Chirped gratings in integrated optics

Gratings with variable periods (chirped gratings) have been fabricated by recording the interference pattern of a collimated laser beam with a converging beam generated by a cylindrical lens. An analysis is presented for the behavior of the chirped gratings as a function of wavelength, the angle between the illuminating beams, the number of the lens, and its position. To calculate the power radiated into air, the coupled-mode equations are solved for the case of a waveguide with chirped surface corrugation. Experimentally, chirped gratings have been etched on the surface of an optical waveguide and used to couple light out of the waveguide. It was found that the light was focused outside the waveguide, and the fraction of the power radiated into air compared favorably with the theoretical calculation. The focal point outside the waveguide was found to move by about 1 cm when the wavelength was changed by 500 Å-in agreement with theoretical estimates.