Principal Refractive Indices Research Articles

Quantum imaging of biological organisms through spatial and polarization entanglement.

Quantum imaging holds potential benefits over classical imaging but has faced challenges such as poor signal-to-noise ratios, low resolvable pixel counts, difficulty in imaging biological organisms, and inability to quantify full birefringence properties. Here, we introduce quantum imaging by coincidence from entanglement (ICE), using spatially and polarization-entangled photon pairs to overcome these challenges. With spatial entanglement, ICE offers higher signal-to-noise ratios, greater resolvable pixel counts, and the ability to image biological organisms. With polarization entanglement, ICE provides quantitative quantum birefringence imaging capability, where both the phase retardation and the principal refractive index axis angle of an object can be remotely and instantly quantified without changing the polarization states of the photons incident on the object. Furthermore, ICE enables 25 times greater suppression of stray light than classical imaging. ICE has the potential to pave the way for quantum imaging in diverse fields, such as life sciences and remote sensing.

Linear and nonlinear optical properties of the langasite crystal Ca3TaAl3Si2O14

We have shown that the optical sign of the uniaxial langasite crystal Ca3TaAl3Si2O14 is positive. We also measured the phase-matching conditions of second-harmonic generation and sum-frequency generation up to 3.5 µm. Simultaneous fitting of these experimental data allowed us to report the Sellmeier equations of the ordinary and extraordinary principal refractive indices, and the magnitude of the nonlinear coefficient.

Calibration of Acousto-Optic Interaction Geometry Based on the Analysis of AOTF Angular Performance.

Acousto-optic interaction geometry determines the spectral and spatial response of an acousto-optic tunable filter (AOTF). The precise calibration of the acousto-optic interaction geometry of the device is a necessary process before designing and optimizing optical systems. In this paper, we develop a novel calibration method based on the polar angular performance of an AOTF. A commercial AOTF device with unknown geometry parameters was experimentally calibrated. The experimental results show high precision, in some cases falling within 0.01°. In addition, we analyzed the parameter sensitivity and Monte Carlo tolerance of the calibration method. The results of the parameter sensitivity analysis show that the principal refractive index has a large influence on the calibration results, while other factors have little influence. The results of the Monte Carlo tolerance analysis show that the probability of the results falling 0.1° using this method is greater than 99.7%. This work provides an accurate and easy-to-perform method for AOTF crystal calibration and can contribute to the characteristic analysis of AOTFs and the optical design of spectral imaging systems.

Universal Method for Determining the Principal Optical Indicatrix Axes in Triclinic Crystals

Determining the orientations of principal optical indicatrix axes is a key prerequisite for the applications of optical crystals, which is still an intriguing challenge for triclinic optical crystals due to the lowest symmetry. The prism method is one of the important ways to determine these directions, but no actual examples are available owing to the complexity and scarcity of the triclinic crystals so far. To solve this remaining problem among seven crystal systems, we proposed a universal method, the so-called “multiple prisms method,” to determine the orientations of principal optical indicatrix axes X, Y, and Z as well as the principal refractive index values nx, ny, and nz in triclinic crystals based on four prisms and demonstrated this method by employing triclinic Nd3+-doped La2CaB8O16 crystals, which is of great significance to the studies and applications of triclinic optical crystals in the future.

Regularization of dielectric tensor tomography.

Dielectric tensor tomography reconstructs the three-dimensional dielectric tensors of microscopic objects and provides information about the crystalline structure orientations and principal refractive indices. Because dielectric tensor tomography is based on transmission measurement, it suffers from the missing cone problem, which causes poor axial resolution, underestimation of the refractive index, and halo artifacts. In this study, we study the application of total variation and positive semi-definiteness regularization to three-dimensional tensor distributions. In particular, we demonstrate the reduction of artifacts when applied to dielectric tensor tomography.

First measurements of second-order frequency conversion phase-matching conditions in the new CTAS crystal

We report that Ca3TaAl3Si2O14 is a positive uniaxial crystal and provides second-order frequency conversion. Indeed, we performed direct measurements of phase-matching conditions for second-harmonic generation and sum-frequency generation up to 3.5 µm. The simultaneous fitting of recorded data provided the Sellmeier equations of the two principal refractive indices and the magnitude of the nonlinear coefficient.

