Group Refractive Index Research Articles

Refractive indices used by the Haag-Streit Lenstar to calculate axial biometric dimensions.

To estimate refractive indices used by the Lenstar biometer to translate measured optical path lengths into geometrical path lengths within the eye. Axial lengths of model eyes were determined using the IOLMaster and Lenstar biometers; comparing those lengths gave an overall eye refractive index estimate for the Lenstar. Using the Lenstar Graphical User Interface, we noticed that boundaries between media could be manipulated and opposite changes in optical path lengths on either side of the boundary could be introduced. Those ratios were combined with the overall eye refractive index to estimate separate refractive indices. Furthermore, Haag-Streit provided us with a template to obtain 'air thicknesses' to compare with geometrical distances. The axial length estimates obtained using the IOLMaster and the Lenstar agreed to within 0.01mm. Estimates of group refractive indices used in the Lenstar were 1.340, 1.341, 1.415, and 1.354 for cornea, aqueous, lens, and overall eye, respectively. Those refractive indices did not match those of schematic eyes, but were close in the cases of aqueous and lens. Linear equations relating air thicknesses to geometrical thicknesses were consistent with our findings. The Lenstar uses different refractive indices for different ocular media. Some of the refractive indices, such as that for the cornea, are not physiological; therefore, it is likely that the calibrations in the instrument correspond to instrument-specific corrections and are not the real optical path lengths.

Coherent-interference-induced transparency based on long-range air-hole assisted subwavelength waveguides

A novel coherent-interference-induced transparency (CIT) system consisting of two coupled and detuned double-sided-branch (DSB) filters in a long-range air-hole assisted subwavelength (LR-AHAS) waveguide has been proposed and numerically demonstrated. The resonant wavelength, maximum transmittance, full width at half maximum (FWHM) and phase dispersion of the transparent window can be effectively tuned by adjusting the detuning and phase-shift between two coupled DSB filters, and FWHM can be suppressed to as small as 1.6 nm, which is much narrower than that of an individual resonator in an LR-AHAS waveguide. The FWHMs of 3.2 nm and 5.2 nm with the corresponding group refractive indices ng of 73 and 45 have been respectively demonstrated. In addition, multiple transparent peaks with an average bandwidth of 3.6 nm and high transmittance of 0.74 can be achieved by cascading more detuned DSB filters into the system. It provides a new approach to develop tunable high-channel-count bandpass filters and optical buffers based on the LR-AHAS waveguide platform for large-scale photonic integrations.

Air etalon facilitated simultaneous measurement of group refractive index and thickness using spectral interferometry.

A simple method based on air etalons of a transparent cavity is proposed to simultaneously measure the group refractive index and thickness of a transparent optical plate by spectral domain low coherence interferometry. In this method, only a single beam path is needed in contrast to the two beam paths, the reference and sample arms, of the conventional Michelson interferometer. An empty cavity is first constructed in the beam path by two glass plates. Then the transparent plate under test is inserted into the cavity, so that two air gaps are formed in the cavity. A beam of light of low coherence length is then transmitted through the cavity in the normal direction. Measurements of the reflected waves by the air gaps before and after the sample plate is put into the cavity allow us to determine the group refractive index (ng) and thickness (d) of the sample simultaneously. The relative precision of the results for d and ng are both approximately 7×10-4.

Simultaneous thickness and group index measurement with a single arm low-coherence interferometer.

We present a single arm low-coherence interferometer to directly measure the physical thickness and group refractive index of optically transparent samples having flat and parallel surfaces. The optical arrangement, resembling a common-path interferometer, is more compact and stable than the usual dual-arm low-coherence interferometer. It has been used to measure samples of Herasil 102 fused silica, Schott B270 Superwhite crown glass and borosilicate cover glass. The results obtained indicate uncertainties in the third decimal place for index values and thicknesses accurate to within 2 μm.

Electromagnetically induced transparency-like optical responses in all-dielectric metamaterials

We investigate numerically the electromagnetically induced transparency-like behavior in all-dielectric planar photonic metamaterials. The proposed metamaterial consists of a periodical array of silicon metamolecules. Each metamolecule comprises a radiative resonator and a subradiant resonator that couple to each other through near field interactions. Resonances with extremely high quality factors of up to several thousands are predicted, and a group refractive index of more than 200 can be realized at the transparency window. This provides an effective platform for slow light, enhanced nonlinearity and sensing applications and presents opportunities for developing new types of active lasing and optomechanical metamaterials.

