Light Wave Vector Research Articles

Invisibility cloaks in relativistic motion

We consider an ideal invisibility cloak which is illuminated by monochromatic light and which moves in vacuum at constant relativistic velocity with respect to the common inertial frame of light source and observer. We show that, in general, the moving cloak becomes detectable by image distortions and by generating a broad frequency spectrum of the scattered light. However, for many special combinations of incident light frequency, wave vector of light, and cloak velocity, ideal cloaking remains possible. It becomes non-reciprocal though. This means that light rays emitted by the light source arrive at the observer as though they have travelled through vacuum, but they take completely different paths after being retro-reflected at the observer position.

Nonlinear terahertz devices utilizing semiconducting plasmonic metamaterials.

The development of responsive metamaterials has enabled the realization of compact tunable photonic devices capable of manipulating the amplitude, polarization, wave vector and frequency of light. Integration of semiconductors into the active regions of metallic resonators is a proven approach for creating nonlinear metamaterials through optoelectronic control of the semiconductor carrier density. Metal-free subwavelength resonant semiconductor structures offer an alternative approach to create dynamic metamaterials. We present InAs plasmonic disk arrays as a viable resonant metamaterial at terahertz frequencies. Importantly, InAs plasmonic disks exhibit a strong nonlinear response arising from electric field-induced intervalley scattering, resulting in a reduced carrier mobility thereby damping the plasmonic response. We demonstrate nonlinear perfect absorbers configured as either optical limiters or saturable absorbers, including flexible nonlinear absorbers achieved by transferring the disks to polyimide films. Nonlinear plasmonic metamaterials show potential for use in ultrafast terahertz (THz) optics and for passive protection of sensitive electromagnetic devices.

Coupling Efficiency of Surface Plasmon Polaritons for 1D Plasmonic Gratings: Role of Under- and Over-Milling

This paper reports the successful excitation of surface plasmon polaritons (SPPs) through 1D metallic grating on higher refractive index GaP substrate. Coupling efficiency (η) of a free-space transverse-magnetic (TM) plane-wave mode into a SPP mode is crucial for many plasmonic devices. This η predominantly depends on the fabrication (milling) parameters and the factors (under- and over-milling) affecting the η is investigated experimentally and numerically. First of all, η is estimated by measuring the transmission spectra obtained through the plasmonic grating structures by varying the slit width (a) for a fixed period (Λ) and the thickness (t) of the gold (Au) film in which the grating is formed. The wave vector of the incident light is tuned to match the wave vector of the SPP, to get maximum η. For an optimum Au film thickness, a slit width of half of the periodicity of 770 nm in the grating device yields a maximum η. Such grating devices support only a fundamental plasmonic mode because the profile/shape of the slit in the grating device is more like a sinusoidal nature. Furthermore, such grating offers intermediate scattering to the incident light and the SPP as well which in-truns couple more incident energy to the SPPs. Moreover, over-milling results in decreased η where the crystalline plane of the substrate is disturbed. Finite element method (FEM) in COMSOL modeling is used to understand the underlying physics. This study is very useful for the development of the device application in real word.

Linear electro-optic effects due to high-order spatial dispersion

Two new types of electro-optic effect that are linear in the applied electric field strength are theoretically predicted to exist in transparent dielectric crystals due to high order spatial dispersion. The first effect, which is quadratic in the wave vector of light, is possible in materials belonging to all noncentrosymmetric crystal classes. The second, which is cubic in the wave vector, is possible in all crystals. In the ${\bm O}(432)$ and $\bm{O_h}(m\bar 3m)$ crystal classes, for which the primary and secondary linear electro-optic effects and linear electrogyration are simultaneously absent, these effects lead, respectively, to qualitatively new behavior and constitute the dominant bulk electro-optic effect in the limit of small fields. Thus, bulk linear electro-optic effects are predicted to exist in a wide range of materials---including many of considerable technological importance, such as silicon---where they were previously considered impossible.

Adequacy of the rigorous coupled-wave approach for thin-film silicon solar cells with periodically corrugated metallic backreflectors: spectral analysis.

