Group Refractive Index Research Articles

Mass-polariton theory of light in dispersive media

We have recently shown that the electromagnetic pulse in a medium is made of mass-polariton (MP) quasiparticles, which are quantized coupled states of the field and an atomic mass density wave (MDW) [M. Partanen et al., Phys. Rev. A 95, 063850 (2017)]. In this work, we generalize the MP theory of light for dispersive media assuming that absorption and scattering losses are very small. Following our previous work, we present two different approaches to the coupled state of light: (1) the MP quasiparticle theory, which is derived by only using the fundamental conservation laws and the Lorentz transformation; (2) the classical optoelastic continuum dynamics (OCD), which is a generalization of the electrodynamics of continuous media to include the dynamics of the medium under the influence of optical forces. We show that the total momentum and the transferred mass of the light pulse can be determined in a straightforward way if we know the field energy of the pulse and the dispersion relation of the medium. In analogy to the nondispersive case, we also find unambiguous correspondence between the MP and OCD theories. For the coupled MP state of a single photon and the medium, we obtain the total MP momentum ${p}_{\mathrm{MP}}={n}_{\mathrm{p}}\ensuremath{\hbar}\ensuremath{\omega}/c$, where ${n}_{\mathrm{p}}$ is the phase refractive index. The field's share of the MP momentum is equal to ${p}_{\mathrm{field}}=\ensuremath{\hbar}\ensuremath{\omega}/({n}_{\mathrm{g}}c)$, where ${n}_{\mathrm{g}}$ is the group refractive index and the share of the MDW is equal to ${p}_{\mathrm{MDW}}={p}_{\mathrm{MP}}\ensuremath{-}{p}_{\mathrm{field}}$. Thus, as in a nondispersive medium, the total momentum of the MP is equal to the Minkowski momentum and the field's share of the momentum is equal to the Abraham momentum. We also show that the correspondence between the MP and OCD models and the conservation of momentum at interfaces gives an unambiguous formula for the optical force. The dynamics of the light pulse and the related MDW lead to nonequilibrium of the medium and to relaxation of the atomic density by sound waves in the same way as for nondispersive media. We also carry out simulations for optimal measurements of atomic displacements related to the MDW in silicon. In the simulations, we consider different waveguide cross sections and optical pulse widths and account for the breakdown threshold irradiance of materials. We also compare the MP theory to previous theories of the momentum of light in a dispersive medium. We show that our generalized MP theory resolves all the problems related to the Abraham-Minkowski dilemma in a dispersive medium.

Why material slow light does not improve cavity-enhanced atom detection

We discuss the prospects for enhancing absorption and scattering of light from a weakly coupled atom in a high-finesse optical cavity by adding a medium with large, positive group index of refraction. The slow-light effect is known to narrow the cavity transmission spectrum and increase the photon lifetime, but the quality factor of the cavity may not be increased in a metrologically useful sense. Specifically, detection of the weakly coupled atom through either cavity ringdown measurements or the Purcell effect fails to improve with the addition of material slow light. A single-atom model of the dispersive medium helps elucidate why this is the case.

Electromagnetically Induced Transparency in an All-Dielectric Metamaterial-Waveguide With Large Group Index

We investigate numerically an analog of electromagnetically induced transparency (EIT) in an all-dielectric metamaterial-waveguide (ADMW) that consists of a two-dimensional silicon rod array on quartz slab waveguide. The EIT-like response is achieved by the destructive interference between a broad magnetic resonance and a narrow guide mode resonance. By tailoring the guided mode through the thickness of the slab waveguide or the lattice period of the metamaterial, an EIT-like transmission window is achieved with both high Q-factor (>104) and high transmission (>94%). And the group refractive index at the EIT-like resonance of the ADMW can be up to several thousands. These results demonstrate that the proposed ADMW has potential applications in low-loss slow-light based devices, bio-chemical sensing, and optical modulations.

Generation of broadband terahertz pulses via optical rectification in a chalcopyrite CdSiP2 crystal.

We report on the generation of broadband (0.07-6THz) terahertz (THz) radiation via optical rectification in a ⟨110⟩ CdSiP2 (CSP) crystal pumped by a 50fs, 780nm central wavelength optical pulse. By measuring the THz phase refractive index and the optical pump group refractive index, good phase matching can be achieved for a crystal thickness ≲200 μm. Due to this crystal's high second order nonlinearity and low absorption losses, it is envisioned that THz generation from CSP could be further enhanced by confining the optical pump pulse to sub-wavelength waveguides.

