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arXiv:1708.00057 · Europhysics Letters (EPL)

Dualism between optical and difference parametric amplification

Wayne Huang, Herman Batelaan

Published Jul 1, 2017• 4 citations
arXivHTMLPDF

Abstract

Breaking the symmetry in a coupled wave system can result in unusual amplification behavior. In the case of difference parametric amplification the resonant pump frequency is equal to the difference, instead of the sum, frequency of the normal modes. We show that sign reversal in the symmetry relation of parametric coupling give rise to difference parametric amplification as a dual of optical parametric amplification. For optical systems, our result can potentially be used for efficient XUV amplification.

DOI
10.1209/0295-5075/119/24002

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Breaking the symmetry in a coupled wave system can result in unusual amplification behavior. In the case of difference parametric amplification the resonant pump frequency is equal to the difference, instead of the sum, frequency of the normal modes. We show that sign reversal in the symmetry relation of parametric coupling give rise to difference parametric amplification as a dual of optical parametric amplification. For optical systems, our result can potentially be used for efficient XUV amplification.
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A recent article [W.C.W. Huang and H. Batelaan, arXiv:1708.0057v1] analysed the dualism between optical and difference parametric amplification, performing a classical analysis of a system where two electromagnetic fields are produced by another of a frequency which is the difference of the frequency of the other two. The authors claimed that this process would not violate energy conservation at the classical level, but that a quantum description would necessarily require a non-Hermitian Hamiltonian and therefore would not exist. In this work we show that the process can proceed quantum mechanically if described by the correct Hamiltonian, that energy conservation is not violated, and that fields are produced with interesting quantum statistics. Furthermore, we show that the process can be thought of as different types of already known three-wave mixing processes, with the actual type depending on either initial conditions or personal preference.
We develop for the first time the quantum theory of parametric image amplification at low-frequency pumping. Such a process can be implemented by coupled consecutive three-frequency optical interactions. As a result, besides the amplified optical image on the signal frequency, there are two other images with frequencies which are below the pumping frequency. The theory developed takes into account the diffraction effect and group mismatch of interacting waves. For the interacting waves the expressions for mean photon numbers and signal-to-noise ratios are deduced and the dependence of these parameters on the interaction length and coordinate at the image plane are studied.
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.
A quantum theory of parametric amplification and frequency conversion of an optical image in coupled nonlinear optical processes that include one parametric amplification process at high-frequency pumping and two up-conversion processes in the same pump field is developed. The field momentum operator that takes into account the diffraction and group velocities of the waves is used to derive the quantum equations related to the spatial dynamics of the images during the interaction. An optical scheme for the amplification and conversion of a close image is considered. The mean photon number density and signal-to-noise ratio are calculated in the fixed-pump-field approximation for images at various frequencies. It has been established that the signal-to-noise ratio decreases with increasing interaction length in the amplified image and increases in the images at the generated frequencies, tending to asymptotic values for all interacting waves. The variance of the difference of the numbers of photons is calculated for various pairs of frequencies. The quantum entanglement of the optical images formed in a high-frequency pump field is shown to be converted to higher frequencies during the generation of sum frequencies. Thus, two pairs of entangled optical images are produced in the process considered.
We develop for the first time a quantum theory of simultaneous amplification and frequency up-conversion of optical images in two coupled three-wave processes. The theory developed takes into account the diffraction effect and the difference of the group velocities of the interacting waves. Due to the degenerate parametric process involved in the nonlinear optical interactions, the up-conversion also possesses phase sensitivity. As a result, the statistical characteristics of the amplified image and the converted one depend on the phase relation between the signal and the pump waves. It is shown that at the output of the nonlinear crystal the signal-to-noise ratios for the amplified image and the converted one may be same as those for the initial image, i.e. transformation of the optical image may be 'noiseless'.