Gain through losses in nonlinear optics

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-organization, 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 summarize 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 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 modulation instability, 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

Magneto-tunnelling in double-barrier structures:the B perpendicular to J configuration

\u3cp\u3eThe peak in the current-voltage (I-V) characteristic of a double-barrier resonant-tunnelling structure is broadened and lowered by the application of a magnetic field parallel to the layers. The broadening of the peak is roughly linear in the field. The lowering is completed at a field strength termed the quenching field. Both effects are described within a model of coherent tunnelling in a self-consistent potential. The calculated I-V curves agree well with experimental data.\u3c/p\u3

Two-period magneto-oscillations in coherent double barrier-resonant tunnelling

\u3cp\u3eApplying a magnetic field B to a double-barrier resonant-tunnelling diode, perpendicular to the layer structure, introduces oscillations in current density and capacitance that are periodic in 1/B. A derivation of this periodicity is given, based on coherent wave propagation. Two magneto-periods are found, corresponding to the electron concentration in emitter and well, respectively. Numerical calculations are presented for a semiconductor model with self-consistently determined electron potential.\u3c/p\u3

Resonant optical amplification in a laser diode:theory and experiment

\u3cp\u3eResonant optical amplification is studied both theoretically and experimentally. Coupled rate equations for the signal field and the spontaneous emission field, valid for input signals with bit rates up to 10 Gb/s are derived. A special weighing procedure based on a dwell-time analysis is used to account for bistable filter operation. The measured amplification characteristics of a λ/4 DFB laser injected with a 2.5 Gb/s signal show good agreement with theory.\u3c/p\u3