• Chinese Optics Letters
  • Vol. 13, Issue 12, 121602 (2015)
Zhensen Wu1、2、*, Qingchao Shang1, Tan Qu1, Zhengjun Li1, and Lu Bai1
Author Affiliations
  • 1School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071, China
  • 2Collaborative Innovation Center of Information Sensing and Understanding at Xidian University, Xi’an 710071, China
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    DOI: 10.3788/COL201513.121602 Cite this Article Set citation alerts
    Zhensen Wu, Qingchao Shang, Tan Qu, Zhengjun Li, Lu Bai. Geometric optics interpretation for rainbow scattering of a chiral sphere[J]. Chinese Optics Letters, 2015, 13(12): 121602 Copy Citation Text show less

    Abstract

    Research on light scattering from a large chiral sphere shows that the rainbow phenomenon is different from that of an isotropic sphere. A chiral sphere with certain chirality generates three first-order rainbows. In this Letter, we present a geometric optics interpretation for the phenomenon and make a calculation of the rainbow angles. The ray traces inside the sphere are determined by the reflection and refraction laws of light at the achiral–chiral interface and the chiral–achiral interface. The calculated rainbow angles achieve good agreements with those obtained by the analytical solutions. The effects of chirality and the refractive index of the sphere on rainbow angles are analyzed.
    n0sinθi=nRsinθR=nLsinθL,(1)

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    sinθR=n0/nRsinθi,sinθL=n0/nLsinθi.(2)

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    nRsinθi=nRsinθrR=nLsinθrL=n0sinθt.(3)

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    θRR=2θi+π4θR,(4)

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    θRL=2θi+π2θR2θL,(5)

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    θLR=2θi+π2θR2θL,(6)

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    θLL=2θi+π4θL,(7)

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    AOC+COE=AOB+BOF,(8)

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    θRR=2θi+π4arcsin(n1/nRsinθi),(9)

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    θLL=2θi+π4arcsin(n1/nLsinθi),(10)

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    θRL/LR=2θi+π2arcsin(n1/nRsinθi)2arcsin(n1/nLsinθi).(11)

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    θRR,LLext=2θiRR,LL+π4arcsin(n1/nR,LsinθiRR,LL),(12)

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    θiRR=arcsin4313(n1/nR)2,(13)

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    θiLL=arcsin4313(n1/nL)2,(14)

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    Zhensen Wu, Qingchao Shang, Tan Qu, Zhengjun Li, Lu Bai. Geometric optics interpretation for rainbow scattering of a chiral sphere[J]. Chinese Optics Letters, 2015, 13(12): 121602
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