Analysis of intermodal coupling in a two-mode fiber with periodic microbends

Abstract

Simple expressions for the coupling between the LP 0 1 and LP 11 modes of a two-mode optical fiber with a periodic microbending structure are developed. Implementation of the microbend structure using a flexural acoustic wave is described. The dependences of the acoustic frequency and power requirements on the pertinent fiber parameters are presented.Work has been done recently on periodic coupling between the LP 01 and LP11 modes in an optical fiber. A theory for computing the coupling between various modes of a multimode fiber at a bending point has been developed' and shows that the LP'i and LP 1 1 modes are strongly coupled at a bend. A static device that couples energy between the modes using periodic microbends, spaced by a beat length between the modes, has been demonstrated. Also, an all-fiber single-sideband frequently shifter that couples energy between the modes by a traveling flexural acoustic wave has been demonstrated. 3 To optimize the performance of these and other potential two-mode fiber devices, it is desirable to develop simple expressions for the coupling between the LP 01 and LP 11 modes at a microbend and to relate them to the pertinent fiber parameters. In this Letter the coupling coefficient is calculated, and the result is compared with experimental results. Implementation of a periodic coupler using a flexural acoustic wave that travels down the fiber is then discussed. Attention is given here to the acoustic frequency and power requirements as functions of the pertinent fiber parameters. Figure 1 shows the geometry of an optical fiber with periodic microbends. 0 (assumed small) is the bend angle of a single microbend, a is the total deflection of the fiber, and LB is the beat length between the LP 01 and the LP 11 modes. For the analysis, the fiber is taken to be step index with core and cladding refractive indices nc and ncl, respectively, and nc1 -nc = n, so that the modes can be assumed to be weakly guided.The LP modes in a straight fiber can be accurately used as approximations to the true mutually orthogonal eigenmodes. A microbend in the fiber will perturb the modes, causing energy to be transferred between them efficiently. Optical energy traveling on the inside of the bend experiences less phase delay than the light traveling on the outside of the bend. Therefore the spatial phase profile of the light is changed as it rounds the bend. If a pure LP 01 mode is incident upon the bend from the left, light will emerge from the right of the bend with the same field intensity versus radius but with a distorted phase front. This distorted LP 01 mode can be decomposed into a true LP 01 mode along with higher-order guided modes and radiation modes.In the case of a two-mode fiber, light will couple to one spatial orientation of the LP 11 mode and to unwanted radiation modes.The amplitude coupling coefficient (K) between the LPo 1 and the LP 1 , modes can be calculated by computing the overlap integral (loveriap) of the LP 01 mode with its phase distortion and the LP 11 mode:where EO(r) i...

An etched two-mode fiber modal coupling element

“…Thus, can be written as (13) Clearly, varies linearly with Except for a term representing the effects of the photoelastic effect, (13) is identical to the expression obtained by Blake et al for the coupling coefficient due to microbends [13].…”

“…To consider the coupling between LP 01 and LP 11 modes explicitly, it is only necessary to substitute the expressions for the electric fields of the two modes in (13). LP modes guided by weakly guided fibers with a circular core and a rotationally symmetric index profile have two orthogonal polarizations.…”

Acousto-optic superlattice modulator using a fiber Bragg grating

“…The ease with which these devices can be spliced into systems, and the consequent low insertion loss, make them an attractive alternative to pigtailed bulk Bragg cells. Previous designs of intermodal coupler include dual-mode fibers supporting an acoustic flexural wave [1,2], coupling between the polarization normal modes of a high-birefringence fiber by means of a torsional acoustic wave [3], and a high-performance device based on a four-port fused-taper null coupler [4]. All these devices share the requirement that the acoustic wavelength must match the intermodal beat length, L = 2B/)$, where )$ = *$ -$ * and $ and $ are the propagation constants of the modes.…”

Ultrafast all-fiber based cylindrical-vector beam laser

“…[21][22][23][24] For a two mode fiber (TMF), it guides the fundamental mode LP 01 (HE 11 ) and the first group higher-order modes LP 11 (TE 01 , TM 01 , and HE 21 ) in the scalar (vector) approximation. As the eigenmodes TM 01 and TE 01 are radially and azimuthally polarized beams, respectively, 25,26 CVBs can be obtained via exciting these modes in TMFs. By offset splicing single-mode fiber (SMF) with TMF or imposing an acoustic flexural wave on TMF to realize the intermodal coupling, continuous, [26][27][28] microseconds, 29 and nanoseconds, 30 CVBs were delivered in TMFs or TMF-based lasers.…”

“…As the eigenmodes TM 01 and TE 01 are radially and azimuthally polarized beams, respectively, 25,26 CVBs can be obtained via exciting these modes in TMFs. By offset splicing single-mode fiber (SMF) with TMF or imposing an acoustic flexural wave on TMF to realize the intermodal coupling, continuous, [26][27][28] microseconds, 29 and nanoseconds, 30 CVBs were delivered in TMFs or TMF-based lasers. The durations of these CVBs are larger than several nanoseconds, and the ultrafast CVB laser has not been realized.…”