Mach-Zehnder Interferometer Setup Research Articles

Detection of polarization-spatial classical optical entanglement in partially coherent light fields using intensity measurements.

Detection of polarization-spatial classical optical entanglement through implementation of partial transpose on measured intensities is explored. A sufficient criterion for polarization-spatial entanglement in partially coherent light fields based on intensities measured at various orientations of the polarizer, as implied through partial transpose, is outlined. Detection of polarization-spatial entanglement using the outlined method is demonstrated experimentally through a Mach-Zehnder interferometer setup.

Fast Quench Detection in SFCL Pancake Using Optical Fibre Sensing and Machine Learning

A fast hotspot detection technique has been implemented and patented at École Polytechnique Fédérale de Lausanne (EPFL) under the European Union project FastGrid. The optical fibre sensing based technique uses the Mach-Zehnder Interferometer (MZI) and can detect even singular hotspots in the superconductor within 15ms. The MZI setup is very sensitive to external perturbations and mechanical stresses, which can manifest in the output along with the response to hotspots. The disturbance the setup is subject to, varies with the sample being tested and the environment it is being tested in. For example, the sample length and configuration, in addition to the routing of the optical fibre can determine the extent of the stresses on the optical fibre. Previous publications, showcased experiment results on relatively simple sample configurations which were straight HTS tapes with short lengths (0.3m or 1m). This manuscript will investigate the technique feasibility for a more complicated sample type: a pancake prototype for a superconducting fault current limiter (SFCL), comprising 12m of HTS tape in a bifilar winding, with taped optical fibre along the length of the conductor. The manuscript will also give a brief overview of a machine learning based post processing technique for the experimental data, developed at EPFL to supplement the MZI based quench detection for easy and reliable quench detection in large scale applications.

Single-shot interferometric measurement of pulse-to-pulse stability of absolute phase using a time-stretch technique.

Measurement of the absolute phase of ultrashort optical pulses in real-time is crucial for various applications, including frequency comb and high-field physics. Modern single-shot techniques, such as dispersive Fourier transform and time-lens, make it possible to investigate non-repetitive spectral dynamics of ultrashort pulses yet do not provide the information on absolute phase. In this work, we demonstrate a novel approach to characterise single-shot pulse-to-pulse stability of the absolute phase with the acquisition rate of 15 MHz. The acquisition rate, limited by the repetition rate of the used free-running mode-locked Erbium-doped fibre laser, substantially exceeds one of the traditional techniques. The method is based on the time-stretch technique. It exploits a simple all-fibre Mach-Zehnder interferometric setup with a remarkable resolution of ∼7.3 mrad. Using the proposed method, we observed phase oscillations in the output pulses governed by fluctuations in the pulse intensity due to Kerr-induced self-phase modulation at frequencies peaked at 4.6 kHz. As a proof-of-concept application of the demonstrated interferometric methodology, we evaluated phase behaviour during vibration exposure on the laser platform. The results propose a new view on the phase measurements that provide a novel avenue for numerous sensing applications with MHz data frequencies.

Self-referenced interference of laterally displaced vortex beams for topological charge determination

The optical vortex beam having helical phasefront carries well-defined orbital angular momentum (OAM) which can be specified by its topological charge (TC). This study demonstrates that interferogram having conjoined forks structure produced by self-referenced interference of laterally displaced vortex beams, allows simpler and unambiguous way of determining the sign and magnitude of TC. The proposed method uses a Mach–Zehnder interferometer set-up with controlled lateral displacement and tilt angles between the interfering beams, which results into an interferogram with better visual inspection. Theoretical description including intensity and phase profile has been presented.

Modified Mach-Zehnder interferometer for determining the high-order topological charge of Laguerre-Gaussian vortex beams.

This study demonstrates a self-referenced interferometric method to estimate the magnitude and sign of a high-order topological charge (TC) carried by incoming optical vortex beams. The proposed method uses a right-angle prism in a Mach-Zehnder interferometer setup with controlled lateral shift and tilt between the wavefronts of interfering beams. The in-line interference with its conjugate results in a petal-shaped fringe pattern, where the number of petals reveals the magnitude of the TC. When the direction of one of the interfering beams is laterally displaced and rotated to emerge at a small angle for off-axis interference such that the vortices overlap at the output plane, then a fork-like interference pattern with better visibility is obtained, which can be used for estimating the magnitude as well as the sign of the TC. Through numerical simulation and optical experiment, it is shown that the technique is capable of estimating the TC of Laguerre-Gaussian beams even with a nonzero radial index.

