Beam combination at any angles with a multilayer grating

Ci Yin; Shiyao Fu; Yahui Zhang; Yanwang Zhai; Heng Zhou; Chunqing Gao

doi:10.3788/COL201816.080502

Journals >Chinese Optics Letters >Volume 16 >Issue 8 >Page 080502 > Article

Chinese Optics Letters
Vol. 16, Issue 8, 080502 (2018)

Beam combination at any angles with a multilayer grating

Ci Yin, Shiyao Fu, Yahui Zhang, Yanwang Zhai, Heng Zhou, and Chunqing Gao^*

Author Affiliations

School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China

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DOI: 10.3788/COL201816.080502 Cite this Article Set citation alerts

Ci Yin, Shiyao Fu, Yahui Zhang, Yanwang Zhai, Heng Zhou, Chunqing Gao. Beam combination at any angles with a multilayer grating[J]. Chinese Optics Letters, 2018, 16(8): 080502 Copy Citation Text

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Abstract

A scheme for beam combination at any angles employing a specially designed multilayer grating is proposed. Such a grating is able to convert noncoaxial laser beams to coaxial ones, and the combined beams are able to output along the normal line of the grating. The intensity and the phase structure of combined beams can also be controlled. The experiments are carried out by loading an encoded grating on a liquid-crystal spatial light modulator. The results agree well with the simulations. This method of beam combination with a multilayer grating serves to simplify the complexity of beam combination.

A \exp [i ϕ (x, y)] = \sum_{m, n = - \infty}^{+ \infty} c_{m, n} \exp [i (m γ_{x} x + n γ_{y} y)],

(1)

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γ_{x} = \frac{2 π}{T_{x}}, γ_{y} = \frac{2 π}{T_{y}},

(2)

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\sum_{m, n = - \infty}^{+ \infty} \sum_{m^{'}, n^{'} = - \infty}^{+ \infty} c_{m, n} c_{m^{'}, n^{'}}^{*} \times \exp [i (m - m^{'}) γ_{x} x + i (n - n^{'}) γ_{y} y)] = {| C |}^{2} .

(3)

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c_{m, n} = | c_{m, n} | \exp (i τ_{m, n}) \exp (i l_{m, n} φ),

(4)

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A \exp [i ϕ (x)] = \sum_{N} c_{m_{N}} \exp (i m_{N} γ_{x} x) .

(5)

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T_{x} \sin α_{1} = m_{1} λ, T_{x} \sin α_{2} = m_{2} λ, T_{x} \sin α_{3} = m_{3} λ, \dots T_{x} \sin α_{N} = m_{N} λ .

(6)

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m_{1} : m_{2} : m_{3} : \dots : m_{N} = \sin α_{1} : \sin α_{2} : \sin α_{3} : \dots : \sin α_{N} .

(7)

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Ci Yin, Shiyao Fu, Yahui Zhang, Yanwang Zhai, Heng Zhou, Chunqing Gao. Beam combination at any angles with a multilayer grating[J]. Chinese Optics Letters, 2018, 16(8): 080502

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