About me

I am a Marie Skłodowska Curie Research Fellow working with Slobodan Žumer in the Soft Matter team of the Faculty of Physics and Mathematics at the University of Ljubljana. We want to develop a new research direction by combining knowledge from photonics and topological soft matter to find novel ways of guiding light using chiral birefringent media. The non-linear optical response of these media allows a laser beam to be self-confined and to propagate over long distances, leading to what is called spatial optical solitons. Our primary objective is to develop a complete model of optical solitons in chiral birefringent media and examine how these light solitons can be steered and controlled using topological solitons — localized and tunable perturbations of the molecular orientational field which cannot be continuously deformed into the uniform state. Our methodology is based on the theoretical and numerical modeling of the non-linear equations for the propagation of light in chiral birefringent media, combined with collaborative experiments. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska Curie grant agreement No. 834256.

Nemaktis - Open-source platform

for microscopy simulations

Nemaktis is an open-source platform that I developed during my postdoctoral stay in Ljubljana. It includes tools for propagating and visualizing optical fields in complex birefringent media such as liquid crystal (LC) layers, with three backends implementing advanced numerical methods for light propagation, as well as an easy-to-use high level interface in python allowing to quickly setup a simulation and visualize optical micrographs of a LC structure as in a real microscope. It goes well beyond the Jones method usually used in LC research, by accurately modeling diffraction, walk-off, focusing effects, Koehler illumination, etc.

If you want a platform for easily comparing experimental images and numerical micrographs from simulated or theoretical birefringent structures, you should definitely check it out!

For more information, see the following links:

GitHub ReadTheDocs

Physics-based multistep beam propagation in inhomogeneous birefringent media

G. Poy, S. Žumer, Optics express, 28, 24327–24342 (2020)

DOI Article Abstract/Bibtex

We present a unified theoretical framework for paraxial and wide-angle beam propagation methods in inhomogeneous birefringent media based on a minimal set of physical assumptions. The advantage of our schemes is that they are based on differential operators with a clear physical interpretation and easy numerical implementation based on sparse matrices. We demonstrate the validity of our schemes on three simple two-dimensional birefringent systems and introduce an example of application on complex three-dimensional systems by showing that topological solitons in frustrated cholesteric liquid-crystals can be used as light waveguides.

@article{poy_physics_2020,
  title={Physics-based multistep beam propagation in inhomogeneous birefringent media},
  author={Poy, Guilhem and Žumer, Slobodan},
  journal={Optics express},
  volume={28},
  number={16},
  pages={24327--24342},
  year={2020},
  doi={10.1364/OE.400984},
}

Ray-based optical visualisation of complex birefringent structures including energy transport

G. Poy, S. Žumer, Soft Matter, 15, 3659–3670 (2019)

DOI Article Abstract/Bibtex

We propose an efficient method to simulate light propagation in lossless and non-scattering uniaxial birefringent media, based on a standard ray-tracing technique supplemented by a newly-derived transport equation for the electric field amplitude along a ray and a tailored interpolation algorithm for the reconstruction of the electromagnetic fields. We show that this algorithm is accurate in comparison to a full solution of Maxwell's equations when the permittivity tensor of the birefringent medium typically varies over a length much bigger than the wavelength. We demonstrate the usefulness of our code for soft matter by comparing experimental images of liquid crystal droplets with simulated bright-field optical micrographs, and conclude that our method is more general than the usual Jones method, which is only valid under polarised illumination conditions. We also point out other possible applications of our method, including liquid crystal based flat element design and diffraction pattern calculations for periodic liquid crystal samples.

@article{poy_ray-based_2019,
  title = {Ray-based optical visualisation of complex birefringent structures including energy transport},
  volume = {15},
  doi = {10.1039/C8SM02448K},
  number = {18},
  journal = {Soft Matter},
  author = {Poy, Guilhem and Žumer, Slobodan},
  year = {2019},
  pages = {3659--3670},
}

PhD - Lehmann effect

You can download my PhD thesis with the following link:

This thesis is focused on the Lehmann effect, an out-of-equilibrium effect which couples a temperature gradient with the rotation of the internal texture of liquid crystal droplets in coexistence with the isotropic phase.

First, we characterized the thermomechanical coupling terms of Leslie, Akopyan and Zel’dovich by measuring the rotation velocity of the molecules in two translationally invariant configura- tions with different orientations, below the cholesteric/isotropic transition.

Then, we characterized the texture of the droplets observed in the Lehmann experiment, both using optical observations and numerical simulations. More important, we showed for the first time that it is possible to observe the Lehmann effect in achiral nematic droplets, providing that the internal texture is chiral. We also used a photobleaching experiment to show that there is no visible flow in the vicinity of the droplet, which implies that the texture rotation is due to a local rotation of the molecules – not to a solid rotation of the droplet.

Finally, we proposed a theoretical model of the Lehmann effect based on the thermome- chanical coupling of Leslie, Akopyan and Zel’dovich. By applying this model to the numerically computed textures, we fitted our experimental data and found values for the thermomechanical coupling constants much bigger than those measured below the cholesteric/isotropic transition. This model is therefore incomplete.

SM1 — (-1/2) disclination line observed under crossed polarizers just below the cholesteric/isotropic temperature in a planar sliding sample of the mixture CCN-37 + 3 % CC. \(d=\) 10.6 µm and \(\Delta T=\) 40 °C. The bar represents 50 µm.

SM2 — Pair of \(\pm\) 1 disclination lines observed under crossed polarizers just below the cholesteric/isotropic temperature in a mixed sample of the mixture CCN-37 + 3 % CC. \(d=\) 10.8 µm and \(\Delta T=\) 40 °C. The bar represents 100 µm.

SM3 — Lehmann rotation of banded droplets observed in a sample of 7CB + 0.6 \% R811. The temperature gradient is oriented towards the internaut. \(d=\) 50 µm and \(\Delta T=\) 5 °C. The bar represents 50 µm.