Structure, electronic, optical and elastic properties of (NH4)2BeF4 crystal in paraelectric phase

The theoretical study of the structure and specific properties of the (NH4)2BeF4 crystal is carried out within the framework of the DFT. The band-energy structure of the (NH4)2BeF4 crystal in paraelectric phase is calculated and discussed. The edge of the fundamental absorption of the crystal is assumed to be associated with direct transitions in the center of Brillouin zone. The real and imaginary parts of the dielectric function as well as spectral dependence of the principal refractive indices of the crystal are calculated. Experimental study of the refractive indices dispersions of the grown crystal is carried out; the calculated dependances reveal good agreement with experimental data. Theoretical elastic coefficients Сij are calculated. The anisotropy of optical and elastic properties, which is important for possible applications, has been highlighted by means of the 2D and 3D graphs. The presented results should be very useful for future anisotropy-based implementations of the crystal.

Theoretical determination of biaxial anisotropy suitable for reducing incident angle dependence of a high-efficiency polarization grating

A theoretical framework for determining biaxial anisotropy suitable for reducing the incident angle dependence of a polarization grating is proposed. The principal refractive indices are uniquely given by quantifying the biaxial anisotropy through the N z coefficient. The numerical analysis based on the finite-difference time-domain method reveals that the incident angle dependences of the diffraction efficiency and the polarization ellipticity of the diffracted light are significantly reduced when N z = 0.5 . This result is expected to contribute to the design of polarization diffractive optical elements and the development of anisotropic materials and structures.

Tomographic measurement of dielectric tensors at optical frequency.

The dielectric tensor is a physical descriptor of fundamental light-matter interactions, characterizing anisotropic materials with principal refractive indices and optic axes. Despite its importance in scientific and industrial applications ranging from material science to soft matter physics, the direct measurement of the three-dimensional dielectric tensor has been limited by the vectorial and inhomogeneous nature of light scattering from anisotropic materials. Here, we present a dielectric tensor tomographic approach to directly measure dielectric tensors of anisotropic structures including the spatial variations of principal refractive indices and directors. The anisotropic structure is illuminated with a polarized plane wave with various angles and polarization states. Then, the scattered fields are holographically measured and converted into vectorial diffracted field components. Finally, by inversely solving a vectorial wave equation, the three-dimensional dielectric tensor is reconstructed. Using this approach, we demonstrate quantitative tomographic measurements of various nematic liquid-crystal structures and their fast three-dimensional non-equilibrium dynamics.

Optical and generation characteristics of new nonlinear Ba2Ga8GeS16 and Ba2Ga8(GeSe2)S14 crystals for the mid-IR range

Ba2Ga8GeS16 and Ba2Ga8(GeSe2)S14 single crystals of large size and good optical quality have been grown for the first time. Their linear optical characteristics – transmission spectra in the range of 0.3 – 25 μm, dispersion of principal refractive indices, and birefringence – have been measured. Irradiation of the crystals by 100-fs laser pulses with a wavelength of 8.3 μm initiated second-harmonic generation with an efficiency comparable with that obtained for the AgGaS2 crystal.

THE COMBINED ELLIPSOMETRIC METHOD OF COMPLETE OPTICAL CHARACTERIZATION OF CRYSTALS. III. EXPERIMENTAL DETERMINATION OF THE ORIENTATION OF OPTICAL AXIS IN CRYSTAL

In the third part of the article, devoted to the description of the combined ellipsometric method for the complete optical characterization of crystals, two variants of the technique for experimentally determining the orientation of optical axes using ellipsometry are presented. The first variant is based on the search for the circular cross section of the optical indicatrix. As is known, this cross section is perpendicular to the optical axis of the crystal. This is done by successive measurements of the dependence of the effective refractive index on the angle of rotation of the crystal around the normal to the plane under study, n eff = f (α). The second variant is based on the fact that the effective refractive index, n eff , does not depend on the angle of incidence φ of the beam on the plane under study, if the angle between the incident beam and the optical axis does not change. Thus, if measurements are performed on the plane of the optical axes of the crystal, then the problem is reduced to finding a plane that is perpendicular to the optical axis. This is done by successive measurements of the dependence of the effective refractive index on the angle of incidence of the beam on the plane of the optical axes, n eff = f (φ). The second variant of this technique was tested by ellipsometric measurements of a CdWO 4 crystal made on the plane of the optical axes. It has been established that the angle between the optical axes (the bisector of the angle is the principal axis N g of the optical indicatrix) is equal to 2V = 92° ± 1°. Since 2V > 90°, the CdWO 4 crystal is an optically negative crystal (the optical sign is minus). Key words : ellipsometry, optical indicatrix, principal refractive indexes, uniaxial and biaxial crystals.

THE COMBINED ELLIPSOMETRIC METHOD OF COMPLETE OPTICAL CHARACTERIZATION OF CRYSTALS. IV. APPLICATION TO UNIAXIAL CRYSTAL.

