Optical vortex discrimination with a transmission volume hologram

Transmissive volume holograms are considered as mode-selective optical elements for the de-multiplexing and detecting of optical vortex modes according to the topological charge or mode number. Diffraction of vortex modes by a fundamental mode hologram is modeled using a physical optics model that treats the volume hologram as an angle-dependent transfer function. Diffracted irradiance profiles and diffraction efficiencies are calculated numerically as a function of the incident mode number. The results of the model are compared with experimental results obtained with volume holograms of fundamental and higher-order vortex modes. When considered as a function of detuning between the incident and recorded mode numbers, the measured diffraction efficiencies are found to be invariant with respect to the recorded mode number, provided that the order difference remains unchanged, and in close agreement with the predictions of the model. Measurements are made with a 1.3 mm thick permanent photo-thermo-refractive glass hologram and a 9 mm thick re-writable photorefractive lithium niobate hologram. A liquid-crystal spatial light modulator generates the vortex modes used to record and read the holograms. The results indicate that a simple volume hologram can discriminate between vortex modes; however, adjacent mode discrimination with low crosstalk would require a very thick hologram. Furthermore, broadening of the vortex angular spectrum, due to diffraction at a finite aperture, can adversely affect diffraction efficiencies.

[1]  Leonid B. Glebov,et al.  Volume Bragg Gratings in PTR glass - New Optical Elements for Laser Design , 2008 .

[2]  J. P. Woerdman,et al.  Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[3]  A. Vaziri,et al.  Entanglement of the orbital angular momentum states of photons , 2001, Nature.

[4]  M. Neifeld,et al.  Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link. , 2008, Applied optics.

[5]  David G Grier,et al.  Structure of optical vortices. , 2003, Physical review letters.

[6]  Raymond C. Dymale,et al.  Holographic generation of complex fields with spatial light modulators: application to quantum key distribution. , 2008, Applied optics.

[8]  G. Swartzlander,et al.  Optical vortex coronagraph. , 2005, Optics letters.

[9]  M. Lavery,et al.  Efficient sorting of orbital angular momentum states of light. , 2010, Physical review letters.

[10]  David L. Fried,et al.  Branch point problem in adaptive optics , 1998 .

[11]  H. Kogelnik.  Coupled wave theory for thick hologram gratings , 1969 .

[12]  A. Vaziri,et al.  Experimental two-photon, three-dimensional entanglement for quantum communication. , 2002, Physical review letters.

[13]  Yuan Luo,et al.  Optimization of multiplexed holographic gratings in PQ-PMMA for spectral-spatial imaging filters. , 2008, Optics letters.

[14]  Pierpaolo Boffi,et al.  Diffraction of optical communication Gaussian beams by volume gratings: comparison of simulations and experimental results. , 2004, Applied optics.

[15]  Thomas Jennewein,et al.  How to create and detect N-dimensional entangled photons with an active phase hologram , 2007, 0707.0061.

[16]  N. Kato,et al.  A theoretical study of pendellösung fringes. I. General considerations , 1961 .

[17]  Jennifer E. Curtis,et al.  Dynamic holographic optical tweezers , 2002 .

[18]  A. Vaziri,et al.  Experimental quantum cryptography with qutrits , 2005, quant-ph/0511163.

[19]  N. Kato.  A theoretical study of pendellösung fringes. II. Detailed discussion based upon a spherical wave theory , 1961 .

[20]  Mark T. Gruneisen,et al.  Programmable diffractive optics for wide-dynamic-range wavefront control using liquid-crystal spatial light modulators , 2004 .

[21]  S. Barnett,et al.  Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon. , 2004, Physical review letters.