SM4 — Lehmann rotation of cholesteric twisted bipolar droplets observed in a sample of CCN-37 + 5.9 \% CC. The temperature gradient is oriented towards the internaut. \(d=\) 50 µm and \(\Delta T=\) 1.25 °C. The bar represents 50 µm.

SM5 — Lehmann rotation of nematic twisted bipolar droplets observed in a sample of water + 28 \% SSY. The temperature gradient is oriented towards the internaut. \(d=\) 110 µm and \(\Delta T=\) 20 °C. The bar represents 10 µm.

SM6 — Fluorescence signal after a laser shot near a banded droplet of 7CB + 0.25 % R811 + 0.05 % NBD C6-ceramide. The droplet rotates at \(\omega_g=\) 0.139 rad/s when \(\Delta T=\) -10 K. The white point represents the center of the gaussian fit and the white circle represents the circle of equation \(|\vec{x}-\vec{x}_0|=\sigma/2\). The bar represents 50 µm.

SM7 — Same as SM6 with a droplet more distorted rotating at \(\omega_g=\) 0.036 rad/s when \(\Delta T=\) -10 °C. Mixture of 7CB + 0.25 % R811 + 0.05 % NBD C6-ceramide. The bar represents 50 µm.

SM8 — Fluorescence signal after a laser shot (left) and images in transmission between crossed polarizers under white light illumination (right) of a cholesteric twisted bipolar droplet. The black circle represents the outer contour of the droplets. The tilted black line gives the orientation of the bipole. The white point and circle have the same meaning as in SM6 and SM7. Mixture of CCN-37 + 5.9 % CC + 0.05 % NBD C6-ceramide, \(\Delta T=\) 2.5 °C. The bar represents 10 µm.

Master 2 - Rheology of

cornstarch suspensions

Rheology correspond to the study of the flow of matter. The simplest case of study is the shear experiment, where you submit a flowing sample to a shear flow by imposing either a force or a velocity on one of the two plates delimiting the sample (schema on the left). We can then define the strain rate \(\dot\gamma\) as the plate velocity \(v\) divided by the thickness \(d\), the stress \(\sigma\) as the place force \(F\) divided by the plate surface \(S\), and the viscosity \(\eta\) as the proportionality factor between the stress and the strain rate:

When the viscosity of a material is independant of the strain rate or the stress, this material is called newtonian (e.g. water). On the other hand, many materials exhibit a dependance of the viscosity with the strain rate ; these materials are called complex fluids. Suspensions (particles suspended in a fluid) are a perfect exemple of a complex fluid. For low packing fraction of particles, the suspension stays newtonian if the carrier-fluid is newtonian, but with an increase of viscosity due to the hydrodynamic interactions between particles. For high packing fraction, the friction and electrostatic interactions becomes relevant, and interesting dependance between the viscosity and the the strain rate appears. One of these behaviours, called shear-thickening, is the increase of viscosity with the strain rate, which can lead to spectacular effects: for example, one can run across a pool filled with a suspension of cornstarch in water

During my internship, I studied two types of suspensions: supensions of cornstarch in water (repulsive interaction between particles) and suspensions of cornstarch in oil (attractive interaction between particles). The repulsive suspensions are found to be shear-thickening, and a comparison with a recent theoretical model for shear-thickening suspensions is proposed. The attractive suspensions display an interesting dynamic behaviour in Large Amplitude Oscillatory Shear (LAOS) experiment, which is interpreted in terms of shear-reversal and structures forming in the compression direction.

Shear Thickening in Dense Suspensions

Report Abstract

The role of friction in the yielding of adhesive non-Brownian suspensions

J. A. Richards, B. M. Guy, E. Blanco, M. Hermes, G. Poy, W. C. Poon, Journal of Rheology, 64, 405–412 (2020)

DOI Article Abstract/Bibtex

Yielding behavior is well known in attractive colloidal suspensions. Adhesive non-Brownian suspensions, in which the interparticle bonds are due to finite-size contacts, also show yielding behavior. We use a combination of steady-state, oscillatory, and shear reversal rheology to probe the physical origins of yielding in the latter class of materials and find that yielding is not simply a matter of breaking adhesive bonds but involves unjamming from a shear-jammed state in which the microstructure has adapted to the direction of the applied load. Comparison with a recent constraint-based rheology model shows the importance of friction in determining the yield stress, suggesting novel ways to tune the flow of such suspensions.

@article{richards_role_2020,
  title={The role of friction in the yielding of adhesive non-Brownian suspensions},
  author={Richards, James A and Guy, Ben M and Blanco, Elena and Hermes, Michiel and Poy, Guilhem and Poon, Wilson CK},
  journal={Journal of Rheology},
  volume={64},
  number={2},
  pages={405--412},
  year={2020},
  doi={10.1122/1.5132395},
}

Unsteady flow and particle migration in dense, non-Brownian suspensions

M. Hermes, B. M. Guy, W. C. K. Poon, G. Poy, M. E. Cates, M. Wyart, Journal of Rheology, 60, 905–916 (2016)

DOI Article Abstract/Bibtex

We present experimental results on dense corn-starch suspensions as examples of non-Brownian, nearly hard particles that undergo continuous and discontinuous shear thickening (DST) at intermediate and high densities, respectively. Our results offer strong support for recent theories involving a stress-dependent effective contact friction among particles. We show, however, that in the DST regime, where theory might lead one to expect steady-state shear bands oriented layerwise along the vorticity axis, the real flow is unsteady. To explain this, we argue that steady-state banding is generically ruled out by the requirement that, for hard non-Brownian particles, the solvent pressure and the normal-normal component of the particle stress must balance separately across the interface between bands. (Otherwise, there is an unbalanced migration flux.) However, long-lived transient shear bands remain possible.

