Interferometers are instruments that work on the principle of interference, which involves the superposition of two or more waves to produce an interference pattern that can be used to extract information about the original waves. Interferometers have been used to study everything from the properties of light to the structure of molecules, and their applications are still expanding.

The Mach-Zehnder interferometer is a type of interferometer that measures the relative phase shift between two collimated light beams. It is also a beam division interferometer based on amplitude, consisting of two beam splitters and two mirrors. In the Mach-Zehnder interferometer, unlike the Michelson-Morley interferometer, each beam follows a different path, and then recombines downstream of the second beam splitter. However, the interference is still due to the coherent superposition of the two waves.

Moreover, aligning this interferometer can be more challenging than aligning the Michelson-Morley interferometer because the Mach-Zehnder interferometer has two separate paths for the light.

Figure 1: Mach-Zehnder interferometer

The incoming light is divided at the first beam splitter into two separate paths. Each beam reflects off a mirror and then recombines at the end of the second beam splitter, producing an interference pattern dependent on the phase difference between the two waves. The phase difference, or equivalent optical path, can be intentionally introduced by slightly modifying either one of the beam splitters or one of the mirrors to create a small asymmetry.

The interference fringes will be generated, if there is a difference in the optical path lengths of the two beams that is less than the coherence length of the light source. The coherence length represents the distance over which the light waves maintain their phase relationship.

When the difference in the optical path lengths of the two beams is within the coherence length of the light source, the waves can still interfere constructively or destructively, resulting in the formation of interference fringes. These fringes can be observed as patterns of bright and dark bands in the interference pattern.

Since the coherence length of a light source can be extremely short, precision components and careful alignment are crucial in the Mach-Zehnder interferometer to ensure that the two beams have nearly identical optical path lengths. This precision is necessary to maintain the visibility and clarity of the interference fringes.

By placing a sample in one of the beam paths, the resulting difference in the optical path length due to the sample can be measured. This measurement is achieved by observing the changes in the interference fringes. These changes provide valuable information about the properties and characteristics of the sample being tested. The Mach-Zehnder interferometer's ability to measure such small differences in optical path length makes it a powerful tool in various scientific and engineering applications.

Phase change during beam propagation

The “outputs” of the Mach-Zehnder apparatus are two, one parallel to the incoming beam and the other one is orthogonal. 

Parallel output

The parallel output shows the two beams both arrive after having undergone two reflections in each paths P₁ and P₂.

Figure 2: Detector 1

• P₁: first reflection from the beam splitter 1 (BS₁) (π phase shift), second from mirror 1 (M₁) also (π phase shift) and transmission from beam splitter 2 (BS₂): total = 2π phase shift
• P₂: transmission from BS₁, first reflection from mirror 2 (M₂) (π phase shift) and second from BS₂ (π phase shift): total = 2π phase shift

Both P₁ and P₂ arrive in phase having both accumulated a phase shift of 2π that corresponds to one wavelength.

Orthogonal output

For the orthogonal output, one beam arrives after three reflections (O₁), while the other after a single reflection (O₂).

Figure 3: Detector 2

• O₁: first reflection from BS₁ (π phase shift), second from M₁ (π phase shift), and third from BS₂ which gives 0 phase shift as it is reflected from the opposite other side of the beam splitter
• O₂: transmission from BS₁, single reflection from M₂ (π phase shift) and second transmission from BS₂

Figure 4: Phase shift

Both O₁ and O₂ beams are therefore out of phase with π. Therefore give rise to destructive interference and no light can be detected at the second output. The outputs can be viewed through detectors D₁ and D₂.

Applications of Mach-Zender Interferometer

The Mach-Zehnder interferometer has become the favored choice for flow visualization studies due to its spacious and accessible working area and its flexibility in locating fringes.

• It is commonly used in the fields of plasma physics, aerodynamics, and heat transfer to measure changes in temperature, density, and pressure in gases.
• In addition, it is used in fiber-optic communication applications as electro-optic modulators, which offer high-bandwidth electro-optic amplitude and phase responses over a multiple-gigahertz frequency range. They are often incorporated in monolithic integrated circuits.
• Furthermore, it is used to investigate quantum entanglement, which is one of the most counterintuitive predictions of quantum mechanics.
• The Mach-Zehnder configuration is also favored in holographic interferometry due to the ability to easily control the light features in the reference channel without disturbing the object channel. Optical heterodyne detection using an off-axis, frequency-shifted reference beam is particularly useful for shot-noise-limited holography, vibrometry, and laser Doppler imaging of blood flow at video-rate cameras.