Active rejection-enhancement of spectrally adaptive liquid crystal geometric phase vortex coronagraphs Nina Kravets1Urban Mur2Miha Ravnik2 3Slobodan Zumer3 2and Etienne Brasselet1

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Active rejection-enhancement of spectrally adaptive liquid crystal geometric phase

vortex coronagraphs

Nina Kravets,1Urban Mur,2Miha Ravnik,2, 3 Slobodan ˇ

Zumer,3, 2 and Etienne Brasselet1, ∗

1Universit´e de Bordeaux, CNRS, Laboratoire Ondes et Mati`ere d’Aquitaine, F-33400 Talence France

2Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia

3Joˇzef Stefan Institute, Jamova 39,1000 Ljubljana, Slovenia

Geometric phase optical elements made of space-variant anisotropic media customarily ﬁnd their

optimal operating conditions when the half-wave retardance condition is fulﬁlled, which allows

imparting polarization-dependent changes to an incident wavefront. In practice, intrinsic limitations

of man-made manufacturing process or the ﬁnite spectrum of the light source lead to a deviation from

the ideal behavior. This implies the implementation of strategies to compensate for the associated

eﬃciency losses. Here we report on how the intrinsic tunable features of self-engineered liquid crystal

topological defects can be used to enhance the rejection capabilities of spectrally adaptive vector

vortex coronagraphs. We also discuss the extent of which current models enable to design eﬃcient

devices.

Electrical and optical properties of liquid crystals make

them attractive material for numerous photonics appli-

cations requiring remote changes of the phase or the

polarization state of light. This is usually achieved by

electrically driven modiﬁcation of orientational state of

the material along the light propagation direction. The

transverse spatial orientation state of material brings ad-

ditional degree of freedom for phase modulation. This

is the case for liquid crystal slabs whose orientational

state (deﬁned locally by the average molecular orienta-

tion to which we assign a unit vector ncalled director)

imparts a half-wave birefringent retardation to an inci-

dent light ﬁeld along its propagation direction and space-

variant phase proﬁle of a geometric nature in the trans-

verse plane. Their complex amplitude transfer function

is given as t= exp(±2iψ), where ±refers to the handed-

ness of the incident circular polarization state and ψis

its eﬀective in-plane optical axis orientation angle. Such

geometric phase optical elements were anticipated in the

late 1990s [1] and experimentally realized a few years

after using space-variant solid-state subwavelength grat-

ings [2, 3] while the advent of their liquid crystal coun-

terparts appeared only a few years later [4, 5].

In the present work we focus on liquid crystal geomet-

ric phase optical vortex generators ideally associated with

t= exp(±2imφ), where mis an interger or half-integer

and φis the polar angle in the (x, y) plane of the op-

tical element, whose technological maturity and ﬁeld of

use have continued to grow since their ﬁrst realization in

2006 [5]. To date there is a trade-oﬀ between, on the one

hand, the tunability of the operating wavelength in order

to satisfy the half-wave plate condition, which is achieved

either by thermal [6] or electrical [7] means and, on the

other hand, the spatial resolution of the structural sin-

gularity for the director orientation that can reach sub-

micrometer size [8]. Since most applications involve op-

tical beams with cross sections in the millimeter range or

∗etienne.brasselet@u-bordeaux.fr

larger, they do not suﬀer from such a compromise. How-

ever, this is a priori no longer true when the geometric

phase vortex mask is required in the focal plane of an

optical system, as is the case for vector optical vortex

coronagraphy.

Optical coronagraphy is a high contrast imaging tech-

nique originally developed more than 80 years ago to cre-

ate artiﬁcial total eclipses of the Sun [9]. The working

principle of the original apparatus is to occult the central

part of the Airy diﬀraction pattern in the Fourier plane

of a telescope in order to strongly reduce the amount of

on-axis stellar light reaching the observer. It was not un-

til nearly sixty years later that the (binary) manipulation

of the phase distribution of the Airy spot rather than its

occultation was considered [10]. Further developments

led to the advent of optical vortex coronagraphy where a

vortex phase mask with integer values of mis centered on

the Airy pattern of the on-axis light source to be rejected.

Scalar and vector coronagraphy have been proposed si-

multaneously in Refs. 11 and 12. Their respective labels

refer to the physical origin of the phase changes oper-

ated by the vortex phase mask: dynamic (scalar case) or

geometric (vector case). The superior chromatic perfor-

mances of the geometric phase option makes vector vor-

tex coronagrahy more attractive. Nowadays, more than

one decade after ﬁrst laboratory [13] and astronomical

[14, 15] demonstrations, spectrally static geometric phase

vortex masks equip several ground based astronomical

observations facilities [16]. Still, it is important to note

that spectroscopic imaging of extrasolar planets to learn

about their atmospheric composition involves developing

broadband vortex masks. This inherently comes with

polarization leakage problems and requires demanding

technological improvements to mitigate the eﬀects, not

only for the vortex mask itself but also for the additional

polarization optics involved [17, 18].

Instead, another approach would be to consider spec-

trally adaptive geometric phase vortex masks that do

not require the use of additional polarization optics and

to use them in a narrowband regime while the operat-

ing wavelength is scanning the desired spectral band-

arXiv:2210.03987v1 [physics.optics] 8 Oct 2022

width. However, spectrally adaptive liquid crystal geo-

metric phase vortex coronagraphs reported so far remain

hampered by central disorientation region trade-oﬀ [19–

21]. Here we report on how the rejection capabilities of

the latter devices can be enhanced.