@article{hermes_unsteady_2016,
	title = {Unsteady flow and particle migration in dense, non-Brownian suspensions},
	volume = {60},
	issn = {0148-6055, 1520-8516},
	doi = {10.1122/1.4953814},
	number = {5},
	journal = {Journal of Rheology},
	author = {Hermes, Michiel and Guy, Ben M. and Poon, Wilson C. K. and Poy, Guilhem and Cates, Michael E. and Wyart, Matthieu},
	year = {2016},
	pages = {905--916},
}

Master 1 - Stability

of relativistic jets

Astrophysical jets correspond to well-calibrated flows of matter and energy whose source can be a galactic object (for example a microquasar, i.e. a binary system with one compact object and an accretion disk) or an extra-galactic object (for example an active galactic nuclei, i.e. a compact region at the center of a glaxy with a high luminosity). These jets can propagate over considerable distances (up to millions of light-year), which raises the following question: how can we explain the remarkable stability of these jets? This question is relevant, because many magnetohydrodynamic effects (such as the Kelvin-Helmholtz instability) can destabilize the jet.

During my internship, I studied theoretically the mechanisms of stability and instability for a simple model of jet, the beam model. Using the linearized equations of the magnetohydrodynamics for a jet, I computed the dispersion relation of the perturbation of a relativistic and compressible jet, and solved this relation under special limit cases. I showed that there is instable modes at all frequencies when there is no magnetic field, and that the effect of a magnetic field is to shift the most unstable modes to lower frequencies.

Stabilité des jets ultrarelativistes

Report Abstract

Bachelor - Rotational

viscosity measurement

Liquid crystals are products which possess a mesophase, i.e. a phase intermediate between a solid and a liquid. The most simple mesophase is the nematic phase, with no positional order and an orientational order. The latter allows us to define the director \({\bf n}\) as the mean direction of the molecules on a mesoscopic volume. Similarly to an isotropic fluid, where a shear is associated with a viscous stress, a rotation of the molecules without flow in a nematic phase is associated with a bulk viscous torque: \[ {\bf\Gamma}_{vb} = \gamma_1 {\bf n} \times \frac{\partial{\bf n}}{\partial t}, \] where \(\gamma_1\) is called the bulk rotational viscosity. When the nematic phase is confined within two parallel plates treated with a sliding planar anchoring (the molecules are parallel to the plates and can freely rotate on the plate surface), we can similaryly describe the rotational friction on the surface with a surface viscous torque: \[ {\bf\Gamma}_{vs} = \gamma_s {\bf n} \times \frac{\partial{\bf n}}{\partial t}, \] where \(\gamma_s\) is called the surface rotational viscosity.

If a rotating magnetic field \({\bf B}\) is applied parallel to the plates, the director will also rotates at the same angular velocity \(\omega\), but will make a small angle \(\alpha\) with \({\bf B}\) due to the dissipation by \(\gamma_1\) and \(\gamma_s\). By measuring this delay angle for different \(\omega\) and \(B\), it is possible to measure both \(\gamma_1\) and \(\gamma_s\). During my internship, I interfaced with Labview the experimental setup designed by Patrick Oswald to apply the rotating magnetic field, and systematically measured the bulk and surface rotational viscosities of a typical liquid crystal in function of the temperature.

Experimental relationship between surface and bulk rotational viscosities in nematic liquid crystals

P. Oswald, G. Poy, F. Vittoz, V. Popa-Nita, Liquid Crystals, 40, 734–744 (2013)

DOI Article Abstract/Bibtex

Systematic measurements of the surface viscosity \(\gamma_s\) of several nematic liquid crystals in contact with a polymercaptan layer show that the latter scales like the bulk rotational viscosity \(\gamma_1\). This result is interpreted in the framework of a ‘delocalized model’ for the surface viscosity.

@article{oswald_experimental_2013,
	title = {Experimental relationship between surface and bulk rotational viscosities in nematic liquid crystals},
	volume = {40},
	issn = {0267-8292, 1366-5855},
	doi = {10.1080/02678292.2013.783936},
	number = {6},
	journal = {Liquid Crystals},
	author = {Oswald, Patrick and Poy, Guilhem and Vittoz, Franck and Popa-Nita, Vlad},
	year = {2013},
	pages = {734--744},
}

Peer-reviewed articles

Surface Stabilized Topological Solitons in Nematic Liquid Crystals

I. Nys, B. Berteloot, G. Poy, Crystals, 10, 840 (2020)

DOI Article Abstract/Bibtex

Photo-alignment is a versatile tool to pattern the alignment at the confining substrates in a liquid crystal (LC) cell. Arbitrary alignment patterns can be created by using projection with a spatial light modulator (SLM) for the illumination. We demonstrate that a careful design of the alignment patterns allows the stabilization of topological solitons in nematic liquid crystal (NLC) cells, without the need for chirality or strong confinement. The created LC configurations are stabilized by the anchoring conditions imposed at the substrates. The photo-aligned background at both substrates is uniformly planar aligned, and ring-shaped regions with a 180° azimuthal rotation are patterned with an opposite sense of rotation at the top and bottom substrate. A disclination-free structure containing a closed ring of vertically oriented directors is formed when the patterned rings at the top and bottom substrate overlap. Thanks to the topological stability, a vertical director orientation in the bulk is observed even when the centra of both patterned rings are shifted over relatively large distances. The combination of numerical simulations with experimental measurements allows identification of the 3D director configuration in the bulk. A finite element (FE) Q-tensor simulation model is applied to find the equilibrium director configuration and optical simulations are used to confirm the correspondence with experimental microscopy measurements. The created LC configurations offer opportunities in the field of optical devices, light guiding and switching, particle trapping and studies of topological LC structures.

