Influence of Interference Deviation on Four-Beam Interference with Circular Polarization

Xiao Wu

doi:10.3788/LOP55.061405

Journals >Laser & Optoelectronics Progress >Volume 55 >Issue 6 >Page 061405 > Article

Laser & Optoelectronics Progress
Vol. 55, Issue 6, 061405 (2018)

Influence of Interference Deviation on Four-Beam Interference with Circular Polarization

Xiao Wu^*

Author Affiliations

School of Science and Technology, Zhejiang International Studies University, Hangzhou, Zhejiang 310021, China

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DOI: 10.3788/LOP55.061405 Cite this Article Set citation alerts

Xiao Wu. Influence of Interference Deviation on Four-Beam Interference with Circular Polarization[J]. Laser & Optoelectronics Progress, 2018, 55(6): 061405 Copy Citation Text

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Fig. 1. (a) Interference beam in rectangular coordinate system; (b) diagram of four beams (B1, B2, B3, B4) interference

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Interference intensity distributions of four symmetrical RC interference beams using MATLAB simulation. (a) 3-dimensional view of intensity distribution; (b) intensity distribution in xy-plane with the incidence angle θ=10° ; (c) intensity distribution in xy-plane with the incidence angle θ=15°

Fig. 2. Interference intensity distributions of four symmetrical RC interference beams using MATLAB simulation. (a) 3-dimensional view of intensity distribution; (b) intensity distribution in xy-plane with the incidence angle θ=10° ; (c) intensity distribution in xy-plane with the incidence angle θ=15°

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Fig. 3. Interference intensity distributions along the xz-axis and yz-axis. (a1)(a2) Symmetrical distribution; (b1)(b2) under incidence deviation; (c1)(c2) under azimuth deviation

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Fig. 4. Interference intensity distributions. (a) Under azimuth deviation; (b) under azimuth deviation; (c) under both incidence and azimuth deviations

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Parameter	l=1	l=2	l=3
S_l	S₁=- $\begin{matrix} \frac{\sin θ_{1} \cos α_{1}}{\sin θ_{1} \sin α_{1} - sinθ} \end{matrix}$	S₂=- $\begin{matrix} \frac{\sin θ_{1} \cos α_{1} + sinθ}{\sin θ_{1} \sin α_{1}} \end{matrix}$	S₃=-1
d_xl	d_x₁= $\begin{matrix} \frac{λ}{\sin θ_{1} \cos α_{1}} \end{matrix}$	d_x₂= $\begin{matrix} \frac{λ}{\sin θ_{1} \cos α_{1} + sinθ} \end{matrix}$	d_x₃= $\begin{matrix} \frac{λ}{sinθ} \end{matrix}$
d_yl	d_y₁= $\begin{matrix} \frac{λ}{\|\sin θ_{1} \sin α_{1} - sinθ\|} \end{matrix}$	d_y₂= $\begin{matrix} \frac{λ}{\sin θ_{1} \sin α_{1}} \end{matrix}$	d_y₃= $\begin{matrix} \frac{λ}{sinθ} \end{matrix}$
d_z	d_z= $\begin{matrix} \frac{λ}{\|\cos θ_{1} - cosθ\|} \end{matrix}$

Table 1. Slope of lines and interference periods where the maximum interference intensity appears

Parameter	Deviation of incident angle	Deviation of azimuth angle
S_l	S₁= $\begin{matrix} \frac{\sin θ_{1}}{sinθ} \end{matrix}$ ,S₂=¥,S₃=-1	S₁=- $\begin{matrix} \frac{\cos α_{1}}{\sin α_{1} - 1} \end{matrix}$ ,S₂=- $\begin{matrix} \frac{\cos α_{1} + 1}{\sin α_{1}} \end{matrix}$ ,S₃=-1
d_xl	d_x₁= $\begin{matrix} \frac{λ}{\sin θ_{1}} \end{matrix}$ ,d_x₂= $\begin{matrix} \frac{λ}{sinθ + \sin θ_{1}} \end{matrix}$ ,d_x₃= $\begin{matrix} \frac{λ}{sinθ} \end{matrix}$	d_x₁= $\begin{matrix} \frac{λ}{sinθcos α_{1}} \end{matrix}$ ,d_x₂= $\begin{matrix} \frac{λ}{sinθ (\cos α_{1} + 1)} \end{matrix}$ ,d_x₃= $\begin{matrix} \frac{λ}{sinθ} \end{matrix}$
d_yl	d_y₁= $\begin{matrix} \frac{λ}{sinθ} \end{matrix}$ ,d_y₂=¥,d_y₃= $\begin{matrix} \frac{λ}{sinθ} \end{matrix}$	d_y₁= $\begin{matrix} \frac{λ}{sinθ (1 - \sin α_{1})} \end{matrix}$ ,d_y₂= $\begin{matrix} \frac{λ}{\sin α_{1} sinθ} \end{matrix}$ ,d_y₃= $\begin{matrix} \frac{λ}{sinθ} \end{matrix}$
d_z	d_z= $\begin{matrix} \frac{λ}{\|\cos θ_{1} - cosθ\|} \end{matrix}$	d_z=¥

Table 2. Slope of lines and interference periods when there is a deviation in the incident angle or azimuth angle

Xiao Wu. Influence of Interference Deviation on Four-Beam Interference with Circular Polarization[J]. Laser & Optoelectronics Progress, 2018, 55(6): 061405

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