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

## TL;DR

This paper introduces a novel method using diffractive transformation optics to efficiently multiply or divide the orbital angular momentum of light beams, enabling advanced optical information processing and telecom applications.

## Contribution

The work presents a new optical approach to multiply and divide OAM states using phase-only diffractive optics with high-resolution fabrication, demonstrating practical implementation and testing.

## Key findings

- Successfully demonstrated integer OAM multiplication and division
- Fabricated phase-only diffractive optical elements with electron-beam lithography
- Confirmed capability for optical OAM manipulation in experiments

## 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 perform the multiplication of 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. The 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, while 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-beams transmission, and optical routing/switching in telecom.

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Source: https://tomesphere.com/paper/1904.09153