@article{nys_surface_2020,
  title={Surface Stabilized Topological Solitons in Nematic Liquid Crystals},
  author={Nys, Inge and Berteloot, Brecht and Poy, Guilhem},
  journal={Crystals},
  volume={10},
  number={9},
  pages={840},
  year={2020},
  publisher={Multidisciplinary Digital Publishing Institute},
  doi={10.3390/cryst10090840},
}

Control of light by topological solitons in soft chiral birefringent media

A. J. Hess, G. Poy, J. B. Tai, S. Žumer, I. I. Smalyukh, Physical Review X, 10, 031042 (2020)

DOI Article Abstract/Bibtex

In practically all branches of physics, different types of solitons, with a number of them enjoying topological protection, are found. Here we explore how one- and two-dimensional topological solitons formed by spatially localized continuous orientational patterns of optical axis in uniaxial birefringent media interact with light. These solitons, in the forms of one-dimensional twist walls and two-dimensional skyrmions, are controllably generated in thin films of cholesteric liquid crystals to introduce spatially localized patterns of effective refractive index. Laser light interacts with these solitons as quasiparticles or extended interfaces of different effective refractive indices seen by ordinary and extraordinary waves propagating within the liquid-crystal medium. Despite our system’s complex nature, our findings can be paralleled with the familiar phenomena of total reflection and refraction at interfaces of optically distinct media, albeit these behaviors arise in a medium with homogeneous density and chemical composition but with spatial variations of molecular and optical-axis orientations. By exploiting the facile response of liquid crystals to external stimuli, we show that the twist walls and skyrmions can be used to steer laser beams and to act as lenses and other optical elements, which can be reconfigured by low-voltage fields and other means. Analytical and numerical modeling, with the latter based on free-energy-minimizing configurations of the topological solitons, closely reproduce our experimental findings. The fundamental insights provided by this work potentially can be extended also to three-dimensional solitons, such as Hopfions, and may lead to technological applications of optical-axis topological solitons in telecommunications, nanophotonics, electro-optics, and so on.

@article{hess_control_2020,
  title={Control of light by topological solitons in soft chiral birefringent media},
  author={Hess, Andrew J and Poy, Guilhem and Tai, Jung-Shen B and Žumer, Slobodan and Smalyukh, Ivan I},
  journal={Physical Review X},
  volume={10},
  number={3},
  pages={031042},
  year={2020},
  publisher={APS},
  doi={10.1103/PhysRevX.10.031042},
}

Chirality-enhanced periodic self-focusing of light in soft birefringent media

G. Poy, A. J. Hess, I. I. Smalyukh, S. Žumer, Physical review letters, 125, 077801 (2020)

DOI Article Abstract/Bibtex

We experimentally and numerically show that chirality can play a major role in the nonlinear optical response of soft birefringent materials, by studying the nonlinear propagation of laser beams in frustrated cholesteric liquid crystal samples. Such beams exhibit a periodic nonlinear response associated with a bouncing pattern for the optical fields, as well as a self-focusing effect enhanced by the chirality of the birefringent material. Our results open new possible designs of nonlinear optical devices with low power consumption and tunable interactions with localized topological solitons.

@article{poy_chirality_2020,
  title={Chirality-enhanced periodic self-focusing of light in soft birefringent media},
  author={Poy, Guilhem and Hess, Andrew J and Smalyukh, Ivan I and Žumer, Slobodan},
  journal={Physical review letters},
  volume={125},
  number={7},
  pages={077801},
  year={2020},
  doi={10.1103/PhysRevLett.125.077801},
}

Physics-based multistep beam propagation in inhomogeneous birefringent media

G. Poy, S. Žumer, Optics express, 28, 24327–24342 (2020)

DOI Article Abstract/Bibtex

We present a unified theoretical framework for paraxial and wide-angle beam propagation methods in inhomogeneous birefringent media based on a minimal set of physical assumptions. The advantage of our schemes is that they are based on differential operators with a clear physical interpretation and easy numerical implementation based on sparse matrices. We demonstrate the validity of our schemes on three simple two-dimensional birefringent systems and introduce an example of application on complex three-dimensional systems by showing that topological solitons in frustrated cholesteric liquid-crystals can be used as light waveguides.

@article{poy_physics_2020,
  title={Physics-based multistep beam propagation in inhomogeneous birefringent media},
  author={Poy, Guilhem and Žumer, Slobodan},
  journal={Optics express},
  volume={28},
  number={16},
  pages={24327--24342},
  year={2020},
  doi={10.1364/OE.400984},
}

The role of friction in the yielding of adhesive non-Brownian suspensions

J. A. Richards, B. M. Guy, E. Blanco, M. Hermes, G. Poy, W. C. Poon, Journal of Rheology, 64, 405–412 (2020)

DOI Article Abstract/Bibtex

Yielding behavior is well known in attractive colloidal suspensions. Adhesive non-Brownian suspensions, in which the interparticle bonds are due to finite-size contacts, also show yielding behavior. We use a combination of steady-state, oscillatory, and shear reversal rheology to probe the physical origins of yielding in the latter class of materials and find that yielding is not simply a matter of breaking adhesive bonds but involves unjamming from a shear-jammed state in which the microstructure has adapted to the direction of the applied load. Comparison with a recent constraint-based rheology model shows the importance of friction in determining the yield stress, suggesting novel ways to tune the flow of such suspensions.

@article{richards_role_2020,
  title={The role of friction in the yielding of adhesive non-Brownian suspensions},
  author={Richards, James A and Guy, Ben M and Blanco, Elena and Hermes, Michiel and Poy, Guilhem and Poon, Wilson CK},
  journal={Journal of Rheology},
  volume={64},
  number={2},
  pages={405--412},
  year={2020},
  doi={10.1122/1.5132395},
}

Ring-shaped liquid crystal structures through patterned planar photo-alignment

B. Berteloot, I. Nys, G. Poy, J. Beeckman, K. Neyts, Soft Matter, 16, 4999–5008 (2020)

DOI Article Abstract/Bibtex

Patterned liquid crystal (LC) configurations find widespread applications in functional devices such as lenses, gratings, displays and soft-robots. In combination with external stimuli such as an applied electric field, photo-alignment at the surfaces offers an attractive way to stabilize different LC structures in the bulk of a device. Herein, a planar LC cell is developed using a photo-alignment layer at the bottom substrate and a rubbed nylon film at the top substrate. Patterned planar photo-alignment is achieved by modulating the linear polarization with a spatial light modulator (SLM) and projecting the pattern onto the bottom substrate. A ring pattern is written into the photo-alignment layer with a continuous rotation between an inner radius and an outer radius. In the other regions the alignment is parallel to the rubbing direction at the top substrate. Four different LC configurations are observed: structure A in which a ring-shaped region is formed with an out of plane (vertical) orientation perpendicular to the substrate, structure B which has a single disclination loop and a 180° twist at the inner region of the photo-patterned ring (r < rin), structure C which has no discontinuities but a 360° twist in the inner region of the photo-patterned ring (r < rin) and structure D with 2 disclination loops. The LC director configuration for all 4 structures is simulated through finite element (FE) Q-tensor simulations and the optical transmission for each structure is simulated using a generalized beam propagation method.

