Polariton Dispersion Research Articles

Bandgaps properties of Ⅲ-phosphides (BP, AlP, GaP, InP) materials excited by ultrasonic

First bandgaps of Ⅲ-Phosphides (BP, AlP, GaP, InP) materials excited by ultrasonic is studied in the present paper, in which ultrasonic and terahertz wave collinear transmission is postulated. Numerical simulation results show that, frequencies range of lower polariton branches in polariton dispersion curves are determined by the transverse optical(TO)-phonon frequencies, phonon frequencies are determined by first-principles calculations. Under the acousto-optic interaction, band gaps of polariton dispersion curves are turned on, this leads to a dis-propagation of TO-phonon polariton in Ⅲ-Phosphides bulk. First bandgaps width and acousto-optic coupling strength are proportional with ultrasonic frequency and its intensity. With the increase of ultrasonic frequency, frequencies of bandgaps are blue-shifted, the bandgaps converge to the restrahlen band infinitely with frequency of ultrasonic exceeding over effective value. As is show above, relevant technology may be available in tunable THz frequency selection and filtering.

Temperature-Dependent Refractive Index of Quartz at Terahertz Frequencies

Characterisation of materials often requires the use of a substrate to support the sample being investigated. For optical characterisation at terahertz frequencies, quartz is commonly used owing to its high transmission and low absorption at these frequencies. Knowledge of the complex refractive index of quartz is required for analysis of time-domain terahertz spectroscopy and optical pump terahertz probe spectroscopy for samples on a quartz substrate. Here, we present the refractive index and extinction coefficient for α-quartz between 0.5 THz and 5.5 THz (17–183 cm− 1) taken at 10, 40, 80, 120, 160, 200 and 300 K. Quartz shows excellent transmission and is thus an ideal optical substrate over the THz band, apart from the region 3.9 ± 0.1 THz owing to a spectral feature originating from the lowest energy optical phonon modes. We also present the experimentally measured polariton dispersion of α-quartz over this frequency range.

Broadband phonon-polariton dispersion relation of ferroelectric LiTaO3 crystals

Lithium tantalate is a well-known optical crystal. The dispersion relation of phonon-polaritons was studied in ferroelectric lithium tantalate crystals. The reflectivity spectra of E//x and E//z polarizations, which are related to E(x,y) and A1(z) symmetry modes respectively, were measured by the FT-IR measurement in the far- and mid-IR regions. The dispersion relation of phonon-polariton frequency against real and imaginary parts of polariton wavevector was determined. E(x,y) and A1(z) symmetry polariton modes were also studied by forward Raman scattering. By the combination with the observed polariton dispersion relation determined by forward Raman scattering and terahertz time-domain spectroscopy, the broadband polariton frequency dispersion was determined between 10 cm−1 and 1200 cm−1.

Surface Plasmon Coupling in GaN:Eu Light Emitters with Metal-Nitrides

Metal-nitrides of hafnium nitride (HfN), zirconium nitride (ZrN) and titanium nitride (TiN) are investigated as plasmonic materials to enhance the internal quantum efficiency of a GaN:Eu red light emitter. Theoretical calculations are performed to evaluate the surface plasmon polariton dispersion relation and Purcell enhancement factor for a single metal-nitride layer on top of the GaN:Eu emitter. Our findings suggest that among the metal-nitrides investigated in this study, TiN is the most promising candidate for use as plasmonic material to increase the internal quantum efficiency in GaN:Eu red light emitters.

