Interferometer Mach-Zehnder

Analogous to the Michelson interferometer, the Mach-Zehnder interferometer is based on the two-beam interference by amplitude splitting of the incoming wave. The two waves travel along different paths (Fig.4.30a). Inserting a transparent object into one arm of the interferometer alters the optical path difference between the two beams. This results in a change of the interference pattern, which allows a very accurate determination of the refractive index of the sample and its local variation. The Mach-Zehnder interferometer may be regarded therefore as a sensitive refractometer. 

If the beam splitters Bj, and the mirrors Mj, Mj are all strictly parallel, the path difference between the two split beams does not depend on the angle of incidence o because the path difference Aj = B Mj = 2acosa between the beam I and 3 is exactly compensated by the sampe path length between M2 and B2 (Fig.4.30b). This means that the interfering waves in the symmetric interferometer (without sample) experience the same path difference on the solid path as on the dashed path in Fig. 4.30a. Without the sample the total path difference is therefore zero, and it is As = (n-l)L with the sample having the refractive index n in one arm of the interferometer. 

The Mach-Zehnder interferometer has found a wide range of applications. Density variations in laminar or turbulent gas flows can be seen with this technique and the optical quality or mirror substrates of interferometer plates can be tested with high sensitivity [4.26,27]. 

A sample in path 3 introduces an additional path difference A ( ) = ( -l)Z/COSy0 

Analogous to the Michelson interferometer, the Mach-Zehnder interferometer is based on the two-beam interference by amplitude splitting of the incoming wave. The two waves travel along different paths with a path difference 

A sample in path 3 introduces an additional path difference 

In order to get quantitative information of the local variation of the optical path through the sample, it is useful to generate a fringe pattern for calibration purposes by slightly tilting the plates and B2, 

2a cos(a - 3). After being recombined, the two beams therefore have a path difference 

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Fig. 1. Representative device configurations exploiting electrooptic second-order nonlinear optical materials are shown. Schematic representations are given for (a) a Mach-Zehnder interferometer, (b) a birefringent modulator, and (c) a directional coupler. In (b) the optical input to the birefringent modulator is polarized at 45 degrees and excites both transverse electric (TE) and transverse magnetic (TM) modes. The appHed voltage modulates the output polarization. Intensity modulation is achieved using polarizing components at the output.

The Mach-Zehnder Interferometer operates in a similar way, except that the input hght is divided into two arms and the pinhole is placed in one of the arms (Fig. 4bb). A disadvantage here is the possibility of having non-common path errors between the two arms. This system was proposed for use in AO by Angel (1994). The Interferometer which has been most commonly used in AO systems is the Lateral Shearing Interferometer (LSI). In this device, the wavefronts are made to coincide with slightly shifted versions of themselves. Let nl(r) and u2(r) represent the original and shifted wavefronts. 

Heideman R.G., H. Kooyman R. P., Greve J., Performance of a highly sensitive optical waveguide Mach-Zehnder interferometer immunosensor, Sensors and Actuators B 1993 10 209-217. 

Figure 3. Mach-Zehnder interferometer One of the arms is covered by inert material (reference arm), the other arm exposes to the sample (measuring arm).

In the following, the application of these concepts is shown both for reffactometric and reflectometric measurements using Mach-Zehnder interferometers and reflectometric interference spectroscopy. 

Mach-Zehnder interferometers allow the monitoring of gas concentrations and even the determination of analytes in liquids. Normally one of the measurement arms is covered with a thin polymer film into which the analyte can sorp. According to Nemst s distribution law, we have an equilibrium between the mobile and the stationary phase if a gas or a liquid pass the measurement window . Figure 12 shows a variety of results. 

Figure 12. Measurement arm of the Mach-Zehnder interferometer covered by a sensitive polymer layer, resulting in a intensity modulation by a change of the refractive index. This schematic changes are combined with the experimental data on the right side on top the curve of uptake of analyte, and its diffuseion out of the layer (right part), in the middle the experimental modulation, and at the bottom the related changes in refractive index. Bottom left shows the result of intensity signal versus the amount of substance for eight different analytes.

