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Nanopropellers and Their Actuation in Complex Viscoelastic Media

Schamel, D., Mark, A. G., Gibbs, J. G., Miksch, C., Morozov, K. I., Leshansky, A. M., Fischer, P.

ACS Nano, 8(9):8794-8801, June 2014, Featured cover article. (article)

Abstract
Tissue and biological fluids are complex viscoelastic media with a nanoporous macromolecular structure. Here, we demonstrate that helical nanopropellers can be controllably steered through such a biological gel. The screw-propellers have a filament diameter of about 70 nm and are smaller than previously reported nanopropellers as well as any swimming microorganism. We show that the nanoscrews will move through high-viscosity solutions with comparable velocities to that of larger micropropellers, even though they are so small that Brownian forces suppress their actuation in pure water. When actuated in viscoelastic hyaluronan gels, the nanopropellers appear to have a significant advantage, as they are of the same size range as the gel’s mesh size. Whereas larger helices will show very low or negligible propulsion in hyaluronan solutions, the nanoscrews actually display significantly enhanced propulsion velocities that exceed the highest measured speeds in Newtonian fluids. The nanopropellers are not only promising for applications in the extracellular environment but small enough to be taken up by cells.

Featured cover article.

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Video - Helical Micro and Nanopropellers for Applications in Biological Fluidic Environments link (url) DOI [BibTex]


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Convertor

Fischer, P., Mark, A.

May 2014 (patent)

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[BibTex]

[BibTex]


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3D nanofabrication on complex seed shapes using glancing angle deposition

Hyeon-Ho, J., Mark, A. G., Gibbs, J. G., Reindl, T., Waizmann, U., Weis, J., Fischer, P.

In 2014 IEEE 27th International Conference on Micro Electro Mechanical Systems (MEMS), pages: 437-440, January 2014 (inproceedings)

Abstract
Three-dimensional (3D) fabrication techniques promise new device architectures and enable the integration of more components, but fabricating 3D nanostructures for device applications remains challenging. Recently, we have performed glancing angle deposition (GLAD) upon a nanoscale hexagonal seed array to create a variety of 3D nanoscale objects including multicomponent rods, helices, and zigzags [1]. Here, in an effort to generalize our technique, we present a step-by-step approach to grow 3D nanostructures on more complex nanoseed shapes and configurations than before. This approach allows us to create 3D nanostructures on nanoseeds regardless of seed sizes and shapes.

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DOI [BibTex]

DOI [BibTex]


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Circular polarization interferometry: circularly polarized modes of cholesteric liquid crystals

Sanchez-Castillo, A., Eslami, S., Giesselmann, F., Fischer, P.

OPTICS EXPRESS, 22(25):31227-31236, 2014 (article)

Abstract
We describe a novel polarization interferometer which permits the determination of the refractive indices for circularly-polarized light. It is based on a Jamin-Lebedeff interferometer, modified with waveplates, and permits us to experimentally determine the refractive indices n(L) and n(R) of the respectively left- and right-circularly polarized modes in a cholesteric liquid crystal. Whereas optical rotation measurements only determine the circular birefringence, i.e. the difference (n(L) - n(R)), the interferometer also permits the determination of their absolute values. We report refractive indices of a cholesteric liquid crystal in the region of selective (Bragg) reflection as a function of temperature. (C) 2014 Optical Society of America

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DOI [BibTex]

DOI [BibTex]


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Self-Propelling Nanomotors in the Presence of Strong Brownian Forces

Lee, T., Alarcon-Correa, M., Miksch, C., Hahn, K., Gibbs, J. G., Fischer, P.

NANO LETTERS, 14(5):2407-2412, 2014 (article)

Abstract
Motility in living systems is due to an array of complex molecular nanomotors that are essential for the function and survival of cells. These protein nanomotors operate not only despite of but also because of stochastic forces. Artificial means of realizing motility rely on local concentration or temperature gradients that are established across a particle, resulting in slip velocities at the particle surface and thus motion of the particle relative to the fluid. However, it remains unclear if these artificial motors can function at the smallest of scales, where Brownian motion dominates and no actively propelled living organisms can be found. Recently, the first reports have appeared suggesting that the swimming mechanisms of artificial structures may also apply to enzymes that are catalytically active. Here we report a scheme to realize artificial Janus nanoparticles (JNPs) with an overall size that is comparable to that of some enzymes similar to 30 nm. Our JNPs can catalyze the decomposition of hydrogen peroxide to water and oxygen and thus actively move by self-electrophoresis. Geometric anisotropy of the Pt-Au Janus nanoparticles permits the simultaneous observation of their translational and rotational motion by dynamic light scattering. While their dynamics is strongly influenced by Brownian rotation, the artificial Janus nanomotors show bursts of linear ballistic motion resulting in enhanced diffusion.

