Mode-mode competition and unstable behavior in a homogeneously broadened ring laser

Competition between Two-Photon Driving, Dissipation, and Interactions in Bosonic Lattice Models: An Exact Solution

We present an exact solution in arbitrary dimensions for the steady states of a class of quantum driven-dissipative bosonic models, where a set of modes is subject to arbitrary two-photon driving, single-photon loss, and a global Hubbard (or Kerr)-like interaction. Our solutions reveal a wealth of striking phenomena, including the emergence of dissipative phase transitions, nontrivial mode competition physics and symmetry breaking, and the stabilization of many-body SU(1,1) pair-coherent states. Our exact solutions enable the description of spatial correlations, and are fully valid in regimes where traditional mean-field and semiclassical approaches break down.

Conversion Efficiency in Kerr-Microresonator Optical Parametric Oscillators: From Three Modes to Many Modes

Optical parametric oscillation in a Kerr nonlinear microresonator can generate coherent laser light with frequencies that are widely separated from the pump frequency, allowing, for example, visible light to be generated using a near-infrared pump. To be practically useful, the pump-to-signal conversion efficiency must be far higher than what has been demonstrated in microresonator-based oscillators with widely-separated output frequencies. To address this challenge, here we theoretically and numerically study parametric oscillations in Kerr nonlinear microresonators, revealing an intricate solution space that arises from an interplay of nonlinear processes. As a start, we use a three-mode approximation to derive an efficiency-maximizing relation between pump power and frequency mismatch. However, realistic devices, such as integrated microring resonators, support far more than three modes. Hence, a more accurate model that includes the entire modal landscape is necessary to determine potential inefficiencies arising from unwanted competing nonlinear processes. To this end, we numerically simulate the Lugiato-Lefever Equation that accounts for the full spectrum of nonlinearly-coupled resonator modes. We observe and characterize two nonlinear phenomena linked to parametric oscillations in multi-mode resonators: Mode competition and cross phase modulation-induced modulation instability. Both processes may impact conversion efficiency. Finally, we show how to increase the conversion efficiency to ≈ 25 % by tuning the microresonator loss rates. Our analysis will guide microresonator designs that aim for high conversion efficiency and output power.

Embedding liquid lasers within or around aqueous microfluidic droplets

In this paper, we demonstrate the incorporation of dye-based liquid lasers within or around flowing aqueous microfluidic droplets. In particular, we use dye solutions in benzyl alcohol, and either disperse an ensemble of small (∼20 μm) lasing droplets within large (∼500 μm) aqueous droplets flowing in a simple glass capillary-based microfluidic device, or 'wrap' a thin (∼10 μm) lasing benzyl alcohol shell around larger (∼560 μm) microfluidic aqueous droplets. We experimentally and theoretically characterize the lasing behavior in both cases, which is supported by whispering-gallery mode (WGM) optical resonances at the droplet interfaces. We showcase a simple application of our method, which highlights the advantages of having embedded, spatially segregated laser sources within a droplet containing a model analyte solution. With this method, each microfluidic droplet now functions not only as an isolated experiment flask, but is also capable of on drop sensing that exploits WGM-based lasing, thus expanding the possibilities for online monitoring of biophysical/biochemical processes and sensitive detection of biomolecules in droplet-based microfluidics.

Analytical comparison of pulses generated by locking three and five longitudinal modes in free-running class B lasers

We consider the coherent oscillation of five longitudinal modes, which leads to the coupling of modes in the frequency domain and generation of short pulses in the time domain. The aim is to audit the mechanism of mode locking in more detail by extending the analytical solution of the Maxwell-Bloch equations of motion from three to five mode states. The characteristics of pulses including height, repetition, and duration have been calculated for a five-mode class B laser, and the changes are compared with respect to the three-mode state. The effects of other parameters, such as the mean damping rate of cavity mirrors, the frequency detuning of cavity longitudinal modes, and the laser pumping rate have also been investigated. The central and adjacent modes supply the energy of pulses. The amplification gains of five oscillating modes, together with the contribution to forming pulses, are evaluated. It is finally demonstrated that the results satisfy the energy conservation law.

Extreme events in the Ti:sapphire laser

We report experimental and theoretical evidence of the existence of extreme value events in the form of scarce and randomly emerging giant pulses in the femtosecond (self-pulsing or Kerr-lens mode-locked) Ti:sapphire laser. This laser displays complex dynamical behavior, including deterministic chaos, in two different regimes. The extreme value pulses are observed in the chaotic state of only one of these two regimes. The observations agree with the predictions of a well-tested theoretical model that does not include noise or self-Q-switching into its framework. This implies that, in this laser, the extreme effects have a nontrivial dynamical origin. The Ti:sapphire laser is hence revealed as a new and convenient system for the study of these effects.

Longitudinal mode multistability in Ring and Fabry-Pérot lasers: the effect of spatial hole burning

We theoretically discuss the impact of the cavity configuration on the possible longitudinal mode multistability in homogeneously broadened lasers. Our analysis is based on the most general form of a Travelling-Wave Model for which we present a method that allows us to evaluate the monochromatic solutions as well as their eigenvalue spectrum. We find, in agreement with recent experimental reports, that multistability is more easily reached in Ring than in Fabry-Pérot cavities which we attribute to the different amount of Spatial-Hole Burning in each configuration.

Optical memory based on ultrafast wavelength switching in a bistable microlaser

We propose an optical memory cell based on ultrafast wavelength switching in coupled-cavity microlasers, featuring bistability between modes separated by several nanometers. A numerical implementation is demonstrated by simulating a two-dimensional photonic crystal microlaser. Switching times of less than 10 ps, switching energy around 15-30 fJ, and on-off contrast of more than 40 dB are achieved. Theoretical guidelines for optimizing the performance of the memory cell in terms of switching time and energy are drawn.

Scale disparities in the complex Swift-Hohenberg equation for lasers

The complex Swift-Hohenberg (CSH) equation is a generic order parameter equation that applies to many physical systems. In the case of class C lasers, it can be obtained from the Maxwell-Bloch equations using the assumptions of slow envelope and small detuning. We show that the resulting CSH equation inevitably contains different asymptotic order terms, associated with the dominance of the effect of dispersion over diffusion. These scale disparities are usually overlooked or simply not mentioned in the literature, assuming that a CSH equation with all terms of the same order still provides qualitative information. In this paper, the asymptotically nonuniform CSH equation is carefully deduced using a simpler scaling-free procedure, and a stability analysis of the simplest solutions together with some numerical simulations are presented, in which the mentioned scale disparities are clearly seen.

Low instability threshold in a laser operating in both states of polarization

We show that the instability threshold for a laser in which both polarizations are active can be much lower than the Haken second threshold and does not require the bad-cavity limit.