Holographic generation of complex fields with spatial light modulators: application to quantum key distribution

Abstract

There has been considerable interest recently in the generation of azimuthal phase functions associated with photon orbital angular momentum (OAM) for high-dimensional quantum key distribution. The generation of secure quantum keys requires not only this pure phase basis but also additional bases comprised of orthonormal superposition states formed from the pure states. These bases are also known as mutually unbiased bases (MUBs) and include quantum states whose wave functions are modulated in both phase and amplitude. Although modulo 2pi optical path control with high-resolution spatial light modulators (SLMs) is well suited to creating the azimuthal phases associated with the pure states, it does not introduce the amplitude modulation associated with the MUB superposition states. Using computer-generated holography (CGH) with the Leith-Upatnieks approach to hologram recording, however, both phase and amplitude modulation can be achieved. We present a description of the OAM states of a three-dimensional MUB system and analyze the construction of these states via CGH with a phase-modulating SLM. The effects of phase holography artifacts on quantum-state generation are quantified and a prescription for avoiding these artifacts by preconditioning the hologram function is presented. Practical effects associated with spatially isolating the first-order diffracted field are also quantified, and a demonstration utilizing a liquid-crystal SLM is presented.

Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings

“…The superior security advantages of OAM channels have also been demonstrated in both classical and quantum communication systems. [14][15][16][17][18][19] OAM-based optical communications can be classified into two different categories: OAM shift keying (OAM-SK) and OAM division multiplexing (OAM-DM). For OAM-SK, the OAM states of the OV beams are regarded as a modulation format that enables the encoding of information by dynamic switching of spatial light modulators.…”

“…For OAM-SK, the OAM states of the OV beams are regarded as a modulation format that enables the encoding of information by dynamic switching of spatial light modulators. 7,[19][20][21][22] For OAM-DM, the OAM states are considered to be fixed channels to be used to carry information with the advantages of high bit rates and low bit error rates (BERs). 13,23 In a state-of-the-art demonstration of an OAM-based FSO communication system, 2.56 Tbit s 21 data transmission was obtained by the multiplexing of four OAM beams with two polarization states.…”

Photonic orbital angular momentum in starlight

“…Allen et al (1992) showed that a HermiteGaussian laser beam (zero OAM) can be transformed into a Laguerre-Gaussian beam (non-zero OAM) using a pair of cylindrical lenses. Subsequently, several other methods have been developed to generate POAM in the laboratory (Oemrawsingh et al 2004;Gibson et al 2004;Gruneisen et al 2008). LaguerreGaussian beams are known as optical vortex beams because of their phase structure which is proportional to e ımφ , using the azimuthal angle, φ, and the OAM index, m. All of the photons in these optical vortex beams carry m of OAM (Harwit 2003).…”

“…LaguerreGaussian beams are known as optical vortex beams because of their phase structure which is proportional to e ımφ , using the azimuthal angle, φ, and the OAM index, m. All of the photons in these optical vortex beams carry m of OAM (Harwit 2003). Identifying the states from such beams however, can be problematic and several different types of OAM sorters have been developed (Gruneisen et al 2008;Lavery et al 2011a,b;Sponselli & Lavery 2013).…”

Optical vortex discrimination with a transmission volume hologram

“…Spatial light modulators (SLMs) have been utilized to generate OAM states and superpositions of OAM states using modulo 2π phase control [9,10] and computergenerated holography [12] to achieve both amplitude and phase modulation. Thin holograms in conjunction with single-mode optical fibers have been used to detect OAM states, but do not provide a means of separating OAM states with high efficiency [7,8,10,11].…”