Non-linear and/or time-dependent media

Nonlinear interactions in disordered media

Exploiting multiple scattering to efficiently generate light by non-linear processes, or even to amplify these processes, is still a very open topic. Drawing on our experience in theoretical modeling and simulation, acquired in particular through previous works on random lasers and photon echoes, we are tackling these questions in collaboration with S. Mujumdar’s team at TIFR in Mumbai (India).

We studied second harmonic generation (SHG) in a highly disordered material such as KDP powder. Such a material illuminated by a laser pulse produces two speckle patterns at the fundamental and double frequencies. The speckles generated by successive pulses gradually decorrelate, thanks to scatterer motion, with a faster decorrelation for the SHG speckle. A theoretical model has been developed to explain this observation, highlighting the main mechanism of SHG in disordered media in the multiple scattering regime [1]. More recently, we have studied the spatial and temporal behavior of IR and SHG scattering intensity with the same model, in excellent agreement with experimental observations by the Indian team [2].

Figure 1 Intensity correlation function for the fundamental and second harmonic signal as a function of incident power.

Time-dependent complex media

Recently, there has been growing interest in the degrees of freedom provided by media with time-dependent optical properties. They offer new possibilities for controlling wave propagation. In 2021, we published our first theoretical and numerical study, in collaboration with Boris Shapiro (Technion, Israel), on the statistical energy distribution of a wave passing through a time-disordered medium. A surprising behavior was observed: the exponential growth of the average energy over time [3].

Figure 2 Evolution of the average logarithm of the wave energy as a function of the number of temporal kicks.

A second, more recent work has enabled us to determine the expressions for the scattering mean free path and time in a medium exhibiting both spatial and temporal disorder [4]. Surprisingly, plugging in the second type of disorder in addition to the first decreases the overall diffusion of the system.

Footnotes

[1]

Speckle Decorrelation in Fundamental and Second-Harmonic Light Scattered from Nonlinear Disorder Samanta, R., R. Pierrat, R. Carminati, and S. Mujumdar Physical Review Applied 18, no. 5 (2022) Abstract: Speckle patterns generated in a disordered medium carry a lot of information despite the apparent complete randomness in the intensity pattern. When the medium possesses ?(2) nonlinearity, the speckle is sensitive to the phase of the incident fundamental light, as well as the light generated within. Here, we examine the speckle decorrelation in the fundamental and second-harmonic transmitted light as a function of the varying power in the fundamental beam. At low incident powers, the speckle patterns produced by successive pulses exhibit strong correlations, which decrease with increasing power. The average correlation in the second-harmonic speckle decays faster than in the fundamental speckle. Next, we construct a theoretical model, backed up by numerical computations, to obtain deeper physical insights into the faster decorrelations in the second-harmonic light. While providing excellent qualitative agreement with the experiments, the model sheds light on the contribution of two effects in the correlations, namely, the generation of second-harmonic light and the propagation thereof.

[2]

Photon diffusion in space and time in a second-order-nonlinear disordered medium Samanta, R., R. Pierrat, R. Carminati, and S. Mujumdar Physical Review A 108, no. 5 (2023) Abstract: We report experimental and theoretical investigations of photon diffusion in a second-order-nonlinear disordered medium under conditions of strong nonlinearity. Experimentally, photons at the fundamental wavelength (λ=1064nm) are launched into the structure in the form of a cylindrical pellet, and the second-harmonic (λ=532nm) photons are temporally analyzed in transmission. For comparison, separate experiments are carried out with incident green light at λ=532nm. We observe that the second-harmonic light peaks earlier compared to the incident green photons. Next, the sideways spatial scattering of the fundamental as well as second-harmonic photons is recorded. The spatial diffusion profiles of second-harmonic photons are seen to peak deeper inside the medium in comparison to both the fundamental and incident green photons. In order to give more physical insights into the experimental results, a theoretical model is derived from first principles. It is based on the coupling of transport equations. Solved numerically using a Monte Carlo algorithm and experimentally estimated transport parameters at both wavelengths, it shows excellent semiquantitative agreement with the experiments for both fundamental and second-harmonic light.

[3]

Universal Statistics of Waves in a Random Time-Varying Medium Carminati, R., H. Chen, R. Pierrat, and B. Shapiro Physical Review Letters 127, no. 9 (2021) Abstract: We study the propagation of waves in a medium in which the wave velocity fluctuates randomly in time. We prove that at long times, the statistical distribution of the wave energy is log-normal, with the average energy growing exponentially. For weak disorder, another regime preexists at shorter times, in which the energy follows a negative exponential distribution, with an average value growing linearly with time. The theory is in perfect agreement with numerical simulations, and applies to different kinds of waves. The existence of such universal statistics bridges the fields of wave propagation in time-disordered and space-disordered media.

[4]

Multiple scattering theory in one dimensional space and time dependent disorder: average field [Invited] Selvestrel, A., J. Rocha, R. Carminati, and R. Pierrat Optical Materials Express 14, no. 3, 801-815 (2024) Abstract: We theoretically study the propagation of light in one-dimensional space- and time-dependent disorder. The disorder is described by a fluctuating permittivity ε(x, t) exhibiting short-range correlations in space and time, without cross correlation between them. Depending on the illumination conditions, we show that the intensity of the average field decays exponentially in space or in time, with characteristic length or time defining the scattering mean-free path ℓs and the scattering mean-free time τs. In the weak scattering regime, we provide explicit expressions for ℓs and τs, that are checked against rigorous numerical simulations.

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Non-linear and/or time-dependent media

Nonlinear interactions in disordered media

Time-dependent complex media

Footnotes