Analytical approach of developing the expression of output of all-optical frequency encoded different logical units and a way-out to implement the logic gates

To implement different all optical logic operations, encoding/decoding of optical signal is a very important issue. Since now there are so many types of optical signal encoding and decoding techniques have been adopted, such as intensity encoding, polarization encoding, phase encoding, symbolic substitution technique etc. All these existing techniques have their own limitations. In this context one may mention the frequency encoding/decoding technique. The basic inherent advantage of frequency encoding technique over all other existing techniques is that as the frequency of a signal is the fundamental character of it, it always preserves its identity throughout the communication of the signal, irrespective of reflection, refraction attenuation etc. Again, different optical signal has different distinct frequency which may be encoded as a distinct state of a logic system to represent the information. Adopting this technique it is possible to implement binary logic system as well as higher order logic system such as tristate logic, quaternary logic system etc. The major advantages of multivalued logic system over Boolean logic system are that in multivalued logic system the states of information is very more and as result information storage capacity is high. Again in multivalued logic system carry free and borrow free operation can be implemented which is less time consuming and therefore speed of operation is very fast. We have already developed methods of implementation of different all-optical frequency encoded logic as well as different optical processor. In this communication we propose an analytical approach to develop the expression of the outputs of frequency encoded different binary logic expression in terms of input frequencies from the stand point of basic laws of reflection, transmission and frequency conversion property of optical devices and of course mention the way-out to implement these logic operations.