Noteworthy, there are two distinct kinds of central

disorientation in liquid crystal geometric phase vortex

masks: (i) the departure from the space-variant pattern

ψ=mφ (to an unimportant constant) and (ii) the de-

parture from the half-wave birefringent retardance, which

could mix in practice. The few previous attempts can be

classiﬁed as being mainly either on type (i) [21] or type

(ii) [19, 20]. In the ﬁrst case, it is diﬃcult to consider

post-reprogramming of the fabrication-limited patterned

anchoring layers that provide liquid crystal alignment.

Nevertheless, the placement of an opaque disk covering

the troublesome region is a rough solution applicable re-

gardless of the nature of the vortex mask [14]. In the

second case, which refers to the use of spontaneously

formed liquid crystal topological defects under the action

of external ﬁelds, an additional backup option consists to

place the vortex masks between crossed circular polariz-

ers at the expense of throughput losses of at least 50%

for unpolarized light observations and additional polar-

ization optics chromatic issues.

In order to get rid of obstruction and polarization ﬁl-

tering backup strategies for type (ii) vortex masks, one of

us suggested a few years ago that adaptive optimization

of the size of the disorientation region is an open option

when using liquid crystal topological defects called umbil-

ics [22], which is quantitatively explored experimentally

in the present work. Also, we discuss the capabilities

of available analytical model and full numerical simula-

tion to describe adaptive downsizing of the core of um-

bilics towards optimal design. Umbilics are nonsingular

topological defects associated with m=±1 unveiled 40

years ago by Rapini [23] in nematic liquid crystal having

negative dielectric anisotropy (a<0) and sandwiched

between two parallel substrates providing uniform per-

pendicular orientational boundary conditions for the di-

rector (n(x, y, z = 0) = n(x, y, z =L) = ezwhere L

is the cell thickness and ezthe unit vector along the

zaxis). These defects spontaneously appear when ap-

plying a quasistatic voltage between the two facets of

the nematic slab that exceeds the Fr´eedericksz thresh-

old value Uth =πpK3/(0|a|) where K3is the bend

elastic constant of the nematic and 0is the vacuum di-

electric permittivity [23]. In our experiments we used a

20 µm-thick sample prepared with the dual frequency ne-

matic mixture 1859A (from Military University of Tech-

nology, Warsaw, Poland) and umbilics are obtained fol-

lowing the magnetic-electric approach proposed in [22],

see Figs. 1(a) and 1(b). The combined action of a static

magnetic ﬁeld from a ring magnet with a quasistatic elec-

tric ﬁeld (square waveform at 200 kHz frequency) enables

robust self-engineering of geometric phase vortex masks

with m= 1 above Uth = 2.85 V.

As shown in Fig. 1(c), the mask is placed in the Fourier

(c)

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(b)

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FIG. 1. (a) Illustrations of the magneto-electric conﬁg-

uration to generate on-demand macroscopic umbilic defect

in a nematic liquid crystal ﬁlm used as a spectrally adap-

tive liquid crystal geometric phase vortex mask (LC-GPVM)

with m= +1. The Nickel-plated Neodymium (grade N50)

ring magnet (not on scale) has internal and external radii

Rint = 2 mm and Rext = 6 mm, respectively, and height

H= 6 mm. Its magnetization is directed along the zaxis

and is associated with a pull force of ∼32 N (manufacturer

datasheet). The magnet is placed at a distance ∼2 mm from

the input facet of the nematic slab. (b) Side view sketch

of the lines of the ideally axisymmetric director ﬁeld under

the combined action of the magnetic and electric ﬁeld. (c)

Sketch of the coronagraphic experimental setup. Pi: planes

i= (1,2,3,4) of interest; Li: lens i= (1,2,3,4) with focal

length fi; CP1,2: circular polarizers. Parameters: the radius

of the circular aperture at P1is R1= 1 mm, the radius of

the circular aperture at P3is R2= 0.75R1, the focal length

are f1=f2= 200 mm and f3= 400 mm. All the lenses are

achromatic doublets. See text for detailed description. Inset

at P2: phase map of the optical vortex mask. Inset at P3:

calculated intensity and phase, where the luminance refers

to the intensity and the colormap refers to the phase. The

dashed circle refers to the aperture with radius R2.

plane (P2) of a lens (L1, focal length f1) illuminated by a

collimated expanded laser beam from a supercontinuum

source that can be spectrally ﬁltered on-demand using

a set of bandpass interferential ﬁlters. The input pupil

plane P1is located right before L1where a metallic circu-

lar aperture with radius R1is placed. A second lens (L2,

focal length f2) placed at a distance f2from P2produces

the image of the input pupil in the plane P3located at a

distance f2(1 + f2/f1) from L2, where a metallic circular

aperture with radius R2is placed. Ideally, full rejection

of on-axis incident light is achieved when the Airy spot is

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Activerejection-enhancementofspectrallyadaptiveliquidcrystalgeometricphasevortexcoronagraphsNinaKravets,1UrbanMur,2MihaRavnik,2,3SlobodanZumer,3,2andEtienneBrasselet1,1UniversitedeBordeaux,CNRS,LaboratoireOndesetMatiered'Aquitaine,F-33400TalenceFrance2FacultyofMathematicsandPhysics,UniversityofL...

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Active rejection-enhancement of spectrally adaptive liquid crystal geometric phase vortex coronagraphs Nina Kravets1Urban Mur2Miha Ravnik2 3Slobodan Zumer3 2and Etienne Brasselet1

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