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DOI [BibTex]


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Shape control in wafer-based aperiodic 3D nanostructures

Hyeon-Ho, J., Mark, A. G., Gibbs, J. G., Reindl, T., Waizmann, U., Weis, J., Fischer, P.

NANOTECHNOLOGY, 25(23), 2014, Cover article. (article)

Abstract
Controlled local fabrication of three-dimensional (3D) nanostructures is important to explore and enhance the function of single nanodevices, but is experimentally challenging. We present a scheme based on e-beam lithography (EBL) written seeds, and glancing angle deposition (GLAD) grown structures to create nanoscale objects with defined shapes but in aperiodic arrangements. By using a continuous sacrificial corral surrounding the features of interest we grow isolated 3D nanostructures that have complex cross-sections and sidewall morphology that are surrounded by zones of clean substrate.

Cover article.

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DOI [BibTex]

DOI [BibTex]


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Active Microrheology of the Vitreous of the Eye applied to Nanorobot Propulsion

Qiu, T., Schamel, D., Mark, A. G., Fischer, P.

In 2014 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION (ICRA), pages: 3801-3806, IEEE International Conference on Robotics and Automation ICRA, 2014, Best Automation Paper Award – Finalist. (inproceedings)

Abstract
Biomedical applications of micro or nanorobots require active movement through complex biological fluids. These are generally non-Newtonian (viscoelastic) fluids that are characterized by complicated networks of macromolecules that have size-dependent rheological properties. It has been suggested that an untethered microrobot could assist in retinal surgical procedures. To do this it must navigate the vitreous humor, a hydrated double network of collagen fibrils and high molecular-weight, polyanionic hyaluronan macromolecules. Here, we examine the characteristic size that potential robots must have to traverse vitreous relatively unhindered. We have constructed magnetic tweezers that provide a large gradient of up to 320 T/m to pull sub-micron paramagnetic beads through biological fluids. A novel two-step electrical discharge machining (EDM) approach is used to construct the tips of the magnetic tweezers with a resolution of 30 mu m and high aspect ratio of similar to 17:1 that restricts the magnetic field gradient to the plane of observation. We report measurements on porcine vitreous. In agreement with structural data and passive Brownian diffusion studies we find that the unhindered active propulsion through the eye calls for nanorobots with cross-sections of less than 500 nm.

Best Automation Paper Award – Finalist.

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[BibTex]

[BibTex]


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Swimming by reciprocal motion at low Reynolds number

Qiu, T., Lee, T., Mark, A. G., Morozov, K. I., Muenster, R., Mierka, O., Turek, S., Leshansky, A. M., Fischer, P.

NATURE COMMUNICATIONS, 5, 2014, Max Planck Press Release. (article)

Abstract
Biological microorganisms swim with flagella and cilia that execute nonreciprocal motions for low Reynolds number (Re) propulsion in viscous fluids. This symmetry requirement is a consequence of Purcell's scallop theorem, which complicates the actuation scheme needed by microswimmers. However, most biomedically important fluids are non-Newtonian where the scallop theorem no longer holds. It should therefore be possible to realize a microswimmer that moves with reciprocal periodic body-shape changes in non-Newtonian fluids. Here we report a symmetric `micro-scallop', a single-hinge microswimmer that can propel in shear thickening and shear thinning (non-Newtonian) fluids by reciprocal motion at low Re. Excellent agreement between our measurements and both numerical and analytical theoretical predictions indicates that the net propulsion is caused by modulation of the fluid viscosity upon varying the shear rate. This reciprocal swimming mechanism opens new possibilities in designing biomedical microdevices that can propel by a simple actuation scheme in non-Newtonian biological fluids.

Max Planck Press Release.

