Editorial Feature

# Interference Patterns in Wave Optics: Applications in Spectroscopy

Interference is an important phenomenon in the field of wave optics. This technique has been employed to develop various robust analytical techniques in the field of science. In wave optics, light is treated as an electromagnetic wave, and its wave-like behavior is studied by interpreting the interference patterns. This article delves into the intricacies of interference patterns in wave optics and their applications in the field of spectroscopy.

Image Credit: Peter Hermes Furian/Shutterstock.com

## What is Wave Optics?

Wave optics is a branch of optics that studies phenomena such as interference, diffraction, and polarization. These phenomena helped in the development of interferometers, holograms, polarizers, gratings, quarter-wave plates, thin-film interference, and other techniques that have hugely contributed to various scientific breakthroughs.

The phenomena observed in wave optics are summarized below:

Interference: Occurs owing to the overlapping of waves that may add or subtract from each other.

Diffraction: When a light wave encounters obstacles, the wave bends around the edges of the obstacle and scatters.

Polarization: This occurs because of the transverse nature of the electromagnetic waves. The electric and magnetic field vectors relevant to electromagnetic waves are at right angles to each other and to the direction of the wave propagation.

## Interference Patterns in Wave Optics

Interference patterns in wave optics occur due to:

• Phase coherence of the two light fields
• Spatial and temporal overlap of the two light fields
• Non-orthogonal (non-perpendicular) polarization states

There are two types of interference in wave optics: constructive and destructive. In the former interference pattern, the amplitude of the resulting wave is greater than that of the individual wave. In the latter interference pattern, the amplitude of the resulting wave was less than that of either of the individual waves.

## How are Interference Patterns Obtained in Wave Optics?

The two main techniques used to obtain interference patterns in wave optics are as follows:

1. Wavefront Splitting Interference: In this method, a light wave from a single source is split into two parts that travel in two different directions and reunite to form interference-fringe patterns. Techniques that employ these methods include Young’s double slit, Lloyd’s mirror, Fresnel’s double mirror, and Fresnel’s biprism.

1. Amplitude Splitting Interference: In this method, the light wave from a single source is split into two parts: partial reflection or refraction, which is reflected and transmitted light. These two parts travel different paths and reunite to produce interference-fringe patterns.  Techniques that employ these methods include interference in thin films and Michelson’s interferometer.

## Relevance of Interference Patterns in Spectroscopy

Spectroscopy deals with the study of the interaction between matter and electromagnetic radiation, such as light, and the output is recorded in the form of a spectrum. In reality, all spectroscopy methods involve interference phenomena, which is how light interacts with matter.

In prisms, the dispersion of light is because different wavelengths of light are obstructed differently by the prism material, resulting in a specific interference pattern. Diffraction grating is also another method of separating light of different wavelengths.

Interferometry uses interference of light waves to extract the information related to the material under study. When more than two waves overlap, they either amplify or cancel on each other. Studying these interference patterns provides information on the materials that interact with light.

A few methods, such as the Michelson interferometer and Fabry–Perot interferometer, use high levels of interference to separate light into different wavelengths. These techniques are referred to as interference spectroscopy (IS).

Michelson Interferometer: This is a precise tool that consists of a mirror and the incident light is split into two different sets of waves that travel through different paths and then reunite. If the total number of oscillations of both waves unites, they amplify each other and are directed toward the detector to create a visible pattern in the form of a spectrum.

The light intensity changes with the movement of the mirror. Hence, the spectrum is also different. Furthermore, a mathematical operation termed the Fourier transform helps to convert the changes in light intensity into the usual frequency domain of the absorption spectrum.

Fabry-Pérot Interferometer: This interferometer is a sophisticated version of the Michelson interferometer. It consists of two mirrors, which are either flat or curved. It is often used as an optical spectrometer with high resolution.

For the proper functioning of the Fabry-Pérot interferometer, the input light wave must be close to the resonance frequency of the resonator. The resonance frequencies could be adjusted by adjusting the distance between the two mirrors.

When the resonance frequency of the resonator and the input light wave match, the light circulates well within the resonator with no reflection. However, under anti-resonance, the light is not circulated well within the resonator and is reflected.

## Recent Trends

In the conventional double-slit experiment, light passed through closely spaced slits. This experiment revealed both the wave and particle nature of light. However, an article published in Nature Physics reported the recreation of this experiment in the realm of time instead of space. In this experiment, physicists from the Imperial College, London, fired a light beam through a thin film of indium tin oxide.

This material (indium tin oxide) changes its properties in femtoseconds, allowing the passage of light only at specific times. This recreation of the experiment has opened doors to new spectroscopy to study and analyze the temporal structure of a light pulse within a single cycle of its radiation.

Another article published in Scientific Reports presented another version of a double-slit experiment in the realm of time. This experiment used high-speed photoelectrons emitted from helium atoms. They showed that a group of high-speed electrons influenced the interference pattern of single particles.

The double-slit arrangement used a couple of light wave packets with attosecond-controlled spacing. The interference pattern observed on the detector depended on the lapse between the two light wave packets, revealing the wave and particle nature of single-photoelectrons emitted from helium atoms.

## Conclusion

Overall, interference patterns play a crucial role in both wave optics and spectroscopy. This technique is intricately related to the underlying principles of wave mechanics. Delving into the technical insights of interference fringes can help us to understand and manipulate light, opening doors to new technologies to achieve breakthroughs in science.

More from AZoOptics: Wavefront Analysis for High-Resolution Imaging Systems

What are Wave Optics? (Accessed on 31 September 2023). Available at https://www.azooptics.com/Article.aspx?ArticleID=763

Interference (Accessed on 31 September 2023). Available at https://www.britannica.com/science/spectroscopy/Interference#ref620163

Michelson Interferometer & Fourier Transform Spectrometry (Accessed on 31 September 2023). Available at http://courses.washington.edu/phys331/michelson/michelson.pdf

Tirole, R., Vezzoli, S., Galiffi, E. et al. (2023). Double-slit time diffraction at optical frequencies. Nature Physics, 1-4. https://doi.org/10.1038/s41567-023-01993-w

Kaneyasu, T., Hikosaka, Y., Wada, S., Fujimoto, M., Ota, H., Iwayama, H., & Katoh, M. (2023). Time domain double slit interference of electron produced by XUV synchrotron radiation. Scientific Reports, 13(1), 6142. https://www.nature.com/articles/s41598-023-33039-9#Sec6

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Written by

### Bhavna Kaveti

Bhavna Kaveti is a science writer based in Hyderabad, India. She has a Masters in Pharmaceutical Chemistry from Vellore Institute of Technology, India, and a Ph.D. in Organic and Medicinal Chemistry from Universidad de Guanajuato, Mexico. Her research work involved designing and synthesizing heterocycle-based bioactive molecules, where she had exposure to both multistep and multicomponent synthesis. During her doctoral studies, she worked on synthesizing various linked and fused heterocycle-based peptidomimetic molecules that are anticipated to have a bioactive potential for further functionalization. While working on her thesis and research papers, she explored her passion for scientific writing and communications.

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