Optical polarized orthogonal matrix

Shujun Zheng; Jiaren Tan; Xianmiao Xu; Hongjie Liu; Yi Yang; Xiao Lin; Xiaodi Tan

doi:10.1364/PRJ.540120

Journals >Photonics Research >Volume 13 >Issue 2 >Page 373 > Article

Photonics Research
Vol. 13, Issue 2, 373 (2025)

Shujun Zheng^1,†, Jiaren Tan^2,†, Xianmiao Xu¹, Hongjie Liu¹..., Yi Yang³, Xiao Lin³ and Xiaodi Tan^3,*|Show fewer author(s)

Author Affiliations

¹Information Photonics Research Center, College of Photonic and Electronic Engineering, Fujian Normal University, Fuzhou 350117, China

²Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA

³College of Photonic and Electronic Engineering, Key Laboratory of Opto-Electronic Science and for Medicine of Ministry of Education, Fujian Provincial Key Laboratory of Photonics Technology, Fujian Provincial Engineering Technology Research Center of Photoelectric Sensing Application, Fujian Normal University, Fuzhou 350117, China

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DOI: 10.1364/PRJ.540120 Cite this Article Set citation alerts

Shujun Zheng, Jiaren Tan, Xianmiao Xu, Hongjie Liu, Yi Yang, Xiao Lin, Xiaodi Tan, "Optical polarized orthogonal matrix," Photonics Res. 13, 373 (2025) Copy Citation Text

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Application diagram of OPOM4×8 in polarization holography. (a) Concept of polarization hologram multi-channel multiplexing, whose numerical result indicates that the unique information can only be output when PCdek=PCenk. (b) Experimental demonstration by illuminating with different input PC reference waves. The input PC reference wave that determines the reconstruction results for the Arabic numerals 1–8 corresponds respectively to the horizontal coordinates in (a).

Fig. 1. Application diagram of OPOM4×8 in polarization holography. (a) Concept of polarization hologram multi-channel multiplexing, whose numerical result indicates that the unique information can only be output when PCdek=PCenk. (b) Experimental demonstration by illuminating with different input PC reference waves. The input PC reference wave that determines the reconstruction results for the Arabic numerals 1–8 corresponds respectively to the horizontal coordinates in (a).

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The construction of OPOM that is derived from the minimum unit, OPOM2×4, and any Hadamard matrix. Each element of the Hadamard matrix is multiplied by the factor OPOM2×4 and then individually mapped to obtain the higher-order OPOM.

Fig. 2. The construction of OPOM that is derived from the minimum unit, OPOM2×4, and any Hadamard matrix. Each element of the Hadamard matrix is multiplied by the factor OPOM2×4 and then individually mapped to obtain the higher-order OPOM.

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Fig. 3. PCenk (k=1−8) from the OPOM4×8 with eight orthogonal pairs, each containing four polarization states. The direction of the arrow indicates the polarization angle of the polarized light. PCen1=(s,p,s,p); PCen2=(p,s,p,s); PCen3=(s,−p,s,−p); PCen4=(p,−s,p,−s); PCen5=(s,p,−s,−p); PCen6=(p,s,−p,−s); PCen7=(s,−p,−s,p); PCen8=(p,−s,−p,s).

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Fig. 4. (a) Experimental setup for multi-dimensional polarization multiplexing. HWP1-HWP6, half wave plates; PBS1, PBS2, polarization beam splitters; M1-M4, mirrors; L1-L3, lenses; BS1-BS3, beam splitters; A-SLM, amplitude-based spatial light modulator; PQ/PMMA, photoinduced polymer; CCD, charge-coupled device. (b) Obtained different PCs according to the different fast axes of HWP1–HWP4.

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Fig. 5. Application of OPOM4×8 in polarization holography and crosstalk analysis between channels. (a) Experimental demonstration by illuminating with different input PC reference waves [PCdek=PCenk (k=1 to 8)]. (b) Information reconstruction ratio under different PCdek illuminating the eight PCen channels.

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Fig. 6. Holographic encoding of OPOM information channels for multiplexed dynamic display. (a)–(h) The results under a single PCen as the PCde; (i)–(k) the results under the PCde formed by combining three different PCen. When PCde=PCen1+PCen2+PCen3+PCen4+PCen5+PCen6+PCen7+PCen8, the entire rectangle is displayed as depicted in (i). When PCde=PCen1+PCen2+PCen3+PCen4, the left half is displayed as depicted in (j). When PCde=PCen5+PCen6+PCen7+PCen8, the right half is displayed as depicted in (k).

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Recording		Reading	Reconstructing
Sig.	Ref.	Ref.	Rec.	Rec. ( $A + B = 0$ )
$a p + b s$	$a p + b s$	$b p - a s$	$- (A + B) a b^{2} s$	0
$a p + b s$	$a p + b s$	$a p + b s$	$(a^{2} + b^{2}) B (a p + b s) + (A + B) b^{3} s$	$(a^{2} + b^{2}) B (a p + b s)$
$a p + b s$	$b p - a s$	$b p - a s$	$(a^{2} + b^{2}) B (a p + b s) + (A + B) a^{2} b s$	$(a^{2} + b^{2}) B (a p + b s)$
$a p + b s$	$b p - a s$	$a p + b s$	$- (A + B) a b^{2} s$	0

Table 1. Polarization Holography with Arbitrary Orthogonal Reference Waves under Fixed Interference Angle of 90°

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Recording		Reading	Reconstructing
Sig.	Ref.	Ref.	Rec.
$p$	$p$	$s$	0
$p$	$p$	$p$	$B p$
$p$	$s$	$s$	$B p$
$p$	$s$	$p$	0

Table 2. Polarization Holography with Orthogonal Reference Waves under Fixed Signal Wave and Interference Angle of 90°

Shujun Zheng, Jiaren Tan, Xianmiao Xu, Hongjie Liu, Yi Yang, Xiao Lin, Xiaodi Tan, "Optical polarized orthogonal matrix," Photonics Res. 13, 373 (2025)

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