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We study the Pancharatnam–Berry geometric phase for polarized light beams of a non-closed cycle on the Poincare sphere. A geometric phase in different states of polarization is of great importance. It is shown that the Pancharatnam in-phase transformation can be regarded as a transformation of basis vectors. Using spherical trigonometry, we provide a new concise method of proving the Pancharatnam theorem.
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Kiko Nakamura (2013) studied this question.
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