Group Refractive Index Research Articles

Measurement of the group refractive index of bulk material using white-light spectral interferometry

It is a radical but pressing problem to measure the group refractive index of dispersive material both accurately and rapidly in optical engineering field. In this paper, a white-light spectral interferometric system employing a fiber-optic spectrometer is developed for solving this problem. The system takes advantage of the characteristic of fiber-optic spectrometer which can get all the interferometric information by a single shot image without any mechanical scanning. Compared with the traditional windowed Fourier transform, a wavelet transform algorithm is used to directly extract the group delay rather than the phase from the interferogram. Therefore, the new method can provide a simple and fast solution, while still maintaining high accuracy. Based on this white-light Michelson interferometric system, fused silica and BK7 glass samples are measured respectively and the results agree well with the theoretical values over a broad spectral range. At the end of this paper, different mirror positions are used to verify the repeatability of our method.

Noninvasive optical coherence tomography monitoring of structure and hydration changes of human corneas in different preservation media

The influence of different tissue preservation (a test solution under development and a standard storage solution) on human cornea morphology, refractive index and hydration was assessed noninvasively by ultrahigh-resolution optical coherence tomography (OCT) over time. For 28 days' or 15 days' storage in the preservation media, corneas in the two media exhibited different structural changes with different onset times including epithelial desquamation, edema-induced cornea thickening and change in tissue refractive index. It was found that the variation of the group refractive index over time was only about 2%, while 25% variation of hydration was observed in the storage and subsequent return to normothermic conditions in both preservation media. The results suggest the two media involved different but correlated preservation mechanisms. This study demonstrates that the noncontact, noninvasive, and high-resolution OCT is a powerful tool for noninvasive characterization of tissue morphological changes and hydration process and for assessment of the effects of preservation media on stored tissue integrity. © 2011 Society of Photo-Optical Instrumentation Engineers.

Characteristics of subluminal for optical resonators

The insertion loss of fiber couplers in the two fiber rings waveguide system is studied. The peak power is the same by matching coupler strength of two couplers at the resonant area. The peak transmittance is inversely proportional to the group refractive index regardless of the two reflection values. Group delay increases at the expense of reduction of the peak transmissivity. The three rings waveguide structure manifests the subluminal properties accompanying normal dispersion by doping gain media. Group delay is analyzed in the frequency domain and the time domain, respectively. This study could be regarded as the significant theoretical foundation for applications in the field of controllable light velocity theory, sensors, filters, optical buffers and so on.

Defect-mode-like transmission and localization of light in photonic crystals without defects

It is shown that far- and near-field effects, which are similar to those arising in transmission through finite-thickness photonic crystals (PCs) with structural defects, can be obtained in the conventional defect-free dielectric square-lattice PCs. Multiple narrow peaks of total transmission can appear within a frequency range, where the noncircular isofrequency dispersion contours of one type are quickly transformed for a higher-order Floquet-Bloch wave to the noncircular contours of the other type, leading to a frequency-domain passband being very narrow within a certain range of variation of the angles of incidence. In this regime, the mirror reflectance of the equivalent Fabry-P\'erot resonator takes rather large values, which correspond to large values of $Q$ factor and group index of refraction, strong field localization, and good isolation of the transmission peaks from each other. In some examples presented, $Q$ factor exceeds ${10}^{4}$.

From a discrete to a continuous model for interpulse interference with a frequency-comb laser

We have investigated correlation patterns generated by a frequency-comb laser in a dispersive unbalanced Michelson interferometer and apply the developed formalism to the case of distance metrology. Due to group velocity dispersion, the position of the brightest fringe of the correlation pattern, which is used for distance determination, cannot be derived by simply using the definition of group refractive index of the dispersive medium. It is shown that the discrete spectrum of the optical frequency comb gives rise to correlation functions which can be represented by a series, namely a discrete correlation series. We have developed a general formalism, valid for any pulse train, extending the discrete model to a continuous model of cross-correlation functions using the Poisson summation. Our model is relevant for any offset and repetition frequency of the frequency comb. From the continuous cross-correlation model we show that, even for a homogeneous dispersive medium the position of the brightest fringe varies nonlinearly for small delay distances and stabilizes for longer ones. We have compared the theoretical results to measurements of pulse propagation in air for path-lengths up to 200 m.