The rigorous coupled-wave approach (RCWA) is extensively used to compute optical absorption and photon absorption in thin-film photovoltaic solar cells backed by 1D metallic gratings when the wave vector of the incident light lies wholly in the grating plane. The RCWA algorithm converges rapidly for incident s-polarized light over the entire 400-1100nm solar spectrum. It also performs well for incident p-polarized light in the 400-650nm spectral regime, but even with a large number of Floquet harmonics in the solution, the total reflectance is underestimated in the 650-1100nm spectral regime. Despite that shortcoming, the RCWA underestimates the solar-spectrum-integrated photon absorption rate only by 5%-10% for p-polarized light. As sunlight is almost unpolarized, the RCWA should be considered adequate to design thin-film silicon solar cells with periodically corrugated metallic backreflectors.

Sensitization of Rare Earth Ions with Carbon Nanotube Plasmonic Antennas

Complexes containing rare earth ions (REI) and single-walled carbon nanotubes (SWNT) functionalized with single stranded DNA show promise to be utilized for the optical sensing of bio-molecules [1]. However, the electromagnetic interactions between the SWNT and the REI have not been sufficiently studied. In this work, we focus on the plasmonic interaction between the SWNT and a REI such as Terbium or Europium for their use as a biosensing complex. The SWNT may act as a plasmonic antenna and generate a local field in the vicinity of the REI. We use the transmission line model [2] to model the plasmonic properties of the SWNT antenna. The incoming light induces a surface current distribution: I(z)=(V0/Zc)sinh[γp(l/2-|z|)] where V0 is the input voltage into the transmission line model determined by the applied electric field, Zc is the characteristic impedance of the SWNT which is approximately 12 kΩ, γp is the plasmon propogation constant, and l is the length of the tube which we take to be 1 μm. We estimate a field enhancement factor of approximately 106in the near field given by: F=ωl(LC/2)1/2/(k2r2) where L is the kinetic inductance of the SWNT, C is the total capacitance including both electrostatic and quantum capacitances, r is the radial distance between the SWNT axis and the REI, and k and ω are the wavevector and frequency of the incoming light, respectively. The electromagnetic fields will be calculated using the electric Hertz potential satisfying the Helmholtz equation with proper boundary conditions. The conductivity of the SWNT antenna in the transmission line model is given by: σ=iωL-1/(ω2+iωL-1R-C-1L-1 γp 2) where R is the resistance of the SWNT. The interaction of these calculated plasmonic fields with the REI will modulate the lifetimes of the REI. The modulated lifetimes of an electric dipole emitter will be calculated to model the allowed optical transitions of the particular REI. To include the modulations of the optically dark REI transitions, a magnetic dipole emitter will be used. To conclude, these results will give a better understanding of the near field electromagnetic interactions that take place in complexes containing SWNTs and REIs and allow for more efficient sensors. Acknowledgement: This work was supported by: NSF ECCS-1202398

Scattering matrix analysis for evaluating the photocurrent in hydrogenated-amorphous-silicon-based thin film solar cells.

A scattering matrix (S-matrix) analysis method was developed for evaluating hydrogenated amorphous silicon (a-Si:H)-based thin film solar cells. In this approach, light wave vectors A and B represent the incoming and outgoing behaviors of the incident solar light, respectively, in terms of coherent wave and incoherent intensity components. The S-matrix determines the relation between A and B according to optical effects such as reflection and transmission, as described by the Fresnel equations, scattering at the boundary surfaces, or scattering within the propagation medium, as described by the Beer-Lambert law and the change in the phase of the propagating light wave. This matrix can be used to evaluate the behavior of angle-incident coherent and incoherent light simultaneously, and takes into account not only the light scattering process at material boundaries (haze effects) but also nonlinear optical processes within the material. The optical parameters in the S-matrix were determined by modeling both a 2%-gallium-doped zinc oxide transparent conducting oxide and germanium-compounded a-Si:H (a-SiGe:H). Using the S-matrix equations, the photocurrent for an a-Si:H/a-SiGe:H tandem cell and the optical loss in semitransparent a-Si:H solar cells for use in building-integrated photovoltaic applications were analyzed. The developed S-matrix method can also be used as a general analysis tool for various thin film solar cells.

