Synthesis of Hadamard transformers by use of multimode interference optical waveguides

Abstract

We propose a synthesis method of optical Hadamard transformer using multimode interference (MMI) couplers. By using the signal transfer matrix of 2 x 2, 4 x 4, and 8 x 8 MMI couplers, we show that sum and difference units of input signals can be synthesized. An interchange unit of two signals can also be synthesized. One synthesis method of Hadamard transformers is a combination of only 2 x 2 units, and the other is a combination of N x N(N > or = 4) units as well as 2 x 2 units. The design examples of operation units are shown, and the size and the output power of Hadamard transformers are estimated.

A Mode MUX/DEMUX for Multicore Fibers With 2D Core Arrays

“…When the width has about 1μm error, which is about 3% of the total width, the mode extinction ratio degrades to 20dB. This is in agreement with the analysis in [16], which indicated that the width error has a stronger impact on the MMI coupler performance and it can be proportionally related to the length error by a factor of 2 [16]. The operation wavelength range can be evaluated by relating the wavelength deviation to the length deviation [16].…”

Optical signal processing using MMI elements

“…In [7], the Hadamard transform based on MMI couplers has been proposed. By controlling the phase of the input signals at the entrance of the MMI coupler, and cascading the MMI couplers, 2×2 and 8×8 Hadamard transformers have been designed.…”

“…It will now be shown how such elements can be formed from MMI structures. We start with a restricted interference (RI) based 2×2 MMI coupler [1] that has a transfer matrix [7] …”

Optical Chirp <italic>Z</italic>-Transform Processor: Design and Application

“…As such, in the last few decades and especially in recent years, there has been an increasing worldwide trend on the research and development of basic optical signal processing devices that can emulate the fundamental functionalities of the much more mature electronic counterparts but with a much higher processing speed/bandwidth. In this direction, a number of basic analog optical signal processors have been reported, which include the temporal optical differentiators [4]− [7], temporal optical integrators [6]− [9], ODFTs [1], [10]− [13], [29]− [32], optical inverse DFTs [1], [12], optical Hilbert transformers [14]− [16], optical discrete sine transformers [17], optical discrete cosine transformers [17], [18], optical discrete Hartley transformer [18], optical Hadamard transformers [13], [19], and optical discrete wavelet transformers [20].…”