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arXiv · 0809.3302

Symplectic-dilation mixed wavelet transform and its correspondence in quantum optics

Hong-yi Fan·Shu-guang Liu·Li-yun Hu
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Abstract

The symplectic wavelet transformation [Opt. Lett. 31 (2006) 3432], which is related to quantum optical Fresnel transform, is developed to the symplectic-dilation mixed wavelet transform (SDWT). The SDWT involves both a real-variable dilation-transform and a complex-variable symplectic transform, and possesses well-behaved properties such as Parseval theorem and inversion formula. The entangled-coherent state representation (ESCR) not only underlies the SDWT, but also helps to derive the corresponding quantum transform operator whose counterpart in classical optics is the lens-Fresnel mixed transform [Phys. Lett. A 357 (2006) 163].

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Hong-yi Fan, Shu-guang Liu, Li-yun Hu. 2008-09-19. Symplectic-dilation mixed wavelet transform and its correspondence in quantum optics. https://doi.org/10.1364/ol.34.000551

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