A Theoretical Study to Realize Solitonic 2: 1 Multiplexer Using Coupling Actions of Optical Pulse

In combinational logic system, multiplexer is an important part where one can select a particular input in the output side. The specific optical input to be selected at the exit side of the scheme is determined by the control or select channel. Here, 2:1 optical multiplexer is proposed by using the coupling action of the optical pulse of a biased optical coupler. The electro-optic nature of the optical wave guide are massively used to convert the optical pulse into optical soliton pulse. Optical soliton pulses are used here as a substitute of ordinary optical pulse as the information carrier due to some superior character of the soliton pulse. Before introducing in the coupling region. Optical pulse should be converted into solitonic one. Such category of multiplex system may be used for ultra-high speed remote operation and for high secure communication system. KeywordsOptical communication, Coupled waveguide, Evanescent optical pulse, EO effect, Optical soliton pulse.


I. INTRODUCTION
Multiplexer is a combinational logic system that has maximum of 2 n data inputs, n controlled channels and only one output line. One of these data inputs will be transferred to the output based on the values of selection lines.  In evanescent wave coupling optical pulses are transmitted from one optical wave guide to another. If the separation between the two wave guides becomes so small that the evanescent waves of the two wave guides overlap to a considerable extent, then there is a conversation of energy between the two wave guides. In this situation, the evanescent field associated with the propagating modes in the two wave guides interact and lead to a periodic exchange of energy between the two wave guides. Such type of wave guides where coupling between two guides follows is designated as directional coupler. There is a wide-ranging transfer of energy from one to other wave guide will occurs if the propagation constant of the modes in the two wave guides are matching and else there is a partial handover of energy [1,2,3]. Again when an optical pulse having a well defined power shape propagates through an optical fiber, at which the dispersion effect and non-linear effect exactly compensate to each other then a stable wave packet is made. These distinct types of pulses are considered as optical soliton pulse (OSP) which does not broaden in time domain or in frequency domain when it travels through the nonlinear optical fiber medium. Due to such inherent character of the OSP, it is better to use as information carrier in place of ordinary optical pulse [4,5].
In this communication, implementation of optical soliton based 2:1 mux is proposed by using the optical coupling nature of the pulse in the coupling region of the directional coupler. Such theoretical approach is suitable for very high speed and highly secure remote operation.

II. METHODS AND MATERIALS
If A 2 (z) represent the amplitude of the evanescent wave in the 2 nd wave guide due to optical pulse of amplitude A 1 (z) incident in 1 st wave guide in a directional coupler,( as shown in fig. 3) then the optical power in 1 st and 2nd waveguide after interaction become respectively as proportional to | ( )| and | ( )| as given in equ. (1) and (2) respectively. where k are the strength of interaction between two modes], are the propagation constants of the mode in the wave guide-1 and wave guide-2 respectively] [6].
Equations (1) and (2) shows the periodic exchange of energy between two couplers whose frequency of exchange of energy depends not only the properties of the couplers materials but also on the dimension of the coupling region. Again maximum energy will be exchanged from one to other wave guide will be happen for a minimum coupling length between two coupler is given as Now, if we place two wave guide such that the coupling length become exactly , then optical pulse will be switched to the other in the coupling region, this case is denoted as cross state. If some how we make √ then the new coupling length will be as ⁄ . In the later case, the energy exchanged will be stopped and optical pulse will be persist in the same guide, this is designated as parallel state.
The electro-optic behavior of the optical wave guides are used here to switch over from cross state to parallel state. Electric field are applied in the coupling region in opposite sense w.r.t each guide, so that, effective refractive index of one guide increases where as for other guide it is decreases (as shown in fig:3). The electric field is applied exactly along the c-axis as the incident light is along the c-axis. Before incident of the optical pulse into the guides, the optical pulses are changed to a precise power profile so that the optical pulse transferred to optical soliton pulse. Already we proposed some very effective process to get OSP from ordinary optical pulse. [6 ].  The 1st coupler is intended by coupling 1 st and 2 nd wave guide, where as the second coupler is shaped by pairing the outlet of 1 st wave guide from first coupler and an another similar 3 rd wave guide. Oppositely focused electric field having a pre-specified values are applied in both the couplers in coupling section, such that the situation √ have been fulfilled in case of each couplers. 1 I , 2 I symbolize the solitonic optical inputs at the input face of the 1 st wave guide and 2 nd wave guide respectively. Before introducing the optical pulse into the waveguide, it is converted into solitonic pulse. The state (present or absent) of the external electric field applied at the coupling region are considered as inputs of the proposed scheme. The state of the triggering field applied to the 1 st coupler is considered as input A and that for 2 nd coupler is considered as input B.

III. RESULT AND DISCUSSION
The input state is considered as state zero (0) only when the triggered field is applied. In this situation the coupler is in parallel state so that almost all the signal remain in the same wave guide i.e. coupling effect becomes very negligible. The input state is considered as state one when the external triggering field is absent. Here the coupler will be in cross state, where almost all the optical signal transfer to another waveguide in the coupling region and the coupling effect will be maximum. The optical soliton signal (Y) emerges from 1 st wave guide after the 2 nd coupling region is considered as out put of the proposed multiplexer. The out put is considered as state one only when a considerable high intense OSP is come out from the optical wave guide. At the same time the output state is considered as state zero when a very low intense or zero intense optical pulse is obtained at the outlet of the 1 st wave guide at Y.

IV. CONCLUSION
Here, the coupling nature of the wave guide and EO effect of the guiding medium are both used extensively. EO effect are used mainly to convert the optical signal to solitonic one. Hence the proposed system will be very much effective for the high distance and high secured operation. The polarization state of the input optical soliton pulse should be maintained in same manner for proper operation. One can also reduce the value of required triggering pulse by suitably alter the electrode dimension. It is very important to note that the coupling length should be adjusted according to the non-linearity of the guiding medium as the intensity of the soliton pulse is high.