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Video - A Swimming Micro-Scallop Video - Winner of the Micro-robotic Design Challenge in Hamlyn Symposium on Medical Robotics DOI [BibTex]

Video - A Swimming Micro-Scallop Video - Winner of the Micro-robotic Design Challenge in Hamlyn Symposium on Medical Robotics DOI [BibTex]


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Nanohelices by shadow growth

Gibbs, J. G., Mark, A. G., Lee, T., Eslami, S., Schamel, D., Fischer, P.

NANOSCALE, 6(16):9457-9466, 2014 (article)

Abstract
The helix has remarkable qualities and is prevalent in many fields including mathematics, physics, chemistry, and biology. This shape, which is chiral by nature, is ubiquitous in biology with perhaps the most famous example being DNA. Other naturally occurring helices are common at the nanoscale in the form of protein secondary structures and in various macromolecules. Nanoscale helices exhibit a wide range of interesting mechanical, optical, and electrical properties which can be intentionally engineered into the structure by choosing the correct morphology and material. As technology advances, these fabrication parameters can be fine-tuned and matched to the application of interest. Herein, we focus on the fabrication and properties of nanohelices grown by a dynamic shadowing growth method combined with fast wafer-scale substrate patterning which has a number of distinct advantages. We review the fabrication methodology and provide several examples that illustrate the generality and utility of nanohelices shadow-grown on nanopatterns.

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Video - Fabrication of Designer Nanostructures DOI [BibTex]


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Chiral Nanomagnets

Eslami, S., Gibbs, J. G., Rechkemmer, Y., van Slageren, J., Alarcon-Correa, M., Lee, T., Mark, A. G., Rikken, G. L. J. A., Fischer, P.

ACS PHOTONICS, 1(11):1231-1236, 2014 (article)

Abstract
We report on the enhanced optical properties of chiral magnetic nanohelices with critical dimensions comparable to the ferromagnetic domain size. They are shown to be ferromagnetic at room temperature, have defined chirality, and exhibit large optical activity in the visible as verified by electron microscopy, superconducting quantum interference device (SQUID) magnetometry, natural circular dichroism (NCD), and magnetic circular dichroism (MCD) measurements. The structures exhibit magneto-chiral dichroism (MChD), which directly demonstrates coupling between their structural chirality and magnetism. A chiral nickel (Ni) film consisting of an array of nanohelices similar to 100 nm in length exhibits an MChD anisotropy factor g(MChD) approximate to 10(-4) T-1 at room temperature in a saturation field of similar to 0.2 T, permitting polarization-independent control of the film's absorption properties through magnetic field modulation. This is also the first report of MChD in a material with structural chirality on the order of the wavelength of light, and therefore the Ni nanohelix array is a metamaterial with magnetochiral properties that can be tailored through a dynamic deposition process.

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DOI [BibTex]

DOI [BibTex]


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Wireless powering of e-swimmers

Roche, J., Carrara, S., Sanchez, J., Lannelongue, J., Loget, G., Bouffier, L., Fischer, P., Kuhn, A.

SCIENTIFIC REPORTS, 4, 2014 (article)

Abstract
Miniaturized structures that can move in a controlled way in solution and integrate various functionalities are attracting considerable attention due to the potential applications in fields ranging from autonomous micromotors to roving sensors. Here we introduce a concept which allows, depending on their specific design, the controlled directional motion of objects in water, combined with electronic functionalities such as the emission of light, sensing, signal conversion, treatment and transmission. The approach is based on electric field-induced polarization, which triggers different chemical reactions at the surface of the object and thereby its propulsion. This results in a localized electric current that can power in a wireless way electronic devices in water, leading to a new class of electronic swimmers (e-swimmers).

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DOI [BibTex]

DOI [BibTex]


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Swelling and shrinking behaviour of photoresponsive phosphonium-based ionogel microstructures

Czugala, M., O’Connell, C., Blin, C., Fischer, P., Fraser, K. J., Benito-Lopez, F., Diamond, D.

SENSORS AND ACTUATORS B-CHEMICAL, 194, pages: 105-113, 2014 (article)

Abstract
Photoresponsive N-isopropylacrylamide ionogel microstructures are presented in this study. These ionogels are synthesised using phosphonium based room temperature ionic liquids, together with the photochromic compound benzospiropyran. The microstructures can be actuated using light irradiation, facilitating non-contact and non-invasive operation. For the first time, the characterisation of the swelling and shrinking behaviour of several photopatterned ionogel microstructures is presented and the influence of surface-area-to-volume ratio on the swelling kinetics is evaluated. It was found that the swelling and shrinking behaviour of the ionogels is strongly dependent on the nature of the ionic liquid. In particular, the {[}P-6,P-6,P-6,P-14]{[}NTf2] ionogel exhibits the greatest degree of swelling, reaching up to 180\% of its initial size, and the fastest shrinkage rate (k(sh) = 29 +/- 4 x 10(-2) s(-1)). (C) 2014 Elsevier B. V. All rights reserved.