@article{berteloot_ring_2020,
  title={Ring-shaped liquid crystal structures through patterned planar photo-alignment},
  author={Berteloot, Brecht and Nys, Inge and Poy, Guilhem and Beeckman, Jeroen and Neyts, Kristiaan},
  journal={Soft Matter},
  volume={16},
  pages={4999--5008},
  year={2020},
  doi={10.1039/D0SM00308E},
}

Lehmann effect in nematic and cholesteric liquid crystals: a review

P. Oswald, A. Dequidt, G. Poy, Liquid Crystals Reviews, 7, 142–166 (2019)

DOI Article Abstract/Bibtex

The Lehmann effect is the continuous rotation of cholesteric droplets subjected to a temperature gradient. Discovered by Otto Lehmann in 1900, this effect was re-observed recently by several authors not only in cholesterics but also in nematics when the director field is twisted inside the droplets. In most experiments, the droplets coexist with their isotropic liquid, but the Lehmann effect can also be observed when the droplets are dispersed in an isotropic liquid in which the LC is partly miscible. After a brief history on the Lehmann effect and its first explanation by Leslie in 1968, we will review the main experimental results obtained on this subject from 2008. In particular, the role of the temperature gradient, of the size of the droplets, of the textures and their orientation with respect to the temperature gradient, of the confinement effects, of the impurities and of the concentration of chiral molecules will be described. A special emphasis will also be placed on the research of hydrodynamic effects to answer the fundamental question of whether it is just the texture or the droplet itself that rotates. We will then review the different models proposed in the literature to explain the Lehmann effect. Among them are two thermomechanical models directly based on the Leslie explanation (named TM1 and TM2 models), a thermomechanical model of rotating texture ‘surfing’ on a heat wave (TM3 model), a model of melting-growth (MG model) that only applies when the droplets coexist with their own isotropic liquid, and a pure hydrodynamic model (H model) based on the existence of Marangoni flows – currently, only evidenced in emulsified cholesterics. The strengths and weaknesses of each model will be discussed in relation with the experimental results.

@article{oswald_lehmann_2019,
  title = {Lehmann effect in nematic and cholesteric liquid crystals: a review},
  volume = {7},
  doi = {10.1080/21680396.2019.1671244},
  number = {2},
  journal = {Liquid Crystals Reviews},
  author = {Oswald, P. and Dequidt, A. and Poy, G.},
  year = {2019},
  pages = {142--166},
}

Ray-based optical visualisation of complex birefringent structures including energy transport

G. Poy, S. Žumer, Soft Matter, 15, 3659–3670 (2019)

DOI Article Abstract/Bibtex

We propose an efficient method to simulate light propagation in lossless and non-scattering uniaxial birefringent media, based on a standard ray-tracing technique supplemented by a newly-derived transport equation for the electric field amplitude along a ray and a tailored interpolation algorithm for the reconstruction of the electromagnetic fields. We show that this algorithm is accurate in comparison to a full solution of Maxwell's equations when the permittivity tensor of the birefringent medium typically varies over a length much bigger than the wavelength. We demonstrate the usefulness of our code for soft matter by comparing experimental images of liquid crystal droplets with simulated bright-field optical micrographs, and conclude that our method is more general than the usual Jones method, which is only valid under polarised illumination conditions. We also point out other possible applications of our method, including liquid crystal based flat element design and diffraction pattern calculations for periodic liquid crystal samples.

@article{poy_ray-based_2019,
  title = {Ray-based optical visualisation of complex birefringent structures including energy transport},
  volume = {15},
  doi = {10.1039/C8SM02448K},
  number = {18},
  journal = {Soft Matter},
  author = {Poy, Guilhem and Žumer, Slobodan},
  year = {2019},
  pages = {3659--3670},
}

Role of impurities in the Lehmann effect of cholesteric liquid crystals: Towards an alternative model

P. Oswald, G. Poy, Physical Review E, 98 (2018)

DOI Article Abstract/Bibtex

The Lehmann effect is the rotation of cholesteric droplets when they are submitted to a temperature gradient. So far, this effect was only observed in the coexistence region between the cholesteric phase and its isotropic liquid. This zone of coexistence is due to the presence in the LC of impurities. In this paper, we show that the rotation velocity of the droplets does not depend on the choice of the impurity and on its concentration, providing that the variations of the equilibrium twist and the rotational viscosity are taken into account. These results were obtained by doping the cholesteric LC (a diluted mixture of 7CB and R811) with nonmesogenic and mesogenic impurities. The nonmesogenic impurities used are the biphenyl, the hexachloroethane, and a fluorinated polyether polymer. The mesogenic impurity is the LC I52. From these experiments we conclude that the Lehmann effect is certainly not due to a chemical torque of the type described by Leslie, Akopyan, and Zel’dovich. Finally, we propose alternative avenues that might be explored to understand the Lehmann effect.

@article{oswald_role_2018,
  title = {Role of impurities in the {Lehmann} effect of cholesteric liquid crystals: {Towards} an alternative model},
  volume = {98},
  doi = {10.1103/PhysRevE.98.032704},
  number = {3},
  journal = {Physical Review E},
  author = {Oswald, Patrick and Poy, Guilhem},
  year = {2018},
}

Dislocations dynamics during the nonlinear creep of a homeotropic sample of smectic-A liquid crystal

P. Oswald, G. Poy, The European Physical Journal E, 41, 73 (2018)

DOI Article Abstract/Bibtex

New creep experiments under sinusoidal compression/dilation deformation of a homeotropic sample of smectic-A liquid crystal (8CB) show that its response is nonlinear at very small amplitude of deformation. This behavior is explained by taking into account the crossing between the edge dislocations that climb parallel to the layers and the screw dislocations joining the two surfaces limiting the sample. The activation energy of the crossing process and the density of the screw dislocations as a function of the sample thickness are estimated experimentally.

