Multiplication and division of the orbital angular momentum of light with diffractive transformation optics

Gianluca Ruffato,Michele Massari,Filippo Romanato

doi:10.1038/s41377-019-0222-2

Abstract

We present a method to efficiently multiply or divide the orbital angular momentum (OAM) of light beams using a sequence of two optical elements. The key element is represented by an optical transformation mapping the azimuthal phase gradient of the input OAM beam onto a circular sector. By combining multiple circular-sector transformations into a single optical element, it is possible to multiply the value of the input OAM state by splitting and mapping the phase onto complementary circular sectors. Conversely, by combining multiple inverse transformations, the division of the initial OAM value is achievable by mapping distinct complementary circular sectors of the input beam into an equal number of circular phase gradients. Optical elements have been fabricated in the form of phase-only diffractive optics with high-resolution electron-beam lithography. Optical tests confirm the capability of the multiplier optics to perform integer multiplication of the input OAM, whereas the designed dividers are demonstrated to correctly split up the input beam into a complementary set of OAM beams. These elements can find applications for the multiplicative generation of higher-order OAM modes, optical information processing based on OAM beam transmission, and optical routing/switching in telecom.

Highlights

Introduction Since the seminal paper ofAllen and coworkers[1], light beams carrying orbital angular momentum (OAM) gave rise to a flourishing field of research, leading to a rich multiplicity of studies and applications:[2] particle trapping, tweezing, and manipulation[3], high-resolution microscopy[4,5], astronomical coronagraphy[6], mode-division multiplexing[7], and security[8,9]
Circular-sector transformation The optical layout of the system consists of a cascade of two optical elements: the former performs a conformal optical transformation, whereas the latter corrects the phase distortion owing to the different paths traveled by the distinct points of the beam and restores the desired phase profile
The key element of OAM multiplication and division is represented by an optical transformation performing a conformal mapping of the whole circle onto a circular sector (Fig. 1a, d)[36]

Summary

Introduction

Introduction Since the seminal paper ofAllen and coworkers[1], light beams carrying orbital angular momentum (OAM) gave rise to a flourishing field of research, leading to a rich multiplicity of studies and applications:[2] particle trapping, tweezing, and manipulation[3], high-resolution microscopy[4,5], astronomical coronagraphy[6], mode-division multiplexing[7], and security[8,9]. Several optical methods and devices have been described and engineered to tailor and control the OAM content of light beams, such as spiral phase plates[10,11], computergenerated holograms[12,13], q-plates[14], transformation optics[15,16], and metasurfaces[17]. All those methods rely on transferring an azimuthal phase gradient exp(ilθ) to the input beam, with θ being the polar angle on a plane transverse to the propagation direction and l being the amount of OAM per photon in units of ħ. The abovementioned conventional methods are useful for implementing only shift operations

Methods

Results

Conclusion