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DOI [BibTex]

DOI [BibTex]

2013


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Hybrid nanocolloids with programmed three-dimensional shape and material composition

Mark, A. G., Gibbs, J. G., Lee, T., Fischer, P.

NATURE MATERIALS, 12(9):802-807, 2013, Max Planck Press Release. (article)

Abstract
Tuning the optical(1,2), electromagnetic(3,4) and mechanical properties of a material requires simultaneous control over its composition and shape(5). This is particularly challenging for complex structures at the nanoscale because surface-energy minimization generally causes small structures to be highly symmetric(5). Here we combine low-temperature shadow deposition with nanoscale patterning to realize nanocolloids with anisotropic three-dimensional shapes, feature sizes down to 20 nm and a wide choice of materials. We demonstrate the versatility of the fabrication scheme by growing three-dimensional hybrid nanostructures that contain several functional materials with the lowest possible symmetry, and by fabricating hundreds of billions of plasmonic nanohelices, which we use as chiral metafluids with record circular dichroism and tunable chiroptical properties.

Max Planck Press Release.

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Video - Fabrication of Designer Nanostructures DOI [BibTex]


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Chiral Colloidal Molecules And Observation of The Propeller Effect

Schamel, D., Pfeifer, M., Gibbs, J. G., Miksch, B., Mark, A. G., Fischer, P.

JOURNAL OF THE AMERICAN CHEMICAL SOCIETY, 135(33):12353-12359, 2013 (article)

Abstract
Chiral molecules play an important role in biological and chemical processes, but physical effects due to their symmetry-breaking are generally weak. Several physical chiral separation schemes which could potentially be useful, including the propeller effect, have therefore not yet been demonstrated at the molecular scale. However, it has been proposed that complex nonspherical colloidal particles could act as ``colloidal molecules{''} in mesoscopic model systems to permit the visualization of molecular phenomena that are otherwise difficult to observe. Unfortunately, it is difficult to synthesize such colloids because surface minimization generally favors the growth of symmetric particles. Here we demonstrate the production of large numbers of complex colloids with glancing angle physical vapor deposition. We use chiral colloids to demonstrate the Baranova and Zel'dovich (Baranova, N. B.; Zel'dovich, B. Y. Chem. Phys. Lett. 1978, 57, 435) propeller effect: the separation of a racemic mixture by application of a rotating field that couples to the dipole moment of the enantiomers and screw propels them in opposite directions. The handedness of the colloidal suspensions is monitored with circular differential light scattering. An exact solution for the colloid's propulsion is derived, and comparisons between the colloidal system and the corresponding effect at the molecular scale are made.

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Video - Nanospropellers DOI [BibTex]

Video - Nanospropellers DOI [BibTex]


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Indirect absorption spectroscopy using quantum cascade lasers: mid-infrared refractometry and photothermal spectroscopy

Pfeifer, M., Ruf, A., Fischer, P.

OPTICS EXPRESS, 21(22):25643-25654, 2013 (article)

Abstract
We record vibrational spectra with two indirect schemes that depend on the real part of the index of refraction: mid-infrared refractometry and photothermal spectroscopy. In the former, a quantum cascade laser (QCL) spot is imaged to determine the angles of total internal reflection, which yields the absorption line via a beam profile analysis. In the photothermal measurements, a tunable QCL excites vibrational resonances of a molecular monolayer, which heats the surrounding medium and changes its refractive index. This is observed with a probe laser in the visible. Sub-monolayer sensitivities are demonstrated. (C) 2013 Optical Society of America

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DOI [BibTex]


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Plasmonic nanohelix metamaterials with tailorable giant circular dichroism

Gibbs, J. G., Mark, A. G., Eslami, S., Fischer, P.