@article{oswald_dislocations_2018,
  title={Dislocations dynamics during the nonlinear creep of a homeotropic sample of smectic-A liquid crystal},
  author={Oswald, P and Poy, G},
  journal={The European Physical Journal E},
  doi = {10.1140/epje/i2018-11684-9},
  volume={41},
  number={6},
  pages={73},
  year={2018},
}

On the existence of the thermomechanical terms of Akopyan and Zel’dovich in cholesteric liquid crystals

G. Poy, P. Oswald, Liquid Crystals (2018)

DOI Article Abstract/Bibtex

We revisit a theoretical paper of Akopyan and Zel’dovich about the thermomechanical coupling terms in nematic liquid crystals. We show that the expressions of these terms given by these authors must be corrected to satisfy the Onsager reciprocity relations, a point already stressed by Pleiner and Brand in 1987. We then extend this calculation to the cholesteric phase and show that there are no additional terms in the uniaxial approximation of this phase. Finally, we give the correspondence between the Akopyan and Zel’dovich terms and those calculated by Pleiner and Brand in 1996 by making a different choice for the forces and the fluxes in the theory.

@article{poy_existence_2018,
  title={On the existence of the thermomechanical terms of Akopyan and Zel’dovich in cholesteric liquid crystals},
  author={Poy, G and Oswald, P},
  journal={Liquid Crystals},
  doi = {10.1080/02678292.2018.1446552},
  year={2018},
}

Role of anchoring energy on the texture of cholesteric droplets: Finite-element simulations and experiments

G. Poy, F. Bunel, P. Oswald, Physical Review E, 96 (2017)

DOI Article Abstract/Bibtex

We present a numerical method to compute defect-free textures inside cholesteric domains of arbitrary shape. This method has two interesting properties, namely a robust and fast quadratic convergence to a local minimum of the Frank free energy, thanks to a trust region strategy. We apply this algorithm to study the texture of cholesteric droplets in coexistence with their isotropic liquid in two cases: when the anchoring is planar and when it is tilted. In the first case, we show how to determine the anchoring energy at the cholesteric-isotropic interface from a study of the optical properties of droplets of different sizes oriented with an electric field. This method is applied to the case of the liquid crystal CCN-37. In the second case, we come back to the issue of the textural transition as a function of the droplet radius between the double-twist droplets and the banded droplets, observed for instance in cyanobiphenyl liquid crystals. We show that, even if this transition is dominated by the saddle-splay Gauss constant \(K_4\), as was recently recognized by Yoshioka et al. [Soft Matter 12, 2400 (2016)], the anchoring energy does also play an important role that cannot be neglected.

@article{poy_role_2017,
	title = {Role of anchoring energy on the texture of cholesteric droplets: {Finite}-element simulations and experiments},
	volume = {96},
	issn = {2470-0045, 2470-0053},
	doi = {10.1103/PhysRevE.96.012705},
	number = {1},
	journal = {Physical Review E},
	author = {Poy, Guilhem and Bunel, Felix and Oswald, Patrick},
	year = {2017},
}

Fréedericksz transition under electric and rotating magnetic field: application to nematics with negative dielectric and magnetic anisotropies

P. Oswald, G. Poy, F. Vittoz, Liquid Crystals, 1–8 (2017)

DOI Article Abstract/Bibtex

We study the action of a rotating magnetic field on the Fréedericksz instability under electric field of a homeotropic nematic sample sandwiched between two parallel electrodes. The liquid crystal (LC) is of negative dielectric and magnetic anisotropies and the magnetic field is parallel to the electrodes used to apply the electric field. We show that the sample destabilises above a critical voltage \(V_c\) that depends on the magnetic field \(B\) and its angular rotation velocity \(\omega\). The relation \(V_c(B,\omega\) is calculated analytically in the synchronous regime, where the director rotates at the same angular velocity as the magnetic field. These predictions are compared to the experiment performed with the LC CCN-37. From this experiment, the values of the bend constant \(K_3\), of the rotational viscosity \(\gamma_1\) and of the magnetic anisotropy \(\chi_a\) are deduced.

@article{oswald_freedericksz_2017,
	title = {Fréedericksz transition under electric and rotating magnetic field: application to nematics with negative dielectric and magnetic anisotropies},
	issn = {0267-8292, 1366-5855},
	doi = {10.1080/02678292.2016.1272722},
	journal = {Liquid Crystals},
	author = {Oswald, P. and Poy, G. and Vittoz, F.},
	year = {2017},
	pages = {1--8},
}

Lehmann rotation of twisted bipolar cholesteric droplets: role of Leslie, Akopyan and Zel’dovich thermomechanical coupling terms of nematodynamics

P. Oswald, G. Poy, A. Dequidt, Liquid Crystals, 1–20 (2016)

DOI Article Abstract/Bibtex

We show that the Leslie and texture-dependent Akopyan and Zel’dovich thermomechanical coupling terms of nematodynamics cannot explain the thermal Lehmann rotation of the twisted bipolar droplets observed in the coexistence region between a cholesteric phase and the isotropic liquid. On the other hand, these terms are pertinent below the transition temperature and can be determined by measuring the director rotation velocity in two different molecular configurations. In addition, a complete characterisation of the liquid crystal used (CCN-37) is also given.

