Petr Hlubina

Dispersion of group and phase modal birefringence in elliptical-core fiber measured by white-light spectral interferometry

We present a white-light spectral interferometric technique employing a low-resolution spectrometer for measurement of the dispersion of the group and phase modal birefringence in an elliptical-core optical fi ber over a wide spectral range. The technique utilizes a tandem con fi guration of a Michelson interferometer and the optical fi ber to record a series of spectral interferograms and to measure the equalization wavelengths as a function of the optical path difference in the Michelson interferometer, or equivalently, the wavelength dependence of the group modal birefringence in the optical fi ber. Applying a polynomial fi t to the measured data, the wavelength dependence of the phase modal birefringence can also be determined.

White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica

Spectral interference fringes resolved at the output of the uncompensated (dispersive) Michelson interferometer by a low-resolution miniature fibre-optic spectrometer are used to measure the equalization wavelength as a function of the displacement in the interferometer. In the spectral range approximately from 500 to 900 nm, it is confirmed that the group refractive index dispersion in the interferometer beam splitter made of fused silica agrees well with that resulting from the Sellmeier dispersion equation. Moreover, the beam splitter effective thickness is determined either by using the slope of a linear fit function for the displacement dependence on the group refractive index or by means of a least-squares fitting of the experimental data to the theoretical differential group refractive indices.

Dispersive white-light spectral interferometry to measure distances and displacements

Processing of the spectral interferograms recorded at the output of a dispersive Michelson interferometer by a low-resolution spectrometer is performed with a knowledge of both dispersion and thickness of the interferometer optical element (beam splitter or optical sample). The recorded spectral interferograms, including the equalization wavelengths, are fitted by using a least-squares method to the theoretical interferograms to obtain the optical path differences (OPDs) between interfering beams. From the OPDs, which vary with both the wavelength-dependent refractive index and the thickness of fused-silica optical element, distances or displacements are determined. Within two different configurations of a dispersive Michelson interferometer we show that the range of measurable distances depends on the thickness of the optical element. We also confirm by this measurement technique that errors of manually adjusted 10 μm displacements of the interferometer mirror are below 1 μm.

White-light spectral interferometry to measure intermodal dispersion in two-mode elliptical-core optical fibres

Abstract White-light spectral interferometric technique employing a low-resolution spectrometer is used to measure intermodal dispersion for LP x 01 and LP x 11 modes of elliptical-core optical fibres in the spectral range approximately from 540 to 870 nm. The technique utilizes a tandem configuration of a Michelson interferometer and an optical fibre to measure the equalization wavelengths as a function of the optical path difference (OPD) between beams of the interferometer, or equivalently, the wavelength dependence of the intermodal group OPD in the optical fibre. A polynomial fit applied to the measured data gives the wavelength dependence of the difference between propagation constants of modes with 2π ambiguity. The wavelength dependences of both the difference between propagation constants of modes and the intermodal group OPDs obtained are used to compare the theoretical spectral interferograms with the recorded ones and to confirm good agreement between theory and experiment.

White-light spectral interferometric technique to measure the wavelength dependence of the spectral bandpass of a fibre-optic spectrometer

Abstract A spectral-domain white-light interferometric technique with channelled spectrum detection is used to measure the wavelength dependence of the spectral bandpass of a fibre-optic spectrometer. In an experimental setup comprising a halogen lamp, a non-dispersive Michelson interferometer and the spectrometer to be measured, spectral interferograms are recorded for different optical path differences (OPDs) between interfering beams. By processing the recorded spectral interferograms using discrete filtering and a fringe amplitude demodulation method, spectral fringe visibilities, first, as a function of the wavelength for given OPDs, and second, as a function of the OPD at given wavelengths, are obtained. It is confirmed, in accordance with theory, that the latter spectral fringe visibility functions are Gaussian functions with maxima and widths dependent on the wavelength. From the widths of the Gaussian spectral fringe visibility functions the wavelength dependence of the spectrometer bandpass is determined over a wide spectral range.