Polarization independent and tunable plasmonic structure for mimicking electromagnetically induced transparency in the reflectance spectrum

This paper proposes a plasmonic metamaterial that is able to mimic electromagnetically induced transparency in the reflectance spectrum within the GHz frequency range. Each meta-atom consists of a cross-slot structure as the bright resonator positioned on one side of the FR-4 substrate, and four spiral structures as the dark resonator located on the opposite side. Free space experimental results demonstrate that at normal incidence of plane wave, the metamaterial possesses the properties of tunability and polarization independence. In addition, based on simulation results the metamaterial also possesses slow wave property, with group refractive index of 56; and refractive-index-based sensing capability, with figure of merit of 6.1. In the strong coupling configuration, the plasma frequency and coupling constant of the metamaterial were calculated to be approximately 5.4 × 1010 rad s−1 and 9.8 × 109 rad s−1 respectively. While the respective damping constants of the bright resonator and dark resonator were calculated to be approximately 4.6 × 1010 rad s−1 and 1.9 × 1010 rad s−1.

High Resolution Optical Frequency Domain Reflectometry for Analyzing Intra-Chip Reflections

We present a method for high-resolution optical frequency domain reflectometry by de-embedding group-velocity dispersion in the device under test. The method is shown to provide an accurate estimation of the wavelength-dependent group refractive index, and provides a spatial resolution of 5.3 ± 1.7 μm for intra-chip reflections. We applied this method to characterize localized reflections from a number of waveguide crossings. The minimum distance of 30 μm between two crossings could easily be resolved. The reflection of waveguide crossings was analyzed to be (2.5 ± 1.2)·10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> .

Advanced analysis of domain walls in Mg doped LiNbO_3 crystals with high resolution OCT

The structure of domain walls (DW) in ferroelectric media is of great interest as this material is used for frequency doublers and other applications. We show that the structure of the DWs can nicely be visualized by high resolution optical coherence tomography (OCT). While the high group refractive index of lithium niobate allows a resolution much better than 1 µm, the large dispersion can blur the image and has to be compensated. Therefore, we developed an adaptive dispersion compensation algorithm based on maximizing the intensity of the DWs. By measuring a group of DWs, the mean period of the DWs could be measured with an accuracy of less than 10 nm differentiating samples with only 30 nm distinct periods. By analyzing the peak position, amplitude and phase shift within a DW, we were able to determine steps in the DW of only 50 nm. Furthermore, the inclined course of the DWs in a fan-shaped frequency doubler could be displayed. Therefore, we conclude that OCT is able to provide valuable information about the structure of domain walls in periodically poled lithium niobate (PPLN).

MODELLING of a two-dimensional photonic crystal with line defect for a laser gas sensor application

Abstract We present the results of a numerical analysis of a two-dimensional photonic crystal with line defect for a laser gas sensor working in a slow light regime. The geometrical parameters of photonic crystals with three different line defects were numerically analyzed: a missing row of holes, a row of holes with changed diameter and air channel. Antireflection sections were also analyzed. The simulations were carried out by MEEP and MPB programs, with the aim to get the values of a group refractive index, transmission and a light-gas overlap as high as possible. The effective refractive index method was used to reduce the simulation time and required computing power. We also described numerical simulation details such as required conditions to work in the slow light regime and the analyzed parameters values’ dependency of the simulation resolution that may influence the accuracy of the results.

Frequency comb calibrated frequency-sweeping interferometry for absolute group refractive index measurement of air.

The absolute group refractive index of air at 194061.02GHz is measured in real time using frequency-sweeping interferometry calibrated by an optical frequency comb. The group refractive index of air is calculated from the calibration peaks of the laser frequency variation and the interference signal of the two beams passing through the inner and outer regions of a vacuum cell when the frequency of a tunable external cavity diode laser is scanned. We continuously measure the refractive index of air for 2h, which shows that the difference between measured results and Ciddor's equation is less than 9.6×10-8, and the standard deviation of that difference is 5.9×10-8. The relative uncertainty of the measured refractive index of air is estimated to be 8.6×10-8. The data update rate is 0.2Hz, making it applicable under conditions in which air refractive index fluctuates fast.