@article{oswald_lehmann_2016,
	title = {Lehmann rotation of twisted bipolar cholesteric droplets: role of {Leslie}, {Akopyan} and {Zel}’dovich thermomechanical coupling terms of nematodynamics},
	issn = {0267-8292, 1366-5855},
	doi = {10.1080/02678292.2016.1255363},
	journal = {Liquid Crystals},
	author = {Oswald, P. and Poy, G. and Dequidt, A.},
	year = {2016},
	pages = {1--20},
}

Unsteady flow and particle migration in dense, non-Brownian suspensions

M. Hermes, B. M. Guy, W. C. K. Poon, G. Poy, M. E. Cates, M. Wyart, Journal of Rheology, 60, 905–916 (2016)

DOI Article Abstract/Bibtex

We present experimental results on dense corn-starch suspensions as examples of non-Brownian, nearly hard particles that undergo continuous and discontinuous shear thickening (DST) at intermediate and high densities, respectively. Our results offer strong support for recent theories involving a stress-dependent effective contact friction among particles. We show, however, that in the DST regime, where theory might lead one to expect steady-state shear bands oriented layerwise along the vorticity axis, the real flow is unsteady. To explain this, we argue that steady-state banding is generically ruled out by the requirement that, for hard non-Brownian particles, the solvent pressure and the normal-normal component of the particle stress must balance separately across the interface between bands. (Otherwise, there is an unbalanced migration flux.) However, long-lived transient shear bands remain possible.

@article{hermes_unsteady_2016,
	title = {Unsteady flow and particle migration in dense, non-Brownian suspensions},
	volume = {60},
	issn = {0148-6055, 1520-8516},
	doi = {10.1122/1.4953814},
	number = {5},
	journal = {Journal of Rheology},
	author = {Hermes, Michiel and Guy, Ben M. and Poon, Wilson C. K. and Poy, Guilhem and Cates, Michael E. and Wyart, Matthieu},
	year = {2016},
	pages = {905--916},
}

Generalized drift velocity of a cholesteric texture in a temperature gradient

A. Dequidt, G. Poy, P. Oswald, Soft Matter, 12, 7529–7538 (2016)

DOI Article Abstract/Bibtex

We propose a general method to calculate the drift velocity of cholesteric textures subjected to a temperature gradient when the backflow effects are negligible. The textures may be Translationally Invariant Configurations (TICs) or localized structures such as cholesteric droplets or cholesteric fingers. For the TICs and for the droplets, the drift is rotational while for the fingers, the drift is translational. We show that for the TICs, the drift is only due to the thermomechanical coupling terms of Leslie (classical term) and of Akopyan and Zel’dovich (which are additional texture-dependent terms). For the localized structures, we show that another mechanism involving the temperature variations of the elastic constants and the existence of a transverse temperature gradient can lead to a drift which adds to the one due the classical thermomechanical effects.

@article{dequidt_generalized_2016,
	title = {Generalized drift velocity of a cholesteric texture in a temperature gradient},
	volume = {12},
	issn = {1744-683X, 1744-6848},
	doi = {10.1039/C6SM01359G},
	number = {36},
	journal = {Soft Matter},
	author = {Dequidt, Alain and Poy, Guilhem and Oswald, Patrick},
	year = {2016},
	pages = {7529--7538},
}

Continuous Rotation of Achiral Nematic Liquid Crystal Droplets Driven by Heat Flux

J. Ignés-Mullol, G. Poy, P. Oswald, Physical Review Letters, 117, 057801 (2016)

DOI Article Abstract/Bibtex

Suspended droplets of cholesteric (chiral nematic) liquid crystals spontaneously rotate in the presence of a heat flux due to a temperature gradient, a phenomenon known as the Lehmann effect. So far, it is not clear whether this effect is due to the chirality of the phase and the molecules or only to the chirality of the director field. Here, we report the continuous rotation in a temperature gradient of nematic droplets of a lyotropic chromonic liquid crystal featuring a twisted bipolar configuration. The achiral nature of the molecular components leads to a random handedness of the spontaneous twist, resulting in the coexistence of droplets rotating in the two senses, with speeds proportional to the temperature gradient and inversely proportional to the droplet radius. This result shows that a macroscopic twist of the director field is sufficient to induce a rotation of the droplets, and that the phase and the molecules do not need to be chiral. This suggests that one can also explain the Lehmann rotation in cholesteric liquid crystals without introducing the Leslie thermomechanical coupling—only present in chiral mesophases. An explanation based on the Akopyan and Zeldovich theory of thermomechanical effects in nematics is proposed and discussed.

@article{ignes-mullol_continuous_2016,
	title = {Continuous Rotation of Achiral Nematic Liquid Crystal Droplets Driven by Heat Flux},
	volume = {117},
	issn = {0031-9007, 1079-7114},
	doi = {10.1103/PhysRevLett.117.057801},
	number = {5},
	journal = {Physical Review Letters},
	author = {Ignés-Mullol, Jordi and Poy, Guilhem and Oswald, Patrick},
	year = {2016},
	pages = {057801},
}

Do Lehmann cholesteric droplets subjected to a temperature gradient rotate as rigid bodies?

G. Poy, P. Oswald, Soft Matter, 12, 2604–2611 (2016)

DOI Article Abstract/Bibtex

We performed a Fluorescence Recovery After Photobleaching (FRAP) experiment during the Lehmann rotation of cholesteric droplets in thermodynamic coexistence with the isotropic liquid and subjected to a temperature gradient. By creating and tracking bleached spots near the surface of banded droplets (in which the cholesteric helix is perpendicular to the gradient) and concentric circle droplets oriented by an electric field (in which the helix is parallel to the gradient), we found that neither type of droplet rotates as a solid. This result shows that the texture rotation is mainly due to the local director rotation.

@article{poy_lehmann_2016,
	title = {Do Lehmann cholesteric droplets subjected to a temperature gradient rotate as rigid bodies?},
	volume = {12},
	issn = {1744-683X, 1744-6848},
	doi = {10.1039/C5SM02906F},
	number = {9},
	journal = {Soft Matter},
	author = {Poy, Guilhem and Oswald, Patrick},
	year = {2016},
	pages = {2604--2611},
}

Droplet relaxation in Hele-Shaw geometry: Application to the measurement of the nematic-isotropic surface tension

P. Oswald, G. Poy, Physical Review E, 92, 062512 (2015)

DOI Article Abstract/Bibtex

Shape measurements after the coalescence of isotropic droplets embedded in a thin sample of a homeotropic nematic phase provides a tool to measure the nematic-isotropic surface tension. In addition, this experiment allows us to check the scaling laws recently given by Brun et al. [P.-T. Brun, M. Nagel, and F. Gallaire, Phys. Rev. E 88, 043009 (2013)] to explain the relaxation of ellipsoidal droplets in a Hele-Shaw cell.

