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Saturation in the principal (excited) channel of four-level medium as an effective two-level configuration

Jihad S. Addasi

Published Jan 1, 2021• 0 citations

Abstract

Saturation of complex molecules affects the nonlinear processes occurring in the medium. The medium can be described by two-, three-, and four-level configurations. The principal singlet-singlet and excited triplet-triplet channels of a four-level, N-type, configuration were used to study a nonlinear medium, which was excited by radiation with two frequencies. Under weak population of energy levels in the triplet-triplet channel (a small ratio of the total probability of spontaneous and irradiate transitions for both channels p23/p31), the principal (singlet-singlet) channel is similar to a two-level configuration. At the same time, the effective population of the energy levels in the triplet-triplet channel (the ratio p23/p31 is large and the radiation intensity in the principal channel is high) makes the excited (triplet-triplet) channel coincide with the two-level configuration. The saturation intensity of radiation in principal (excited) channel, as effective two-level configuration, and nonlinear processes in this channel can be controlled by external radiation acting on excited (principal) channel. Finally, the average excitation of molecules into the energy levels in the triplet-triplet channel (ratio p23/p31 ≈ 1) makes the four-level configuration similar to the three-level configuration with effective level as a result of combination between second singlet level S2 and first triplet level T1.

DOI: 10.37190/oa210207

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Saturation of complex molecules affects the nonlinear processes occurring in the medium. The medium can be described by two-, three-, and four-level configurations. The principal singlet-singlet and excited triplet-triplet channels of a four-level, N-type, configuration were used to study a nonlinear medium, which was excited by radiation with two frequencies. Under weak population of energy levels in the triplet-triplet channel (a small ratio of the total probability of spontaneous and irradiate transitions for both channels p23/p31), the principal (singlet-singlet) channel is similar to a two-level configuration. At the same time, the effective population of the energy levels in the triplet-triplet channel (the ratio p23/p31 is large and the radiation intensity in the principal channel is high) makes the excited (triplet-triplet) channel coincide with the two-level configuration. The saturation intensity of radiation in principal (excited) channel, as effective two-level configuration, and nonlinear processes in this channel can be controlled by external radiation acting on excited (principal) channel. Finally, the average excitation of molecules into the energy levels in the triplet-triplet channel (ratio p23/p31 ≈ 1) makes the four-level configuration similar to the three-level configuration with effective level as a result of combination between second singlet level S2 and first triplet level T1.

The four-level model is used to study the nonlinear media with coincident absorption and emission bands in both principal (S0S1) and excited (T1T2) channels.The excitation of molecules occurred by two light elds: radiations with intensity I12 at frequency ω0 tuned at the centre of absorption band of principal singletsinglet channel and radiations with intensity I34 at frequency ω tuned at the centre of absorption band of excited triplettriplet channel.The monotonic dependence of phase response of media in both principal and excited channels and the saturation processes are studied theoretically and numerically for four-level model.

Three typical excited-state nonlinear absorption effects in molecular systems with weak ground-state absorption (at 532 nm) are experimentally demonstrated: (a) reverse saturable absorption (RSA) caused by strong triplet first-to-second excited-state absorption in a copper phthalocyanine solution with 15-ns laser pulses; (b) RSA caused by strong singlet first-to-second excited-state absorption in a

{\mathrm{C}}_{60}

solution with 21-ps laser pulses; (c) the RSA-SA turnover caused by strong singlet first-to-second excited-state absorption and weak singlet second-to-third excited-state absorption in a metallo-porphyrin-like solution with 21-ps laser pulses. To simulate these excited-state nonlinear absorption behaviors we propose a general ten-level density-matrix model and its simplified models for the three cases. All simulations are in good agreement with the experimental results.

A theoretical study of the nonlinearity reduction in a four-level system of a potassium atom in the presence of a strong nanosecond laser field, which excites the transition |4S 1/2 ⟩↔|6S 1/2 ⟩ with two photons, is presented. It is shown that the destructive quantum interference between the laser field and the internally generated radiations results in a linear response of the atomic path-1 (|4S 1/2 ⟩↔|6S 1/2 ⟩↔|5P 3/2 ⟩↔|4S 1/2 ⟩) emitted parametric fields. For sufficiently high laser intensities and/or atomic densities, the path-1 emitted fields are driven into saturation, a regime accompanied by a substantial population redistribution among the states. Reasonable agreement between earlier experimental results and the theoretical ones is obtained. It is also shown that upon saturation of path-1, for low atomic density, the path-2 (|4S 1/2 ⟩↔|6S 1/2 ⟩↔|4P 3/2 ⟩↔|4S 1/2 ⟩) is activated. A subtle interplay between laser intensity and atomic density may determine the activation of path-2. Also, it is shown that the path-2 emission |6S 1/2 ⟩↔|4P 3/2 ⟩ is an amplified spontaneous emission process which induces a |4P 3/2 ⟩↔|4S 1/2 ⟩ emission, without population inversion, in a cascade scheme.

The main achievements in our research on the physical phenomena of the excited-state nonlinear absorption in a molecular system and its applications in photonic technology are described. In the first part of this paper, some energy-level models and rate-equations are used to explain various mechanisms of the excited-state nonlinear absorption under different conditions, such as reverse saturable absorption caused by the triplet and/or the singlet excited-state absorption; saturable absorption due to the first and/or the second singlet excited-state absorption; and the excited-state nonlinear absorption induced by two-photon absorption. The experimental results for metal-organic and C 60 materials irradiated by ps and ns laser pulses are consistent with the simulated curves of the transmittance versus fluences. In the second part, the applications of excited-state nonlinear absorption in photonic techniques including optical bistability, optical switching, optical limiting, optical modulation, optical logic and optical storage are introduced. The working principles of the photonic devices based on the excited-state nonlinear absorption are presented. The experimental characteristic curves are found in good agreement with the theoretical simulations for these devices.