Straightforward retrieval of dispersion in a dense atomic vapor helped by buffer gas-assisted radiation channeling

Strong enhancement of group refractive index in a dense buffered atomic vapor is recorded using a technique of reflection from a low-finesse Fabry–Perot cavity filled with dense atomic vapor allowing the retrieval of a dispersion curve for the hyperfine structure of Rb D2 line buffered by a high-density Cs vapor. Oscillations of the recorded signal resulting from interference of beams reflected from the front and rear windows of the cell appearing with the laser frequency scanning across the resonance allow easy reconstruction of the dispersion curve. Contribution from concomitant interconnected processes, in particular, the determinative role of radiation channeling in enhancement of the resonator Q-factor, is analyzed.

Phase-resolved pulse propagation through metallic photonic crystal slabs: plasmonic slow light.

We characterized the electromagnetic field of ultra-short laser pulses after propagation through metallic photonic crystal structures featuring photonic and plasmonic resonances. The complete pulse information, i.e. the envelope and phase of the electromagnetic field, was measured using the technique of cross-correlation frequency resolved optical gating. In good agreement, measurements and scattering matrix simulations show a dispersive behaviour of the spectral phase at the position of the resonances. Asymmetric Fano-type resonances go along with asymmetric phase characteristics. Furthermore, the spectral phase is used to calculate the dispersion of the sample and possible applications in dispersion compensation are investigated. Group refractive indices of 700 and 70 and group delay dispersion values of 90 000 fs2 and 5000 fs2 are achieved in transverse electric and transverse magnetic polarization, respectively. The behaviour of extinction and spectral phase can be understood from an intuitive model using the complex transmission amplitude. An associated depiction in the complex plane is a useful approach in this context. This method promises to be valuable also in photonic crystal and filter design, for example, with regards to the symmetrization of the resonances.This article is part of the themed issue 'New horizons for nanophotonics'.

Beyond the effective mass approximation: A predictive theory of the nonlinear optical response of conduction electrons

We present an experimental and computational study of the nonlinear optical response of conduction electrons to intense terahertz (THz) electric field. Our observations (saturable absorption and an amplitude-dependent group refractive index) can be understood on the qualitative level as the breakdown of the effective mass approximation. However, a predictive theoretical description of the nonlinearity has been missing. We propose a model based on the semiclassical electron dynamics, a realistic band structure, and the free electron Drude parameters to accurately calculate the experimental observables in InSb. Our results open a path to predictive modeling of the conduction-electron optical nonlinearity in semiconductors, metamaterials, as well as high-field effects in THz plasmonics.

Simultaneous interferometric measurement of the absolute thickness and surface shape of a transparent plate using wavelength tuning Fourier analysis and phase shifting

The absolute optical thickness and surface shape of optical devices are considered as the fundamental characteristics when designing optical equipment. The thickness and surface shape should be measured simultaneously to reduce cost. In this research, the absolute optical thickness and surface shape of a 6–mm-thick fused silica transparent plate of diameter 100mm was measured simultaneously by a three-surface Fizeau interferometer. A measurement method combining the wavelength tuning Fourier and phase shifting technique was proposed. The absolute optical thickness that corresponds to the group refractive index was determined by wavelength tuning Fourier analysis. At the beginning and end of the wavelength tuning, the fractional phases of the interference fringes were measured by the phase shifting technique and optical thickness deviations with respect to the ordinary refractive index and surface shape were determined. These two kinds of optical thicknesses were synthesized using the Sellmeier equation for the refractive index of fused silica glass, and the least square fitting method was used to determine the final absolute optical thickness distribution. The experimental results indicate that the all the measurement uncertainties for the absolute optical thickness and surface shape were approximately 3nm and 35nm, respectively.

Investigation of the laser acetylene sensor based on two-dimensional photonic crystal

We have developed the laser acetylene sensor based on a two-dimensional photonic crystal. The interaction of optical wave with the analyzed gas was enhanced by the use of the slow light effect. We carried out a numerical analysis to get the optimal structure of the sensor, including the photonic crystal forming an active element of the sensor and anti-reflection sections to maximize transmission. We considered geometric features of photonic crystals such as a line defect formed by a missing row of holes, a row of holes with changed diameter and air channel. High values of group refractive index and overlap integral as well as low attenuation of the crystal are required for the sensor operation; we carried the suitable simulations to achieve the best performance of the sensor. After the simulations, photonic crystal sensor was fabricated with electron beam lithography and reactive ion etching in the silicon layer of SOI heterostructure. Finally, the laser acetylene sensor was characterized experimentally.