Semiconductor saturable absorbers for ultrafast terahertz signals

We demonstrate saturable absorber behavior of n-type semiconductors GaAs, GaP, and Ge in the terahertz (THz) frequency range at room temperature using nonlinear THz spectroscopy. The saturation mechanism is based on a decrease in electron conductivity of semiconductors at high electron momentum states, due to conduction band nonparabolicity and scattering into satellite valleys in strong THz fields. Saturable absorber parameters, such as linear and nonsaturable transmission, and saturation fluence, are extracted by fits to a classic saturable absorber model. Further, we observe THz pulse shortening, and an increase in the group refractive index of the samples at higher THz pulse peak fields.

Group Velocity Modulation Based on Electrooptic Photonic Crystal With Waveguide Structure

We propose an electrooptic photonic crystal with a periodically poled lithium niobate (PPLN) waveguide structure based on electrooptic effect, where the group velocity of input optical beam can be continuously modulated from subluminal to superluminal by adjusting the applied external electric field in the z-direction of the crystal. The slow light propagation at the band edges was investigated and analyzed, in which a large group index in a PPLN waveguide was obtained, and the group refractive index or the transmission as a function of the applied electric field, operation temperature, and different input wavelength were also presented and discussed in detail.

Simultaneous measurement of group refractive index and thickness of optical samples using optical coherence tomography

Optical coherence tomography (OCT), based on a Michelson interferometer and utilizing low coherence light as the optical source, is a novel technique for the noninvasive imaging of optical scattering media. A simple OCT scheme based on a 3 x 3 fiber coupler is presented for the simultaneous measurement of the refractive index and thickness of optical samples. The proposed system enables the refractive index and thickness to be determined without any prior knowledge of the sample parameters and is characterized by a simple and compact configuration, a straightforward measurement procedure, and a low cost. The feasibility of the proposed approach is demonstrated experimentally using BK7 and B270 optical glass samples.

Measurement of the Absolute Optical Thickness Distribution of a Mask-blank Glass by a Phase-shifting, Wavelength Tuning Interferometry

The uniformity of the surface flatness, optical thickness distribution, and refractive index have been requested in semi-conductor industry. The absolute optical thickness of a mask-blank glass of seven-inch square and 3.1 mm thickness was measured by three-surface interferometry in a wavelength tuning Fizeau interferometer. Wavelength-tuning interferometry can separate three interference signals of the front surface shape, the rear surface shape and the optical thickness in frequency space. The wavelength of a tunable laser diode source was scanned linearly from 632 nm to 642 nm and a CCD detector recorded two thousand interference images. The number of phase variation of the interference fringes during the wavelength scanning was counted by a temporal discrete Fourier transformation. The initial and final phases of the interferograms before and after the scanning were measured by a phase shifting technique with fine tunings of the wavelengths at 632nm and 642 nm. The optical thickness defined by the group refractive index at the central wavelength of 637 nm can be measured by this technique. Experimental results show that the cross talk in multiple-surface interferometry caused a systematic error of 0.6 microns in the measured optical thickness.

Grating-Assisted Spectrally-Narrowed Emissions from an Organic Slab Crystal Excited with a Mercury Lamp

We report spectrally-narrowed emissions that take place from an organic semiconductor slab crystal of 2,5-bis(4-biphenylyl)thiophene (BP1T) under a low excitation-intensity regime. These emissions are caused with a mercury lamp that operates on a household power supply with an electric current approximately 1 A. The BP1T slab crystal is equipped with a distributed Bragg reflector. To complete this structure the slab crystal is attached to a diffraction grating that is engraved on a surface of a quartz glass substrate. The diffraction gratings have precisely been formed using a focused ion beam with a nanometer-defined precision. The spectral narrowing accompanied by the emission intensity increment is related to the strong mode-coupling between the forward electromagnetic wave and the backward (i.e., reflected) wave within the grating zone. Using a laser we also carried out the emission measurements on the BP1T crystals under a high excitation-intensity regime. The emissions are characterized as the longitudinal multimode laser oscillation, enabling us to determine the group refractive index of 4.56 for the BP1T slab crystal. Under both the low and high excitation-intensity regimes excitons are dominant species of the emission. Their participation in the spectrally-narrowed emissions is briefly discussed.

