Moving Coordinate Frame FDTD Analysis of Long Range Tracking of Pulsed Fields in Graded Index Waveguides

Hybrid Ray-Fdtd Moving Coordinate Frame Approach for Long Range Tracking of Collimated Wavepackets

“…At the front boundary ζ = ζ max , [18] we show that this instability occurs also for the case where + W is not stationary and does impinge upon the front boundary). Thus, the solution is to specify − W and U on the front boundary according to our knowledge of their behavior.…”

“…Modeling of pulses along curved trajectories has already been demonstrated in [25], and initial steps have been taken towards incorporation of these tools into a 3D code along the lines discussed above. The problem of pulse propagation in a graded index waveguide, simulating structures such as fiber optics, is presented in another paper [18].…”

“…(c) A graded index waveguiding structure (e.g., an optical fiber) with the general form c(z, r) =c(z)/n(z, r), r = x 2 + y 2 , where the profile functionn(z, r) is monotonously decreasing away from the z axis withn(0, r) = 1 , so thatc(z) is the wavespeed on the axis. Since the modal propagation speed is close toc(z) , we choose here c w (z) =c(z) (see [18]). …”

“…So far this approach has been studied for 1D inhomogeneous medium in [15,16] and for 1D homogeneous, nonlinear optical medium [17]. In this paper we consider long range tracking of 3D space-time wavepackets in plane stratified media, using Pulsed Beams (PB's) [5][6][7] in the numerical examples, while a recent paper [18] considers the problem of wavepacket propagation in longitudinally inhomogeneous graded index media, such as optical fibers. The applications in theses two papers differ both physically and numerically.…”

“…The applications in theses two papers differ both physically and numerically. In the problem considered here, the spatial collimation of the wavepacket is due to the wavepacket structure; in [18], on the other hand, the spatial guiding is due to the graded medium (thereby introducing a temporal dispersion which becomes significant at very large distances yet is properly modeled by our moving frame FDTD scheme), Also, in the guiding medium problem the off-axis field is evanescent, whereas in the collimated wavepacket problem considered here there are no evanescent fields. This leads to a different numerical implementations, in particular for the ABC at the side walls of the moving frame.…”