Coupled wave analysis of obliquely incident waves in thin film gratings

Abstract

The problem of a guided wave obliquely incident on a grating etched in a thin film guide is considered. Two-dimensional coupled wave equations for the incident and reflected beams are derived for the cases of TE-TE, TE-TM, and TM-TM coupling. Two methods, a ray optic approximation and a coupled beam method, are proposed for the numerical solution of the coupled wave equations. Both methods are illustrated by a number of calculated examples.

Beam propagation in an active planar waveguide with an angled Bragg grating ( α laser)

“…Taking into account [8], we start with the Helmholtz equation for the scalar factor E of the general mode ®eld which depends on the coordinates x and z in the propagation plane. The vector character of the ®eld is contained in a second factor 1538 R. G uther which depends on the function of the vertical coordinate y containing the ground mode distribution.…”

“…The two-dimensional wave propagation in planar waveguides was treated in [8,9]. A possible model can be constructed using a geometrical approximation omitting the second spatial derivatives of the ®elds in the waveguides (slowly varying envelopes).…”

“…The problem of applying the volume holographic technique to a vertical singlemode planar waveguide was solved by Van Roey and Lagasse [8]. Therefore, the combination of [8], [14] and [15] is the tool used to understand some features of the ¬ laser.…”

“…Therefore, the combination of [8], [14] and [15] is the tool used to understand some features of the ¬ laser.…”

<title>Holoplanar optical interconnects</title>

“…Using the appropriate criteria for the first zero of diffraction efficiency, = 2it, we obtain from Eqs. (6) and (7), the following Bragg angular tolerance: 1 X AO= -=y- (8) ntanaL L This angle determines the required angular separation between two hologram grating vectors to avoid crosstalk between channels. In a practical system a full width of half maximum AOFWHM iS measured, and the angular separation between channels is defined as AO = 1OAOFWHM to achieve crosstalk <-30dB.…”