Compact representation of the spatial modes of a phase-sensitive image amplifier

Abstract

We compute the eigenmodes of a spatially-broadband optical parametric amplifier with elliptical Gaussian pump and show that the well-amplified eigenmodes can be compactly represented by a low-dimensional subspace of the first few Laguerre- or Hermite-Gaussian (LG or HG, respectively) modes of an appropriate waist size. We also show that the first few eigenmodes are well matched to single LG or HG modes. For sufficiently large pump waists, the optimum waist size of the compact basis is in the vicinity of the geometric average of the pump waist size and the inverse spatial bandwidth of the nonlinear crystal in the parametric amplifier. The use of such compact representation can greatly simplify numerical computation of the spatial eigenmodes of the amplifier and thus lead to improving the experiments on traveling-wave image amplification and spatially-broadband vacuum squeezing.

Devices for quantum communication over mode-division-multiplexing systems

“…First, based on our previous studies of the nonlinear mode interactions in spatially-multimode optical parametric amplifiers in free space [6][7][8][9] and multimode waveguides [10], we have developed a scheme for a spatial-mode demultiplexer based on sum-frequency generation (SFG) in a two-mode PPLN waveguide [11,12]. We have experimentally demonstrated such a demultiplexer, in which, by adjusting the spatial profile of a 1560-nm pump wave, we could selectively upconvert either mode TM00, or mode TM01, or any superposition of these two modes of a 1540-nm signal to TM01 mode at 775 nm, for both classical [13,14] and single-photon-level [14,15] signals.…”

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].…”

“…The first three cases use standard √ 2 ratio between the waists of the signal and pump mode bases, which ensures equal wavefront curvatures of the signal and pump modes. The last case provides expressions for an arbitrary ratio between the signal and pump beam waists, which is important for compact representation of the PSA eigenmodes [7].…”

“…2 ) often yields a far more compact representation of the eigenmodes [7]. For the latter (non-standard) basis, the overlap integrals of Eqs.…”