光纤中慢光群折射率限定特性研究

光纤中慢光群折射率限定特性研究

Selection of numerical differentiation method for calculation of group refractive index of air over all calculable wavelengths

In this study, we attempt the selection of a difference approximation method to facilitate calculation of the group refractive index of air (GRA) over all calculable wavelengths. Based on calculation and error analysis, we test the performance of the three-point forward, three-point backward, and four-point central difference methods. We find that the GRA computation over the range of all calculable wavelengths (320–1680nm) can be easily approximated by the four-point central difference method with a step size of 10nm and an approximation accuracy of less than 30×10−9.

Generation of efficient THz radiation by optical rectification in DAST crystal using tunable femtosecond laser pulses

We report the efficient THz generation by optical rectification from an indigenously grown organic DAST crystal using the 140 fs oscillator laser pulses tunable in between 780 and 850 nm. The generated THz pulse profile and powers have been measured using the photoconductive (PC) antennas and pyroelectric detector, respectively. The highest THz peak amplitude and power is obtained at 825 nm central wavelength. We have theoretically explained the enhancement of THz radiation based on the matching of average optical group refractive index and average THz refractive index of the DAST crystal at 825 nm. In addition, the dependence of THz peak amplitude and THz power on laser power have been carried out. The measured quantum conversion efficiency (QCE) of 0.5 and 1.5 THz bands are of the order 3.7 × 10−3, 1.4 × 10−3, respectively. Finally, an attempt has been made to study the effect of polarizations on generated THz signal.

On-Chip Multiple Electromagnetically Induced Transparencies in Photon–Plasmon Composite Nanocavities

Chip-integrated multiple electromagnetically induced transparencies are realized using a photon–plasmon composite nanocavity (composed of a single photonic crystal nanocavity coupled with a single plasmonic nanocavity), i.e., comprehensively utilizing the superiorities of photonics as well as plasmonics. The destructively interferential coupling of one broad-band plasmonic nanocavity mode with two narrow-band silicon photonic crystal nanocavity modes generates two electromagnetically induced transparency windows. The two transparency windows simultaneously have a narrow line width of 15 nm, a high transmission contrast of 70%, and a strong slow light effect. A large group refractive index of more than 400 is obtained at the transparency window center, indicating a 10-fold increase in comparison with earlier results. The photon–plasmon composite nanocavity has a feature size of only 2 μm. The transparency window shifts 30 nm for the photon–plasmon composite nanocavity covered with a monolayer of graphene e...

Uncovering dispersion properties in semiconductor waveguides to study photon-pair generation

We investigate the dispersion properties of ridge Bragg-reflection waveguides to deduce their phasematching characteristics. These are crucial for exploiting them as sources of parametric down-conversion (PDC). In order to estimate the phasematching bandwidth we first determine the group refractive indices of the interacting modes via Fabry–Perot experiments in two distant wavelength regions. Second, by measuring the spectra of the emitted PDC photons, we gain access to their group index dispersion. Our results offer a simple approach for determining the PDC process parameters in the spectral domain, and provide important feedback for designing such sources, especially in the broadband case.

Light-Matter Interactions in Cesium Lead Halide Perovskite Nanowire Lasers.

Light-matter interactions in inorganic perovskite nanolasers are investigated using single-crystalline cesium lead halide (CsPbX3, X = Cl, Br, and I) nanowires synthesized by the chemical vapor transport method. The perovskite nanowires exhibit a uniform growth direction, smooth surfaces, straight end facets, and homogeneous composition distributions. Lasing occurs in the perovskite nanowires at low thresholds (3 μJ/cm(2)) with high quality factors (Q = 1200-1400) under ambient atmospheric environments. The wavelengths of the nanowire lasers are tunable by controlling the stoichiometry of the halide, allowing the lasing of the inorganic perovskite nanowires from blue to red. The unusual spacing of the Fabry-Pérot modes suggests strong light-matter interactions in the reduced mode volume of the nanowires, while the polarization of the lasing indicates that the Fabry-Pérot modes belong to the same fundamental transverse mode. The dispersion curve of the exciton-polariton model suggests that the group refractive index of the polariton is significantly enhanced.