Imaging Michelson interferometer for a low-density gas jet characterization.

A new optical probing method with increased interferometric sensitivity for a low-density gas jet characterization is presented. The proposed technique employs a Michelson interferometer with a self-imaging object arm, which enables the relay imaging of the object on itself, and in this way, the phase sensitivity of the device is increased by a double propagation of the object laser beam through the gas jet. The wavelength of 405 nm was chosen to further increase the sensitivity by increasing the probe wavenumber. A low-density argon gas jet with various backing pressures was characterized by our method and by a commonly used Mach-Zehnder interferometer setup showing the expected twofold increase in the signal to noise ratio in the double pass configuration.

Weak-measurement Mach-Zehnder interferometer for testing wave-particle duality

The Mach-Zehnder interferometer (MZI) is a regular yet simple instrument to test wave-particle duality. One key device in a standard MZI is the beam splitter 2 (BS2). Here we make a simple quantum mechanics analysis about the wave function evolution and find that the strong and exclusive interaction of BS2 with the incident microscopic particle beam (photons, electrons, etc.) is the fundamental reason why standard MZIs could not allow for the simultaneous observation of wave and particle properties of these particles. A weak-measurement (WM) MZI setup is then proposed, where BS2 is replaced with a deliberately designed highly transparent interference screen operating via either weak absorption or weak-scattering effect. Quantum-mechanical analysis on this WM-MZI shows that the overall power to make simultaneous observation of interference fringe (wave nature) and which-path information (particle nature) of microscopic particles can be significantly enhanced compared with the standard MZIs.

Phase estimation using phase gradients obtained through Hilbert transform.

An algorithm to extract phase in its unwrapped form from an interferogram having perturbed straight line fringes is proposed and studied. Phase gradients are extracted from an interferogram using the Hilbert transform, and the phase is then estimated from their gradients using the method of least squares for the Hudgin geometry. The matrix inversion required in implementing the method of least squares for the Hudgin geometry is carried out analytically by exploiting the additional symmetries available in the Hudgin matrix. The consistency of the proposed algorithm is demonstrated through its implementation, both on numerically generated interferograms, as well as on interferograms measured in a Mach-Zehnder interferometric setup, where the respective imparted phases were random, and corresponded to atmospheric turbulence-like models.

Determination of the glass wall effect in optical measurement of temperature in liquid using Mach–Zehnder interferometer

For optical experiments in which the change of refractive index is monitored, the refractive index of glass would change due to the change of temperature along the walls, and, as a result, the measurements of temperature and concentration would be affected. Because of this, one may use another temperature measurement technique parallel with a Mach–Zehnder interferometer (MZI). For instance, thermocouples or thermometers can be implemented inside the walls to obtain the temperature at the walls and close to the liquid region. The main limitation of this technique is that it provides information at a specific location and not along the walls or inside the liquid zone. On the other hand, the measurement is performed at the location close to the liquid region and not inside the liquid. Thus, in this study, we suggest using the optical method with some modifications that clear up the mentioned limitations. Accordingly, the optical effect of glass in the laser interferometry experiment is first studied. Then, we suggest two experimental methods based on modifications in the experimental setup and the image processing technique of MZI to accurately determine the glass effect and remove this effect from the temperature and concentration measurements. Implementing any of these techniques results in accurate measurement of the temperature and concentration of the liquid in any rectangular cell. Finally, according to the results of this study, it can be claimed that a temperature profile can be obtained precisely using MZI, and the existence of other apparatus to measure the temperature is redundant for the MZI setup. This outcome offers a simpler and more precise measurement of either temperature or concentration profiles of any transparent liquid.

Development of measuring diffusion coefficients by digital holographic interferometry in transparent liquid mixtures.