Switching from subluminal to superluminal light propagation via a coherent pump field in a four-level atomic system

We theoretically investigate the influence of a coherent pump field on the propagation of a weak light pulse of a probe field in a four-level atomic system. Due to the modulation of the pump field, the light pulse can be manipulated from subluminal to superluminal with negligible distortion. This scheme can be realized in both the ultracold and Doppler-broadened atomic systems. We also demonstrate that the spectral linewidth with an anomalous dispersion is reduced by thermal averaging; therefore, one can obtain a larger negative group refractive index in room-temperature vapor than the largest value achieved in ultracold atomic gas.

Influence of external magnetic field on magnon–plasmon polaritons in negative-index antiferromagnet–semiconductor superlattices

The peculiarities of the negative refraction in periodic multilayered antiferromagnet–semiconductor nanostructures are investigated in the presence of an external magnetic field parallel to the plane of the layers. Effective material tensors are obtained using method of anisotropic homogeneous medium. Dispersion and energetic relations for the mixed magnon–plasmon polaritons are investigated in the case of the Voigt geometry. Frequency regions of anomalous dispersion are found and studied in various regimes of the applied magnetic field. The necessary conditions are found under which the structure behaves as a left-handed negative-index metamaterial. Analytical expressions for the frequency-dependent phase and group refractive indices are obtained.

Broadband near-infrared fibers dispersion measurement using white-light spectral interferometry

A new technique for an experimental determination of the effective refractive index, group refractive index and dispersion of fibers in a broad near-infrared spectral range is presented. The method is based on a white-light spectral interference which utilizes an unbalanced Michelson interferometer. The effective refractive index is obtained by a direct fitting the cosine function to the spectral interference pattern recorded by a low resolution spectrometer. The method has been tested in the spectral range of 1000–1700 nm both with standard telecommunication fibers and a sample of a photonic fiber. The accuracy of dispersion measurement ( 0.16 ps nm · km ) exceeds those from the previously reported near-infrared white-light spectral interference methods.

Spectral Properties of High-Power Distributed Bragg Reflector Lasers

In this paper, spectral data of distributed Bragg reflector lasers emitting around 974 nm and 1084 nm are presented. The devices are fabricated by a single-growth molecular beam epitaxy step, and the gratings are defined by holographic interferometry. Spectral dependencies on the grating and gain section lengths are systematically investigated in the so-called cleaved-back experiments. Experimental data for the side-mode suppression ratio, mode spacing, and group refractive index are given for devices emitting around 974 nm. In addition, the coupling efficiency between the grating and gain section is derived experimentally for devices emitting around 1084 nm.

A spectral interferometric method to measure thickness with large range

We present a spectral interferometric method to measure the thickness of an optical plate or a film with a single layer. The system is based on the Michelson interferometer configuration, and the spectral interference signal of a broadband light source is recorded by a spectrometer. The optical path difference (OPD) between two interfering beams can be obtained by Fourier transform from the spectral interferogram. Gaussian fitting is used to find the exact peak of fringe to enhance the precision of the measurements. When the sample is inserted into the sample beam, the film’s thickness can be calculated by comparing the change of OPD, provided that the sample group refractive index is known. Only a single measurement is needed to determine a film’s thickness after the initial OPD of the system is calibrated. As no moving parts are required, the system has good stability. In particular, a large range of thicknesses, from micrometers up to several millimeters, can be measured. Such a large range is valuable for optical measurements. For demonstration, we measured the thicknesses of preservative film, cover glass and carrier glass, which were 9.6 ± 0.55, 156.1 ± 0.75, 1008.44 ± 0.96 μm, respectively.

