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 F 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 tight 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 A-in agreement with theoretical estimates. P I . INTRODUCTION ERIODIC STRUCTURES, and in particular corrugated structures, play a significant role in integrated optics [ I ] . Corrugated waveguides serve as narrow-band filters, which reflect wavelengths which satisfy Bragg's law [2]. Such reflectors may be incorporated in laser structures to form distributed feedback lasers [3] or distributed Bragg reflectors [4] . Periodic structures with longer periods have been used to couple between guided modes and air, such as in the cases of input or output couplers [5] . In this paper, we consider the problem of gratings with large and monotonic variation in the period. We describe a method for fabricating such chirped gratings, present a theory for treating them, and present experimental results demonstrating some of their unique applications. 11. GRATING FABRICATION CONSIDERATIONS The gratings are fabricated, as in the case of uniform gratings, by the interference of two laser beams. The period chirp is obtained by cylindrical focusing of one of the two beams, as shown in Fig. 1. The recording plate is located at the x = 0 plane, the angle of incidence of the plane wave is 612, and the angle subtended by the collimated beam and the bisector of the converging beam angle is 8. The interference pattern is recorded over a distance L on the recording plate. The converging wave is generated by a cylindrical lens of focal length f and width d, and the focus is located at point Simple geometrical calculations relate the focal line coP(Xf? Zf). ordinates with f , L , d, and 0 , namely Manuscript received November 16, 1976;revised December 16, 1976. This research was supported by AFOSR. The work of one of the authors ( J . B. S . ) was supported in part by the Hertz Foundation. The authors are with the California Institute of Technology, Pasadena,CA91125. Fig. 1. Recording arrangement and geometry for the fabrication of chirped gratings.