As for the measurement of diffusion coefficient in transparent liquids by digital holographic interferometry, there are many kinds depending on the mathematical model and experimental setup. The method of using the distance of the peaks in concentration difference profile to determine diffusion coefficient by Mach-Zehnder interferometric experimental setup, is easy to handle. In order to improve the accuracy and convenience of measurement in this method, we combine procedures of hologram analysis used by Mialdun et al (2011) and those by He et al (2009). By using polynomial to fit the continuous phase difference (interference phase) of object beam, it can be more convenient and accurate to determine the distance between the two peaks. Besides, the shift of initial time has been discussed as a separated topic at the first time and two functions for minimization have been given for determination of the initial time in this paper. With the development, diffusion coefficient of KCl in water at 0.33mol/L and 25 °C has been measured. The diffusion coefficient is 1.844 × 10(-9) m2/s with the uncertainty of ± 0.012 × 10(-9) m2/s. Our measurement has more similar result with other methods than holographic interferometry. The relative uncertainty of diffusion coefficient in our experiment is less than 1% and total uncertainty of temperature is within ± 0.04 K.

Phase-sharing using a Mach-Zehnder interferometer.

A phase-sharing scheme using the Mach-Zehnder interferometric setup is demonstrated. Two coherent light fields of the same wavelength which have orthogonal polarizations are used as sources at the two ends of a Mach-Zehnder interferometer. They are made to interfere independently at the opposing ends of the interferometer so that the phase estimated by two observers at the two opposing ends of the interferometer is nearly identical. The scheme could in principle be used by two observers to simultaneously monitor and study a phase object inserted in one of the arms of the interferometer. A pseudorandom phase plate which mimics atmospheric turbulence is inserted in one of the arms of the interferometer to demonstrate that such a phase-sharing scheme could be converted to a secret-key sharing scheme. Shared secret-key generation is demonstrated through evaluation of the phase correlates of the shared phase samples available at their respective ends. The shared random phases could also be used in a more direct manner by the respective observers for random phase encryption of images.

Simultaneous measurement of refractive index and temperature using multimode microfiber-based dual Mach-Zehnder interferometer.

A multimode microfiber (MMMF)-based dual Mach-Zehnder interferometer (MZI) is proposed and demonstrated for simultaneous measurement of refractive index (RI) and temperature. By inserting a section of MMMF supporting a few modes in the sensing arm of the MZI setup, an inline interference between the fundamental mode and the high-order mode of MMMF, as well as the interference between the high-order mode of MMMF and the reference arm, i.e., the dual MZI, is realized. Due to different interference mechanisms, the former interferometer achieves RI sensitivity of 2576.584 nm/RIU and temperature sensitivity of -0.193 nm/°C, while the latter one achieves RI sensitivity of 1001.864 nm/RIU and temperature sensitivity of 0.239 nm/°C, demonstrating the ability to attain highly accurate multiparameter measurements.

Enhanced Electro-Optic Property in ${\rm LiNbO}_{3}$ by Electric Field Domain Inversion

Change in the value of half-wave voltage of ${\rm LiNbO}_{3}$ ( $z$ -cut) before and after high electric field domain inversion at room temperature has been reported. For verification, a Mach–Zehnder interferometric setup is used and the voltage required for phase reversal of the fringe pattern is noted for single domain and domain inverted sample. The technique of the used domain inversion process is discussed and confirmation of the domain inversion is also done. As the half-wave voltage decreases after domain inversion, it may be assumed that the overall electro-optic property of ${\rm LiNbO}_{3}$ has been enhanced. This might possibly been caused by the internal field compensating the spontaneous polarization of the crystal.

2-step Quadrature Phase-shifting Digital Holographic Optical Encryption using Orthogonal Polarization and Error Analysis

In this paper, a new 2-step quadrature phase-shifting digital holographic optical encryption method using orthogonal polarization is proposed and tolerance errors for this method are analyzed. Unlike the conventional technique using a PZT mirror, the proposed optical setup comprises two input and output polarizers, and one λ/4-plate retarder. This method makes it easier to get a phase shift of π/2 without using a mechanically driven PZT device for phase-shifting and it simplifies the 2-step phase-shifting Mach-Zehnder interferometer setup for optical encryption. The decryption performance and tolerance error analysis for the proposed method are presented. Computer experiments show that the proposed method is an alternate candidate for 2-step quadrature phase-shifting digital holographic optical encryption applications.