Anisotropy of the Linear Magnetic Birefridence of Europium Iron Garnet

The results of investigation of magnetic linear birefringence (MLB) and magnetic linear dichroism (MLD) of Eu3Fe5O12 (EuIG) iron garnet on 7F07F6 optical transitions upon variation of the directions of the magnetization vector I relative to the electric vector E linearly polarized light that propagates through single crystal iron garnets are presented. The measurements were made on Eu3Fe5O12 single-crystal samples in the form of plates 100 μm thick cut in the (110) and (100) plane at the temperatures T = 82 and in a magnetic field H= 25 kOe. The absorption spectra of the linearly polarized light were studied. It is shown that MLB and dichroism in the region of the 7F07F6 absorption band reach values 10-3. First experimentally discovered nonreciprocity of MLB spectra and dichroism with the change of the relative orientation of the magnetization vector I and the light wave vector. This effect may use as a base for the design of the different transducers, for example, magnetooptical optical channels commutator.

Specific Futures of Optical Anisotropy in Terbium Iron and Terbium Gallium Garnets

We reported magnetooptical properties of Tb3+ in single crystals of Tb3Fe5O12 and Tb3Ga5O12 for ion occupying sites of D2 symmetry in the garnets structure. It is shown that in the employed Voigt geometry the magnetic linear birefringence and the dichroism reach values 10-4, and have a strong dependence on the wavelength and a strong anisotropy. The absorption spectra were obtained at temperatures of 30K, 100K using magnetic field up to 25 kOe applied parallel and perpendiculare to the electric vector E linearly polarized light on the 7F67F0 and 7F67F1 optical transitions region. The aim of this research was revealing of a role of contributions of exchange interaction and a crystal field in splitting of energy levels of the basic condition 7F6 ion Tb3+ multiplet in Tb ferrite-garnet by studying of character of spectra magnetic linear dichroism (MLD) paramagnetic and ferrimagnetic crystals placed in an external magnetic field. More over, the assumption about nonreciprocity of magnetic linear birefringence (MLB) spectra and dichroism with the change of the relative orientation of the magnetization vector I and the light wave vector has been experimentally confirmed. This effect may use as a base for the design of the different transducers, for example, magnetooptical optical channels commutator.

Specific Features of ${\hbox{Tb}}{^{3+}}$ Magnetooptics in Terbium Iron and Terbium Gallium Garnets (${\hbox{Tb}}_{3}{\hbox{Fe}}_{5}{{\hbox{O}}_{12}}$ and ${\hbox{Tb}}_{3}{\rm Ga}_{5}{{\hbox{O}}_{12}}$)

We reported magnetooptical properties of Tb3+ in single crystals of Tb3Fe5O12 and Tb3Ga5O12 for ion occupying sites of D2 symmetry in the garnets structure. It is shown that in the employed Voigt geometry the magnetic linear birefringence and the dichroism reach values 10-4, and have a strong dependence on the wavelength and a strong anisotropy. The absorption spectra were obtained at temperatures of 30 K, 82 K, 100 K using magnetic field up to 25 kOe applied parallel and perpendicular to the electric vector E linearly polarized light on the 7F6-7F0 and 7F6-7F1 optical transitions region. The aim of this research was revealing of a role of contributions of exchange interaction and a crystal field in splitting of energy levels of the basic condition 7F6 ion Tb3+ multiplet in Tb ferrite-garnet by studying of character of spectra of magnetic linear dichroism (MLD) paramagnetic and ferrimagnetic crystals placed in an external magnetic field. Moreover, the assumption about nonreciprocity of magnetic linear birefringence (MLB) spectra and dichroism with the change of the relative orientation of the magnetization vector I and the light wave vector has been experimentally confirmed. This effect may be used as a base for the design of the different transducers, for example, magnetooptical optical channels commutator.

