Synthesis of circuits based on all-optical Mach-Zehnder Interferometers using Binary Decision Diagrams

Abstract

The advancement of fabrication technology in VLSI (Very Large Scale Integration) and photonic industry has gained significant interest due to the feasibility of performing functional computations on-chip using ultra-high speed optical devices and low-power interconnects. Here, the necessity of optical circuits arises as they are inevitable components in developing optical Integrated Circuits (ICs). In this conjuncture, methodologies to design highly scalable optical circuits and their synthesis schemes have received interest. In recent years, several works and their findings have been reported in various research articles where researchers have mainly designed combinational and sequential memory elements using optical devices. The use of Binary Decision Diagrams (BDDs) to construct optical circuits has been reported recently. However, the costs of the resulting circuits are still rather high. Furthermore, they include a substantial amount of splitters, which is a significant drawback as they degrade the signal strength in the circuits.

In this paper, we propose an improved design technique where we use BDDs to construct optical circuits. Rather than generating a single graph for multi-output functions, we consider individual graphs for each output separately which, afterwards are combined to realize the entire function. In our experiments, we find that this approach performs better in comparison to related techniques – a cost improvement of approx. 34% is observed on average. As these optical circuits are mainly designed with MZIs, beam combiners and beam splitters, the use of beam splitters in the circuit degrades the signal quality at the receiver end. To address this concern, in a second phase of our design, we make all the circuits free from splitters. Experimental results for both the design schemes are given and analyzed.

Introduction

The present day's computing system demands high end fabrication technologies to develop high speed computing systems to perform faster logic computations. In this conjuncture optical computing has emerged as one of the alternatives in this highly challenging field. Silicon-based optical components and interconnects have a very high speed [9], [18] which empower them to perform very fast computations using ultrafast (speed of light) photon particles.

In recent years, several progresses [15], [26] are seen in development of optical logic modules, where optical devices like Terahertz optical asymmetric de-multiplexer (TOAD), MZI, optical fiber have been used immensely [8], [29].

The applications of such optical devices are not restricted to the theoretical domain only but physical realizations of optical circuits in on-chip units have been initiated [3], [12], [13], [14], [16]. Like implementation of MZI using 2-D electron gas in the quantum hall regime is shown in Ref. [14], successful fabrication of MZI using Polymer [33], Ion exchange [2], Laser radiation [17] have been reported recently. In a current development, industry specific fabrication of photonic MZI using SiO2 clad [29] is claimed.

At the same time logic synthesis [25] using optical components has come out as a major investigating field before researcher and in current years several such advancements have been reported.

Not only logic synthesis, but designing logic modules like multiplexers [11], adders [5], [22], universal logic blocks, sequential memory elements [6], [8] with optical components have received significant attention.

But a generalized way to design optical circuits for arbitrary logic functions remains essential as most of the logic modules that are previously made being basically done on a specific type of functional blocks and manually designed.

To address these concerns, an alternate way has been developed in Ref. [25], where BDDs have been used to generalize the design procedure. But significant drawbacks still prevails in that scheme: The resulting circuits are of rather high costs and the loss of signal power due to the presence of signal splitting devices. In an attempt to alleviate these problems, a novel design approach has been introduced in Ref. [30], where a reverse BDD-based traversal technique is being incorporated to design splitter-free circuits composed with Crossbar switches – an electro-optical device. In this conjuncture, efficient scalable design approaches for optical circuits are one of the priorities in this domain.

In this paper, we are proposing a scalable synthesis scheme to realize optical circuits. In our design method, we use MZIs as primary device to build such circuits. Initially, we represent the input function in terms of a Binary Decision Diagrams where separate BDD trees are formed for all individual functions. The reason behind this separation of BDD trees is that, in our experiment, we interestingly find that a BDD node can be replaced with a functional equivalent MZI switch only when separated trees are formed. If shared BDD trees are considered, a single BDD node cannot be replaced with a single MZI component but requires more than one MZI. Due to this reason, in our design first we generate separate BDD trees for all individual functions and then we perform a very straight-forward mapping which maps each BDD tree to its equivalent optical circuit by replacing BDD nodes with MZI switches.

Though this design considerably improves the cost parameters of the circuit, it still suffers from signal degradation since such designs contain signal splitters as one of the circuit components. To overcome this problem, we generate a splitter-free design of the circuit, where rather than using signal splitters, we duplicate the signal lines from the source signal and forwarded it to both the destinations nodes. By this, we ensure that there is hardly any loss of signal power at the expense of an increase in the optical costs.

The rest of the work is organized as follows. Section 2 provides the background details of the optical technologies especially SOA based MZI switch and brief idea on BDD data structure. Section 3 presents proposed techniques. In Section 4, a discussion over our approaches is made and experimental results have been presented in Section 5. Finally, the work has been concluded in Section 6.