Researching | Fast-forming focused spots through a multimode fiber based on an adaptive parallel coordinate algorithm

Journals >Chinese Optics Letters >Volume 13 >Issue 7 >Page 071404 > Article

Chinese Optics Letters
Vol. 13, Issue 7, 071404 (2015)

Fast-forming focused spots through a multimode fiber based on an adaptive parallel coordinate algorithm

Zhe Yin, Guodong Liu, Fengdong Chen, and Bingguo Liu^*

Author Affiliations

Instrument Science and Technology, Harbin Institute of Technology, Harbin 150001, China

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DOI: 10.3788/COL201513.071404 Cite this Article Set citation alerts

Zhe Yin, Guodong Liu, Fengdong Chen, Bingguo Liu. Fast-forming focused spots through a multimode fiber based on an adaptive parallel coordinate algorithm[J]. Chinese Optics Letters, 2015, 13(7): 071404 Copy Citation Text

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Abstract

We propose an adaptive parallel coordinate (APC) algorithm for quickly forming a series of focused spots at a multimode fiber (MMF) output by controlling the MMF input field with a spatial light modulator (SLM). Only passing over the SLM once, we can obtain SLM reflectance to form focused spots on different positions. Compared with the transmission matrix method, our APC does not require iterations and massive calculations. The APC does not require as much access device time as the adaptive sequential coordinate ascent (SCA) algorithm. The experiment results demonstrate that the time taken to form 100 spots with our APC is 1/54th the time with the SCA.

E_{fiber, in} = L (E_{SLM, out}) = e^{i ϕ_{L}} E_{SLM, out},

(1)

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E_{fiber, in, ref} = L (E_{SLM, ref}) = A_{fiber, in, ref} e^{i (ϕ_{L} + ϕ_{SLM, ref})},

(2)

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E_{fiber, in, test} = L (E_{SLM, test}) = A_{fiber, in, test} e^{i (ϕ_{L} + ϕ_{SLM, test})},

(3)

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u_{n} = E_{fiber, in, ref} + E_{fiber, in, test} .

(4)

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v_{m} = \sum_{n} P_{m n} u_{n} = \sum_{n} P_{m n} (E_{fiber, in, ref} + E_{fiber, in, test}) .

(5)

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v_{m} = \sum_{n} P_{m n} (A_{fiber, in, ref} e^{i (ϕ_{L} + ϕ_{SLM, ref})} + A_{fiber, in, test} e^{i (ϕ_{L} + ϕ_{SLM, test})}) = A_{ref} e^{i (ϕ_{L} + ϕ_{SLM, ref} + ϕ_{m, ref})} + A_{test} e^{i (ϕ_{L} + ϕ_{SLM, test} + ϕ_{m, test})},

(6)

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I_{fiber, out} (x, y) = {| A_{ref} |}^{2} + {| A_{test} |}^{2} + 2 | A_{ref} | | A_{test} | \cos [(ϕ_{SLM, ref} + ϕ_{m, ref}) - (ϕ_{SLM, test} + ϕ_{m, test})] = a (x, y) + b (x, y) \cos (ϕ_{SLM, test} - ϕ_{SLM, ref}) \cos δ (x, y) + b (x, y) \sin (ϕ_{SLM, test} - ϕ_{SLM, ref}) \sin δ (x, y),

(7)

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I_{fiber, out, sum} = \iint_{R_{1} {+ R}_{2}} I_{fiber, out} (x, y) d x d y .

(8)

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I_{fiber, out, norm} = I_{fiber, out} (x, y) / I_{fiber, out, sum} .

(9)

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I_{des} (x, y) = I_{0} \exp [- a ({(x - x_{m})}^{2} + {(y - y_{m})}^{2})],

(10)

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F (ϕ_{SLM, test}) = \iint_{R_{1} {+ R}_{2}} | I_{des} - I_{fiber, out, norm} | d x d y = A + B \cos (ϕ_{SLM, test} - ϕ_{SLM, ref}) + C \sin (ϕ_{SLM, test} - ϕ_{SLM, ref}),

(11)

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A = \iint_{R_{1}} I_{des} d x d y - \iint_{R_{2}} I_{des} d x d y + (\iint_{R_{2}} a (x, y) d x d y - \iint_{R_{1}} a (x, y) d x d y) / I_{fiber, out, sum}, B = 2 (\iint_{R_{2}} b (x, y) \cos δ (x, y) - \iint_{R_{1}} b (x, y) \cos δ (x, y) d x d y) / I_{fiber, out, sum}, C = 2 (\iint_{R_{2}} b (x, y) \sin δ (x, y) d x d y - \iint_{R_{1}} b (x, y) \sin δ (x, y) d x d y) / I_{fiber, out, sum} .

(12)

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φ_{test, opt} = {\begin{cases} θ & if B \cos θ + C \sin θ < 0 \\ θ + π & otherwise \end{cases} .

(13)

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Zhe Yin, Guodong Liu, Fengdong Chen, Bingguo Liu. Fast-forming focused spots through a multimode fiber based on an adaptive parallel coordinate algorithm[J]. Chinese Optics Letters, 2015, 13(7): 071404

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