Measuring dispersion between two modes of an optical fibre using low-coherence spectral interferometry with a Michelson interferometer

Abstract

It is demonstrated experimentally that even if the spectral interference between two modes of an optical fibre excited by a low-coherence source is not resolved at its output by a spectrometer of a given resolving power, it is resolved in the Michelson interferometer configuration. In a tandem configuration of a dispersive Michelson interferometer and a two-mode optical fibre, the optical path difference (OPD) in the interferometer is adjusted close to the group OPD between modes to produce a low-frequency spectral modulation that can be processed. Thus, using the Fourier-transform method in processing the measured spectral modulations and subtracting the effect of the dispersive Michelson interferometer, the wavelength dependence of the group OPD between two modes of the optical fibre over a limited spectral region is obtained.     

Far zone spectral shifts in light propagation from the exit face of a few-mode fibre waveguide guiding the frequency-dependent linearly polarized modes

Abstract

Far zone spectral shifts, including free space propagation of light from a planar secondary, partially coherent source represented by the exit face of a few-mode fibre waveguide, are investigated in the paraxial regime by using frequency-dependent linearly polarized (LP) modes guided by the fibre waveguide. The origin of the far zone blue or red spectral shift of individual frequency-dependent LP modes, as well as of their superposition at the particular observation point, is clarified. In particular, the dependence of the wavelength shifts of spectra on the position of the observation point in the far zone plane and the primary source linewidth is studied for the two-mode, weakly guiding, step-index fibre waveguide.     

Near-field characterization of thin planar optical waveguides

Abstract

A detailed near-field analysis of planar waveguides supporting two modes has been carried out. Theoretical calculations for both step- and gradedindex profiles, have shown the near-field features produced by interference of the two mode wavefunctions, which depend on their phase difference and intensity ratio. Theoretical results have been experimentally confirmed by performing an independent control of the two last magnitudes during the measurements. Fitting the calculated near-field intensity distribution to the measured one, the index profile of the waveguide has been reconstructed. The profile parameters differ by less than 5% from those obtained with the m-line method. Theoretical and experimental single mode analysis, also included for comparison, result in less accurate parameters showing index jump deviations, with respect to the m-line method, of the order of 10%.     

Experimental Demonstration of Spectral Modification in a Mach-Zehnder Interferometer

Abstract

We illustrate here the experimental verification of the spectral modulation arising from interference of light beams having different degrees of correlation in a Mach-Zehnder interferometer for which the theoretical study was done by Agarwal and James (1993, J. mod. Optics, 40 1431). Through a theoretical fitting for the observed spectral modification, path difference between the beams in the two arms is calculated and compared with the experimental values.     

Nonlinear Dispersion Coefficients of a Cylindrical Optical Waveguide

Abstract

The nonlinear carrier wave dispersion relation at weak nonlinearity is derived for the linearly polarized (LP) modes of a step-index optical fibre that has both a nonlinear core and a nonlinear cladding. The calculation begins with the exact equations for the nonlinear fibre and the nonlinear shift (coefficient), from its linear value, of the propagation wave-number is given in closed analytical form. The nonlinear coefficient is completely general and accounts both for the nonlinearity and the structure of the guided mode. Some numerical results for the LP₀₁ mode are presented which show that significant deviations occur from the conventionally accepted (averaged) nonlinear coefficient.     

Measuring dispersion between two modes of an optical fibre using time-domain and spectral-domain low-coherence interferometry

Abstract

Group optical path difference (OPD) between two modes of an optical fibre excited by a low-coherence source characterized by a multimode spectrum is evaluated measuring both the visibility dependence in the Michelson interferometer configuration and the spectral modulation at the output of the optical fibre. Using the Fourier-transform method in processing the measured spectral modulations, a slight wavelength dependence in the group OPD between two modes of the optical fibre is resolved. Comparing the group OPD corresponding to a central wavelength of the measured spectral region with the group OPD obtained from the measured visibility dependence, good agreement between results of the measurements in the spectral domain and in the time domain is achieved.     