Second-harmonic generation spectroscopy of excitons in ZnO

Nonlinear optics of semiconductors is an important field of fundamental and applied research, but surprisingly the role of excitons in the coherent processes leading to harmonics generation has remained essentially unexplored. Here we report results of a comprehensive experimental and theoretical study of the three-photon process of optical second-harmonic generation (SHG) involving the exciton resonances of the noncentrosymmetric hexagonal wide-band-gap semiconductor ZnO in the photon energy range of $3.2$--$3.5$ eV. Resonant crystallographic SHG is observed for the $1s(A,B)$, $2s(A,B)$, $2p(A,B)$, and $1s(C)$ excitons. We show that SHG signals at these exciton resonances are induced by the application of a magnetic field when the incident and the SHG light wave vectors are along the crystal $z$ axis where the crystallographic SHG response vanishes. A microscopic theory of SHG through excitons is developed, which shows that the nonlinear interaction of coherent light with excitons has to be considered beyond the electric-dipole approximation. Depending on the particular symmetry of the exciton states SHG can originate from the electric- and magnetic-field-induced perturbations of the excitons due to the Stark effect, the spin as well as orbital Zeeman effects, or the magneto-Stark effect. The importance of each mechanism is analyzed and discussed by confronting experimental data and theoretical results for the dependences of the SHG signals on photon energy, magnetic field, electric field, crystal temperature, and light polarization. Good agreement is obtained between experiment and theory proving the validity of our approach to the complex problem of nonlinear interaction of light with ZnO excitons. This general approach can be applied also to other semiconductors.

Manipulation of ferromagnets via the spin-selective optical Stark effect

We investigate the non-resonant all-optical switching of magnetization. We treat the inverse Faraday effect (IFE) theoretically in terms of the spin-selective optical Stark effect for linearly or circularly polarized light. In the dilute magnetic semiconductors (Ga,Mn)As, strong laser pulses below the band gap induce effective magnetic fields of several teslas in a direction which depends on the magnetization and light wave vectors. Our theory demonstrates that the polarized light catalyzes the angular momentum transfer between lattice and the magnetization.

Features of optical anisotropy of europium and terbium iron garnets

The results of investigation of magnetic linear birefringence (MLB) and magnetic linear dichroism of Tb3Fe5O12 (TbIG) iron garnet (IG) on 7F6–7F0 and 7F6–7F1 optical transitions and Eu3Fe5O12 (EuIG) iron garnet on 7F0–7F6 at the variation of the directions of the magnetization vector I relative to the electric vector E linearly polarized light that propagates through single crystal iron garnets are presented. The measurements were made on Tb3Fe5О12 and Eu3Fe5O12 single-crystal samples in the form of plates 100μm thick cut in the (110) and (100) plane a temperature of T=82K and in a magnetic field H=22kOe. The absorption spectra of the linearly polarized light were studied. It is shown that MLB and dichroism in the region of the 7F6–7F0 and 7F0–7F6 absorption bands reach values 10−3. The nonreciprocity of MLB spectra and dichroism with the change of the relative orientation of the magnetization vector I and the light wave vector is first experimentally discovered. This effect may be used as a base for the design of the different transducers such as a magnetooptical optical channels commutator.

Faraday rotation and circular dichroism spectra of gold and silver nanoparticle aggregates

We study the magneto-optical response of noble metal nanoparticle clusters. We consider the interaction between the light-induced dipoles of particles. In the presence of a magnetic field, the simplest achiral cluster, a dimer, exhibits circular dichroism (CD). The CD of a dimer depends on the directions of the magnetic field and the light wave vector. The CD of a populous cluster weakly depends on the magnetic field. Upon scattering from the cluster, an incident linearly polarized light with polarization azimuth $\ensuremath{\varphi}$ becomes elliptically polarized. The polarization azimuth rotation and ellipticity angle variation are sinusoidal functions of $2\ensuremath{\varphi}$. The anisotropy and the chirality of the cluster control the amplitude and offset of these sinusoidal functions. The Faraday rotation and Faraday ellipticity are also sinusoidal functions of $2\ensuremath{\varphi}$. Near the surface plasmon frequency, Faraday rotation and Faraday ellipticity increase.

Deep-subwavelength imaging of the modal dispersion of light

Numerous optical technologies and quantum optical devices rely on the controlled coupling of a local emitter to its photonic environment, which is governed by the local density of optical states (LDOS). Although precise knowledge of the LDOS is crucial, classical optical techniques fail to measure it in all of its frequency and spatial components. Here, we use a scanning electron beam as a point source to probe the LDOS. Through angular and spectral detection of the electron-induced light emission, we spatially and spectrally resolve the light wave vector and determine the LDOS of Bloch modes in a photonic crystal membrane at an unprecedented deep-subwavelength resolution (30-40 nm) over a large spectral range. We present a first look inside photonic crystal cavities revealing subwavelength details of the resonant modes. Our results provide direct guidelines for the optimum location of emitters to control their emission, and key fundamental insights into light-matter coupling at the nanoscale.

