Gain through losses in nonlinear optics

Auro M Perego,Sergei K Turitsyn,Kestutis Staliunas

doi:10.1038/s41377-018-0042-9

Auro M Perego, Sergei K Turitsyn + Show 1 more

Open Access

https://doi.org/10.1038/s41377-018-0042-9

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Abstract

Instabilities of uniform states are ubiquitous processes occurring in a variety of spatially extended nonlinear systems. These instabilities are at the heart of symmetry breaking, condensate dynamics, self-organisation, pattern formation, and noise amplification across diverse disciplines, including physics, chemistry, engineering, and biology. In nonlinear optics, modulation instabilities are generally linked to the so-called parametric amplification process, which occurs when certain phase-matching or quasi-phase-matching conditions are satisfied.In the present review article, we summarise the principle results on modulation instabilities and parametric amplification in nonlinear optics, with special emphasis on optical fibres. We then review state-of-the-art research about a peculiar class of modulation instabilities (MIs) and signal amplification processes induced by dissipation in nonlinear optical systems. Losses applied to certain parts of the spectrum counterintuitively lead to the exponential growth of the damped mode themselves, causing gain through losses. We discuss the concept of imaging of losses into gain, showing how to map a given spectral loss profile into a gain spectrum. We demonstrate with concrete examples that dissipation-induced MI, apart from being of fundamental theoretical interest, may pave the way towards the design of a new class of tuneable fibre-based optical amplifiers, optical parametric oscillators, frequency comb sources, and pulsed lasers.

Highlights

Instabilities of uniform states are ubiquitous processes occurring in a variety of spatially extended nonlinear systems
To better demonstrate the Gain through losses (GTL) dynamics in OPOs, we analytically show that dissipation can induce amplification in situations where standard parametric amplification should in principle be absent
We have included some novel results and extended the concept of modulation instabilities (MIs) induced by losses to various important systems and models: the nonlinear Schrödinger equation (NLSE) coupled to a two-level distributed system; the NLSE with periodic lumped filtering, leading to ILG, which opens the possibility for a new class of fibre-optic-based tuneable amplifiers; the coupled wave equations describing OPOs; and the GLLE that models an externally driven ring fibre resonator with an intracavity spectral filter

Summary

Introduction

Instabilities of uniform states are ubiquitous processes occurring in a variety of spatially extended nonlinear systems. The latter phenomenon can be routinely observed in an optical fibre, where phase-matching conditions are achieved in case of anomalous dispersion: a sufficiently intense pump field amplifies two spectral sidebands symmetrically located with respect to the pump wave frequency, which, in this context, are called the signal and idler.

Results

Conclusion