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Highly efficient and polarization-independent Fresnel lens based on dye-doped liquid crystal

Liang-Chen Lin, Hung-Chang Jau, Tsung-Hsien Lin, and Andy Y.-G. Fuh

Open Access Open Access

Abstract

We demonstrated a highly efficient, polarization-independent and electrically tunable Fresnel lens based on dye-doped liquid crystal using double-side photoalignment technique. The maximum diffraction efficiency reaches 37%, which approaches the theoretical limit ~41%. Such a lens functions as a half-wave plate, and this feature could be well preserved under the applied voltage. In addition, the device is simple to fabricate, and has fast switching responses between focusing and defocusing state.

©2007 Optical Society of America

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Figures (7)
Fig. 1.
Fig. 1. Schematic fabrication method of the DDLC Fresnel lens.

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Fig. 2.
Fig. 2. Schematic diagram of the orthogonally alternating binary configuration of the DDLC Fresnel lens. The top layer is a Fresnel zone plate mask.

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Fig. 3.
Fig. 3. Microscopic images of the fabricated DDLC Fresnel lens observed under a crossed-polarizer optical microscope with the rubbing direction of the cell making an angle of, (a) 0°, and (b) 45° to the polarizer axis.

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Fig. 4.
Fig. 4. Schematic experimental setup for analyzing the focusing properties of the DDLC Fresnel lens.

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Fig. 5.
Fig. 5. The measured primary diffraction efficiency of the DDLC Fresnel lens as a function of the applied voltage.

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Fig. 6.
Fig. 6. The measured intensity of the DDLC Fresnel lens as a function of the analyzer axis in reference to the director axis of LCs in the odd zones under various voltages.

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Fig. 7.
Fig. 7. Measured diffraction efficiency at the primary focal point of the DDLC Fresnel lens as a function of the incident linearly polarization angle at the applied voltages of V = 0Vrms and 1.8 Vrms.

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Equations (5)

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[ T in ] = [ E o cos ⁡ θ E o sin ⁡ θ ] ; [ T out ] odd − zone = [ E o cos ⁡ θ ∙ e in o 2 π λ d E o sin ⁡ θ ∙ e in e 2 π λ d ] ; [ T out ] even − zone = [ E o cos ⁡ θ ∙ e in e 2 π λ d E o sin ⁡ θ ∙ e in o 2 π λ d ]
D m = 1 2 A 1 ∫ 0 2 A 1 [ T out ] e − i 2 m π A 2 A 1 dA
= 1 2 πr 1 2 ∫ 0 2 π ∫ 0 r 1 [ T out ] odd − zone e − im π r 2 r 1 2 rdrd θ + ∫ 0 2 π ∫ r 1 2 r 1 [ T out ] even − zone e − im π r 2 r 1 2 rdrd θ
= 1 im π e in o 2 π λ d ( e i ( n e − n o ) 2 π λ d − 1 ) [ − E o cos ⁡ θ E o sin ⁡ θ ] , m = odd integers
η m = ∣ D m ∣ ∣ T in ∣ 2 2 = ∣ D m ∣ 2 E 0 2 = ( sin ⁡ ( n e − n o ) 2 π λ d 2 m π 2 ) 2 , m = odd integers
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