Dalibor Ciprian

Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film.

We present a white-light spectral interferometric technique for measuring the absolute spectral optical path difference (OPD) between the beams in a slightly dispersive Michelson interferometer with a thin-film structure as a mirror. We record two spectral interferograms to obtain the spectral interference signal and retrieve from it the spectral phase, which includes the effect of a cube beam splitter and the phase change on reflection from the thin-film structure. Knowing the effective thickness and dispersion of the beam splitter made of BK7 optical glass, we use a simple procedure to determine both the absolute spectral phase difference and OPD. The spectral OPD is measured for a uniform SiO(2) thin film on a silicon wafer and is fitted to the theoretical spectral OPD to obtain the thin-film thickness. The theoretical spectral OPD is determined provided that the optical constants of the thin-film structure are known. We measure also the nonlinear-like spectral phase and fit it to the theoretical values in order to obtain the thin-film thickness.

Spectral-domain measurement of phase modal birefringence in polarization-maintaining fiber

We report on a new and simple method for measuring the wavelength dependence of phase modal birefringence in a polarizationmaintaining fiber. The method is based on application of a lateral pointlike force on the fiber that causes strong coupling between polarization modes and utilizes their interference resolved as the channeled spectrum. The change of the phase retrieved from two recorded channeled spectra that are associated with the known displacement of coupling point is used to determine the phase modal birefringence as a function of wavelength. A windowed Fourier transform is applied to reconstruct precisely the phase change and the phase ambiguity is removed provided that we know the phase change of the spectral fringes at one specific wavelength. The measured wavelength dependence of phase modal birefringence is compared with that resulting from the group modal birefringence measurement.

Measurement and modelling of dispersion characteristics of a two-mode birefringent holey fibre

Employing several interferometric methods, we measured in a broad spectral range the wavelength dependences of the phase modal birefringence and the polarization mode dispersion for the LP01 and even LP11 spatial modes supported by a birefringent holey fibre. We also determined the wavelength dependence of the intermodal dispersion between the X- and Y-polarized LP01 and even LP11 spatial modes. Furthermore, using a full-vector finite-element method, we modelled all the measured dispersion characteristics and demonstrated good agreement between experimental and theoretical results.

Measurement of chromatic dispersion of polarization modes in optical fibres using white-light spectral interferometry

We report on a white-light interferometric technique for a broad spectral range measurement (e.g. 500–1600 nm) of chromatic dispersion of polarization modes in short-length optical fibres. The technique utilizes an unbalanced Mach–Zehnder interferometer with a fibre under test of known length inserted in one of the interferometer arms and the other arm with adjustable path length. We record a series of spectral interferograms by VIS–NIR and NIR fibre-optic spectrometers to measure the equalization wavelength as a function of the path length difference, or equivalently the differential group index dispersion of one polarization mode. The differential group dispersion of the other polarization mode is obtained from measurement of the group modal birefringence dispersion. We verify the applicability of the method by measuring the chromatic dispersion of polarization modes in a birefringent holey fibre. We apply a five-term power series fit to the measured data and confirm by its differentiation that the chromatic dispersion agrees well with that specified by the manufacturer. We also measure by this technique the chromatic dispersion of polarization modes in an elliptical-core fibre.

Spectral interferometric technique to measure the ellipsometric phase of a thin-film structure

A two-step white-light spectral interferometric technique is used to retrieve the ellipsometric phase of a thin-film structure from the spectral interferograms recorded in a polarimetry configuration with a birefringent crystal. In the first step, the phase difference between p- and s-polarized waves propagating in the crystal alone is retrieved. In the second step, the additional phase change that the polarized waves undergo on reflection from the thin-film structure is retrieved. The new method is used in determining the thin-film thickness from ellipsometric phase measured for SiO(2) thin film on a Si substrate in a range from 550 to 900 nm. The thicknesses of three different samples obtained are compared with those resulting from polarimetric measurements, and good agreement is confirmed.

