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arXiv:2609.22905

Loss induced dynamics of optical pulses in saturable nonlinear media

Golam Ali Sekh

Published Sep 19, 2026• 0 citations
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Abstract

We consider pulse propagation in a saturable nonlinear coupler whose other arm is dissipative and other is transparent. A flow of energy from transparent to dissipative arm takes place for weak value of dissipation and the coupler losses its energy. The energy loss of the coupler reduces for strong dissipation. This energy loss depends on the saturable nonlinearity. We find that the flow of relative energy at the output of a finite-sized coupler has a peak at a particular value of nonlinear strength. The peak value decreases with the increase of dissipation and it vanishes for stronger dissipation due to Zeno effect.

DOI
10.48550/arxiv.2609.22905

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We consider pulse propagation in a saturable nonlinear coupler whose other arm is dissipative and other is transparent. A flow of energy from transparent to dissipative arm takes place for weak value of dissipation and the coupler losses its energy. The energy loss of the coupler reduces for strong dissipation. This energy loss depends on the saturable nonlinearity. We find that the flow of relative energy at the output of a finite-sized coupler has a peak at a particular value of nonlinear strength. The peak value decreases with the increase of dissipation and it vanishes for stronger dissipation due to Zeno effect.
It is shown that, in a simple coupler where one of the waveguides is subject to controlled losses of the electric field, it is possible to observe an optical analog of the linear and nonlinear quantum Zeno effects. The phenomenon consists in a counterintuitive enhancement of transparency of the coupler with an increase of the dissipation and represents an optical analog of the quantum Zeno effect. Experimental realization of the phenomenon based on the use of chalcogenide glasses is proposed. The system allows for observation of the crossover between the linear and nonlinear Zeno effects, as well as the effective manipulation of light transmission through the coupler.
We theoretically demonstrate the possibility of observing the macroscopic Zeno effect for nonlinear waveguides with localized dissipation. We show the existence of stable stationary flows, which are balanced by losses in the dissipative domain. The macroscopic Zeno effect manifests itself in the nonmonotonic dependence of the stationary flow on the strength of the dissipation. In particular, we highlight the importance of the dissipation parameters in observing the phenomenon. Our results are applicable to a large variety of systems, including the condensates of atoms or quasiparticles and optical waveguides.
Pulse propagation in maser-type traveling-wave amplifiers with a homogeneously broadened transition is treated by a formalism analogous to the Bloch equations. Phenomenological dephasing (T2) and recovery (T1) times are defined, and a linear (nonsaturable) loss mechanism is included. In the numerical calculations, only the case of negligible excitation during the time it takes a pulse to pass is considered. When pulses are allowed to grow until the amplifier is ``saturated,'' steady-state pulses having a unique shape and intensity independent of the initial pulse are found. The parameters of these steady-state pulses depend only on the ratio of the linear loss and gain coefficients. Steady-state pulses have a peak intensity that decreases monotonically from infinity to zero as the linear loss coefficient varies from zero to the gain coefficient, while the pulse width correspondingly varies from zero to infinity, and the pulse energy varies from a finite value to zero. Steady-state pulses propogate at a velocity less than that of the small signal velocity in the medium.
A theoretical investigation is reported of the behavior of optical pulses under quasiresonant adiabatic tracking conditions. It is shown that dispersion of the group velocity and saturation of the populations of the resonant levels may give rise to soliton propagation of light. The exact solution for the envelope of a soliton is obtained for the first time subject to the saturation effect. Expressions are derived for the critical energy density in a soliton and for its duration. A study is made of the influence of the resonant saturation on the shape of a soliton envelope and its parameters. An analysis is reported of the behavior of light pulses of energies higher and lower than the critical value. It is shown that these pulses exhibit three types of quasisoliton propagation: weak, strong, and steady-state. The results for the pulses are generalized to two-dimensional light beams in a nonlinear waveguide.
We discuss the inevitable dissipation of energy that must accompany the creation of a pulse-medium excitation state in a passive dielectric. We show that there is a minimum amount of energy that an optical pulse must deposit in the medium to create a given pulse-medium state and that energy deposited beyond this minimum value must be dissipated in the medium. We compare this notion of dissipation to a related concept found by determining the fraction of energy stored in a medium that is irrecoverable by future fields. These two notions of dissipation are model-independent and form upper and lower bounds for real-time loss. Any model-dependent notion of loss that falls outside these bounds has serious conceptual difficulties. We show that a traditional notion of real-time loss based on a multiple-Lorentz oscillator model fails to give reasonable results in classes of passive linear media near EIT, while the notions of loss we introduce give sensible results for all passive media.
Above a critical power threshold for a given pulse width, a short pulse of coherent traveling-wave optical radiation is observed to propagate with anomalously low energy loss while at resonance with a two-quantum-level system of absorbers. The line shape of the resonant system is determined by inhomogeneous broadening, and the pulse width is short compared to dissipative relaxation times. A new mechanism of self-induced transparency, which accounts for the low energy loss, is analyzed in the ideal limit of a plane wave which excites a resonant medium with no damping present. The stable condition of transparency results after the traversal of the pulse through a few classical absorption lengths into the medium. This condition exists when the initial pulse has evolved into a symmetric hyperbolic-secant pulse function of time and distance, and has the area characteristic of a "$2\ensuremath{\pi}$ pulse." Ideal transparency then persists when coherent induced absorption of pulse energy during the first half of the pulse is followed by coherent induced emission of the same amount of energy back into the beam direction during the second half of the pulse. The effects of dissipative relaxation times upon pulse energy, pulse area, and pulse delay time are analyzed to first order in the ratio of short pulse width to long damping time. The analysis shows that the $2\ensuremath{\pi}$ pulse condition can be maintained if losses caused by damping are compensated by beam focusing. In an amplifying inhomogeneously broadened medium an analytic "$\ensuremath{\pi}$ pulse area" solution is presented in the limit of a sharp leading edge of the pulse. The dynamics of self-induced transparency are studied for the particular effects of Doppler velocities upon a resonant gas. The analysis of transparency for random orientations of dipole moments associated with degenerate rotational states yields modified forms of self-induced transparency behavior, which indicates a finite pulse energy loss as a function of distance in some cases. The effect of self-induced transparency on the photon echo is considered. Experimental observations of self-induced transparency have been made in a ruby sample at resonance with a pulsed ruby-laser beam. Single and multiple $2\ensuremath{\pi}$ pulse outputs have been observed, and pulse areas measured in the range of $2\ensuremath{\pi}$. The experimental results are compared with the predictions of the ideal-plane-wave theory. Deviations from the ideal-plane-wave theory are discussed. An analysis is made of the effect of a transverse mode of the propagating beam upon the transparency properties of the pulse.