μrad/√Hz, enabling dependable detection down to a quantum-limited noise floor. The method can resolve various noise mechanisms that cause specific CEP noise spectral shapes. The underlying mechanisms are further analyzed in terms of spurious temporal correlation to distinguish between technical and stochastic noise signatures. Moreover, a Hadamard deviation analysis reveals a varying degree of frequency stability in the measured CEP time series.

Breather soliton dynamics in microresonators

The generation of temporal cavity solitons in microresonators results in coherent low-noise optical frequency combs that are critical for applications in spectroscopy, astronomy, navigation or telecommunications. Breather solitons also form an important part of many different classes of nonlinear wave systems, manifesting themselves as a localized temporal structure that exhibits oscillatory behaviour. To date, the dynamics of breather solitons in microresonators remains largely unexplored, and its experimental characterization is challenging. Here we demonstrate the excitation of breather solitons in two different microresonator platforms based on silicon nitride and on silicon. We investigate the dependence of the breathing frequency on pump detuning and observe the transition from period-1 to period-2 oscillation. Our study constitutes a significant contribution to understanding the soliton dynamics within the larger context of nonlinear science.

Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators

Dissipative temporal Kerr solitons in optical microresonators enable to convert a continuous wave laser into a train of femtosecond pulses. Of particular interest are single soliton states, whose $\mathrm{sech}^{2}$ spectral envelope provides a spectrally smooth and low noise optical frequency comb, and that recently have been generated in crystalline, silica, and silicon-nitride resonators. Here, we study the dynamics of multiple soliton states containing ${N}$ solitons and report the discovery of a novel, yet simple mechanism which makes it possible to reduce deterministically the number of solitons, one by one, i.e. ${N\! \to\! N\!-\!1\! \to\! \dots \!\to\! 1}$. By applying weak phase modulation, we directly characterize the soliton state via a double-resonance response. The dynamical probing demonstrates that transitions occur in a predictable way, and thereby enables us to map experimentally the underlying multi-stability diagram of dissipative Kerr solitons. These measurements reveal the "lifted" degeneracy of soliton states as a result of the power-dependent thermal shift of the cavity resonance (i.e. the thermal nonlinearity). The experimental results are in agreement with theoretical and numerical analysis that incorporate the thermal nonlinearity. By studying two different microresonator platforms (integrated $\mathrm{Si_{3}N_{4}}$ microresonators and crystalline $\mathrm{MgF_{2}}$ resonators) we confirm that these effects have a universal nature. Beyond elucidating the fundamental dynamical properties of dissipative Kerr solitons the observed phenomena are also of practical relevance, providing a manipulation toolbox which enables to sequentially reduce, monitor and stabilize the number ${N}$ of solitons, preventing it from decay. Achieving reliable single soliton operation and stabilization in this manner in optical resonators is imperative to applications.

Temporal solitons in optical microresonators

Dissipative solitons can emerge in a wide variety of dissipative nonlinear systems throughout the fields of optics, medicine or biology. Dissipative solitons can also exist in Kerr-nonlinear optical resonators and rely on the double balance between parametric gain and resonator loss on the one hand and nonlinearity and diffraction or dispersion on the other hand. Mathematically these solitons are solution to the Lugiato-Lefever equation and exist on top of a continuous wave (cw) background. Here we report the observation of temporal dissipative solitons in a high-Q optical microresonator. The solitons are spontaneously generated when the pump laser is tuned through the effective zero detuning point of a high-Q resonance, leading to an effective red-detuned pumping. Red-detuned pumping marks a fundamentally new operating regime in nonlinear microresonators. While usually unstablethis regime acquires unique stability in the presence of solitons without any active feedback on the system. The number of solitons in the resonator can be controlled via the pump laser detuning and transitions to and between soliton states are associated with discontinuous steps in the resonator transmission. Beyond enabling to study soliton physics such as soliton crystals our observations open the route towards compact, high repetition-rate femto-second sources, where the operating wavelength is not bound to the availability of broadband laser gain media. The single soliton states correspond in the frequency domain to low-noise optical frequency combs with smooth spectral envelopes, critical to applications in broadband spectroscopy, telecommunications, astronomy and low phase-noise microwave generation.

Processing of optical combs with fiber optic parametric amplifiers

Low noise optical frequency combs consist of equally spaced narrow-linewidth optical tones. They are useful in many applications including, for example, line-by-line pulse shaping, THz generation, and coherent communications. In such applications the comb spacing, extent of spectral coverage, degree of spectral flatness, optical tone power and tone-to-noise ratio represent key considerations. Simultaneously achieving the level of performance required in each of these parameters is often challenging using existing comb generation technologies. Herein we suggest and demonstrate how fiber optic parametric amplifiers can be used to enhance all of these key comb parameters, allowing frequency span multiplication, low noise amplification with simultaneous comb spectrum flattening, and improvement in optical tone-to-noise ratio through various phase insensitive as well as phase sensitive implementations.

Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb

We describe a radio-frequency (RF) discriminator, or frequency-to-voltage converter, based on a voltage-controlled oscillator phase-locked to the signal under test, which has been developed to analyze the frequency noise properties of an RF signal, e.g., a heterodyne optical beat signal between two lasers or between a laser and an optical frequency comb. We present a detailed characterization of the properties of this discriminator and we compare it to three other commercially available discriminators. Owing to its large linear frequency range of 7 MHz, its bandwidth of 200 kHz and its noise floor below 0.01 Hz(2)/Hz in a significant part of the spectrum, our frequency discriminator is able to fully characterize the frequency noise of a beat signal with a linewidth ranging from a couple of megahertz down to a few hertz. As an example of application, we present measurements of the frequency noise of the carrier envelope offset beat in a low-noise optical frequency comb.

Sub-THz Wave Generation Using Photonics Technology and Its Application

We describe a technique for generating millimeter- and submillimeter-waves by using photonics technology focusing on the generation of optical beat signals with such a frequency range. We also describe an optical beat signal generation technique that utilizes an optical frequency comb with a spectral bandwidth of over 1 THz. To obtain a low-noise optical frequency comb, a phase modulator and a single-mode fiber are used for optical pulse generation. The frequency interval of the optical frequency comb can be tuned from 30 to 40 GHz. We can obtain an optical beat signal with an arbitrary frequency from 100 GHz to 1 THz by selecting and mixing two appropriate line spectra from the optical frequency comb.