Abstract
We use the Fourier transform and Snell’s law to demonstrate how refraction at a flat interface induces astigmatism and transforms the spatial distribution of a stigmatic beam. Refraction makes the beam parameters for the transverse dimensions perpendicular and parallel to the plane of incidence grow differently and gives rise astigmatism. The decompositions of the orbital angular momentum of the beam before and after refraction are different. A single-value state of orbital angular momentum of the incident photon in a Laguerre–Gaussian mode is transformed into a superposition state.
Highlights
It is well established that an optical beam with a helical phase front, characterized by an azimuthal phase dependence of exp(ilφ) of its transverse spatial profile, carries an orbital angular momentum (OAM) of ħl per photon [1,2,3]
The OAM light has attracted a lot of interest in the fields of quantum optics and quantum information in recent years as it is regarded as a physical realization of higher-dimensional quantum systems [4, 5], which enable us to go beyond twodimensional Hilbert spaces
We study astigmatism resulting from refraction and its effect on the OAM of the outgoing beam after it passes through an optical element
Summary
It is well established that an optical beam with a helical phase front, characterized by an azimuthal phase dependence of exp(ilφ) of its transverse spatial profile, carries an orbital angular momentum (OAM) of ħl per photon [1,2,3]. The incident beam in a Laguerre-Gaussian (LG) mode with a topological charge l is transformed into a superposition of LG beams after it passes through a Dove prism, instead of the expected LG beam with the inverse topological charge −l [10, 11]. This undesired change of the orbital angular momentum increases the error rate in quantum information algorithms and protocols that make use of Dove prisms without being aware of this effect.
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