Multispectral Management of the Photon Orbital Angular Momentum

Mikaël Ghadimi Nassiri and Etienne Brasselet

Phys. Rev. Lett. 121, 213901 – Published 20 November 2018

Abstract

We report on a programmable liquid crystal spatial light modulator enabling independent orbital angular momentum state control on multiple spectral channels. This is done by using electrically controllable “topological pixels" that independently behave as geometric phase micro-optical elements relying on self-engineered liquid crystal defects. These results open interesting opportunities in optical manipulation, sensing, imaging, and communications, as well as information processing. In particular, spectral vortex modulation allows considering singular spatiotemporal shaping of ultrashort pulses which may find applications in many areas such as material processing, spectroscopy, or elementary particles acceleration.

Received 21 August 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.213901

Physics Subject Headings (PhySH)

Light-matter interaction Optical vortices

Liquid crystals

Angular momentum

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Mikaël Ghadimi Nassiri and Etienne Brasselet^*

Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France

^*etienne.brasselet@u-bordeaux.fr

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Issue

Vol. 121, Iss. 21 — 23 November 2018

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Images

Figure 1
(a) Illustration of a usual optical device made of a two-dimensional matrix of electrically controlled liquid crystal pixels having a uniform molecular orientation, $ψ = ψ_{0}$ . (b) Topological counterpart where every pixel acts as an electrically controlled microscopic $q$ plate ( $q = + 1$ for the enlarged pixel).
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Figure 2
(a) Multispectral modulation of the orbital angular momentum content of a discrete spectral channel $λ_{n}$ by an array of $q$ plates of order $q_{n}$ . (b) Fabricated LC-SLM based on self-engineered electrically controlled LC topological defects with $q = + 1$ . The ruler is in centimeter units. (1) $2 \times 5$ electrical cables supplying applied voltage; (2) ground; (3) Teflon holder. Top Teflon holder not shown here. (c) Typical observation of a matrix of 49 $q$ plates observed between crossed linear polarizers and white light incoherent illumination. (d) Interferometric demonstration of the orbital angular momentum state change by an increment of two units performed by an individual structured pixel, here, at 550 nm wavelength. The forked pattern results from the far-field superposition of a processed circularly polarized Gaussian beam with a reference Gaussian beam.
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Figure 3
(a) Sketch of the experimental setup for ultrabroadband scalar and vectorial vortex beam shaping. The optical fiber array consists of 12 multimode step-index fibers with numerical aperture 0.2 and core radius $50 μ m$ . The detection system is either a camera or a fiber spectrometer. Scalar vortex (b) and vectorial (c) beam shaping when incident light is, respectively, circularly and linearly polarized. In both cases, the observation is made by placing an output polarizer that selects the polarization state orthogonal to the incident one. The image on the left corresponds to the seven spectral channels $λ_{n} = 485$ , 511, 533, 555, 575, 595, and 617 nm with $\sim 10 nm$ full width at half maximum in the plane of the LC-SLM and the image on the right refers to the far field of the polychromatic structured light field.
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Figure 4
Demonstration of on-demand polychromatic superposition of orbital angular momentum states. (a) Spectrum of the incident light that consists of five spectral channels at $λ_{n} = 485$ , 515, 546, 578, and 614 nm. (b) Chart of the on-axis power $P$ collected with a fiber spectrometer having a clear aperture of diameter $D = 200 μ m$ , see leftmost panel (c) for the five chosen configurations labeled $# m$ , with $m = (1, 2, 3, 4, 5)$ . The vortex states of every channel is optimized for $Δ_{n}^{vortex} = 7 π$ , $7 π$ , $5 π$ , $5 π$ , and $5 π$ , respectively. The nonvortex states correspond to $Δ_{n}^{nonvortex} = Δ_{n}^{vortex} - π$ . The collected power values are normalized to the reference power $P_{ref} (λ)$ associated to the nonvortex state. (c) Total far-field intensity profiles for the five configurations.
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Figure 5
Four-dimensional optical pulse shaping by spectral vortex modulation. (a) Electric field temporal waveform of a chirped ultrashort optical Gaussian pulse characterized by central wavelength $λ_{0} = 500 nm$ , spatial waist $r_{0} = 500 μ m$ , temporal waist $t_{0} = 21 fs$ , and chirp parameter $δ ω = 0.60 rad / fs$ , whose intensity spectrum is shown in panel (b) (black curve). The spectral dependence of the optical vortex purity for three cases, $η_{i}$ with $i = (1, 2, 3)$ , is shown in panel (b) (colored curves). (c) Total far field intensity profile of the spatiotemporally shaped pulse for the three cases, which are associated with parameters $β_{i}$ , in the case $q = + 1$ . An optical bottle pulse is obtained for $i = 2$ while only transverse and longitudinal spatial modulation is obtained for $i = 1$ and $i = 3$ , respectively. $κ$ refers to the spatial frequencies in the transverse plane (arbitrary units). (d) Intensity profiles of the field component carrying distinct orbital angular momentum per photon, here $0 ℏ$ (red color) and $2 σ ℏ$ (green color) per photon.
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