Fano resonances in THz metamaterials composed of continuous metallic wires and split ring resonators.

We demonstrate theoretically and experimentally that Fano resonances can be obtained in terahertz metamaterials that are composed of periodic continuous metallic wires dressed with periodic split ring resonators. An asymmetric Fano lineshape has been found in a narrow frequency range of the transmission curve. By using a transmission line combined with lumped element model, we are able to not only fit the transmission spectra of Fano resonance which is attributed to the coupling and interference between the transmission continuum of continuous metallic wires and the bright resonant mode of split ring resonators, but also reveal the capacitance change of the split ring resonators induced frequency shift of the Fano resonance. Therefore, the proposed theoretical model shows more capabilities than conventional coupled oscillator model in the design of Fano structures. The effective parameters of group refractive index of the Fano structure are retrieved, and a large group index more than 800 is obtained at the Fano resonance, which could be used for slow light devices.

Fizeau-type interferometric probe to measure geometrical thickness of silicon wafers.

We developed an optical interferometric probe for measuring the geometrical thickness and refractive index of silicon wafers based on a Fizeau-type spectral-domain interferometer, as realized by adopting the optical fiber components of a circulator and a sheet-type beam splitter. The proposed method enables us to achieve a much simpler optical composition and higher immunity to air fluctuations owing to the use of fiber components and a common-path configuration as compared to a bulk-type optical configuration. A femtosecond pulse laser having a spectral bandwidth of 80 nm at a center wavelength of 1.55 µm and an optical spectrum analyzer having a wavelength uncertainty of 0.02 nm were used to acquire multiple interference signals in the frequency domain without a mechanical phase-shifting process. Among the many peaks in the Fourier-transformed signals of the measured interferograms, only three interference signals representing three different optical path differences were selected to extract both the geometrical thickness and group refractive index of a silicon wafer simultaneously. A single point on a double-sided polished silicon wafer was measured 90 times repetitively every two seconds. The geometrical thickness and group refractive index were found to be 476.89 µm and 3.6084, respectively. The measured thickness is in good agreement with that of a contact type method within the expanded uncertainty of contact-type instruments. Through an uncertainty evaluation of the proposed method, the expanded uncertainty of the geometrical thickness was estimated to be 0.12 µm (k = 2).

Interference enhancement in spectral domain interferometric measurements on transparent plate

In spectral domain interferometry, the interference signal generated by directly reflected waves from the two surfaces of a sample plate under test is greatly enhanced by the blockage of those light waves reflected by the two arm mirrors in the Michelson interferometer. This sample surface-reflected interference signal, being the optical path length of the plate, is therefore identifiable directly from the Fourier-transformed interference spectrum. Consequently, the group refractive index and physical thickness of the plate can be obtained simultaneously without any prior information of them. Moreover, subsequent in situ angular scanning on the interference spectra helps to retrieve the wavelength-dependent phase refractive index and first-order dispersion. The order of magnitude of the relative error for the group refractive index is 10(-4), while that for the phase refractive index and the physical thickness is 10(-3).

First Results in Near and Mid IR Lithium Niobate-Based Integrated Optics Interferometer Based on SWIFTS-Lippmann Concept

High-resolution spectrometers are nowadays achievable in compact devices using integrated optics. The approach developed here consists in obtaining a static interferogram by means of a Fresnel reflection at the waveguide output (Lippmann interference between forward and backward beams) and then sample the fringes by periodically etching the waveguide with transverse nanogrooves, that will collect a negligible part of the flux. We present the first SWIFTS-Lippmann interferometer in the near and mid-infrared, thanks to high form factor grooves obtained by focused ion beam in lithium niobate, which opens the way to electrooptic modulation of the interferogram and thus, sampling on-chip, without any moving part. Possible applications are high-resolution spectroscopy and accurate measurement of effective refractive index of a waveguide. A measurement of the effective group refractive index of the guided mode is presented.

Dual-mode electromagnetically induced transparency and slow light in a terahertz metamaterial.

