Interferometric model for phase analysis in fiber couplers

Abstract

An interferometric model is proposed to estimate the phase differences in lossless, strongly coupled biconical fiber couplers. This approximate method is simpler than the traditional s-parameter network theory-based analysis technique and minimizes the number of unknowns. The phase difference between the transmitted and coupled light fields is directly related to the field interaction and can be estimated by employing the energy conservation and mode orthogonality principles. The maximum coupling coefficient and dependence of phase difference on coupling conditions can be analyzed for multiport single-mode fiber couplers.

Achromatic design of a photonic tricoupler and phase shifter for broadband nulling interferometry

“…The conservation of energy between the inputs and the outputs implies 22 Hence the transmission coefficient is expressed with respect to the coupling coefficient as:…”

“…Hence mode field orthogonality is generally needed, in addition to energy conservation and symmetry arguments, to determine the phase shift. However, by assuming mode orthogonality principle, 22 the transfer matrix can be written as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 6 ; 4 2 6…”

“…Furthermore, the conservation of energy inside the device 22 itself implies that E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 8 ; 1 1 6 ; 5 4 0…”

“…Hence mode field orthogonality is generally needed, in addition to energy conservation and symmetry arguments, to determine the phase shift. However, by assuming mode orthogonality principle, 22 the transfer matrix can be written as M=(trueTfalse˜1trueCfalse˜1trueCfalse˜2trueCfalse˜1trueTfalse˜2trueCfalse˜1trueCfalse˜2trueCfalse˜1trueTfalse˜1),where trueC˜1, trueC˜2, trueT˜1, and trueT˜2 are the complex coupling coefficients from the input waveguide to the central and outer output waveguides, and transmission coefficients in the outer and central waveguides, respectively (Fig. 2).…”

“…A tricoupler with asymmetric coupling or tapered waveguides 14 , 22 requires the treatment of coupling to the center and unfed outer waveguides, C1 and C2, separately. As a result, expressions for the differential phases between channels become complicated to compute in terms of the coupling and transmission coefficients, which in turn makes the transfer matrix complicated and potentially impacts the efficiency of phase calculations for fringe tracking.…”