A compact diffractive sorter for high-resolution demultiplexing of orbital angular momentum beams

Abstract

The design and fabrication of a compact diffractive optical element is presented for the sorting of beams carrying orbital angular momentum (OAM) of light. The sorter combines a conformal mapping transformation with an optical fan-out, performing demultiplexing with unprecedented levels of miniaturization and OAM resolution. Moreover, an innovative configuration is proposed which simplifies alignment procedures and further improves the compactness of the optical device. Samples have been fabricated in the form of phase-only diffractive optics with high-resolution electron-beam lithography (EBL) over a glass substrate. A soft-lithography process has been optimized for fast and cheap replica production of the EBL masters. Optical tests with OAM beams confirm the designed performance, showing excellent efficiency and low cross-talk, with high fidelity even with multiplexed input beams. This work paves the way for practical OAM multiplexing and demultiplexing devices for use in classical and quantum communication.

Figure 1

Comparison of high-resolution OAM sorter configurations. In the original configuration, at least four elements were required: an unwrapper and a phase-corrector, followed by a fan-out array and a second phase-corrector, as well as the ubiquitous lenses for Fourier transform. In the new configuration, high-resolution OAM sorting is performed with two diffractive optics: the first encoding both the optical operations of the unwrapper and the fan-out, and the second performing phase-correction. The inset sketches the output intensity and phase with/without (w/o) the fan-out element.

Figure 2

Schematic of the compact high-resolution sorter. The input OAM beam impinges on the outer annular region (A) of the diffractive optics that encodes the fan-out focusing unwrapper. Subsequently, a mirror reflects the beam towards the optical element again through its inner zone (B), where double phase-correction is performed. A Fourier lens completes the demultiplexing. A beam-splitter (BS) is used to separate input and output beams.

Figure 3

(a) Phase pattern of log-pol sorter with three-copies fan-out. Parameters of the optical transformation: a = 64 μm, b = 900 μm, f = 8.5 mm, phase-corrector radius (red dashed line) ρ₂ = 700 μm, unwrapper outer radius ρ₁ = 1200 μm. (b.1-3) Details of the fan-out unwrapper zone at optical microscope. (c.1-2) Details of the double phase-corrector region at optical microscope.

Figure 4

SEM inspection of the 3-copy sorter fabricated with electron-beam lithography and designed for λ = 632.8 nm. Number of phase levels: 256. Maximal thickness step: 1289.0 nm. (a) Zone of transition from the inner (double phase-corrector) to the outer (fan-out unwrapper) region marked by a green line in Fig. 3(a). (b–e) Details. (f) Region marked by an orange line in Fig. 3(a). (g) Exposure of a limited part (40 × 40 μm²) of the region in figure (f) in order to highlight the edge profile.

Figure 5

Experimental data for OAM beams in the range ℓ = −{9, …, +9} focused after the fan-out log-pol sorter for (a) N = 1 (b), N = 3 and (c), N = 5. As expected, a reduction in spot width is evident as the fan-out multiplication factor N increases. Coordinates have been normalized by the parameter Δy = λf/2πa, such that the vertical position of each spot corresponds to the OAM content of the corresponding beam, according to Eq. (2).

Figure 6

(a) Cross-sections of the experimental far-field plots in Fig. 5. The vertical coordinate has been normalized by Δy = λf/2πa. (b) Intensity profile of the single peak corresponding to ℓ = 0. (c) Position of the spots as a function of the input OAM value and theoretical curve.

Figure 7

Output relative power in all detector regions for pure input OAM-beams in the set ℓ = {−9, …, +9}, for different number of copies N of the integrated fan-out log-pol sorter: (a) N = 1, (b) N = 3, (c) N = 5.

Figure 8

Average inter-channel cross-talk XT for the fan-out log-pol sorter as a function of copies number N = {1, 3, 5} and channel separation Δℓ = {1, 2}. Error bars: standard deviation calculated over the total channel set in the range ℓ = {−9, …, +9}.

Figure 9

Encoded (multiplexed) and measured (de-multiplexed) superposition weightings for multiplexed OAM modes sent through (a) N = 1, (b) N = 3 and (c) N = 5 integrated copies of the fan-out log-pol mode sorter. The similarity between the multiplexed and de-multiplexed detected modes are S = 0.791, S = 0.968 and S = 0.971 for the cases of N = 1, 3 and 5, respectively.

Figure 10

Comparison between the experimental cross-section of the far field distribution of the master and replica for the sorter with a three-copies fan-out.