Rate equation analysis and non-Hermiticity in coupled semiconductor laser arrays

Abstract

Optically-coupled semiconductor laser arrays are described by coupled rate equations. The coupled mode equations and carrier densities are included in the analysis, which inherently incorporate the carrier-induced nonlinearities including spatial hole burning and amplitude-phase coupling. We solve the steady-state coupled rate equations and consider the cavity frequency detuning and the individual laser pump rates as the experimentally controlled variables. We show that the carrier-induced nonlinearities play a critical role in the mode control, and we identify gain contrast induced by cavity frequency detuning as a unique mechanism for mode control. Photon-mediated energy transfer between cavities is also discussed. Parity-time symmetry and exceptional points in this system are studied. Unbroken parity-time symmetry can be achieved by judiciously combining cavity detuning and unequal pump rates, while broken symmetry lies on the boundary of the optical locking region. Exceptional points are identified at the intersection between broken and unbroken parity-time symmetry.

Dynamics of Laterally-Coupled Pairs of Spin-VCSELs

“…These behaviours are shown in Fig. 15 where the square points show the ellipticity in guide (1), the diamond points show the ellipticity in guide (2) and the red arrows indicate the directions in which P (2) is varied. the pump power is stepped down to η (i) = 12, leading to oscillations in the ellipticity with an angular frequency of approximately 66 rad·ns −1 .…”

“…For this particular set of parameters, the switching time is quite slow, taking around 100 ns to settle down to the steady-state solutions. show the sequence in which the pump ellipticity in guide 2, P (2) , was varied.…”

Radically tunable ultrafast photonic oscillators via differential pumping

“…It is worth mentioning that for laser separation distances larger than those typically occurring in PICs or in cases where delays are intentionally introduced, such systems are described by delay-differential equations having a rich set of dynamical features [21][22][23][24].The introduction of topological characteristics in coupled lasers in terms of differential pumping and frequency detuning between the lasers [ Fig. 1(d)] enables the onchip implementation of a large set of key functionalities such as reconfigurable beam forming and steering [25], coherence tuning and enhanced phase-locking [26][27][28], localized syncrhonization [27,29], enhanced bandwidth and tailored modulation response [30,31] as well as existence of exceptional points allowing for ultra-sensitivity [32][33][34][35].In this work we consider the fundamental non-Hermitian optical meta-molecule consisting of two mutually coupled and differentially pumped semiconductor lasers as the basic reconfigurable oscillator element of a photonic integrated circuit exhibiting an extreme frequency tunability spanning over 100 GHz and controlled by minute changes of the electrically injected differential pumping. The latter is shown to control not only the frequency but also the shape of the underlying limit cycle providing a remarkable flexibility for the RF properties of the emited light beam.The time evolution of the electric fields and the number densities of two evanescently coupled diode lasers is governed by the following coupled single-mode rate equations for the amplitude of their normalized electric fields E 1 , E 2 , their phase difference θ and the normalized excess…”

“…The introduction of topological characteristics in coupled lasers in terms of differential pumping and frequency detuning between the lasers [ Fig. 1(d)] enables the onchip implementation of a large set of key functionalities such as reconfigurable beam forming and steering [25], coherence tuning and enhanced phase-locking [26][27][28], localized syncrhonization [27,29], enhanced bandwidth and tailored modulation response [30,31] as well as existence of exceptional points allowing for ultra-sensitivity [32][33][34][35].…”

Antiresonances and Ultrafast Resonances in a Twin Photonic Oscillator

“…The coupling introduces a rich set of complex dynamical features in the system such as phase locking, instabilities, bifurcations and limit cycles [2][3][4][5][6]. From the technological point of view, systems of coupled semiconductor lasers offer capabilities for numerous integrated photonics applications [7] as transmitters in high-speed optical communications and optical interconnects, high-power laser sources, tunable photonic oscillators, controllable optical beam shaping and steering elements and ultrasensitive sensors [8][9][10][11][12]. The underlying model of such structures is a system of coupled rate equations governing the time evolution of the electric fields amplitudes and phases as well as the carrier dynamics, with the carrier-induced nonlinearity playing a crucial role due to a non-zero linewidth enhancement factor describing an amplitudephase coupling mechanism [13].…”