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Chinese Physics B

Polarization control of multi-photon absorption under intermediate femtosecond laser field

Wenjing Cheng, Pei Liu, Guo Liang, Ping Wu, Tianqing Jia, Zhenrong Sun, Shian Zhang

Published Aug 1, 2017• 1 citation
Publisher

Abstract

It has been shown that the femtosecond laser polarization modulation is a very simple and well-established method to control the multi-photon absorption process by the light–matter interaction. Previous studies mainly focused on the multi-photon absorption control in the weak field. In this paper, we further explore the polarization control behavior of multi-photon absorption process in the intermediate femtosecond laser field. In the weak femtosecond laser field, the second-order perturbation theory can well describe the non-resonant two-photon absorption process. However, the higher order nonlinear effect (e.g., four-photon absorption) can occur in the intermediate femtosecond laser field, and thus it is necessary to establish new theoretical model to describe the multi-photon absorption process, which includes the two-photon and four-photon transitions. Here, we construct a fourth-order perturbation theory to study the polarization control behavior of this multi-photon absorption under the intermediate femtosecond laser field excitation, and our theoretical results show that the two-photon and four-photon excitation pathways can induce a coherent interference, while the coherent interference is constructive or destructive that depends on the femtosecond laser center frequency. Moreover, the two-photon and four-photon transitions have the different polarization control efficiency, and the four-photon absorption can obtain the higher polarization control efficiency. Thus, the polarization control efficiency of the whole excitation process can be increased or decreased by properly designing the femtosecond laser field intensity and laser center frequency. These studies can provide a clear physical picture for understanding and controlling the multi-photon absorption process in the intermediate femtosecond laser field, and also can provide a theoretical guidance for the future experimental realization.

DOI
10.1088/1674-1056/26/8/083201

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It has been shown that the femtosecond laser polarization modulation is a very simple and well-established method to control the multi-photon absorption process by the light–matter interaction. Previous studies mainly focused on the multi-photon absorption control in the weak field. In this paper, we further explore the polarization control behavior of multi-photon absorption process in the intermediate femtosecond laser field. In the weak femtosecond laser field, the second-order perturbation theory can well describe the non-resonant two-photon absorption process. However, the higher order nonlinear effect (e.g., four-photon absorption) can occur in the intermediate femtosecond laser field, and thus it is necessary to establish new theoretical model to describe the multi-photon absorption process, which includes the two-photon and four-photon transitions. Here, we construct a fourth-order perturbation theory to study the polarization control behavior of this multi-photon absorption under the intermediate femtosecond laser field excitation, and our theoretical results show that the two-photon and four-photon excitation pathways can induce a coherent interference, while the coherent interference is constructive or destructive that depends on the femtosecond laser center frequency. Moreover, the two-photon and four-photon transitions have the different polarization control efficiency, and the four-photon absorption can obtain the higher polarization control efficiency. Thus, the polarization control efficiency of the whole excitation process can be increased or decreased by properly designing the femtosecond laser field intensity and laser center frequency. These studies can provide a clear physical picture for understanding and controlling the multi-photon absorption process in the intermediate femtosecond laser field, and also can provide a theoretical guidance for the future experimental realization.
We extend the third perturbation theory to study the polarization control behavior of the intermediate state absorption in Nd 3+ ions. The results show that coherent interference can occur between the single-photon and three-photon excitation pathways, and depends on the central frequency of the femtosecond laser field. Moreover, single-photon and three-photon absorptions have different polarization control efficiencies, and the relative weight of three-photon absorption in the whole excitation processes can increase with increasing the laser intensity. Therefore, the enhancement or suppression of the intermediate state absorption can be realized and manipulated by properly designing the intensity and central frequency of the polarization modulated femtosecond laser field. This research can not only enrich theoretical research methods for the up-conversion luminescence manipulation of rare-earth ions, but also can provide a clear physical picture for understanding and controlling multi-photon absorption in a multiple energy level system .
Abstract We theoretically and experimentally demonstrate the control of the intermediate state absorption in an ( n + m ) resonance-mediated multi-photon absorption process by the polarization-modulated femtosecond laser pulse. An analytical solution of the intermediate state absorption in a resonance-mediated multi-photon absorption process is obtained based on the time-dependent perturbation theory. Our theoretical results show that the control efficiency of the intermediate state absorption by the polarization modulation is independent of the laser intensity when the transition from the intermediate state to the final state is coupled by the single-photon absorption, but will be affected by the laser intensity when this transition is coupled by the non-resonant multi-photon absorption. These theoretical results are experimentally confirmed via a two-photon fluorescence control in (2 + 1) resonance-mediated three-photon absorption of Coumarin 480 dye and a single-photon fluorescence control in (1 + 2) resonance-mediated three-photon absorption of IR 125 dye.
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.
Weak-field coherent phase control of atomic non-resonant multiphoton excitation induced by shaped femtosecond pulses is studied theoretically in the single-cycle regime. The carrier-envelope phase (CEP) of the pulse, which in the multi-cycle regime does not play any control role, is shown here to be a new effective control parameter that its effect is highly sensitive to the spectral position of the ultrabroad spectrum. Rationally chosen position of the ultrabroadband spectrum coherently induces several groups of multiphoton transitions from the ground state to the excited state of the system: transitions involving only absorbed photons as well as Raman transitions involving both absorbed and emitted photons. The intra-group interference is controlled by the relative spectral phase of the different frequency components of the pulse, while the inter-group interference is controlled jointly by the CEP and the relative spectral phase. Specifically, non-resonant two- and three-photon excitation is studied in a simple model system within the perturbative frequency-domain framework. The developed intuition is then applied to weak-field multiphoton excitation of atomic cesium (Cs), where the simplified model is verified by non-perturbative numerical solution of the time-dependent Schrödinger equation. We expect this work to serve as a basis for a new line of femtosecond coherent control experiments.
With femtosecond laser spectral phase shaping technique and polarization modulation technique,the coherent control of two-photon fluorescence(TPF)in Rhodamine B solution is studied.By shaping the femtosecond pulse with simple phase patterns(cosinusoidal andπphase step-function shape),two-photon fluorescence intensity of Rhodamine B can be controlled effectively.Theoretical simulation and calculation show that the variation of twophoton fluorescence intensity for Rhodamine B solution is ascribed to the constructive and destructive interference of various quantum paths in two-photon transitions.TPF of Rhodamine B solution displays periodical change by polarization modulation.TPF decreases when the laser polarization changes from linear through elliptical to circular.These experimental results are theoretically confirmed to be caused by the variation of laser polarization.
Femtosecond coherent phase control of resonance mediated (2+1)(2+1)(2+1) three-photon absorption is studied both theoretically and experimentally. The regime is perturbative of third order. The photoexcitation coherently combines elements of both nonresonant and resonance-mediated multiphoton transitions. By proper simple pulse shaping the three-photon absorption in Na is effectively controlled experimentally, enhanced up to $\ensuremath{\sim}300%$ of the absorption induced by the transform-limited pulse. It is achieved by phase manipulating intra- and intergroup interferences involving two groups of three-photon excitation pathways: (i) on resonance and (ii) near resonance with the intermediate resonance state accessed by nonresonant two-photon transition.