Design of All-Optical Universal Gates Using Plasmonics Mach-Zehnder Interferometer for WDM Applications

Abstract

All optical integrated circuits have great application in high-speed computing and information processing to overcome the limitation of conventional electronics. In this work, a novel design of all optical universal gates using optical Kerr-effect and optical bistability of a plasmonics-based Mach-Zehnder interferometer (MZI) has been proposed. A MZI is capable for switching of light which depends on the intensities of optical input signal. The study of device is carried out using finite-difference-time-domain (FDTD) method and verified using MATLAB simulation.

Appendix: Mathematical formulation of single MZI

When signal is propagated through 3-dB coupler, it splits into two ports, and mathematically can be written as [27,28,29,30]

$$ \begin{array}{c} A=\sqrt{1-{\alpha}_1}\left({E}_{in}\right)+ j\sqrt{\alpha_1}(0)\\ {} B= j\sqrt{\alpha_1}\left({E}_{in}\right)+\sqrt{1-{\alpha}_1}(0)\end{array} $$

(6)

where E _in is the input optical signal intensity and α ₁ is attenuation constant of first directional coupler shown in Fig. 1. Equation (6) can be rewritten in matrix form as

$$ \left[\begin{array}{c} A\\ {} B\end{array}\right]=\left[\begin{array}{c}\sqrt{1-{\alpha}_1}\kern0.5em j\sqrt{\alpha_1}\\ {}\begin{array}{cc} j\sqrt{\alpha_1}& \sqrt{1-{\alpha}_1}\end{array}\end{array}\right]\left[\begin{array}{c}{E}_{in}\\ {}0\end{array}\right] $$

(7)

Further propagation of signals from output of first directional coupler through two linear arms of MZI will reach at point C and D and can be written as

$$ \begin{array}{c} C= A{e}^{- j{\varphi}_1}\\ {} D= B{e}^{- j{\varphi}_2}\end{array} $$

(8)

where φ ₁ has value equal to zero since there is no phase difference occur in first linear arm and φ ₂ is phase difference in second linear arm due to Kerr material [36],

$$ {\varphi}_2=\varDelta \varphi =\left(2\pi /\lambda \right)\left({\overset{\sim }{n}}_x-{\overset{\sim }{n}}_y\right) L $$

(9)

whereas λ is wavelength of operation and L is length of second linear arm of MZI and

$$ \left.\begin{array}{c}{\overset{\sim }{n}}_x={n}_x+\varDelta {n}_x\\ {}{\overset{\sim }{n}}_y={n}_y+\varDelta {n}_y\end{array}\right\} $$

(10)

where n _x and n _y are linear different refractive indices in second arm of MZI occur due to modal birefringence with low and high intensity of signal, respectively. ∆n _x and ∆n _y are nonlinear parts of refractive indices because of signal-induced birefringence. If signal is given with low intensity then,

$$ {\varDelta n}_x={2 n}_2{\left|{E}_{in}\right|}^2 $$

(11)

When signal is provided with high intensity then due to cross-phase modulation, refractive index becomes,

$$ {\varDelta n}_y={2 n}_2 b{\left|{E}_{in}\right|}^2,\kern3.75em b={\chi}_{xxyy}^{(3)}/{\chi}_{xxxx}^{(3)} $$

(12)

${\chi}_{xxyy}^{(3)}$ and ${\chi}_{xxxx}^{(3)}$ is third-order susceptibility of nonlinear Kerr material, and b = 1/3 when origin of signal is purely electronic. Using Eq. (9) and (12), phase shift becomes,

$$ {\varphi}_2\equiv {\varDelta \varphi}_L+{\varDelta \varphi}_{NL}=\left(2\pi L/\lambda \right)\left(\varDelta {n}_L+{n}_{2 B}{\left|{E}_{in}\right|}^2\right) $$

(13)

where ∆n _L  = n _x  − n _y and Kerr coefficient n _2B  = 2n ₂(1 − b). For high intensity of light ∆φ ≠ 0 and maximum transmission of signal is through second linear arm of MZI and its transmittivity can be obtained as,

$$ {T}_{out1}=\frac{1}{4}{\left|1-{e}^{i{\varphi}_2}\right|}^2={sin}^2\left(\frac{\varDelta \varphi}{2}\right) $$

(14)

When low-intensity of optical signal arrives, the output can be obtained as

$$ {T}_{out2}={cos}^2\left(\frac{\varDelta \varphi}{2}\right) $$

(15)

Thus, Eqs. (14) and (15) give the output of single MZI, when high- and low-intensity signal is fed at its first input port, respectively. This exclusive switching property of MZI has been used for designing the circuit of universal gates.