Spatial modes of phase-sensitive image amplifier with higher-order Gaussian pump and phase mismatch

Abstract

We compute eigenmodes of spatially-broadband optical parametric amplifier either with fundamental Hermite-Gaussian pump and phase mismatch k0, or with higher-order pump and k=0. Both cases are capable of shifting the maximum gain to higher-order modes. © 2011 IEEE Photonics Society OCIS codes: (190.4970) Parametric oscillators and amplifiers; (270.6570) Squeezed states; (999.9999) Optical image amplification.Traveling-wave phase-sensitive optical parametric amplifiers (PSAs) have large spatial bandwidths, and hence, when pumped by a wide pump beam, can operate in a spatially multimode regime, serving as noiseless image amplifiers [1,2] and sources of multimode squeezed-light. However, for pumping by realistic focused beams, the analysis of PSA is difficult due to spatial mode mixing dynamics (also known as gain induced diffraction) [3].We have recently developed a procedure for finding the orthogonal set of independently squeezed (or amplified) modes of a traveling-wave PSA [4]. It is based on solving the parametric amplifier equation via a 2D Hermite-Gaussian (HG) expansion over HG mn modes, originally developed for cavities [5] and for 1D travelingwave PSAs [6]. Unlike the previous work, our method can a) handle amplification by an elliptical HG 00 pump with potentially different 1/e intensity radii a 0px and a 0py in x-and y-dimensions, respectively, and b) find the eigenmodes of the spatially-broadband PSA once the Greens' function of the PSA is computed [7]. For convenience, we initially expanded the signal over HG mn modes with the same Rayleigh ranges z Rx =k p a 0px 2 and z Ry =k p a 0py 2 as the pump (i.e. with 2 1/2 larger waist) and found the PSA Green's function by solving the resulting system of coupled-HG-mode equations. A later-found compact representation of the eigenmodes in the HG basis with a Rayleigh range significantly shorter than the pump's simplifies their experimental detection by properly matched local oscillator [8].In this paper, we study the PSA under two new situations: first, under HG 00 pump-mode pumping, but with a non-zero phase mismatch, and second, under pumping by a higher-order HG mode, but with perfect phase matching.Let us understand what happens in the first situation. Non-zero phase mismatch k = k p -k s -k i , in the simplest case of a plane-wave pump, moves the maximum gain from low spatial frequencies (low-pass-filtering behavior of a PSA with k = 0) to higher spatial frequencies (bandpass-filtering behavior of a PSA with k  0). This only happens for k < 0, because negative phase mismatch compensates the diffractive term in the effective phase mismatch k eff (q) = k + q 2 / k s , making k eff (q) = 0 at some high spatial frequency q of interest. It is reasonable to expect that, with a Gaussian pump, a similar shift of the highest gain from the fundamental HG 00 signal mode toward higher-order HG modes (i.e. modes with larger presence of high spatial frequencies) will take place.In the second situation (pumping by a higher-order mode), the coupled-mode theor...

Mode coupling in phase-sensitive amplifier with generalized pump mode and spot size

“…Following the coupled-mode PSA theory [4,5], we have recently developed procedure for finding the PSA's spatial eigenmodes [6] and their compact representation [7], based on singularvalue decomposition of the Green's function of the PSA [8,9]. While our previous analysis was based on a fundamental Gaussian pump, in this paper we present the generalizations of our theory for arbitrary Hermite-and Laguerre-Gaussian (HG or LG) pump orders, which have led to some of the recently published numerical results [10].…”