Resonances between fundamental frequencies for lasers with large delayed feedbacks

Abstract

High-order frequency locking phenomena were recently observed using semiconductor lasers subject to large delayed feedbacks [1,2]. Specifically, the relaxation oscillation (RO) frequency and a harmonic of the feedback-loop round-trip frequency coincided with the ratios 1:5 to 1:11. By analyzing the rate equations for the dynamical degrees of freedom in a laser subject to a delayed optoelectronic feedback, we show that the onset of a two-frequency train of pulses occurs through two successive bifurcations. While the first bifurcation is a primary Hopf bifurcation to the ROs, a secondary Hopf bifurcation leads to a two-frequency regime where a low frequency, proportional to the inverse of the delay, is resonant with the RO frequency. We derive an amplitude equation, valid near the first Hopf bifurcation point, and numerically observe the frequency locking. We mathematically explain this phenomenon by formulating a closed system of ordinary differential equations from our amplitude equation. Our findings motivate new experiments with particular attention to the first two bifurcations. We observe experimentally (1) the frequency locking phenomenon as we pass the secondary bifurcation point, and (2) the nearly constant slow period as the two-frequency oscillations grow in amplitude. Our results analytically confirm previous observations of frequency locking phenomena for lasers subject to a delayed optical feedback.

Effective production of gammas, positrons, and photonuclear particles from optimized electron acceleration by short laser pulses in low-density targets

“…The corresponding nonlinear structure looks like an empty cavity of pulse length with an electrostatic field filled with a laser field (a "laser bullet"). The considered relativistic laser pulse satisfies the condition of complete electron cavitation immediately at the entrance of the light into the target, which supports almost the same pulse radius over entire propagation length until pulse depletion in accordance with the most advanced theory, where self-focusing is associated with plasma nonlinearities due to both relativistic electron mass variation and relativistic charge displacement [20]. Acceleration of electrons in laser bullet occurs as a combination of direct laser acceleration and electrostatic wake acceleration with a stochastic feature.…”

“…where self-focusing is associated with plasma nonlinearities due to both relativistic electron mass variation and relativistic charge displacement [20].…”

Generation of high-charge electron beam in a subcritical-density plasma through laser pulse self-trapping

“…To understand condition (1) for stable relativistic self-channeling of a Gaussian laser beam entering a plasma, we use a commonly used model based on the nonlinear Schrödinger equation (NLSE) for the complex amplitude of the laser electric field [11]. Although this model is based on a simple stationary envelope treatment, it can shed light on the physics of the propagation of a short laser pulse.…”

“…The influence of both mechanisms on the propagation mode for a relativistic laser beam has been discussed in detail in various papers [14,[16][17][18][19] and monographs [20,21]. A recent work [11] gives an analytical description of a self-focusing structure formation for a laser beam having a given form of the radial intensity distribution at the plasma entrance which can be plasma-vacuum interface, as in our PIC model. This work which includes the mentioned relativistic nonlinearities has taken an important step towards the solution of the boundary-value problem for the incident Gaussian light beam, that is exactly what corresponds to PIC simulations with parameter R inside plasma.…”

“…This matching condition is shown to be the condition for a self-trapping regime of relativistic self-channeling, which we prove in Sec. IV using a recently developed theory [11]. We discuss the results and conclusions in Sec.…”