The Mutual Interference of Modes of a Few-mode Fibre Waveguide Analysed in the Frequency Domain

The interference between modes of a few-mode weakly guiding fibre waveguide is investigated in the frequency domain at the exit face of a fibre waveguide as well as at the output of a Michelson interferometer by using classical coherence formalism and the coherent-mode representation. It is revealed that a variable sinusoidal spectral modulation is present at the exit of a two-mode fibre waveguide and that the mutual interference of modes analysed at the output of a Michelson interferometer by a low-resolution spectrometer gives the interference fringes of suitable visibility. A comparison is made between the interference in the frequency domain and that in the time domain with particular emphasis on possible sensor applications.

Dispersive spectral-domain two-beam interference analysed by a fibre-optic spectrometer

Abstract The effect of a fibre-optic spectrometer on analysed spectral interference of two beams from a white-light source is studied theoretically and experimentally, including the effect of dispersion in an interferometer. First, the spectral interference law is expressed analytically under the condition of a Gaussian response function of a fibre-optic spectrometer, and then second, the theoretical analysis is accompanied by three experiments employing a fibre-optic spectrometer and a Michelson interferometer with different amounts of dispersion. Within one experiment the interference fringes are resolved over a wide spectral range and within two experiments the interference fringes are resolved only in a narrow spectral range around a wavelength at which the group optical path difference between interfering beams is zero. Knowing dispersion in the interferometer and the bandpass of the spectrometer, the positions of the interferometer mirror in the corresponding range are determined and good agreement between the recorded spectral interferograms and the theoretical ones is found.

Spectral and Dispersion Analysis of Laser Sources and Multimode Fibres Via the Statistics of the Intensity Pattern

Abstract The statistics of an intensity pattern at the exit face of a multimode fibre excited by a quasimonochromatic source is analysed by means of an expression for speckle pattern contrast. Theoretical considerations that take advantages of both classical coherence formalism and guided-mode field representation of light propagating in multimode fibres lead to two equivalent expressions for speckle pattern contrast; the first is expressed in the time domain by using a source temporal coherence function and the second is expressed in the frequency domain by using a frequency correlation function of the source spectral density. Moreover, the modal guiding conditions in multimode fibre are in both expressions governed by a maximum group delay time difference. The feasibility of both expressions, especially the second, is demonstrated by analytic expressions for the speckle pattern contrast for seven different spectra, that is the influence of the source temporal coherence as well as the modal dispersion is...

Measuring intermodal dispersion in optical fibres using white-light spectral interferometry with the compensated michelson interferometer

Abstract Employing a low-resolution miniature fibre-optic spectrometer, it is demonstrated that the spectral interference fringes are resolved at the output of a tandem configuration of the compensated (non-dispersive) Michelson interferometer and a two-mode optical fibre only in the vicinity of two different equalization wavelengths. Namely, the overall equalization wavelength at which the optical path difference (OPD) in the interferometer is the same as the group OPD between modes, and the fibre equalization wavelength at which the group OPD between modes is zero. Moreover it is shown that the OPD adjusted in the interferometer and measured as a function of the overall equalization wavelength gives directly the spectral dependence of the intermodal group OPD in an optical fibre. Thus the new technique of white-light spectral interferometry is used to measure intermodal dispersion in two different two-mode optical fibres in the spectral range approximately from 620 to 850 nm.

Evaluation of spectral modulated interferograms using a Fourier transform and the iterative phase-locked loop method

Spectral modulated interference fringes are observed in the form of the periodical modulation of a broadband spectrum at the output of an interferometer provided with a subsequent spectrometer. The group optical path difference of interfering light waves corresponding to the distance from the surface to be measured is characterized by the spectral fringe phase function. To recover the phase functions, a standard, Fourier-transform method, or parametric methods like a phase-locked loop (PLL) method, can be used. In the former case, the Fourier spectrum in the wavelength domain is computed and filtered out to obtain the reference spectrum and the overall phase information using a phase-unwrapping algorithm. In the latter case, the fringe phase deviations are traced dynamically in the independent variable domain, i.e. in the wavelength domain when the PLL method is applied to spectral interferometry. The PLL method was used to demodulate spectral fringes iteratively. A spectral fringe signal with a priori unknown carrier fringe frequency is considered and at the first iteration step a fringe phase equal to zero is supposed. The second iteration takes the demodulated phase found from the first iteration etc. As a result, the unwrapped phase function of the spectral fringes is found.