Temperature and voltage sensings by mode‐mode interference in polarization‐maintaining optical fibers

Abstract

Two optic fiber sensing systems for temperature and voltage have been developed which utilize the mode‐mode interference of the two orthogonally polarized modes, HE^x _II and HE^y _II, in two commencal polarization‐maintaining fibers (bow‐tie and elliptical core fibers). A package of controlled programs in a Macintosh computer, which can record and process all related data automatically, is established for temperature sensing. The signal drifting problem in voltage sensings has been investigated, and the elimination of signal drifting is obtained by the phase tracking with direct current technology The agreement between the sensing results for temperature and dynamic voltage and those predicted by experimental principles is satisfactory, which confirms the validity of the developed sensing systems.     

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.     

The role of hyper-Raman transitions in the radiation spectrum of a strongly driven two-level atom

Abstract

Numerical results are presented on the spectrum of the light scattered into the vacuum modes by a two-level atom driven by a strong ramped field of frequency smaller than the natural atomic frequency. The attention is focused on the role of the hyper-Raman part of the spectrum, which is shown to decrease dramatically with increasing ramp time. It is suggested that this may explain lack of experimental observation of the hyper-Raman lines. For zero ramp time, the numerical intensity of both high-order harmonics and hyper-Raman peaks is shown to agree satisfactorily with previous analytical predictions except in the region of overlap of the two series of peaks. This lends support for the suggestion that the plateau in the spectrum is related to quantum-mechanical interference between high-order harmonics and hyper-Raman processes. There is also good agreement between the numerical amplitude of the plateau and previous analytical predictions. A physical mechanism for the cut-off frequency which terminates the plateau, based on approximate energy conservation in hyper-Raman transitions, is presented and is shown to be in agreement with present numerical and previous analytical results.     

Analysis of time-domain and spectral-domain two-beam interference including the effect of a variable spectral bandpass of a detecting system

Abstract

The effect of a variable Gaussian response function of a monochromator in a detecting system with a broadband detector is included in the theoretical and experimental analysis of time-domain and spectral-domain interference of two light beams from a source of a multimode Gaussian spectrum. The time-domain theoretical analysis gives the analytic expressions for the measured complex degree of temporal coherence of the light with and without the effect of variable spectral bandpass of the detecting system. The spectral-domain theoretical analysis of the two-beam interference gives the spectral interference law from which the visibility of the spectral interference fringes resolved for a given delay in the interferometer by a spectrometer is expressed as a function of the bandpass of the spectrometer. The theoretical conclusions are confirmed experimentally in the Michelson interferometer configuration using a laser diode operated below the threshold, a prism monochromator and a p-i-n photodetector. From the width of the central peak in the measured visibility dependence that narrows with increasing slit width of the monochromator, the spectral bandpass of the monochromator is evaluated. It is also shown how the visibility of the spectral interference fringes decreases as the slit width of the prism spectrometer increases.     

General Implementation of the Incoherent Optical Fourier Transform by Interference

Abstract

The possibility of performing an incoherent optical Fourier transform with interferometers comprising two arms optically centred on the same axis has been investigated. Any interferometer of this type is suitable provided two conditions are met: the centre of the source should be imaged through both arms onto the same point, and the centre of the observation plane should be the image through both arms of the same point. One possible experimental set-up is introduced and results are presented.     

Indirect interference of two modes with different frequencies at the one-photon level

Abstract

The possibility of observing interference with two modes of different frequencies in a one-photon state by means of parametric up-conversion is studied. This phenomenon could be utilized for discernment between pure and mixed states. There is also a close connection to the question of the extent of indefiniteness of the photon's path.     

Spontaneous emission from a three-level atom in two-band photonic crystals

Abstract

We investigate the spontaneous emission from a V three-level atom embedded in two-band isotropic photonic crystals. The dipoles of the two transitions from the two upper levels to the lower level are parallel. Due to the quantum interference between the two transitions and the existence of two bands, the populations in the upper levels display some novel properties, such as anti-trapping and continuous oscillation, which differ from that of a two-level atom (with two bands) and also differ from that if only one band (for three-level atom) is considered. The spontaneous emission field is composed of two parts: localized field and travelling field. The localized field is composed of one or two localized modes, and the travelling field is composed of no, one, two or three propagating modes depending on different conditions. The conditions for different combinations of localized modes and propagating modes are discussed.     

