Photon-pair generation by intermodal spontaneous four-wave mixing in birefringent, weakly guiding optical fibers

Abstract

We present a theoretical and experimental study of the generation of photon pairs through the process of spontaneous four wave mixing (SFWM) in a few-mode, birefringent fiber. Under these conditions, multiple SFWM processes are in fact possible, each associated with a different combination of transverse modes for the four waves involved. We show that in the weakly guiding regime, for which the propagation modes may be well approximated by linearly polarized modes, the departure from circular symmetry due to the fiber birefringence translates into conservation rules which retain elements from azimuthal and rectangular symmetries: both OAM and parity must be conserved for a process to be viable. We have implemented a SFWM source based on a "bow-tie" birefringent fiber, and have measured for a collection of pump wavelengths the SFWM spectra of each of the signal and idler photons in coincidence with its partner photon. We have used this information, together with knowledge of the transverse modes into which the signal and idler photons are emitted, as input for a genetic algorithm which accomplishes two tasks: i) the identification of the particular SFWM processes which are present in the source, and ii) the characterization of the fiber used.

Fiber-based photon-pair source capable of hybrid entanglement in frequency and transverse mode, controllably scalable to higher dimensions

“…Let us note that with M supported modes, in principle M 4 processes are possible, which in our case (M = 6) translates into 1296 processes. As we discussed in Ref., 34 Fig. 4 (d),(g),(j), the slight shift is probably due to calibration error in the monochromators.…”

“…In order to analyze our experimental results, we consider a fiber that supports the linearly polarized modes LP 01 and LP 11 ; fiber birefringence then implies the existence of two non-degenerate LP 01 modes: LP 01x and LP 01y , polarized along the x and y directions, and four non-degenerate LP 11 modes: LP 11ex , LP 11ey , LP 11ox , and LP 11oy , with even(e) and odd(o) parity. 33 We have used a simple dispersion model where, for polarization i = x, y and parity j = e, o, the index of refraction is given as n i j (ω) = n(ω) + δ ix ∆ + δ jo ∆ p , where δ i j is a Kronecker delta; here, n(ω) is obtained for a step-index fiber characterized by radius r and numerical aperture NA, while ∆ is the birefringence and ∆ p is the "parity birefringence" 34 (with ∆ p = n xo − n xe = n yo − n ye ).…”

Counter-propagating spontaneous four wave mixing: photon-pair factorability and ultra-narrowband single photons

“…Another interesting possibility is for the four waves to propagate in different transverse modes (in a fewmode or multi-mode fiber), likewise leading to an offset of the generation frequencies from the pump frequencies. Thus, let us discuss the case of CP-SFWM implemented in a few-mode optical fiber [33,34] leading to an intermodal process; this means allowing some of the waves involved in the SFWM process to travel in higher-order transverse modes. As an example, if the forward propagating pump travels in the fundamental fiber mode and the signal photon travels in a certain higher-order mode X, while the backward-propagating pump mode travels in the same higher-order mode X and the idler photon travels in the fundamental mode, then perfect phasematching will occur for signal and idler frequencies that are shifted from those of the pumps.…”

Perspectives for Applications of Quantum Imaging

“…In addition, we would like to mention several review papers and overview articles covering topics that are touched on here but are beyond the scope of this review: single photon sources and detectors, integrated‐optical sources of entangled photons, and generation of photon pairs via spontaneous four wave mixing …”