In this Letter, we construct a metamaterial with dual-mode electromagnetically induced transparency (EIT)-like behavior by introducing "bright atoms," "quasi-dark atoms," and "dark atoms" simultaneously. The dual-mode EIT-like behavior has been demonstrated both experimentally and theoretically in terahertz (THz) regime. At two EIT-like modes, slow light is also observed as two time-delayed wave packets, and the effective group refractive index can reach 10(2). Furthermore, stable dual-mode EIT-like behavior is verified in this metamaterial for a wide range of oblique incident angles. Our work provides a design approach to mimic dual-mode EIT, and such an approach may achieve potential applications on miniaturized and versatile THz devices.

Optical interferometric approach for measuring the geometrical dimension and refractive index profiles of a double-sided polished undoped Si wafer

In this investigation, we propose a technique to obtain not only the dimensional profile of an undoped double-side polished silicon (Si) wafer but also its refractive index profile simultaneously. This technique is based on low coherence scanning interferometry using a near-infrared light around 1 µm wavelength, for which transmission is non-zero for undoped silicon and also detectable by the typical visible CCD camera. As the experimental results show, the profiles of optical thicknesses, geometrical thicknesses, group refractive indices and phase refractive indices were successfully obtained by the proposed technique, and the mean values were 1869.6 µm, 490.45 µm, 3.8121 and 3.516, respectively. Compared to the reference values of the group refractive index and the phase refractive index of the Si wafer given by the previous researches, the deviations were 0.055 and 0.04, respectively. The deviations were attributed to the position error of the scanning stage. In addition, the combined technique with spectrally-resolved interferometry was also discussed to improve the measurement accuracy of the system.

Demonstration of slow sound propagation and acoustic transparency with a series of detuned resonators

We present experimental results demonstrating the phenomenon of acoustic transparency with a significant slowdown of sound propagation realized with a series of paired detuned acoustic resonators (DAR) side-attached to a waveguide. The phenomenon mimics the electromagnetically induced transparency in atomic physics. By arranging four identical DAR pairs along the waveguide with an equal subwavelength separation between adjacent pairs, we show that this arrangement features unique properties of narrow-band transmission and strong dispersion. In particular, we demonstrate side-lobe suppression of more than 20 dB on both sides of the transparency window, and we quantify directly (using a pulse propagation) the acoustic slowdown effect, resulting in the sound group velocity of \ensuremath{\sim}9.8 m/s (i.e. in the group refractive index of 35). We find very similar values of the group refractive index by using measurements of the phase of the transmitted wave. It is also shown that a direct coupling exists between the DAR in each pair, which cannot be explained by the interference of waves radiated from those resonators. This detrimental coupling becomes noticeable for small values of detuning and also if the cross-sectional area of the neck of the resonators is increased.

Ultracompact Slow Surface Plasmon Polaritons Superlattice with Broad Bandwidth and Super-High Normalized Delay-Bandwidth Product

In this paper, we propose an ultracompact low-loss plasmonic superlattice for slow surface plasmon polaritons. The superlattice consists of a two-dimensional metal gap waveguide (Ag-SiO2-Ag) inserted with thin metal films working as coupled reflectors. Theoretical calculations indicate that the device is working on a broad bandwidth of 37 THz including the two telecom wavelengths of 1,310 and 1,550 nm and with mean group refractive index of 3.5 and mean transmission of 60 %. As the total geometric thickness is only 1.6 μm, the normalized delay-bandwidth product of the superlattice is as high as 0.44. All the theoretical prediction based upon the transfer matrix method is validated by the finite-difference time-domain numerical simulation on surface plasmon polaritons propagating in the superlattice.

Optically Pumped Lasing from Single Crystals of a Cyano‐Substituted Thiophene/Phenylene Co‐Oligomer

Room temperature optically pumped lasing is achieved for a new n-type molecular crystal of 2,5-bis(4′-cyanobiphenyl-4-yl)­thiophene (BP1T-CN). Efficient stimulated emission in the Fabry–Pérot crystal cavity is supported with a high group refractive index (4.18–4.98), Q factor (910–1860), material gain coefficient (120 cm-1), and a high stimulated emission rate demonstrated by pump–probe measurements.

Precise measurement of the thermo-optical coefficients of various Nd-doped vanadates with an intracavity self-mode-locked scheme

We employ an intracavity self-mode-locked laser to precisely measure the group refractive indices and thermo-optic coefficients for Nd-doped vanadates at 1064 nm. The samples include Nd:GdVO4, Nd:YVO4 and Nd:LuVO4 crystals. We make a detailed comparison between the present results and those currently reported in the literature. We confirm that the present results are in good agreement with the currently available data with the best precision.