Selective excitation and imaging of ultraslow phonon polaritons in thin hexagonal boron nitride crystals

We selectively excite and study two new types of phonon-polariton guided modes that are found in hexagonal boron nitride thin flakes on a gold substrate. Such modes show substantially improved confinement and a group velocity that is hundreds of times slower than the speed of light, thereby providing a new way to create slow light in the mid-infrared range with a simple structure that does not require nano-patterning. One mode is the fundamental mode in the first Restrahlen band of hexagonal boron nitride thin crystals on a gold substrate; the other mode is equivalent to the second mode of the second Restrahlen band of hexagonal boron nitride flakes that are suspended in vacuum.The new modes also couple efficiently with incident light at the hexagonal boron nitride edges, as we demonstrate experimentally using photo-induced force microscopy and scanning near-field optical microscopy. The high confinement of these modes allows for Purcell factors that are on the order of tens of thousands directly above boron nitride and a wide band, with new perspectives for enhanced light-matter interaction. Our findings demonstrate a new approach to engineering the dispersion of polaritons in 2D materials to improve confinement and light-matter interaction, thereby paving the way for new applications in mid-infrared nano-optics.

Impact of temperature on exciton-cavity detuning and polariton relaxation kinetics in monolayer Tungsten Disulphide ([formula omitted]) based microcavity

Monolayer Tungsten Disulphide (WS2) with strongly confined 2D Wannier-Mott excitons exhibits a large binding energy and oscillator strength. This monolayer is currently emerging as a good candidate for studying strong light–matter coupling at high temperature. Here, we investigate the formation of exciton-polaritons in a monolayer WS2 based semiconductor microcavity under non-resonant excitation. Our results show that the cavity detuning changes from negative to positive values over a temperature range of 130–230 K, which allow the tuning of polariton dispersion. The Hopfield coefficient show that the Upper branch (UP) can be tuned from a more excitonlike (130 K), to a more photonlike (230 K) at small wave vector k. Thus, the UP states have a faster lifetime which enhances the relaxation mechanisms towards lower polariton (LP) states. A Rabi splitting of 40 meV is observed, which corresponds to energy of longitudinal optical (LO) phonon. To show how polaritons states are populated, we investigate a semiclassical model that treats the temporal dynamics of polaritons in which LO phonon-assisted polariton emission is taken into account. The results reveals that the UP occupation starts to decrease, for increasing the occupation factor in the LP branch.

Spatially resolved measurement of plasmon dispersion using Fourier-plane spectral imaging

We show that Fourier-plane imaging in conjunction with the Kretschmann-Raether configuration can be used for measuring polariton dispersion with spatial discrimination of the sample, over the whole visible spectral range. We demonstrate the functionality of our design on several architectures, including plasmonic waveguides, and show that our new design enables the measurement of plasmonic dispersion curves of spatially-inhomogeneous structures with features as small as 3{\mu}m, in a single shot.

Analysis of polariton dispersion in metal nanocomposite based novel superlattice system

Abstract The influence of metal nanoparticles in tuning the polaritonic gap in a novel piezoelectric superlattice is studied. Dielectric function of the metal nanoparticles is analyzed using Kawabata-Kubo effect and Drude’s theory. The effective dielectric function of the nanocomposite system is studied using Maxwell Garnett approximation. Nanocomposite based LiTaO 3 novel superlattice is formed by arranging the nanocomposite systems in such a way that their orientations are in the opposite direction. Hence there are two additional modes of propagation. The top most modes reflect the metal behavior of the nanoparticles. It is found that these modes of propagation vary with the filling factor. These additional modes of propagations can be exploited in the field of communication.

Vacuum Bloch–Siegert shift in Landau polaritons with ultra-high cooperativity

A two-level system resonantly interacting with an a.c. magnetic or electric field constitutes the physical basis of diverse phenomena and technologies. However, Schrodinger’s equation for this seemingly simple system can be solved exactly only under the rotating-wave approximation, which neglects the counter-rotating field component. When the a.c. field is sufficiently strong, this approximation fails, leading to a resonance-frequency shift known as the Bloch–Siegert shift. Here, we report the vacuum Bloch–Siegert shift, which is induced by the ultra-strong coupling of matter with the counter-rotating component of the vacuum fluctuation field in a cavity. Specifically, an ultra-high-mobility two-dimensional electron gas inside a high-Q terahertz cavity in a quantizing magnetic field revealed ultra-narrow Landau polaritons, which exhibited a vacuum Bloch–Siegert shift up to 40 GHz. This shift, clearly distinguishable from the photon-field self-interaction effect, represents a unique manifestation of a strong-field phenomenon without a strong field. The Bloch–Siegert shift—a strong-field phenomenon that implies a failure of the rotating-wave approximation—is observed in the polariton dispersion diagram of a two-dimensional electron gas system inside a high-Q terahertz photonic crystal cavity.