Wide spectral range measurement of modal birefringence in polarization-maintaining fibres

We report on a substantially improved white-light spectral interferometric technique for measurement of the group and phase modal birefringence in polarization-maintaining fibres (PMFs) over a wide wavelength range (e.g. 480–1600 nm). The technique utilizes a tandem configuration of a Michelson interferometer and a PMF placed between Glan–Taylor polarizer and analyzer. Spectral signals are recorded by VIS–NIR and NIR fibre-optic spectrometers to measure the equalization wavelength as a function of the path length difference adjusted in the interferometer, or equivalently, the wavelength dependence of the group modal birefringence in the PMF. Moreover, a new procedure is used to specify the sign of the group modal birefringence. A polynomial fit is applied to the measured data to determine also the wavelength dependence of the phase modal birefringence in the PMF over a wide spectral range.

Absolute phase birefringence dispersion in polarization-maintaining fiber or birefringent crystal retrieved from a channeled spectrum

We report on a simple method for retrieving the wavelength dependence of the phase birefringence in a polarization-maintaining fiber or a birefringent crystal from a channeled spectrum. The method utilizes interference of polarized modes or waves resolved as the channeled spectrum and its processing by a windowed Fourier transform to reconstruct precisely the phase as a function of wavelength. The ambiguity of the phase is removed provided that we know both the approximative function for the birefringence dispersion and the length of the fiber or the thickness of the crystal. The method is used in measuring the wavelength dependence of the phase birefringence in an elliptical-core fiber or in a quartz crystal in a range from 500 to 900 nm. The dependences are compared with those resulting from the available data, and very good agreement is confirmed.

Differential group refractive index dispersion of glasses of optical fibres measured by a white-light spectral interferometric technique

We report on a white-light interferometric technique employing a low-resolution spectrometer to measure the differential group refractive index of glasses of optical fibres over a wide wavelength range. The technique utilizes an unbalanced Mach–Zehnder interferometer with a fibre under test of known length inserted in one of the interferometer arms and the other arm with adjustable path length. We record a series of spectral interferograms to measure the equalization wavelength as a function of the path length difference, or equivalently the group dispersion. Subtracting the group dispersion of the optical components present in the interferometer along with the fibre, we measure the wavelength dependence of differential group refractive index for pure silica and SK222 glasses. We confirm that the differential group dispersion measured for pure silica glass agrees well with that described by the dispersion equation.

Spectral interferometry and reflectometry used for characterization of a multilayer mirror

A white-light spectral interferometric technique is used to retrieve a relative spectral phase and group delay of a multilayer mirror from the spectral interferograms recorded in a dispersive Michelson interferometer. The phase retrieval is based on the use of a windowed Fourier transform in the wavelength domain, and characterization of the multilayer mirror is completed by a three-step measurement of the reflectance spectrum of the mirror in the same interferometer.

Linear and quadratic magneto-optical effects in reflection from a medium with an arbitrary direction of magnetization

Three basic configurations are usually distinguished in calculations of the light propagation in magneto-optical media: polar, longitudinal and transverse direction of the magnetization. In these particular cases the fourth order equations for normal components of the wave vectors reduce to bi-quadratic ones. Analytic solutions of this equation are obtained also for a mixture of longitudinal and transverse effects (magnetization in the plane of interface) and for a mixture of polar and transverse effects. These configurations are discussed in details. If the magnetization is in general direction, the fourth-order characteristic equation has to be solved by using numerical methods. Permittivity tensor is considered for the case of cubic magneto-optical crystal. Its linear and quadratic terms in magnetization are included. The magneto-optical medium is described by the index of refraction and by linear and quadratic epitaxial Fe layer on MgO substrate. The magnetization component effects in general direction are studied by numeric calculations of the reflection coefficients. The mixture of the polar, longitudinal and transverse magneto-optical effects is analyzed taking into account the second order terms. The effects of the magnetization components are specified at normal incidence geometry, because in this case the calculation becomes simpler.