Easily tuneable nonlinear optical loop mirror including low-birefringence, highly twisted fibre with invariant output polarisation

Analysis of the nonlinear optical loop mirror with feedback and low-birefringence twisted fiber in the loop

“…The input of the system in this paper consists of solely a right-circularly polarized input [C + = 0], but it should be noted that this system can be similarly derived with a left-circularly polarized input with the same output behavior of the NOLM [17]. The couplers in the system are assumed to not affect the polarization state, and their behavior at the NOLM at coupler K 1 can therefore be described as…”

“…The QWP in the fiber loop is seen differently by each clockwise and counter-clockwise beam, and is defined in matrix form [17] with angle α as…”

“…The equations are normalized to the distance s = L/L b where L is the length of the fiber (in meters) and L B is the beat length of the fiber. Following [6,17], it is defined that µ = π 2 + g 2 where g is the ratio of circular to linear birefringence, given as g = γπ/k, with γ = [h/(2n) − 1]q being the circular birefringence term (h ∼ 0.13 − 0.16 for silica fibers [8]), and k = πδn/λ is the linear birefringence term. The normalized power is given as P N = bπP in /k where P in is the input power in the fiber, and b = 4πn 2 /3λA ef f is the nonlinearity where n 2 ∼ 2.5 × 10 −20 m 2 /W is the Kerr coefficient [12] and A ef f is the effective modal area.…”

“…Using this, and a weak nonlinearity approximation, Kuzin et al showed [8] that when a polarization controller is placed asymmetrically in the NOLM loop, the output of the NOLM can be tuned. As noted by Pottiez et al, [17] this approach lends itself to empirical adjustments and does not offer a simple mathematical description of the tunability of the NOLM. They instead propose a novel approach to analyzing the NOLM with low birefringence, by replacing the polarization controller with a Figure 1.…”

“…This paper uses the analysis approach of [17] to examine the effect on the output of a NOLM with feedback when using a low birefringence twisted fiber in the loop. It is shown that rotation of the QWP allows the tuning of the output bistable and chaotic regions of the NOLM with feedback.…”