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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Two-photon absorption induced optical power limiting behavior of strong femtosecond hyper-Gaussian pulses

Ji‐Cai Liu, Xing-Zhe Li, Ying Zhang

Published Nov 3, 2016• 1 citation
Publisher

Abstract

Propagation of strong femtosecond hyper-Gaussian pulses in an organic molecular medium is studied by solving numerically the Maxwell-Bloch equations using an iterative predictor-corrector finite-difference time-domain technique. The carrier-wave frequency of the field is tuned in two-photon resonance with the molecular system simplified by a cascade three-level model. Strong two-photon absorption induced optical power limiting behavior is observed for the hyper-Gaussian pulses of different orders. For the ultrashort hyper-Gaussian pulses, it is found that the ”two-photon area” is no further the deciding quantity of the two-photon induced dynamics, and pulses with different temporal profiles will induce different two-photon absorption dynamics and optical limiting processes. With the same pulse duration and field amplitude, pulses of a lower order is found to have a larger input ”two-photon area” but a smaller output area, and therefore show a better optical limiting behavior. The population distribution and the generation of new fields during pulse propagation also depend on the shape of the incident field.

DOI
10.1117/12.2247665

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Propagation of strong femtosecond hyper-Gaussian pulses in an organic molecular medium is studied by solving numerically the Maxwell-Bloch equations using an iterative predictor-corrector finite-difference time-domain technique. The carrier-wave frequency of the field is tuned in two-photon resonance with the molecular system simplified by a cascade three-level model. Strong two-photon absorption induced optical power limiting behavior is observed for the hyper-Gaussian pulses of different orders. For the ultrashort hyper-Gaussian pulses, it is found that the ”two-photon area” is no further the deciding quantity of the two-photon induced dynamics, and pulses with different temporal profiles will induce different two-photon absorption dynamics and optical limiting processes. With the same pulse duration and field amplitude, pulses of a lower order is found to have a larger input ”two-photon area” but a smaller output area, and therefore show a better optical limiting behavior. The population distribution and the generation of new fields during pulse propagation also depend on the shape of the incident field.
Propagation of strong femtosecond hyper-Gaussian pulses in a cascade three-level molecular system is studied by solving numerically the Maxwell–Bloch equations by the iterative predictor-corrector finite-difference time-domain method. Optical power limiting behavior induced by strong nonlinear two-photon absorption is observed for different orders of the femtosecond hyper-Gaussian pulses. Pulses of a higher order temporal profile are found to have a wider power range of optical limiting but a larger output saturation intensity. Both the output saturation value and the damage threshold of optical power limiting decrease with pulse duration increasing. The decrease of the pulse area along the pulse propagation is much slower than that obtained from the two-photon area theorem due to invalidity of the slowly varying amplitude approximation and the monochromatic field hypothesis.
The interference resonant propagation of two-color 4π-4π femtosecond Gaussian pulses in three-level Λ-type atomic medium with different values of the relative phase φ is investigated by using numerical solution, which is obtained by the finite-difference time domain (FDTD) method and the iterative predictor–corrector (PC) method for the full Maxwell-Bloch equations. It is found that, for a smaller value of the φ, the pulse splitting occurs, and when the value of the φ increases to a certain value, only the variation of pulse shape present but the pulse splitting no longer occurs; accordingly, their spectral strengths and frequency ranges of the two-color pulses decrease remarkably with the value of φ increasing; Moreover, the relative phase also has an obvious effect on population, different population evolutions can be achieved by adjusting the value of φ.
The interference resonant propagation and spectral properties of a superposition of two femtosecond chirped Gaussian pulses with equal pulse area and same size but opposite sign of the chirp coefficient (C) in a three-level Λ-type atomic medium is investigated by using the numerical solution, which is obtained by the finite-difference time-domain (FDTD) method and the iterative predictor–corrector (PC) method for the full Maxwell–Bloch equations. It is found that, for the double pulses with smaller area, (2π, 2π) double pulses, the pulse splitting occurs when the value of the |C| is smaller, and only the variation of pulse shape is present but the pulse splitting no longer occur when the value of the |C| increases to a certain value; New high frequency component doesn’t basically appear and the strength of the spectral component near the central frequency decreases considerably but the strength of blue shift component is not varied obviously with the value of |C| increasing. For the double pulses with larger areas, the case of pulse splitting is similar to that of (2π, 2π) pulses, but the strength of the spectral component with higher frequency increase evidently comparing with the case of (2π, 2π) double pulses. Moreover, the value of the |C| also has an obvious effect on population, different population evolutions can be achieved by adjusting the value of |C|.
Coherent control of femtosecond two-photon absorption in the intermediate-field regime is analyzed in detail in the powerful frequency domain using an extended 4th-order perturbative description. The corresponding absorption is coherently induced by the weak-field non-resonant two-photon transitions as well as by four-photon transitions involving three absorbed photons and one emitted photons. The interferences between these two groups of transitions lead to a difference between the intermediate-field and weak-field absorption dynamics. The corresponding interference nature (constructive or destructive) strongly depends on the detuning direction of the pulse spectrum from half the two-photon transition frequency. The model system of the study is atomic sodium, for which both experimental and theoretical results are obtained. The detailed understanding obtained here serves as a basis for coherent control with rationally-shaped femtosecond pulses in a regime of sizable absorption yields.
Propagation of single- and two-color hyperbolic secant femtosecond laser pulses in a three-level $\ensuremath{\Lambda}$-type quantum system is investigated by solving the Maxwell and density matrix equations with the finite-difference time-domain and Runge-Kutta methods. As a first study of our modeling, we simulate pulse self-induced transparency (SIT) in two-level systems and see how this phenomenon can be controlled by manipulating the initial relative phase between the SIT pulse and a second control pulse, provided the ratio between both pulse frequencies obeys the relation ${\ensuremath{\omega}}_{1}∕{\ensuremath{\omega}}_{2}=3$. We then examine frequency down-conversion processes that are observed with single- and two-color pulses the envelope area of which is equal to or a multiple of $2\ensuremath{\pi}$, for pulse frequencies close to resonance with the transitions of a three-level $\ensuremath{\Lambda}$ medium. Also, phase-sensitive phenomena are discussed in the case of two-color $\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ pulses propagating resonantly in the three-level system. In particular, possibilities for such coherent control are found for frequency down-conversion processes when the ratio of the frequencies of optical transitions is ${\ensuremath{\omega}}_{13}∕{\ensuremath{\omega}}_{12}=3$. The conditions for quantum control of four-wave mixing processes are also examined when the pulse frequencies of two-color $\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ pulses are far from any resonance of the three-level system. We demonstrate the possibility to cancel the phase sensitivity of the four-wave coupling in a $\ensuremath{\Lambda}$-type system by competition effects between optical transitions.
Propagation of dichromatic femtosecond laser pulses tuned respectively in single-photon resonances with the cascade three-level system is studied. The initial areas of the two pulses are both equal to 2π, which makes them respectively an optical soliton in ideal two-level systems. When the dichromatic solitons are synchronized into the medium, both the temporal shapes and the spectral distributions of the pulses are strongly distorted during propagation. The delay time between the dichromatic solitons plays an important role on the evolution of the fields.