Comparison of two-color methods based on wavelength and adjacent pulse repetition interval length

This paper describes the characteristics of a two-color method based on the adjacent pulse repetition interval length (APRIL), which functions as a length unit for femtosecond optical frequency combs (FOFCs), and compares the results to the wavelength-based two-color method. The wavelength-based two-color method can eliminate the inhomogeneous disturbance of effects caused by the phase refractive index; therefore, the APRIL-based two-color method can eliminate the air turbulence of errors induced by the group refractive index. Our numerical analysis of the APRIL-based two-color method will contribute to the pulse-laser-based two-color method, which secures traceability to the definition of the meter via APRIL.

Sub-sampling low coherence scanning interferometry and its application: refractive index measurements of a silicon wafer

In this investigation, refractive indices of a silicon (Si) wafer were measured by low-coherence scanning interferometry adopting the sub-sampling technique to reduce measurement time. Based on Fourier domain analysis method, the sub-sampled correlogram was analyzed and the refractive indices were calculated by the simple refractive index model and curve fitting of the phase extracted from the sub-sampled correlogram. In the experiment to verify the proposed technique, near-infrared light emitted by a super-luminescent diode with 1050nm center wavelength was used as an optical source because it is partially transparent to an undoped Si wafer. As the result of measuring an undoped double-side polished Si wafer, group and phase refractive indices were successfully obtained with the sub-sampled correlogram, and the deviations from the reference value were within 0.001.

Characteristics of an adjacent pulse repetition interval length as a scale for length

This paper describes the characteristics of the adjacent pulse repetition interval length (APRIL), which is used as a scale for femtosecond optical frequency comb (FOFC)-based length measurements. This approach is based on the analogy between the phase refractive index and the group refractive index. Because the former influences the wavelength, which is the basic parameter used to describe monochromatic light in terms of length measurement, we investigated the latter to analyze the theoretical properties of the APRIL when used as a length standard. The results of theoretical analyses and numerical investigations show that when the air parameters change, the changes in the wavelength of a He–Ne laser and the APRIL of an FOFC laser are of the same order of magnitude. The difference between the effects of the phase refractive index on the wavelength and the group refractive index on the APRIL was also confirmed. The proposed concept and analysis pave the way for developing a length traceability system based on the APRIL via optical fibers.

An integrated solution for mold shape modification in precision glass molding to compensate refractive index change and geometric deviation

In precision glass molding, refractive index change and geometric deviation (or curve change as often referred to in industry) occurred during molding process can result in substantial amount of aberrations. Previously, refractive index change and geometric deviation were investigated in separate studies by the authors. However, optical performance of a molded glass lens depends on both refractive index and geometry. In order to mold lenses with optimal performance, both refractive index change and geometric deviation have to be taken into consideration simultaneously and compensated. This paper presented an integrated compensation procedure for modifying molds to compensate both refractive index change and geometric deviation. Group refractive index change predicted by the finite element method simulation was used to provide a modified geometry design for a desired lens. Geometric deviations of molded glass lenses with the modified design were analyzed with a previously developed numerical simulation approach, which is used to modify the mold shape. This procedure was validated by molding a generic aspherical glass lens. Both geometry and optical measurement results confirmed that the molded lens performed as specified by the original design. It also demonstrated that finite element method assisted compensation procedure can be used to predict the final optical performance of compression molded glass components. This research provided an opportunity for optics manufacturers to achieve better performance lens while maintaining lower cost and a shorter cycle time.

Emission and charge transport properties of thiophene-terminated thiophene/phenylene co-oligomer crystals

We have grown the crystals of two thiophene/phenylene co-oligomers (TPCOs) composed of in-line five and seven alternating thiophene and benzene rings. These TPCOs are characterized by thiophenes located at both molecular terminals. The grown crystals had several pairs of parallel crystal faces that function as optical resonators. These produced interference fringes in their emission and reflectance spectra. We measured the emission spectra in both weak broadband excitation and intense laser excitation regimes. From these spectra we determined the phase refractive index dispersion and the anisotropic group refractive indices. We made field-effect transistor devices using the above TPCO crystals and carried out their electrical measurements. These optical and charge transport properties are compared with those of crystals of other alternating TPCOs with phenylenes located at both molecular terminals.