Observation of phonon-polaritons in thin flakes of hexagonal boron nitride on gold

Hexagonal Boron Nitride (hBN) is a layered van der Waals material able to sustain hyperbolic phonon-polaritons within its mid-infrared reststrahlen bands. We study the effect of a metallic substrate adjacent to hBN flakes on the polariton dispersion and on the standing wave patterns in nanostructures by means of mid-infrared nanospectroscopy and nanoimaging. We exploit the gold-coated tip apex for atomic force microscopy to launch polaritons in thin hBN flakes. The photo-thermal induced mechanical resonance is used to detect the amplitude profile of polariton standing waves with a lateral resolution of 30 nm. We observe the polariton excitation spectra on hBN flakes as thin as 4 nm, thanks to the infrared field enhancement in the nanogap between the gold-coated tip apex and an ultraflat gold substrate. The data indicate no major effect of remote screening of the free electrons in gold on the phonon-polariton excitation that appears robust also against geometrical imperfections.

The Exciton–Polariton Dispersion Law under the Action of Strong Pumping in the Region of the M-Band of Luminescence

The double-pulse interaction with excitons and biexcitons in semiconductors is studied theoretically. It is shown that the dispersion law of carrier wave has three branches under the action of a powerful pumping in the region of the M-band of luminescence. Values of parameters at which the dispersion law branches can intersect due to the degeneration of the exciton level energy have been found. The effect of a significant change in the force of coupling between the exciton and photon of a weak pulse with a change in the pumping intensity is predicted.

Controlling Level Splitting by Strong Coupling of Surface Plasmon Resonances with Rhodamine-6G on a Gold Grating

Strongly coupled system is known to pose challenges, particularly those involving multitude of levels as in molecules. Surface plasmons offer intense and localized electromagnetic fields, wherein molecules placed in such environment exhibit generic features of strongly coupled system. We demonstrate the control over the splitting of surface plasmon polaritons dispersion branches in strong coupling regime within the absorption and fluorescence bands of Rhodamine-6G molecules placed on top of gold grating structures. The enhanced electromagnetic near-fields of surface plasmon polaritons excited on top of gold gratings have been calculated by numerical simulation and various aspects related to the coupling have been captured by modelling the Rhodamine-6G molecule as a theoretical three level Λ–system which support the experimentally observed variation in splitting with varying periods of gratings. The plasmonically enhanced electromagnetic field plays the role of a control field applied across one leg of the Λ–system. Experimentally measured spectral features, including level splitting and dispersions of the strongly coupled system of molecule-gold grating are consistently described by the model for a variety of samples, with different periodicities, different molecule-grating separations obtained through a dielectric spacer layer, and coupling to higher order diffraction modes of the grating.

Ultrafast Dynamics of Polariton Cooling and Renormalization in an Organic Single-Crystal Microcavity under Nonresonant Pumping

Microcavity systems with organic luminescent materials have a hot prospect for room-temperature cavity-polariton devices. The polariton dispersion relation of organic microcavities is significantly different from that of inorganic microcavities due to the strong localization of Frenkel excitons. Also photoexcited particles will undergo a different cooling mechanism until they reach the polariton ground state. In the characterization of efficient polariton condensates, therefore, the polariton cooling dynamics as well as the kinetics of the polariton eigenstate should be measured. Here we present experimental studies on ultrafast dynamics of cavity polaritons in an organic single-crystal microcavity under nonresonant pumping. In time-resolved photoluminescence measurements we observed, for the first time, an ultrafast dynamics of stimulated cooling of the organic cavity polariton. Transient transmission measurement enabled us to investigate the detailed renormalization dynamics of the polariton eigenstate....