Light scattering from a magnetically tunable dense random medium with dissipation: ferrofluid

We present a semi-phenomenological treatment of light transmission through and its reflection from a ferrofluid, which we regard as a magnetically tunable system of dense random dielectric scatterers with weak dissipation. Partial spatial ordering is introduced by the application of a transverse magnetic field that superimposes a periodic modulation on the dielectric randomess. This introduces Bragg scattering which effectively enhances the scattering due to disorder alone, and thus reduces the elastic mean free path towards Anderson localization. Our theoretical treatment, based on invariant imbedding, gives a simultaneous decrease of transmission and reflection without change of incident linear polarisation as the spatial order is tuned magnetically to the Bragg condition, namely the light wave vector being equal to half the Bragg vector (Q). Our experimental observations are in qualitative agreement with these results. We have also given expressions for the transit (sojourn) time of light and for the light energy stored in the random medium under steady illumination. The ferrofluid thus provides an interesting physical realization of effectively a "Lossy Anderson-Bragg" (LAB) cavity with which to study the effect of the interplay of spatial disorder, partial order and weak dissipation on light transport. Given the current interest in propagation, optical limiting and storage of light in ferrofluids, the present work seems topical.

Silver clusters insert into polymer solar cell for enhancing light absorption

As an employment of surface plasmonic effect, the consequence of insertion of a layer of Ag clusters into polymer solar cell on the enhancement of light absorption and power conversion efficiency is investigated. Optical analysis based on the finite-difference time-domain (FDTD) is performed with experiments to evaluate the effect of the interaction between the Ag clusters and incident light on light absorption in polymer solar cell. Ag clusters modify the light wave vector and the electromagnetic field inside the device is redistributed and enhanced. As a result, polymer solar cells achieve an overall increase in absorption, short-circuit current density, and power conversion efficiency.

Novel coherent two-dimensional optical spectroscopy probes of chirality exchange and fluctuations in molecules

We demonstrate how stochastic transitions between molecular configurations with opposite senses of chirality may be probed by 2D optical signals with specific pulse polarization configurations. The third-order optical response of molecular dimers (such as biphenyls) with dynamical axial chirality is calculated to order of k(2) in the wavevector of light. Spectroscopic signatures of equilibrium chirality fluctuations are predicted for three dynamical models (Ornstein-Uhlenbeck, two-state jump, and diffusion in double well) of the dihedral angle that controls the chirality.

Wave-coupling theory of linear electro-optic effect for ultrashort laser pulses

A wave-coupling theory of linear electro-optic (EO) effect for ultrashort laser pulses has been developed. As one of its applications, the linear EO effect of ultrashort Gaussian pulses propagating in LiNbO3 crystal is demonstrated, with the intensity lower than the damage threshold. It is found that the EO effect is sensitive to both the azimuth angle and the polar angle of wave vector of light. And the larger the applied electric field, the shorter the crystal used for optimization of EO coupling is. The numerical results show that, with the duration of input pulse changing from 150 fs to 5 fs, the durations of output pulses are broadened due to the group-velocity dispersion, as well as the first- and second-order refractive dispersion. In addition, when input pulse duration is larger than 20 fs, in contrast with zero chirp, the output durations can be slightly compressed if a positive chirp input pulse is used. The validities of slowly varying amplitude approximation and continuous wave approximation are also discussed. The influence of self-phase modulation and cross-phase modulation on the EO effect is also discussed briefly.

Excitonic fine structure of out-of-plane nitrogen dyads in GaAs

We report on the excitonic photoluminescence from a nitrogen dyad of C 2v symmetry located in a plane parallel to the emitted light wavevector (out-of-plane). We determine that the spectral signature of out-of-plane dyads is composed of five transitions linearly polarized along [1 0 0] or [0 1 0]. A sixth transition is in principle allowed but could not be observed due to its relatively low oscillator strength. However, a perturbation in the close vicinity of a dyad can significantly influence the fine structure and the polarization sequence of the emission and can bring out this sixth transition.