APPLIED PHYSICS LETTERS, 103(21), 2013, Featured cover article. (article)

Abstract
Plasmonic nanohelix arrays are shown to interact with electromagnetic fields in ways not typically seen with ordinary matter. Chiral metamaterials (CMMs) with feature sizes small with respect to the wavelength of visible light are a promising route to experimentally achieve such phenomena as negative refraction without the need for simultaneously negative e and mu. Here we not only show that giant circular dichroism in the visible is achievable with hexagonally arranged plasmonic nanohelix arrays, but that we can precisely tune the optical activity via morphology and lattice spacing. The discrete dipole approximation is implemented to support experimental data. (C) 2013 AIP Publishing LLC.

Featured cover article.

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DOI [BibTex]

DOI [BibTex]

2010


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Magnetic Nanostructured Propellers

Fischer, P., Ghosh, A.

July 2010 (patent)

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[BibTex]

2010


[BibTex]


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Molecular QED of coherent and incoherent sum-frequency and second-harmonic generation in chiral liquids in the presence of a static electric field

Fischer, P., Salam, A.

MOLECULAR PHYSICS, 108(14):1857-1868, 2010 (article)

Abstract
Coherent second-order nonlinear optical processes are symmetry forbidden in centrosymmetric environments in the electric-dipole approximation. In liquids that contain chiral molecules, however, and which therefore lack mirror image symmetry, coherent sum-frequency generation is possible, whereas second-harmonic generation remains forbidden. Here we apply the theory of molecular quantum electrodynamics to the calculation of the matrix element, transition rate, and integrated signal intensity for sum-frequency and second-harmonic generation taking place in a chiral liquid in the presence and absence of a static electric field, to examine which coherent and incoherent processes exist in the electric-dipole approximation in liquids. Third- and fourth-order time-dependent perturbation theory is employed in combination with single-sided Feynman diagrams to evaluate two contributions arising from static field-free and field-induced processes. It is found that, in addition to the coherent term, an incoherent process exists for sum-frequency generation in liquids. Surprisingly, in the case of dc-field-induced second-harmonic generation, the incoherent contribution is found to always vanish for isotropic chiral liquids even though hyper-Rayleigh second-harmonic generation and electric-field-induced second-harmonic generation are both independently symmetry allowed in any liquid.

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DOI [BibTex]


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Chiral molecules split light: Reflection and refraction in a chiral liquid

Ghosh, A., Fischer, P.

PHYSICAL REVIEW LETTERS, 97(17), 2006, Featured highlight ‘Fundamental optical physics: Refraction’ Nature Photonics, Nov. 2006. (article)

Abstract
A light beam changes direction as it enters a liquid at an angle from another medium, such as air. Should the liquid contain molecules that lack mirror symmetry, then it has been predicted by Fresnel that the light beam will not only change direction, but will actually split into two separate beams with a small difference in the respective angles of refraction. Here we report the observation of this phenomenon. We also demonstrate that the angle of reflection does not equal the angle of incidence in a chiral medium. Unlike conventional optical rotation, which depends on the path-length through the sample, the reported reflection and refraction phenomena arise within a few wavelengths at the interface and thereby suggest a new approach to polarimetry that can be used in microfluidic volumes.

Featured highlight ‘Fundamental optical physics: Refraction’ Nature Photonics, Nov. 2006.

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DOI [BibTex]

DOI [BibTex]


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Direct chiral discrimination in NMR spectroscopy

Buckingham, A., Fischer, P.

CHEMICAL PHYSICS, 324(1):111-116, 2006 (article)

Abstract
Conventional nuclear magnetic resonance spectroscopy is unable to distinguish between the two mirror-image forms (enantiomers) of a chiral molecule. This is because the NMR spectrum is determined by the chemical shifts and spin-spin coupling constants which - in the absence of a chiral solvent - are identical for the two enantiomers. We discuss how chirality may nevertheless be directly detected in liquid-state NMR spectroscopy: In a chiral molecule, the rotating nuclear magnetic moment induces an electric dipole moment in the direction perpendicular to itself and to the permanent magnetic field of the spectrometer. We present computations of the precessing electric polarization following a pi/2 pulse. Our estimates indicate that the electric polarization should be detectable in favourable cases. We also predict that application of an electrostatic field induces a chirally sensitive magnetization oscillating in the direction of the permanent magnetic field. We show that the electric-field-perturbed chemical shift tensor, the nuclear magnetic shielding polarizability, underlies these chiral NMR effects. (c) 2005 Elsevier B.V. All rights reserved.

