Two-Dimensional Discrete Sine Transform and Discrete Cosine Transform Based on Two-Dimensional Multimode Interference Couplers

In this letter, all-optical two-dimensional discrete sine transform and discrete cosine transform (2DDST/DCT) are proposed to be realized on two-dimensional multimode interference (2DMMI) couplers. Similar to the one-dimensional case, the 2DDST/DCT requires only one 2DMMI coupler and a few phase shifters.

I. Introduction

Orthogonal transforms are very useful techniques in signal processing. They can be either one-dimensional (1-D) or two-dimensional (2-D), both of which are extremely useful for video/image processing, filtering, and orthogonal frequency-division multiplexing (OFDM) [1], [2]. Recently, studies have been focused on realizing orthogonal transforms all-optically [3]– [9]. All-optical discrete Fourier transform (DFT) is proposed to be realized on planar lightwave circuits (PLCs) [3], [4] using the concept of DFT [3] or fast Fourier transform (FFT) [4]. Tseng et al. proposed to realize an all-optical Hardamad transform based on long-period fiber gratings (LPFGs) [5]. The MMI coupler, an ultracompact device [10], can also realize orthogonal transforms, such as the Hadamard transform [6], [7], the DST/DCT [8], and the DFT [9]. However, all of the existing studies focus on the 1-D orthogonal transforms and few studies have been conducted on the 2-D case.