Characterization of the interference coupling technique into single mode fibers

Abstract

192 / CLEO 2002 / TUESDAY AFTERNOON ization. Eq. (1) yields for the dispersion relation of linear waveswhere K is the Bloch vector. The group velocity vf' ( K ) = o$yl k sin(KR) is a good measure for the velocity of the motion of an excitation along the chain and is slower than the group velocity of a channel waveguide by a factor of up to 10 and more. Its sign can be altered by changing the seperation of two defects. The temporal behavior (e.g. hopping times) obtained from Eq. (1) is compared with direct simulations of Maxwell's equations in the time domain by means of finitedifference time-domain calculations (FDTD).Assuming a Kerr-type perturbative polarization we get the following discrete Schrodinger equation for the scaled amplitudes A,fi 1 where 6,, 6,, describe self-phase and cross-phase modulation, respectively. We find stable localized solutions as in similar discrete systems? For a focusing nonlinearity localized modes or discrete solitons exist for frequencies below the miniband. The lower the frequency the more localized is the solution and the higher is the energy. Fig. 2 shows the modal amplitudes of a discrete soliton for two different frequencies assuming equal amplitudesThe possibility of using a two-or even threedimensional superstructure of defects may lead 4 1 = 0,o -10 -5 0 5 10 Defect JTuC6 Fig. 2. Discrete solitons for different frequencies (a) w = -($/2 + 5?d4)o0, (b) w = -(&2 + 2$)0,. (Amplitudes are given in units of m., to applications such as steering, routing and switching.Coupling light into a waveguide or a fiber is typically based on using a lens with a small f-number to focus the input beam into the waveguide. Such 2 coupling scheme becomes increasingly complex and lossy for Single-Mode Fibers (SMF).' We show that this problem can be overcome by launching the central fringe, generated by the interference pattern of two Gaussian beams, into a SMF or a waveguide. In an earlier publication, we have demonstrated that using interference schemes, it is possible to enhance the coupling efficiency in a quasi-phase matched second-har-monic generation process by as much as 67% in 4 pm wide waveguides.2 In this paper, we propose a comparison of the single beam and the interference coupling schemes into single mode fibers. Coupling efficiency calculations, based on the overlapping integrals of the fiber mode field and the distribution of the input light intensity are presented? This study takes into account the light coupling and propagation in the fiber core and cladding. Marcuse has shown that a Gaussian radial distribution fits (Err < 1%) the mode field of a stepindex fiber! The diameter, 2wD, of the SMF Gaussian mode field profile can be determined empirically using Marcusse equation relating the radius of the mode field, to the core size, a, and the normalized fiber number, K4 Hence, the coupling efficiency, q, can be obtained by calculating the normalized integral: Jo . . n = (1) where fir) is the incident light intensity profile function and exp -( ? / w i ) is the fiber mode distribu...