In the fourth part of the article, the application of the proposed method for the complete optical characterization of crystals to optically uniaxial crystals is considered. The object of the study was lithium niobate (LiNbO 3 ) crystals. Refining the orientation of the optical indicatrix in the samples under study, we confirmed the conclusion by direct measurements that for the implementation of the proposed combined ellipsometric method, knowledge of the crystallographic orientation of the crystal under study is completely optional. The obtained values of the optical constants of the undoped LiNbO 3 crystal [ n o = 2.280(±0.003), n e = 2.202(±0.002), Δ n = – 0.0775(±0.0015)] fully confirmed the correctness of the proposed method and its efficiency in the investigation of uniaxial crystals. The sensitivity of the combined ellipsometric method was tested on LiNbO 3 crystals subjected to high-temperature annealing in an H 2 O atmosphere. The optical constants obtained for an undoped LiNbO 3 crystal [ n o = 2.2455(±0.0015), n e = 2.1965(±0.0015), Δn = – 0.049(±0.001)] and a magnesium-doped LiNbO 3 crystal [ n o = 2.2445(±0.0015), n e = 2.1756(±0.0007), Δ n = – 0.069(±0.001)] is significantly less than the optical constants of the as grown crystal. It is assumed that the main reason that caused such significant changes is high-temperature annealing in an H 2 O atmosphere. Our main goal was to show the applicability of the method to the analysis of possible changes in the optical constants of a crystal caused by the influence of various factors on its properties. The results obtained show that the goal has been achieved. Key words : ellipsometry, optical indicatrix, principal refractive indexes, uniaxial crystals, lithium niobate.

Obliquely Bideposited TiN Thin Film with Morphology-Dependent Optical Properties

TiN thin films were obliquely bideposited with different subdeposit thicknesses. The morphology of the bideposited film was varied from a nano-zigzag array to a vertically grown columnar structure by reducing the subdeposit thickness. The principal index of refraction and extinction coefficient were obtained to explain the measured reflectance and transmittance spectra. The loss of the bideposited thin film decreased as the thickness of the subdeposit decreased. The principal indices for normal incidence were near or under unity, indicating the low reflection by the bideposited thin films. A TiN film with a subdeposit thickness of 3 nm demonstrated an average index of refraction of 0.83 and extinction coefficient of below 0.2 for visible wavelengths. The retrieved principal refractive indexes explained the anisotropic transmission and reflection. For most normal incident cases, the analysis offers the tunable anisotropic property of a TiN nanostructured film for multilayer design in the future.

Unusual ferroelectric-dependent birefringence in 2D trilayered perovskite-type ferroelectric exploited by dimensional tailoring

<h2>Summary</h2> Ferroelectrics with switchable spontaneous polarization have taken a dominant position as the nonlinear optical candidates, of which birefringence is an essential merit to optical devices. Despite the increasing advance of hybrid perovskite ferroelectrics, it remains a great challenge to control and tune their birefringence, thus hindering their practical optical applications. Here, we present a 2D trilayered hybrid perovskite-type ferroelectric obtained by 3D-to-2D dimensional tailoring, [(CH₃)₂CH(CH₂)₂NH₃]₂(CH₃NH₃)₂Pb₃Cl₁₀, showing biaxial polarizations of ∼5 μC/cm² and a relatively wide optical band gap. The intrinsic 2D architecture results in highly anisotropic principal refractive indices, namely, the optical birefringence. Interestingly, its birefringence can be reversibly switched through ferroelectric-to-paraelectric symmetry breaking. The birefringence tuning is further established by virtue of pretransitional modulation of ferroelectricity, exhibiting unusual polarization-dependent behaviors. In our judgment, this study on the polarization-dependent birefringence of hybrid perovskite ferroelectrics will provide a new pathway toward modulating nonlinear optical properties for smart devices.

Thermo-optic parameters of potassium titanyl phosphate crystals

This paper presents results of a comparative analysis of thermo-optic parameters of potassium titanyl phosphate (KTP) crystals. We demonstrate that some relations for temperature derivatives of their principal refractive indices have limited applicability. We propose that, to more accurately determine these parameters, temperature-noncritical phase matching should be taken into account.

Group velocity of light in biaxial crystals.

Based on the wave vector surface, we have derived the analytical expressions for the group velocity of light traveling in an optically biaxial crystal in an arbitrary direction. Our formulas are in terms of either the wave vector direction or the ray direction. An axis dispersion vector is introduced to specify the rotation of the dielectric frame in monoclinic and triclinic crystals, which is found to be responsible for the asymmetry of the group velocity surfaces of these two crystal systems when compared to their phase and ray velocity surfaces. Our formulas confirm that the group velocity of light in a nondissipative medium equals the ratio between the Poynting vector and the total energy density of the electromagnetic field. The group index of light is found to be decomposable into three parts: the ray index, the group index due to principal refractive index dispersion, and that due to axis dispersion. Numerical calculations are performed for the group velocity of light in ${\rm Sn}_2{\rm P}_2{\rm S}_6$ crystal at 550 nm wavelength. Our results show that the dispersion of the principal refractive indices has a considerable contribution to the group index.

