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2298 Vol. 50,No. 7 /1 April 2025 / Optics Letters Letter
Shaped vector beams generated with a phase-only
modulation—retarder optical configuration
Ignacio Moreno,1,2,∗Jeffrey A. Davis,3María del Mar Sánchez-López,1,4 AND Don
M. Cottrell3
1Instituto de Bioingeniería Universidad Miguel Hernández de Elche, 03202 Elche, Spain
2Departamento de Ciencia de Materiales, Óptica y Tecnología Electrónica, Universidad Miguel Hernández de Elche, 03202 Elche, Spain
3Department of Physics, San Diego State University, San Diego, California 92182, USA
4Departamento de Física Aplicada, Universidad Miguel Hernández de Elche, 03202 Elche, Spain
*i.moreno@umh.es
Received 5 November 2024; revised 26 February 2025; accepted 26 February 2025; posted 27 February 2025; published 25 March 2025
This work presents a new configuration to generate vector
beams, with shaped intensity and polarization distributions,
based on two liquid-crystal spatial light modulators (SLM).
The first device is used in a scalar mode to shape an input lin-
early polarized beam with a phase-only computer-generated
hologram. Then, the Fourier transform is optically formed
onto the second SLM, which operates as a pixelated retarder
to spatially modify the state of polarization. The proposed
optical architecture allows shaping the amplitude profile,
while easily generating the cylindrically polarized vector
beam pattern. Experimental results demonstrate the ver-
satility of the approach. © 2025 Optica Publishing Group. All
rights, including for text and data mining (TDM), Artificial Intelligence
(AI) training, and similar technologies, are reserved.
https://doi.org/10.1364/OL.546144
Cylindrically polarized vector beams have been a subject of
great interest in the past two decades [1–3], with potential in
classical and quantum systems [4,5]. Many different techniques
have been developed for their generation [6,7]. Among them,
systems based on spatial light modulators (SLMs) are attractive
because they can be reconfigured in real-time from a computer.
However, standard phase-only liquid-crystal (LC) SLMs only
modulate the linear polarization component parallel to the LC
director axis [8]. Therefore, SLM-based systems for generating
vector beams typically modulate two orthogonal polarization
components either by beam splitting and using two parts of the
SLM screen [9] or by modulating the beam twice [10–12]. Other
methods use SLMs to generate two versions of the beam whose
polarization is modified in an intermediate Fourier transform
(FT) plane [13,14]. All these systems share as a common feature
that two orthogonal polarization components are independently
modulated in phase. In many situations, it is also required to
shape the beam’s amplitude, which is achieved by applying
techniques that encode the amplitude information onto the dis-
played phase-only functions [15–17]. Such techniques typically
diffract the beam away from the main direction in areas requiring
low amplitude and then are filtered, thus leading to significant
efficiency losses.
In this work we go beyond the standard modulation scheme
to generate vector beams. We employ two LC-SLMs, but we
demonstrate a different configuration where the first SLM is
operated as a phase-only modulator that encodes a FT computer-
generated hologram (CGH) designed to shape the input beam
but maintaining a uniform polarization. Next, the system forms
the optical FT on the second SLM. By means of a half-wave
plate (HWP) that rotates the linear polarization, the second SLM
is operated as a linear retarder where the retardance is spatially
controlled with a displayed pattern. By addressing a spiral phase
function to this second SLM, a cylindrically polarized version
is produced. Thus, this configuration results in a very effective
way to generate vector beams where the use of standard CGH
techniques allows efficiently structuring the beam with arbitrary
shapes different to the classical Gaussian profile or plane wave
approximation.
The proposed system is shown in Fig. 1. A He–Ne laser is spa-
tially filtered and collimated with lens L1. Two parallel-aligned
liquid-crystal on silicon (LCOS) SLMs are employed. These
are reflective pixelated linear retarders where the retardance is
controlled through the addressed gray level image [8]. When
illuminated with linear polarization parallel to the LC director,
they act as phase-only modulators. We use two LCOS-SLMs
from Hamamatsu, model X10468-01, with 792 ×600 pixels and
pixel spacing ∆=20 µm. In both devices, the LC director is
oriented horizontal in the laboratory framework. The trans-
mission axis of the input polarizer (P1) is set horizontal, so
SLM1 phase-only modulates the input beam, without changing
its polarization. The phase-only function displayed on SLM1 is
an inverse FT CGH calculated to shape the optical FT obtained
on SLM2 by means of lens L2. Despite introducing losses,
we use two non-polarizing beam splitters (BS1 and BS2) to
make a compact system and ensure normal incidence onto the
SLMs.
The polarization of the beam impinging onto SLM2 is rotated
by +45oby the HWP, which is oriented at +22.5o. Then SLM2
modifies the state of polarization according to its retardance ϕ2.
A quarter-wave plate (QWP) oriented at +45o, placed on the
beam reflected by SLM2, provides an additional transformation
that leads to output linear states of variable orientation as a
function of ϕ2[18,19]. Finally, lens L3 images the SLM2 plane
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