Optical switches and logic gates based on self-collimated beams in two-dimensional photonic crystals

Yuanliang Zhang; Yao Zhang; Baojun Li

doi:10.1364/OE.15.009287

Optics Express
Vol. 15,
Issue 15,
pp. 9287-9292
(2007)
•https://doi.org/10.1364/OE.15.009287

Optical switches and logic gates based on self-collimated beams in two-dimensional photonic crystals

Yuanliang Zhang, Yao Zhang, and Baojun Li

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Yuanliang Zhang, Yao Zhang, and Baojun Li, "Optical switches and logic gates based on self-collimated beams in two-dimensional photonic crystals," Opt. Express 15, 9287-9292 (2007)

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Abstract

A device for optical switches and logic gates is proposed in two-dimensional photonic crystals based on self-collimated beams. The main structure of the device is a line-defect-induced 3 dB splitter. Operating principle, as revealed by both theoretical calculation and finite-difference time-domain simulation, is based on the interference of reflected and transmitted self-collimated beams. This device is potentially applicable for photonic integrated circuits.

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Fig. 1. Schematic diagram of the proposed optical switches and logic gates. The defect region (green area, the reducing Si rods) and the surrounding region (cyan area, the host rods) corresponds to an optically thinner medium (low refractive index, nL) and an optically denser medium (high refractive index, nH), respectively.

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Fig. 2. (a). Band diagram of the PC structure for E -polarized mode. The inset shows the PC structure, which consists of square lattice of Si rods in air. The frequency 0.194(a/λ) is marked by the orange line. (b) Equifrequency contours of the first band.

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Fig. 3. Simulated steady-state field distribution of the E -polarized mode at 0.194(a/λ) when incident beams propagate along the Γ-M direction. (a) and (b) for the case that the incident beam is only launched into face I₁ and I₂, respectively.

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Fig. 4. (a). Schematic diagram of the switch. Two beams with different phases are incident on the input faces I₁ and I₂. (b) and (c) Simulated steady-state field distribution of the E -polarized mode at 0.194(a/λ) when incident beams propagate along the Γ-M direction. The phase difference φ₁-φ₂ of the two incident beams particularly sets as π/2 and -π/2, respectively.

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Fig. 5. (a). The normalized intensity spectra of faces O₁ (green line) and O₂ (violet line) for Fig. 3(a). The red line represents the total output efficiency. (b) The normalized intensity and extinction ratio spectra for Fig. 4(b).

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Tables (1)

Table 1. The total device functions.

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Equations (4)

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t^{2} + r^{2} = 1

\begin{matrix} T_{I_{1}} = E_{1} \cdot {te}^{i φ} = uE e^{- i (φ_{1} - φ)} ⁄ \sqrt{2} \\ R_{I_{1}} = E_{1} \cdot {re}^{i (φ + π ⁄ 2)} = uE e^{- i (φ_{1} - φ - π ⁄ 2)} ⁄ \sqrt{2} \\ T_{I_{2}} = E_{2} \cdot {te}^{i φ} = uE e^{- i (φ_{2} - φ)} ⁄ \sqrt{2} \\ R_{I_{2}} = E_{2} \cdot {re}^{i (φ + π ⁄ 2)} = uE e^{- i (φ_{2} - φ - π ⁄ 2)} ⁄ \sqrt{2} \end{matrix}}

\begin{matrix} O_{1} = R_{I_{1}} + T_{I_{2}} = uE e^{- i (φ_{1} - φ - π ⁄ 2)} ⁄ \sqrt{2} + {uEe}^{- i (φ_{2} - φ)} ⁄ \sqrt{2} \\ = \sqrt{2} uE \cos (- \frac{φ_{1} - φ_{2}}{2} + \frac{π}{4}) e^{- i (\frac{φ_{1} + φ_{2}}{2} - φ - \frac{π}{4})} \\ O_{2} = R_{I_{2}} + T_{I_{1}} = uE e^{- i (φ_{2} - φ - π ⁄ 2)} ⁄ \sqrt{2} + {uEe}^{- i (φ_{1} - φ)} ⁄ \sqrt{2} \\ = \sqrt{2} uE \cos (\frac{φ_{1} - φ_{2}}{2} + \frac{π}{4}) e^{- i (\frac{φ_{1} + φ_{2}}{2} - φ - \frac{π}{4})} \end{matrix}}

\begin{matrix} I_{O_{1}} = {∣ O_{1} ∣}^{2} = 2 {∣ uE ∣}^{2} \cos^{2} (- \frac{φ_{1} - φ_{2}}{2} + \frac{π}{4}) = {∣ uE ∣}^{2} [1 + \sin (φ_{1} - φ_{2})] \\ I_{O_{2}} = {∣ O_{2} ∣}^{2} = 2 {∣ uE ∣}^{2} \cos^{2} (\frac{φ_{1} - φ_{2}}{2} + \frac{π}{4}) = {∣ uE ∣}^{2} [1 - \sin (φ_{1} - φ_{2})] \end{matrix}}

		for φ₁-φ₂ =2kπ+π/2					for φ₁ -φ₂=2kπ-π/2
Input	I₁	0	1	0	1	I₁	0	1	0	1
signal	I₂	0	0	1	1	I₂	0	0	1	1
Comparison			Fig. 3(a)	Fig. 3(b)	Fig. 4(b)			Fig. 3(a)	Fig. 3(b)	Fig. 4(c)
Output	O₁/OR	0	1	1	1	O₁/XOR	0	1	1	0
signal	O₂/XOR	0	1	1	0	O₂/OR	0	1	1	1

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Equations (4)

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