Contents I. Introduction
Waveguide gratings (WGGs) have shown their value for many years in filters and mirrors [1], sensors [2], lasers [3], second-harmonic generation [4], tunable time-delays [5], and many more applications and theoretical studies. In a WGG, a guided mode is manipulated through a one-dimensional periodic variation of the dielectric constant along the propagation direction. An important property of finite uniform periodic structures in lossless media is the occurrence of fringes in the transmission and reflection spectra near the stopband edges. It is well known that these oscillations in the transfer function (near the edges outside the stopband) of a uniform grating are due to Fabry–Pérot resonance modes of the grating Bloch modes [6]. These fringes which are undesired for many applications, e.g., wavelength filtering, can be strongly reduced by apodization, i.e., making gradual transitions between the grating region and the unperturbed waveguide [7]. The optimum shape of the apodization function depends on the application and the grating parameters, and in general requires numerical optimization [8]–[10]. In this letter, we propose a fabrication scheme which provides a straightforward way of implementing two types of apodization: 1) chirping through varying the width of the ridge-WGG [11], [12], and 2) strength modulation by varying the width or location of the grating [12]. The main difference of our approach compared to most other approaches known from literature, e.g., [9], [10], [13], is that we first pattern the waveguides and the apodization function using conventional UV lithography, and then use laser interference lithography (LIL) [14] in combination with an image reversal bake for defining the grating with the desired shape. In this letter, we will show that these relatively strong low-loss WGGs can have a high quality factor for a first-order longitudinal Fabry–Pérot resonance in the case of no apodization. We demonstrate the potential of our fabrication method only for the chirp-based apodization method, because of its larger misalignment tolerance. We did not attempt to optimize the apodization function, but just chose to linearly taper the waveguide width to chirp the effective index. This led to an evident reduction of the fringes near the lower wavelength side of the stopband edge. This is shown by both transmission and scatter measurements using an end-fire and an infrared-camera setup [15], respectively.