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DOI [BibTex]

DOI [BibTex]


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NONLINEAR OPTICAL PROPERTIES OF CHIRAL LIQUIDS Electric-dipolar pseudoscalars in nonlinear optics

Fischer, P., Champagne, B.

In NON-LINEAR OPTICAL PROPERTIES OF MATTER: FROM MOLECULES TO CONDENSED PHASES, 1, pages: 359-381, Challenges and Advances in Computational Chemistry and Physics, 2006 (incollection)

Abstract
We give all overview of linear and nonlinear optical processes that can be specific to chiral molecules in isotropic media. Specifically, we discuss the pseudoscalars that underlie nonlinear optical activity and chiral frequency conversion processes in fluids. We show that nonlinear optical techniques open entirely new ways of exploring chirality: Sum-frequency-generation (SFG) at second-order and BioCARS at fourth-order arise in the electric-dipole approximation and do not require circularly polarized light to detect chiral molecules in solution. Here the frequency conversion in itself is a measure of chirality. This is in contrast to natural optical activity phenomena which are based on the interference of radiation from induced oscillating electric and magnetic dipoles, and which are observed as a differential response to right and left circularly polarized light. We give examples from our SFG experiments in optically active solutions and show how the application of an additional static electric field to sum-frequency generation allows the absolute configuration of the chiral solute to be determined via all electric-dipolar process. Results from ab initio calculations of the SFG pseudoscalar are presented for a number of chiral molecules

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[BibTex]

[BibTex]


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Ring-resonator-based frequency-domain optical activity measurements of a chiral liquid

Vollmer, F., Fischer, P.

OPTICS LETTERS, 31(4):453-455, 2006 (article)

Abstract
Chiral liquids rotate the plane of polarization of linearly polarized light and are therefore optically active. Here we show that optical rotation can be observed in the frequency domain. A chiral liquid introduced in a fiber-loop ring resonator that supports left and right circularly polarized modes gives rise to relative frequency shifts that are a direct measure of the liquid's circular birefringence and hence of its optical activity. The effect is in principle not diminished if the circumference of the ring is reduced. The technique is similarly applicable to refractive index and linear birefringence measurements. (c) 2006 Optical Society of America.

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DOI [BibTex]


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Sign of the refractive index in a gain medium with negative permittivity and permeability

Chen, Y., Fischer, P., Wise, F.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, 23(1):45-50, 2006 (article)

Abstract
We show how the sign of the refractive index in any medium may be derived using a rigorous analysis based on Einstein causality. In particular, we consider left-handed materials, i.e., media that have negative permittivities and permeabilities at the frequency of interest. We find that the consideration of gain in such media can give rise to a positive refractive index. (c) 2006 Optical Society of America.

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DOI [BibTex]

DOI [BibTex]

2001


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Isotropic second-order nonlinear optical susceptibilities

Fischer, P., Buckingham, A., Albrecht, A.

PHYSICAL REVIEW A, 64(5), 2001 (article)

Abstract
The second-order nonlinear optical susceptibility, in the electric dipole approximation, is only nonvanishing for materials that are noncentrosymmetric. Should the medium be isotropic, then only a chiral system. such as an optically active liquid, satisfies this symmetry requirement. We derive the quantum-mechanical form of the isotropic component of the sum- and difference-frequency susceptibility and discuss its unusual spectral properties. We show that any coherent second-order nonlinear optical process in a system of randomly oriented molecules requires the medium to be chiral. and the incident frequencies to be different and nonzero. Furthermore, a minimum of two nondegenerate excited molecular states are needed for the isotropic part of the susceptibility to be nonvanishing. The rotationally invariant susceptibility is zero in the static field limit and shows exceptionally sensitive resonance and dephasing effects that are particular to chiral centers.

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DOI [BibTex]

2001


DOI [BibTex]


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Reply to “Comment on ‘Phenomenological damping in optical response tensors’”

Buckingham, A., Fischer, P.

PHYSICAL REVIEW A, 63(4), 2001 (article)

Abstract
We show that damping factors must not be incorporated in the perturbation of the ground state by a static electric field. If they are included, as in the theory of Stedman et al. {[}preceding Comment. Phys. Rev. A 63, 047801 (2001)], then there would be an electric dipole in the y direction induced in a hydrogen atom in the M-s = + 1/2 state by a static electric field in the x direction. Such a dipole is excluded by symmetry.

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DOI [BibTex]