Measuring a spectral bandpass of a fibre-optic spectrometer using time-domain and spectral-domain two-beam interference

Abstract

Spectral bandpasses of a miniature spectrometer with three read fibres of different core diameters are obtained using the visibility functions for both spatial and spectral fringes resolved in the interference of two light beams from a laser diode operated below the threshold. From a width of the central peak of the visibility function for the spatial interference fringes measured in the Michelson interferometer configuration with a broadband detector, the source spectral width is evaluated. From widths of the visibility functions for the spectral interference fringes measured in the Michelson interferometer configuration by the spectrometer with the different read fibres, the overall spectral bandpasses are evaluated. Subtracting the effect of the source spectral width, the spectral bandpasses of the fibre-optic spectrometer are determined. These are compared with the directly measured bandpasses using the delta-function spectrum of the same laser diode operated far above the threshold.     

Design of a compact dual-mode ring resonator bandpass filter with harmonic suppression

Abstract

An approach to suppress the harmonic responses in a dual-mode circular ring resonator bandpass filter is presented. Feed lines with one-sided coupling arms are suitably relocated around the ring resonator to introduce phase interference between two degenerate modes for simultaneously suppressing the second and third harmonics. Three open loop resonators at the rim of the ring are adopted to further suppress the second harmonic. By fabricating on a FR4 glass-epoxy base, this approach is demonstrated to have effectiveness in broadening the filter's rejection band in both simulations and measurements without affecting the fundamental response or increasing the device size.     

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.     

Low-frequency Beats Produced by Interference of Laser Modes

Abstract

A helium-neon laser operating in three or more axial modes can generate, at a photo detector with a nonlinear response to intensity, beat signals with frequencies corresponding to the second differences between the frequencies of these modes. This paper presents a quantum-field theoretical treatment of the formation of such low-frequency beats, as well as experimental data demonstrating that interference effects corresponding to the production of such beats can be observed even at light levels at which the probability of at least one photon from each of the three modes being present simultaneously in the optical path is negligible.     

Intensity Distribution Across a Source from Spectral Measurements

Abstract

The degree of spectral coherence (μ₁₂(ω)) over the plane of a double slit is determined from the measurement of spectral changes in Young's interference experiment using the spectral interference law. The experimental and theoretically calculated values of μ₁₂(ω)) for the experimental parameters agree well within experimental error, thus supporting the theoretical prediction of D. F. V. James and E. Wolf (1991, Phys. Lett. A, 157 6). The degree of spectral coherence determined is used for estimating the intensity distribution across a source. This new approach, being a simple spectral measurement technique, might find its application in astronomy, particularly for the study of intensity distribution across stars.     

Diffraction Properties of Absorbing Cylinders Suspended in Outside Absorbing Media

The forms of the diffracted E and H fields, for absorbing cylinders with radii small compared to the wavelength and suspended in outside absorbing media, have been determined from Maxwell's equations and boundary conditions, when these cylinders are illuminated by plane periodic electromagnetic waves in a direction perpendicular to their axes, and the electric vector is parallel or perpendicular to the axes. From these E and H fields the time averages of the radiant flux and the electric field energy densities consist of exponentially increasing or decreasing background terms, characteristic of the incident and diffracted waves, and interaction terms, which generate exponentially decreasing maxima and minima or interference fringes, whose radial spacings increase with the angle from the direction of incidence. The radiant fluxes have properties characteristic of creeping waves. Particular attention has been devoted to determining the boundary conditions for each of the vector fields and retaining the proper coefficients, so that direct comparisons can be made between the two polarizations. In all cases the magnitudes and forms of these vector fields are functions of the material constants of both media, the wavelength, the modes being excited, the cylinder radius and the polarization used.     

Influence of Kerr-like medium on the dynamics of a two-mode Raman coupled model

Abstract

We study the quantum dynamics of an effective two-level atom interacting with two modes via Raman process inside an ideal cavity in the presence of Kerr non-linearity. The cavity modes interact both with the atom as well as the Kerr-like medium. The unitary transformation method presented here, not only solves the time-dependent problem, but also provides the eigensolutions of the interacting Hamiltonian at the same time. We study the atomic-population dynamics and the dynamics of the photon statistics in the two cavity modes. The influence of the Kerr-like medium on the statistics of the field is explored and it is observed that Kerr medium introduces antibunching in mode 1 and this effect is enhanced by a stronger interaction with the non-linear medium. In the high non-linear coupling regime anticorrelated beam become correlated. Kerr medium also introduces non-classical correlation between the two modes.