Comparison of two partial coherence interferometers for corneal pachymetry in high myopia and after LASIK

We aimed to compare the Haag-Streit optical low-coherence reflectometry (OLCR) pachymeter and the Zeiss Anterior Chamber Master (ACMaster) for measuring central corneal thickness (CCT) in high myopes and after laser in situ keratomileusis (LASIK) for myopia. Central corneal thickness was measured in 55 eyes of 30 myopic subjects (spherical equivalent refraction of - 5.25 D to - 10.75 D, maximal astigmatism of - 2 D), and in 37 eyes of 21 patients 3 months after LASIK for myopia (preoperative spherical equivalent refraction of - 6.0 D to - 10.75 D, maximal astigmatism of - 2 D). All measurements were performed with the Haag-Streit OLCR pachymeter and the Zeiss ACMaster, using group refractive indices of 1.376 and 1.3851, respectively. Thickness measurements were compared using paired t-tests, Pearson's correlation, linear regression and Bland-Altman plots. In myopic subjects, CCT measured 531 +/- 28 microm and 533 +/- 27 microm with the OLCR pachymeter and the ACMaster, respectively (p < 0.01); all measurements correlated closely (r = 0.99, p < 0.01). In LASIK-treated eyes, CCT measured 472 +/- 24 microm using the OLCR pachymeter and 475 +/- 23 microm using the ACMaster (p < 0.01), again with close correlation between the two instruments (r = 0.99, p < 0.01). Measurements of CCT in high myopes and after myopic LASIK were very similar with the Haag-Streit OLCR pachymeter and the Zeiss ACMaster. Using the current group refractive indices, the observed difference between the two instruments of < 3 microm is of little clinical importance. Thus, it would seem safe to use the OLCR pachymeter and the ACMaster interchangeably for CCT measurements in myopia as well as after myopic LASIK.

Fabry-Pérot microcavity modes observed in the micro-photoluminescence spectra of the single nanowire with InGaAs/GaAs heterostructure

We report on the fabrication of the nanowires with InGaAs/GaAs heterostructures on the GaAs(111)B substrate using selective-area metal organic vapor phase epitaxy. Fabry-Pérot microcavity modes were observed in the nanowires with perfect end facets dispersed onto the silicon substrate and not observed in the free-standing nanowires. We find that the calculated group refractive indices only considering the material dispersion do not agree with the experimentally determined values although this method was used by some researchers. The calculated group refractive indices considering both the material dispersion and the waveguide dispersion agree with the experimentally determined values well. We also find that Fabry-Pérot microcavity modes are not observable in the nanowires with the width less than about 180 nm, which is mainly caused by their poor reflectivity at the end facets due to their weak confinement to the optical field.

Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index

We present a method for simultaneously measuring the thickness and the group refractive index of a specimen using self-referenced spectral-domain fiber-based interferometry. By removing the scanning part and using the fiber-based configuration, the system complexity and stability could be significantly improved. To minimize the system drift, we utilized the signals originated from the fiber ends of both arms. Implementing in a self-referenced configuration, we could improve the measurement accuracy down to a decimal place. Experimental measurements were made with a 1.555 mm thick fused silica plate. At 814 nm the thickness was measured as 1.5546 +/- 0.0002 mm, and at the same time, the group index was obtained as 1.4627 +/- 0.0002.

Heterodyne near-field scanning optical microscopy with spectrally broad sources

We propose to use low-coherence-length cw optical sources with a broad spectrum in heterodyne near-field scanning microscopy in order to imitate optical pulse propagation and to obtain information about spectrally variant properties of nanophotonic components. The dispersion difference in the interferometer arms for a symmetric acousto-optic modulator arrangement is shown to be negligible over appreciable bandwidths. Demonstration of the principle of operation and viability of this approach is provided by measurement of the group refractive index of a silicon channel waveguide.

Strongly subluminal regime of optical-to-terahertz conversion in GaP

We introduce and investigate a special regime of terahertz generation in electro-optic crystals with ultrashort laser pulses, in which neither phase-matching nor Cherenkov radiation mechanism are efficient. This regime occurs under the conditions that the optical group refractive index is larger than the low-frequency phase refractive index of the crystal, and the spectral bandwidth of the laser pulse is smaller than the frequency of the phase-matched terahertz wave. In this regime, that can be realized for a Ti:sapphire laser in GaP, terahertz generation is provided by transient processes at the crystal boundaries. We study the peculiarities of the terahertz emission from a slab of GaP excited with a Ti:sapphire laser. In particular, we demonstrate a possibility to implement a pointlike source of terahertz radiation that can increase the resolution of terahertz apertureless near-field microscopy.