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

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.

Broad‐Bandwidth Micro‐Diffractive Optical Elements

“…[ 6 ] Micro‐diffractive optical elements (M‐DOEs), widely used in integrated optics, are a type of ultrathin phase elements operating via interfering and diffracting for generating the desired light field. [ 7,8 ] In particular, the diffractive element changes the propagation path of incident light utilizing the geometry of flat grating patterns, [ 9,10 ] in contrast to the refractive element [ 11–13 ] that uses the 3D curved surface to deflect light paths. Because a diffractive element does not have a substantial thickness, an optical system including such elements can be designed to have the following characteristics: small size, light weight, and compact configuration.…”

Multiplexed Generation of Generalized Vortex Beams with On‐Demand Intensity Profiles Based on Metasurfaces

“…[ 10 ] Based on the specificities of vortex beams, many modulating methods have been explored for OAM, such as beam reshape of Laguerre Gaussian mode, [ 11,12 ] composite beam obtained by multichannel superposition, [ 13 ] and OAM multiplication and division calculations. [ 14 ] Over the last several decades, various approaches have been developed for generating vortex beams, such as using spatial light modulators, whispering rings, [ 15 ] segmented gratings, [ 13 ] and optical modes modulation within Laser cavity. [ 16 ] Recently, the rapid development in the field of metasurfaces has provided a flexible and compact platform for generating and manipulating vortex beams for various applications.…”

Design for a New “Dipole-sorter” for Direct and Dose Effective Magnetic Dipole Measurement

“…In this contribution we consider a more general class of conformal transformations recently described in optics [4] and demonstrate how to introduce them in electron microscopy trough electrostatic elements [5]. For a given n, the new conformal mapping transforms a circle in the plane into a circular sector in the destination plane ( Fig.…”

“…It is worth noting the similarity of the phase elements with integer and fractional multipole fields. (b) Scheme of OAM multiplication and division with combined circular-sector transformations[4].…”

“…This transformation is generated by a phase element of the type , where m=1-1/n and , being k the wavevector. The second element has substantially the same functional dependence, after the substitution m=1-n. A combination of those elements has been demonstrated to perform multiplication and division of OAM beams in a compact and effective manner [4] (Fig. 1(b)).…”