All-optical symmetric ternary logic gate Tanay Chattopadhyay à Mechanical Operation (Stage-II), Kolaghat Thermal Power Station, WBPDCL, Mecheda, Purbamedinipur, KTPP Sub Post Office, 721137 West Bengal, India article info Article history: Received 3 October 2009 Received in revised form 21 December 2009 Accepted 12 January 2010 Available online 1 February 2010 Keywords: Optical ternary logic Polarization Terahertz optical asymmetric demultiplexer (TOAD) abstract Symmetric ternary number (radix = 3) has three logical states (1 ¯ , 0, 1). It is very much useful in carry free arithmetical operation. Beside this, the logical operation using this type of number system is also effective in high speed computation and communication in multi-valued logic. In this literature all-optical circuits for three basic symmetrical ternary logical operations (inversion, MIN and MAX) are proposed and described. Numerical simulation verifies the theoretical model. In this present scheme the different ternary logical states are represented by different polarized state of light. Terahertz optical asymmetric demultiplexer (TOAD) based interferometric switch has been used categorically in this manuscript. & 2010 Elsevier Ltd. All rights reserved. 1. Introduction In the present era electronic computers are based on conven- tional binary number system (radix-2), such computers are not suitable for parallel arithmetic computing due to the carry generation and propagation. Many techniques have been pro- posed in the literature to alleviate and or solve this problem such as, negative radix representation [1], radix-2 modified signed digit (MSD) [2,3], reduced number system (RNS) [3], modified trinary number (MTN) [4,5], etc. All of these proposals are based on radix- 2 number system. In general, as radix of the number system increases, smaller number of digits necessary to express a given quantity. A number of N-range expressed as N=R d where d is the necessary number of digits and R is the radix. Multi-valued system (radix 42) is the best alternative for generation to come for increasing the data carrying capacities, large information storage and high speed arithmetic operations [6]. Ternary logic (radix = 3) system has a great contribution in this regard. A ternary number is an ordered string of symbol a i and an optional digit. The symbol a i is either a signed digit (it may be positive or negative), which is called the signed ternary number or all positive with set of number {0, 1, 2}, which is called ordinary ternary (OT) number. In general the decimal equivalent of an n-bit ternary number (a n 1 ya 1 a 0 ) 3 can be written as D ¼ X n1 i ¼ 0 a i 3 i ð1Þ Various signed ternary logical states have been proposed in various literatures such as, the radix-3 modified signed digit (MSD) [7], ternary signed digit (TSD) [8,9], negabinary trinary signed digit (NSD) (where a i A f2; 1; 0; 1; 2g) [10] and balance ternary digit (BTD) or symmetric ternary digit (STD) (where a i A f 1; 0; 1g, which is ‘symmetrical’ about zero (hence the term ‘balanced’), here 1 ¯ =  1 and 1 = + 1) [11–13]. Yi et al. [12] designed ‘ternary optical computer’ (TOC) which follows ordinary ternary (OT) logic system. The so called ‘Brousentsov’s Ternary Principle’ of computer design was initially realized the Setun computer [13] and this computer was based on the ‘ternary-symmetrical number system’ or symmetrical ternary digit (STD). STD has the following advantageous properties:  ‘Ternary inversion’ [14] is easily changeable from 1 ¯ with 1 and vice versa. As an example ðþ 23Þ 10 ¼ð10 1 1Þ 3 and ð23Þ 10 ¼ ð 1011Þ 3 .  We can easily understand the sign of the number with viewing the most significant digit (‘trit’ [14]). As from the previous example most significant digit of (+23) 10 is 1 and ( 23) 10 is  1.  Addition and subtraction are in fact the same operations: just the rule of ‘ternary inversion’ is applied to one of the operands and then an adding operation is done. Beside arithmetic operation, logical operation is also very important. Many proposals have already been created for ternary logical operation, such as binary coded ternary (BCT) [15], ordinary ternary (OT) [12,16,17], etc. in photonics technology. But very few literatures are there on symmetrical all-optical logical operation. In this paper some basic logical operations ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/optlastec Optics & Laser Technology 0030-3992/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2010.01.023 à Tel.: + 91 9432075035; fax: + 91 3228231256. E-mail address: tanay2222@rediffmail.com Optics & Laser Technology 42 (2010) 1014–1021