IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 11, NO. 5, MAY 1999 569 Second- and Third-Order Dispersion Compensator Using a High-Resolution Arrayed-Waveguide Grating Hiroyuki Tsuda, Katsunari Okamoto, Senior Member, IEEE, Tetsuyoshi Ishii, Kazunori Naganuma, Yasuyuki Inoue, Member, IEEE, Hirokazu Takenouchi, and Takashi Kurokawa, Member, IEEE Abstract—We have proposed a dispersion compensation scheme that uses a high-resolution arrayed-waveguide grating (AWG). When the diffraction order of the AWG is 59 and the number of waveguides in an arrayed-waveguide is 340, the calculated max- imum second- and third-order dispersion compensation range is 8.0 ps/nm and 6.0 ps/nm , and 100 ps/nm and 937.5 ps/nm , for a 1 ps-pulse and a 12.5 ps-pulse, respectively. In experiments, second-order dispersion ( 0.8 to 5.2 ps/nm) is effectively compensated for 1.1-ps pulses; and pulse compression by third-order dispersion compensation is successfully demon- strated. Index Terms—Arrayed-waveguide grating, dispersion compen- sation, dispersion compensator, gratings, optical communication, optical pulse compression, optical pulse shaping, optical equaliz- ers, optical waveguide components, time–space conversion. I. INTRODUCTION G ROUP velocity dispersion (GVD, second-order disper- sion) and GVD slope (third-order dispersion) compensa- tion are indispensable for high-speed optical communication systems. The dispersion of the optical transmission line can be compensated by a fiber grating (FG) [1] or a dispersion compensating fiber (DCF). However, the former creates a dispersion ripple while the latter can not be tuned when compensating dispersion. The dispersion equalizer with cas- caded Mach–Zhender interferometers by Takiguchi et al. [2] is promising because of its tunability, however, its bandwidth is limited to about 400 GHz. A dispersion compensator using two cascaded AWG’s was proposed by Lee [3], but it generates satellite pulses due to its nonflat transmission characteristics. This letter proposes a dispersion compensator that uses an AWG and we theoretically and experimentally investigate its feasibility [4]. The proposed dispersion compensator is useful because it has a bandwidth of several terahertz, can compensate both positive and negative dispersion, and offers tunability if a spatial light modulator is used for phase control [5]. The proposed device is suitable for transmission systems with a pulsewidth of about 5–20 ps and can, theoretically, Manuscript received November 10, 1998; revised January 20, 1999. H. Tsuda, T. Ishii, K. Naganuma, and H. Takenouchi are with the NTT Opto-Electronics Laboratories, Kanagawa 243-0198, Japan. K. Okamoto and Y. Inoue are with the NTT Opto-Electronics Laboratories, Ibaragi 319-1196, Japan. T. Kurokawa is with the Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan. Publisher Item Identifier S 1041-1135(99)03616-2. Fig. 1. Schematic view of the reflection-type dispersion compensator using an AWG. compensate second- and third-order dispersion of 100 ps/nm and 937.5 ps/nm , respectively, for a 12.5-ps pulse. II. DISPERSION COMPENSATION USING AN AWG The schematic view of the reflection-type dispersion com- pensator using an AWG is shown in Fig. 1. Dispersion com- pensation is performed by decomposing the input waveform into its frequency components, modulating the phase of each component by a spatial filter, reflecting them from a mirror, and reforming the waveform by combining the components. To achieve accurate phase compensation, the phase variation within the resolution bandwidth has to be sufficiently small for all spectral components. This condition is described as follows: (1) where is the resolution of the AWG, is the relative phase compared to the phase at the center frequency and is a constant determined by the required accuracy. This condition is sufficient when the free spectral range (spectral window), , is broad enough compared to the input signal bandwidth. is described as follows: (2) where is the diffraction order, and is the number of waveguides in the arrayed-waveguide. To compensate second-order dispersion, a parabolic phase filter that satisfies the following equation is used (3) 1041–1135/99$10.00  1999 IEEE