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Journal of Optics

Optical parametric amplification near resonance transition in two-level system

Serguei I. Stepanov, Nayeli Casillas, Manuel Ocegueda, Jorge Montoya-Cardona, Francisco A. Domínguez-Serna, K Garay Palmett

Published Feb 28, 2025• 0 citations
Publisher

Abstract

Abstract We present results of a theoretical analysis of an optical parametric amplification (OPA) in a collinear nearly degenerate four-wave mixing configuration close to the resonance of a two-level transition in χ ′ ′ ′ media. It is performed both for homogeneously and for inhomogeneously broadened spectral line using a standard set of Bloch equations in the semiclassical approximation. Unlike the traditional approach of a coupled propagation of the signal/idler waves, we treat OPA as a coupled propagation of the amplitude and phase modulations of the pump wave with the signal/idler waves as the modulation sidebands. We show that for low frequency off-sets between the pump and the signal/idler waves, OPA process is basically manifested in a unidirectional transformation of the input amplitude modulation of the pump wave into the output phase modulation. The frequency band of the OPA is determined by detuning the pump wave from the resonance transition. The obtained results are applied to evaluate the expected OPA gain for the acetylene-filled micro-structured fiber with the resonance vibration-rotational transitions in the 1500–1550 nm spectral range.

DOI
10.1088/2040-8986/adbb7c

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Abstract We present results of a theoretical analysis of an optical parametric amplification (OPA) in a collinear nearly degenerate four-wave mixing configuration close to the resonance of a two-level transition in χ ′ ′ ′ media. It is performed both for homogeneously and for inhomogeneously broadened spectral line using a standard set of Bloch equations in the semiclassical approximation. Unlike the traditional approach of a coupled propagation of the signal/idler waves, we treat OPA as a coupled propagation of the amplitude and phase modulations of the pump wave with the signal/idler waves as the modulation sidebands. We show that for low frequency off-sets between the pump and the signal/idler waves, OPA process is basically manifested in a unidirectional transformation of the input amplitude modulation of the pump wave into the output phase modulation. The frequency band of the OPA is determined by detuning the pump wave from the resonance transition. The obtained results are applied to evaluate the expected OPA gain for the acetylene-filled micro-structured fiber with the resonance vibration-rotational transitions in the 1500–1550 nm spectral range.
Experimental results on parametric optical processes in saturable ytterbium-doped fibers (YDFs) at the wavelength of 1064 nm are reported. Significant photoinduced change of the refractive index under saturation of the fiber-optical absorption in the near-infrared range enables us to consider this medium as an effective optical Kerr ( χ ′′′ ) medium. For pumping, it needs continuous-wave Nd:YAG laser power of 10-mW scale, but the saturation process has the characteristic time ≤1ms, governed by the metastable level lifetime in YDF. We investigate the nearly degenerate collinear configuration of the optical parametric amplification (OPA). Here we focus on unidirectional transformation of the initial amplitude modulation in the incident pump wave to the output phase modulation as a manifestation of OPA in a narrowband case. This effect results from the conventional coupled-wave equations for the signal and idler waves—if one considers them as the modulation sidebands. It can also be treated as a result of the self-phase modulation of the periodically modulated pump in the Kerr medium. OPA gain of about 0.64 with the net gain ≈0.29 was experimentally estimated for the utilized 2-m-long YDF in the frequency band ≈200Hz.
We present experimental advances in comparative studies of optical parametric amplification (OPA) in microstructured fused silica solid-core fibers and hollow-core fibers filled with acetylene (C2H2). Both media exhibit third-order nonlinearity, enabling the OPA process in collinear configurations with a high spatial concentration of light power. In the former, non-resonant case, we investigated the parametric amplification via four-wave mixing (FWM) with a degenerate pump by picosecond laser pulses centered at a wavelength of 737 nm. This process ensured the generation of the correlated signal/idler photon pairs that could be parametrically amplified in a similar nonlinear micro-structured fiber. For the resonant acetylene-filled fibers, we present an experimental evaluation of the OPA gain in a degenerate collinear FWM at 1530 nm near the P9 acetylene absorption line. We specifically studied the transformation of amplitude modulation in the quasi-continuous W-scale input pump wave to output phase modulation and vice versa. Our research compares OPA efficiencies and the potential to generate squeezed and entangled light states in resonant and non- resonant fiber-based media.
In the presence of a nonzero idler beam or, equivalently, in the collinear degenerate configuration, optical parametric amplification (OPA) can be phase sensitive. When the photon deamplification mode is selected in the OPA process, amplification of the optical phase occurs instead of the usual amplification of photon number. We demonstrate for the first time, to the best of our knowledge, that the operation of a spatially multimodal optical parametric amplifier in the phase-sensitive mode can result in a significant redistribution of spatial frequencies and near-ideal beam angle amplification. A numerical model is presented for phase-sensitive parametric amplification via three-wave mixing. The model is applied to monochromatic beams and finite beam apertures. The sensitivity of gain to the incident phase, noncollinear angle, and aperture size is studied in particular. Simple conditions are derived for the operation of the optical parametric amplifier in the phase-sensitive mode. Potential applications of the concept are discussed.
The behaviour of collinear signal, idler and pump waves in a non-linear medium without inversion symmetry is investigated under small-signal conditions when the frequency ω of either the signal or the idler approaches a transition frequency of the medium. The three waves are coupled together by the first-, second- and third-order susceptibility tensors of the medium. All three tensors exhibit a resonance in the case under consideration. The first-order resonance creates an absorption band and the third-order resonance produces stimulated Raman amplification. It is shown that the strength of the second-order resonance, which enters into the parametric effect, is determined by the product of the strengths of the other two. The growth constant of the signal and idler waves is a maximum when the mismatch of the propagation constants Δ k in the presence of the pump field takes a non-zero value equal to the decay constant at frequency ω times the ratio of the imaginary and real parts of the complex parametric growth constant, a quantity which is independent of the pump field strength. Except in the immediate neighbourhood of resonance, the frequency dependence of the optimum growth constant is controlled by the ratio of the peak Raman growth constant to the off-resonance parametric growth constant. When this ratio is small the optimum growth constant is never significantly larger than the off-resonance parametric value; when it is large the optimum growth constant slightly exceeds the peak Raman growth constant over a frequency range of 10-10 3 linewidths on one side of resonance. In the immediate neighbourhood of the resonance the optimum growth constant exhibits structure which is controlled by the anomalous dispersion and absorption resulting from the first-order resonance.
Phase-sensitive amplification (PSA) is a particular type of optical parametric amplification (OPA) that features a low-noise property such that the quantum-limited noise figure is 0 dB. The PSA operation is typically achieved when the signal and idler spectra are degenerate in optical parametric interactions, i.e., the degenerate OPA condition. However, for a spectrally broadened incident light, these two spectra can be partially degenerate. The present work investigates the noise property of OPA in such conditions in terms of quantum mechanics. The results quantitatively indicate the intermediate properties between PSA and phase-insensitive amplification.