Controlling terahertz surface plasmon polaritons in Dirac semimetal sheets

We theoretically investigate the dispersion and coupling characteristics of terahertz surface plasmons polaritons (SPPs) in bulk Dirac semimetals (BDS) sheets, which indicate that symmetric and anti-symmetric modes are attributed to the odd and even superpositions of the anti-symmetric eigenmode supported by the single-layer BDS sheet. Interestingly, the symmetric mode has better confinement than the eigenmode and anti-symmetric mode. By introducing two silicon bars, the highly-confined symmetric mode is modulated in resonance frequency and transmission intensity by the designed novel band-pass filter. Numerical results show good agreement with the theoretical analysis based on the coupled mode theory and the Fabry-Perot resonance theory. The developed Dirac semimetal plasmonic structures pave the way to the development of novel THz active devices for light modulation platform.

Photonic-crystal exciton-polaritons in monolayer semiconductors

Semiconductor microcavity polaritons, formed via strong exciton-photon coupling, provide a quantum many-body system on a chip, featuring rich physics phenomena for better photonic technology. However, conventional polariton cavities are bulky, difficult to integrate, and inflexible for mode control, especially for room-temperature materials. Here we demonstrate sub-wavelength-thick, one-dimensional photonic crystals as a designable, compact, and practical platform for strong coupling with atomically thin van der Waals crystals. Polariton dispersions and mode anti-crossings are measured up to room temperature. Non-radiative decay to dark excitons is suppressed due to polariton enhancement of the radiative decay. Unusual features, including highly anisotropic dispersions and adjustable Fano resonances in reflectance, may facilitate high temperature polariton condensation in variable dimensions. Combining slab photonic crystals and van der Waals crystals in the strong coupling regime allows unprecedented engineering flexibility for exploring novel polariton phenomena and device concepts.

Tuning the dispersion of effective surface plasmon polaritons with multilayer systems.

Recently, effective surface plasmon polaritons (ESPPs) induced by structural dispersion in bounded waveguides were theoretically demonstrated and experimentally verified. Despite the theoretical and experimental efforts, whether ESPPs can mimic real SPPs in every aspect still remains an open question. In this work, we go one step further to study the hybridization of ESPPs in multilayer systems. We consider transverse electric (TE) modes in a conventional rectangular waveguide and a parallel-plate waveguide (PPW) and derive analytically the dispersion relations and asymptotic frequencies of the corresponding ESPPs modes in sandwiched structures consisting of alternating dielectrics of different permittivities. Our results show that the ESPPs can be categorized into odd and even parities (owing to the 'plasmon' hybridization) in a similar way as natural SPPs supported by the insulator/metal/insulator (IMI) and metal/insulator/metal (MIM) heterostructures in the optical regime. The similarities and differences between ESSPs and their optical counterparts are also discussed in details, which may provide valuable guidance for future application of ESPPs at the microwave and terahertz frequencies.

Surface polaritons in grating composed of left-handed materials

In this work, we developed a unique mathematical model to solve dispersion relation for surface polaritons (SPs) in artificial composite materials grating. Here, we have taken two types of materials for analysis. In the first case, the grating composed of epsilon-negative (ENG) material and air interface. In second case, grating composed of left-handed materials (LHMs) and ENG medium interface is considered. The dispersion curves of both p and s polarized SPs modes are obtained analytically. In the case of ENG grating and air interface, polaritons dispersion curves exist for p-polarization only, whereas for LHM grating and ENG medium interface, the polaritons dispersion curves for both p and s polarization are observed.