@article{oswald_droplet_2015,
	title = {Droplet relaxation in Hele-Shaw geometry: Application to the measurement of the nematic-isotropic surface tension},
	volume = {92},
	issn = {1539-3755, 1550-2376},
	doi = {10.1103/PhysRevE.92.062512},
	number = {6},
	journal = {Physical Review E},
	author = {Oswald, Patrick and Poy, Guilhem},
	year = {2015},
	pages = {062512},
}

Lehmann rotation of cholesteric droplets: Role of the sample thickness and of the concentration of chiral molecules

P. Oswald, G. Poy, Physical Review E, 91, 032502 (2015)

DOI Article Abstract/Bibtex

We study the role of the sample thickness \(d\) and of the concentration \(C\) of chiral molecules during the Lehmann rotation of cholesteric droplets of radius \(R\) subjected to a temperature gradient \(\vec{G}\). Two configurations are studied depending on how the helix is oriented with respect to \(\vec{G}\). The first result is that, at fixed \(C\) and \(R\), the rotation velocity \(\omega\) increases with \(d\) when the helix is parallel to \(\vec{G}\), whereas it is independent of \(d\) when the helix is perpendicular to \(\vec{G}\). The second result is that, for a given \(C\), \(\omega_0=\lim_{R\rightarrow0}\omega(R)\) is the same for the two types of droplets independently of \(d\). This suggests that the, as yet unknown, physical mechanism responsible for the droplet rotation is the same in the two types of droplets. The third result is that the Lehmann coefficient \(\bar\nu\) defined from the Leslie-like relation \(\omega_0=−\bar\nu G/\gamma_1\) (with \(\gamma_1\) the rotational viscosity) is proportional to the equilibrium twist \(q\). Last, but not least, the ratio \(\bar R=\bar\nu/q\) depends on the liquid crystal chosen but is independent of the chiral molecule used to dope the liquid crystal.

@article{oswald_lehmann_2015,
	title = {Lehmann rotation of cholesteric droplets: Role of the sample thickness and of the concentration of chiral molecules},
	volume = {91},
	issn = {1539-3755, 1550-2376},
	doi = {10.1103/PhysRevE.91.032502},
	number = {3},
	journal = {Physical Review E},
	author = {Oswald, Patrick and Poy, Guilhem},
	year = {2015},
	pages = {032502},
}

Experimental relationship between surface and bulk rotational viscosities in nematic liquid crystals

P. Oswald, G. Poy, F. Vittoz, V. Popa-Nita, Liquid Crystals, 40, 734–744 (2013)

DOI Article Abstract/Bibtex

Systematic measurements of the surface viscosity \(\gamma_s\) of several nematic liquid crystals in contact with a polymercaptan layer show that the latter scales like the bulk rotational viscosity \(\gamma_1\). This result is interpreted in the framework of a ‘delocalized model’ for the surface viscosity.

@article{oswald_experimental_2013,
	title = {Experimental relationship between surface and bulk rotational viscosities in nematic liquid crystals},
	volume = {40},
	issn = {0267-8292, 1366-5855},
	doi = {10.1080/02678292.2013.783936},
	number = {6},
	journal = {Liquid Crystals},
	author = {Oswald, Patrick and Poy, Guilhem and Vittoz, Franck and Popa-Nita, Vlad},
	year = {2013},
	pages = {734--744},
}

Conferences (talks & posters)

Chirality in soft matter: from out-of-equilibrium physics to non-linear optics

G. Poy, L2C, Montpellier, France, 2020 (Invited seminar)

Lensing and deflection of light with soft topological solitons

G. Poy, A. J. Hess, J. B. Tai, S. Žumer, I. I. Smalyukh, N.I.C.E. conference - Optics and Photonics symposia, Nice, France, 2020 (Invited keynote talk)

Website Abstract Slides

Chirality in soft matter: from out-of-equilibrium physics to non-linear optics

G. Poy, LOMA, Bordeaux, France, 2019 (Invited seminar)

A new operator-splitted beam propagation method with application to non-linear optics in liquid crystals

G. Poy, Optics of Liquid Crystals, Quebec city, Canada, 2019 (Oral presentation)

Nemaktis: a numerical platform for light propagation in liquid crystals

G. Poy, A. Petelin, European Conference on Liquid Crystals, Wrocław, Poland, 2019 (Oral presentation)

Simulation of polarized optical micrographs including light-deviation effects in slowly-varying birefringent structures

G. Poy, Workshop on Liquid Crystals for Photonics, Jastrzębia Góra, Poland, 2018 (Oral presentation)

Improved ray-tracing for slowly varying director field: Simulation of optical micrographs of nematic and cholesteric droplets

G. Poy, International Liquid Crystal Conference, Kyoto, Japan, 2018 (Oral presentation)

On the pertinence of the thermomechanical model in the Lehmann rotation of cholesteric and nematic droplets

G. Poy, Faculty of Mathematics and Physics, Ljubljana, Slovenia, 2018 (Seminar)

Lehmann effect: The end of the Leslie paradigm

G. Poy, J. Ignés-Mullol, P. Oswald, International Liquid Crystal Conference, Kent, Ohio, 2016 (Invited talk)

Website Abstract Slides

Heat-flux-driven rotation of nematic and cholesteric twisted bipolar droplets

G. Poy, F. Bunel, J. Ignés-Mullol, P. Oswald, StatPhys, Lyon, France, 2016 (Poster)

Du nouveau sur l'effet Lehmann thermique dans des gouttes cholestériques

G. Poy, J. Ignés-Mullol, P. Oswald, 17ème Colloque sur les systèmes anisotropes auto-organisés, Autrans, France, 2015 (Oral presentation)

Website Abstract Slides