Interferometric sensors frequently have also been applied to biosensor measurements. Thereby, the evanescent field technique (Mach-Zehnder interferometer) has been compared with other optical detection principles regarding information on layer structure and in case of biosensing30. The... 

Figure 13. A Mach-Zehnder interferometer used to measure the isomers para- and meta-xvlene at various concentrations.

Fabricius N., Gauglitz G. and Ingenhoff J., A gas sensor based on an Mach-Zehnder interferometer, Sensors Actuators B 1992 7 672-676. 

Drapp B., Piehler J., Brecht A.. Gauglitz G., Luff B.J., Wilkinson J.S., Ingenhoff J., Integrated optical Mach-Zehnder interferometers as simazine immunoprobes, Sensors Actuators B 1997 39 277-282. 

Heideman R.G., Lambeck P.V., Remote opto-chemical sensing with extreme sensitivity design, fabrication and performance of a pigtailed integrated optical phase-modulated Mach-Zehnder interferometer system, Sens, and Actuat. B 1999 61 1 GO-127. 

The electron density of the produced plasma was diagnosed by means of a Mach-Zehnder interferometer, operated with a small portion of the main pulse, doubled in frequency [29,30]. The electron density along the pulse path was measured to be ne 2 x 1019 cm-3. At this density, the electron plasma wave has a period Tp 25 fs and wavelength Ap ss 7.5 j,m. 

Mach-Zehnder interferometer, 144 Medical applications, 153 Metal-insulator transitions, 52 Monte Carlo procedure, 135 Multi-energy X-ray imaging, 131 Multilayer targets, 131 Multiphoton absorption, 85 Multiphoton ionization, 82 Multiple filamentation, 91, 92 Multipulse techniques, 152... 

Paloczi, G. T. Huang, Y. Yariv, A. Mookherjea, S., Polymeric Mach Zehnder interferometer using serially coupled microring resonators, Opt. Express 2003, 11, 2666 2671... 

Based on the way the interferometer is configured, CCMI sensors can be categorized into two groups, namely the Mach-Zehnder interferometer (MZI) type and the Michelson interferometer (MI) type. The MZI sensor works in transmission mode, i.e., the transmitted interference signal is detected. The MI sensor works in reflection mode, where the light passes the interferometer twice and the reflected interference signal is detected. 

Allsop, T. Reeves, R. Webb, D. J. Bennion, I. Neal, R., A high sensitivity refractometer based upon a long period grating Mach Zehnder interferometer, Rev. Sci. Instrum. 2002, 73, 1702 1705... 

Tian, Z. Yam, S. S. Barnes, J. Bock, W. P. Greig J. M. Fraser H. P. Loock R. D. Oleschuk, Refractive index sensing with Mach Zehnder interferometer based on concatenating two single mode fiber tapers, IEEE Photon. Technol. Lett. 2008, 20, 626... 

Fig. 9.11 The calculated response of a 1.5 mm long silicon PWEF sensor in a Mach Zehnder interferometer configuration, as a film of final thickness d 2 nm and index n 1.5 grows on the waveguide surface. The normalized fractional surface coverage is also shown...

Fig. 9.13 Mach Zehnder interferometer (MZI) sensor interrogation circuit using (a) conventional linear waveguide geometry and (b) folded spiral waveguide geometry. The dashed line in (b) indicates the sensor window boundaries in this infra red camera image...

Fig. 9.14 (a) The measured variation of the Mach Zehnder interferometer (MZI) output intensity as a monolayer of streptavidin is bound to the surface, and (b) the optical phase change calculated from this intensity data... 

Weisser, M. Tovar, G. Mittler Neher, S. Knoll, W. Brosinger, F. Freimuth, H. Lacher, M. Ehrfeld, W., Specific biorecognition reactions observed with and integrated Mach Zehnder interferometer, Biosens. Bioelectron. 1999, 14,405 411... 

One of the main advantages of the optical-based sensors is their high resolution. Integrated optical sensors16, especially the interferometric ones that have been developed in recent years, such as the Mach-Zehnder interferometer (MZI)17 and the Young interferometer 18-21, show an extremely high refractive index resolution in the range of 10 1—10 8 RIU (refractive index units)17,21, which is equivalent to... 

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