Group velocity of light in uniaxial crystals.

Using the wave vector surface, we have derived the analytical expressions for the group velocities of the extraordinary light and the ordinary light traveling in an optically uniaxial crystal. Our formulas are in terms of either the wavevector direction or the ray direction, and they use only the principal refractive indices and their frequency dispersions. The algebraic equation for the group velocity surface of the crystal is also derived. While the group velocity is in the same direction as the ray velocity, numerical calculation shows that in the visible region the group velocity is slower than the ray velocity, and the difference between them becomes significant at short wavelengths.

THE COMBINED ELLIPSOMETRIC METHOD OF COMPLETE OPTICAL CHARACTERIZATION OF CRYSTALS. II. DETERMINATION OF THE OPTICAL CONSTANTS OF CRYSTAL

This part of the article describes the second stage of the combined ellipsometric method of complete optical characterization of crystals. The testing of the second stage was carried out on crystals of lithium niobate (LiNbO 3 ) and cadmium tungstate (CdWO 4 ). The obtained results of measurements of an optically uniaxial LiNbO 3 crystal fully confirmed the correctness of the proposed method and its applicability for optical characterization of crystals. In particular, the values of the principal refractive indices { n o = 2.280(±0.003), n e = 2.202(±0.002)} and birefringence {Δ n = – 0.0775(±0.0015)} of the LiNbO 3 crystal are in good agreement with the values of these quantities, obtained by other researchers by other methods. Studies of the optically biaxial CdWO 4 crystal were important for analyzing the accuracy of determining the optical constants. For generality of this analysis, measurements were performed in different measurement configurations at several angles of incidence of the laser beam. In particular, according to the results of measurements in two configurations (angle of incidence 45°), the following values of the principal refractive indices of the CdWO 4 crystal (doped from the melt 0.375 wt.% PbO) were obtained: n g = 2.249±0.002, n m = 2.185±0.002, n p = 2.130±0.008. Based on these values of n g , n m , and n p , the angle between the optical axes and the optical sign of the crystal were determined. It has been shown experimentally that the CdWO 4 crystal is a pronounced biaxial crystal with an angle between the optical axes close to 90°. Possible ways to improve the accuracy of determining the optical constants of crystals are also analyzed. Key words : ellipsometry, optical indicatrix, principal refractive indexes, uniaxial and biaxial crystals.

Microstructure-Induced Anisotropic Optical Properties of YF3 Columnar Thin Films Prepared by Glancing Angle Deposition.

Yttrium fluoride (YF3) columnar thin films (CTFs) were fabricated by electron beam evaporation with the glancing angle deposition method. The microstructures and optical properties of YF3 CTFs were studied systematically. The YF3 films grown at different deposition angles are all amorphous. As the deposition angle increases, the columns in YF3 CTFs become increasingly separated and inclined, and the volume fraction of YF3 decreases, resulting in lower refractive indices. This phenomenon is attributed to the self-shadowing effect and limited adatom diffusion. The YF3 CTFs are optically biaxial anisotropic with the long axis (c-axis) parallel to the columns, the short axis (b-axis) perpendicular to the columns, and the other axis (a-axis) parallel to the film interface. The principal refractive index along the b-axis for the 82°-deposited sample is approximately 1.233 at 550 nm. For the 78°-deposited sample, the differences of principal refractive indices between the c-axis and the b-axis and between the a-axis and the b-axis reach the maximum 0.056 and 0.029, respectively. The differences of principal refractive indices were affected by both the deposition angle and the volume fraction of YF3.

SPECTROSCOPIC ELLIPSOMETRY ANALYSIS OF A ANTIMONY TRISULFIDE (Sb2S3) THIN FILM

In the present research paper, thin films of antimony trisulfide (Sb2S3) were successfully deposited on glass substrates. The effect of thickness on the structural and optical properties of antimony trisulfide (Sb2S3) thin films is studied. The optical constants (n, k) and film thicknesses of Sb2S3 thin films were obtained by fitting the ellipsometric parameters ( and ) data using three-layer model systems in the wavelength range of 400–1800 nm. It is found that the refractive index n increases with an increase of the film thickness. The structural investigations are performed by Scanning electron microscopy SEM (the Grain size increased with the film thickness). We demonstrate generalized ellipsometry for precise measurement of the principal indices of refraction and the extinction coefficients.