Approximate expressions for estimation of four-wave mixing efficiency in slow-light photonic crystal waveguides

Abstract

We present approximate analytical expressions for the estimation of the degenerate four-wave mixing conversion efficiency in slow light photonic crystal waveguides. The derived formulas incorporate the different effective modal areas and the frequency-dependent linear and nonlinear parameters of the pump, signal and idler waves. The influence of linear loss, two-photon absorption and free-carrier generation is also accounted for. Numerical solution of the coupled propagation equations is used to verify the validity of the proposed expressions under different values of the linear and nonlinear parameters of the waveguide. It is shown that the derived expressions provide an accurate estimation of the conversion efficiency and are thus expected to be very useful in the design of photonic crystal waveguides for nonlinear signal processing applications.

Slow Light in Photonic Crystal Waveguides as a Key Enabler for Future Optical Network Technologies

“…In its degenerate form, FWM occurs when part of the optical power of the data packet is transferred to an idler optical pulse located at another frequency through the mediation of a strong optical pump pulse located at a third frequency. This energy transfer depends on the linear and nonlinear phase mismatch between the three waves [36]. The FWM performance is usually quantified by the conversion efficiency factor, η=P i (L)/P s (0), where P s (0) is the incident optical power of the input data packet and P i (L) is the wavelength converted optical power at the output of the PCSW, of total length L. The power of each wave can be estimated either by using an an embedded Runge-Kutta scheme [37] or by using an analytical approximation [16].…”

Designing photonic crystal waveguides for broadband four-wave mixing applications

“…In its degenerate form, FWM involves the interaction between a signal and an idler wave, located at different wavelengths, mediated through a strong pump wave located at a third wavelength [3]. Nano-photonic structures such as photonic crystals [4] may enable the realization of such functionalities in compact form.…”

“…In Eq. (4), κ tot and g are the total phase mismatch and the parametric gain given by [3] κ tot κ ImfF s F i − 2F p gP 2 p ;…”

“…The FC density N C is given by N C β TPA S 3 p τ C P 2 p ∕2ℏω p A 2 ppp [12], S μ is the slow-down factor for μth wave [12], λ 0 1550 nm, ω μ 2πc∕λ μ , τ C is the FC lifetime and for silicon waveguides C 1 1.35 × 10 −27 m 3 , and C 2 1.45 × 10 −21 m 3 [13]. The FC lifetime τ C is assumed to be 600 ps [3], while the effective modal areas A ρκψ are given by [11] A ρκψ…”

“…In Eq. (6), κ is the phase mismatch in the presence of linear loss only, given by [3] κ Δk 4πn 2Pp A −1…”