Tunable terahertz reflection spectrum based on band gaps of GaP materials excited by ultrasonic

Tunable terahertz (THz) reflection spectrum, ranged from 0.2 to 8 THz, in band gaps of gallium phosphide (GaP) materials excited by ultrasonic is investigated in the present paper, in which tunable ultrasonic and terahertz wave collinear transmission in the same direction is postulated. Numerical simulation results show that, under the acousto-optic interaction, band gaps of transverse optical phonon polariton dispersion curves are turned on, this leads to a dis-propagation of polariton in GaP bulk. On the other side, GaP material has less absorption to THz wave according to experimental studies, as indicates that THz wave could be reflected by the band gaps spontaneously. The band gaps width and acousto-optic coupling strength are proportional with ultrasonic frequency and its intensity in ultrasonic frequency range of 0–250 MHz, in which low-frequency branch of transverse optical phonon polariton dispersion curves demonstrate periodicity and folding as well as. With the increase of ultrasonic frequency, frequency of band gap is blue-shifted, and total reflectivity decreased with −1-order and −2-order reflectivity decrease. The band gaps converge to the restrahlen band infinitely with frequency of ultrasonic exceeding over 250 MHz, total reflectivity of which is attenuated. As is show above, reflection of THz wave can be accommodated by regulating the frequency and its intensity of ultrasonic frequency. Relevant technology may be available in tunable THz frequency selection and filtering.

Exciton-polaritons in cuprous oxide: Theory and comparison with experiment

The observation of giant Rydberg excitons in cuprous oxide $\left(\mathrm{Cu_{2}O}\right)$ up to a principal quantum number of $n=25$ by T.~Kazimierczuk \emph{et al.} [Nature \textbf{514}, 343, (2014)] inevitably raises the question whether these quasi-particles must be described within a multi-polariton framework since excitons and photons are always coupled in the solid. In this paper we present the theory of exciton-polaritons in $\mathrm{Cu_{2}O}$. To this end we extend the Hamiltonian which includes the complete valence band structure, the exchange interaction, and the central-cell corrections effects, and which has been recently deduced by F.~Schweiner \emph{et al.} [Phys.~Rev.~B \textbf{95}, 195201, (2017)], for finite values of the exciton momentum $\hbar K$. We derive formulas to calculate not only dipole but also quadrupole oscillator strengths when using the complete basis of F.~Schweiner \emph{et al.}. Very complex polariton spectra for the three orientations of $\boldsymbol{K}$ along the axes $[001]$, $[110]$, and $[111]$ of high symmetry are obtained and a strong mixing of exciton states is reported. The main focus is on the $1S$ ortho exciton-polariton, for which pronounced polariton effects have been measured in experiments. We set up a $5\times 5$ matrix model, which accounts for both the polariton effect and the $K$-dependent splitting, and which allows treating the anisotropic polariton dispersion for any direction of $\boldsymbol{K}$. We especially discuss the dispersions for $\boldsymbol{K}$ being oriented in the planes perpendicular to $[1\bar{1}0]$ and $[111]$, for which experimental transmission spectra have been measured. Furthermore, we compare our results with experimental values of the $K$-dependent splitting, the group velocity, and the oscillator strengths of this exciton-polariton.

Backward Cherenkov radiation emitted by polariton solitons in a microcavity wire

Exciton-polaritons in semiconductor microcavities form a highly nonlinear platform to study a variety of effects interfacing optical, condensed matter, quantum and statistical physics. We show that the complex polariton patterns generated by picosecond pulses in microcavity wire waveguides can be understood as the Cherenkov radiation emitted by bright polariton solitons, which is enabled by the unique microcavity polariton dispersion, which has momentum intervals with positive and negative group velocities. Unlike in optical fibres and semiconductor waveguides, we observe that the microcavity wire Cherenkov radiation is predominantly emitted with negative group velocity and therefore propagates backwards relative to the propagation direction of the emitting soliton. We have developed a theory of the microcavity wire polariton solitons and of their Cherenkov radiation and conducted a series of experiments, where we have measured polariton-soliton pulse compression, pulse breaking and emission of the backward Cherenkov radiation.