Duality relations in a two-path interferometer with an asymmetric beam splitter

We investigate quantitatively the wave-particle duality in a general Mach-Zehnder interferometer setup with an asymmetric beam splitter. The asymmetric beam splitter introduces additional a priori which-path knowledge, which is different for a particle detected at one output port of the interferometer and a particle detected at the other. Accordingly, the fringe visibilities of the interference patterns emerging at the two output ports are also different. Hence, in sharp contrast with the symmetric case, here we should concentrate on one output port and distinguish two possible paths taken by the particles detected at that port among four paths. It turns out that two nonorthogonal unsharp observables are measured jointly in this setup. We apply the condition for joint measurability of these unsharp observables to obtain a trade-off relation between the fringe visibility of the interference pattern and the which-path distinguishability.

Vibration detection using focus analysis of interferograms

This paper proposed an automated technique for vibration detection using statistical focus measure to evaluate interferogram contrast. An interferogram sequence from a Mach-Zehnder interferometer setup is recorded (frame rate: 24 fps) and the gray-level variance (GLVA) is plotted versus time. Occurrence of induced vibration in the setup causes a decrease in the interferogram contrast which, in turn, manifests as an evident rapid drop in the variance plot. The technique is demonstrated experimentally using periodic microvibrations (frequency range, ≤6 Hz) and aperiodic disturbances.

Development of a time-resolved white-light interference microscope for optical phase measurements during fs-laser material processing

A modified Mach-Zehnder interferometer set-up combined with microscope objectives has been developed for the measurement of phase changes in the processed ma- terial sample, like modification and melting of glass. The white light is generated by focusing ultrafast laser radiation (tp = 80 fs) in a sapphire crystal using a micro-lens array to minimize temporal and spatial fluctuations in the white- light continuum. Lateral and coaxial pump-probe measure- ments of the phase changes during material processing are performed using two coupled ultrafast laser sources at dif- ferent repetition rates (frep = 1 Hz-1 MHz). The optical phase shift and therefore the refractive index of the material are calculated from the interference images using two ap- proaches. The knowledge of the refractive index during the laser processing with a temporal resolution in the ps-range and a spatial resolution of several microns leads to a bet- ter understanding of the initial processes for the permanent material modifications.

Comparisons of multi-wavelength oscillations using Sagnac loop mirror and Mach-Zehnder interferometer for ytterbium doped fiber lasers

A multiwavelength Ytterbium-doped fiber ring laser operating at 1030 nm region is demonstrated using a Sagnac loop mirror and a Mach-Zehnder interferometer. We report the Performance comparisons of multi-wavelength oscillations in Yb3+ doped fiber lasers (YDFL) with typical commercial ytterbium doped silica fibers. By adjusting the polarization controller (PC), a widely tunable laser range of 22 nm from 1030 nm to 1050 nm is obtained. The Mach-Zehnder interferometer (MZI) design has exhibited simplicity in the operation for controlling the smallest wavelength spacing compared to Sagnac loop mirror method. In our observations, the smallest achieved stable wavelength spacing in Sagnac loop mirror setup and MZI setup were 2.1 nm and 0.7 nm, respectively. In case of nine-wavelength operation with a MZI setup, the stability, Full Width at Half Maximum (FWHM) and side mode suppression ratio (SMSR) of laser lines are not affected by increasing pump power, While for above four wavelength operation, the laser stability with Sagnac loop mirror becomes worse specially for higher input pump power and the power fluctuation among the wave-lengths would be also slightly larger.

Duality relation and joint measurement in a Mach-Zehnder interferometer

The Mach-Zehnder interferometric setup quantitatively characterizing the wave-particle duality implements in fact a joint measurement of two unsharp observables. We present a necessary and sufficient condition for such a pair of unsharp observables to be jointly measurable. The condition is shown to be equivalent to a duality inequality, which for the optimal strategy of extracting the which-path information is more stringent than the Jaeger-Shimony-Vaidman-Englert inequality.

Precision refractive index measurements of air, N_2, O_2, Ar, and CO_2 with a frequency comb

We report precision measurements of the refractive indices of dry air, N(2), O(2), Ar, and CO(2), performed by using a frequency comb as the light source in a Mach-Zehnder interferometer setup. Improved dispersion formulas for all gases are derived with a sensitivity level of 10(-9). These results are valid for a wavelength range from 740 to 860 nm and are in good agreement with measurements from other groups.