Nirmal K. Viswanathan is a senior professor of physics at the University of Hyderabad, specializing in structured light and topological optics. His work includes diverse areas of optics, including Structured light, singular optics, topological effects, spin-orbit interaction, fiber optics, vector vortex beams, fundamental optical phenomena and Brewster angle structures.
In this episode, we discuss his diverse career, research insights, and the importance of rethinking traditional optical paradigms in education.
Every year when I teach the Optics course for physics majors, I start with the treatment of electromagnetic theory and then build on it a variety of optical phenomena and effects. Let me present three aspects related to it:
1. The impact and effect of Heaviside-Maxwell’s equations in understanding how fields can evolve and interact with matter is noteworthy. The foundations of field theory are already there to see, and the arguments of locality and causality take their form in an intuitive way. It shows the power of combining physical intuition with mathematical techniques, and in the process, the flavor of classical physics at its best.
2. To see optics from a framework of a comparison between the wavelength of light and the size of an interacting object. This is usually termed the ‘size parameter’ viewpoint. The size parameter has an intuitive connection to the approximations that we use. For example, the foundation principles on which scattering theory is based for discriminating between Rayleigh and Mie scattering processes are mainly based on size. It is also amazing to see how the dipole approximation can solve or at least give an opening to understand a variety of optical effects. It reveals the power of the method and its effectiveness. Lord Rayleigh had a significant role to play in this way of attacking a problem, and it continues to be one of the most powerful methods to introduce concepts not only in electromagnetic theory but also in applications of quantum mechanics, including atomic and molecular physics.
3. The elegance of mathematics that one must use to understand the electromagnetic theory of light. Of course, a good foundation in vector calculus is necessary, but what intrigues me and several of my students is the effectiveness of vector calculus in trying to understand a variety of processes. Every time we use a Laplacian or a curl of curl type of transformation, we observe how important physical effects emerge from that mathematical operation. One of the most effective ways to study vector calculus is to apply it in electromagnetic theory, and if one needs to broaden the scope of this study, optical effects provide an excellent playground. Ultimately, there is an amazing coherence between what is computed, what is theorized, and what is measured. It is a great model and an advertisement for physics.
Of course, there are many more observations related to teaching this course, which I wish to share, but I will keep them for future blogs. One thing is for sure: there is no end to getting surprised, learning new things, and finally looking at an old phenomenon (literally and metaphorically) in a new light.
I propose to point out what I conceive to be the error which vitiates his reasoning, and afterwards to show that, after all, his theory is substantially correct.
Reference: Note on the explanation of Coronas, as given in Verdet’s Legons d Optique Physique, and other works; London Math. Soc. Proc. 11. pp. 267—269, 1871
If radiation pressure is indeed a genuine electromagnetic phenomenon, then why don’t we observe it in our everyday lives?
The reason is that the magnitude of the radiation pressure from the natural light source on Earth (the Sun) is feeble.
from electromagnetic theory, this tiny amount of pressure can be calculated by the formula \(\frac{E}{c}\), where ‘E’ is the energy of sunlight on earth and ‘c’ is the speed of light in vaccum (which is \(3 \times 10^8 \text{ ms}^{-1}\) [\(9.83 \times 10^8 \text{ ft s}^{-1}\)]).
Maxwell himself recognized the low value of this energy, which he assumed to be \(83.4 \frac{\text{ft} \cdot \text{pound}}{\text{sec} \cdot (\text{ft})^2}\)
Taking this value and dividing it by ‘c’ gives us a radiation pressure of \(10^{-7} \frac{\text{pound}}{(\text{ft})^2}\).
Poynting, who extensively worked on radiation pressure from an electromagnetic theory viewpoint, compared this tiny pressure to the size of a grain in an area of \(200,0000 \text{ (ft)}^2\)!
This highlights why radiation pressure is hard to measure experimentally, and it took some trial and error to ascertain the value and the method. More on this later…
Reference :
Loudon, R., and C. Baxter. ‘Contributions of John Henry Poynting to the Understanding of Radiation Pressure’. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2143 (2012): 1825–38. https://doi.org/10.1098/rspa.2011.0573.
My latest research grant from ANRF is on “Opto-Thermal Binding of Plasmonic Matter”. This is a topic that is at the interface of optical momentum, thermodynamics, statistical physics, and advanced optical microscopy in the real and momentum spaces.
Optical momentum and its measurement have a rich history in understanding electromagnetic waves and their interaction with matter. Over the past century, multiple applications have emerged that harness the transfer of momentum from light to matter. Interestingly, the light that is scattered off this interaction also carries relevant information not only about the interaction but also about certain parameters of light and the participating matter.
These lectures are my attempt to give an overview of the field. My main target audience is my PhD group members and senior undergraduates who are working with me. But these lectures can be followed by anyone who is seriously interested in physics. The discussion involves theoretical optical physics (including elements of statistical and quantum optics), experimental techniques (including advanced microscopy methods) and a few computational techniques connected to the interaction. The goal of the lectures is to reveal the interesting questions in research papers, review articles, monographs and conference papers related to the field and their possible application in industries, including biophotonics and astro and space-photonics. From time to time, I will also discuss our research results from the project.
My previous blog discussed some historical papers related to the intensity interferometer and its connection to quantum optics. Here, I explain the basic physics of an intensity interferometer.
In the context of spatial coherence, the coherence theory expresses the degree of spatial coherence as,
with \( U_i(t) \) representing the fields of sources \( i = 1 \) and \( 2 \).
An intensity interferometer measures the intensity correlation function between such sources. If \( I_1(t) \) is the intensity of source 1 and \( I_2(t) \) is the intensity of source 2, then the intensity correlation function is given by:
If one ignores the background (the first term in the sum of the above equation) and considers only the fluctuations in the signal (the second term), then the term of relevance will be:
The signal in the intensity interferometer is thus proportional to \( \left| \gamma_{12} \right|^2 \).
A conventional interferometer measures a signal that is proportional to \( \left| \gamma_{12} \right| \), which includes the amplitude and phase, whereas an intensity interferometer measures a signal proportional to \( \left| \gamma_{12} \right|^2 \), which is not sensitive to the phase.
Intensity interferometers have certain advantages compared to conventional interferometers (such as the Michelson interferometer). Below is a partial list:
Intensity measurements (unlike amplitude or phase) can be done directly using optoelectronic instruments.
They do not require precise, sub-wavelength optical alignment, unlike amplitude- or wavefront-dividing interferometers.
They can be used with two detectors that are placed far apart, thereby improving the spatial resolution of the measurement (relevant in astronomy).
A constraint of an intensity interferometer is that the intensity of the participating source should be bright.
There is an important connection between quantum optics and radio astronomy. Hanbury Brown and Twiss in the 1950s devised the intensity interferometer.
Particularly, they were interested in measuring the ‘diameter of discrete radio sources’. The title of their seminal paper reads “A new type of interferometer for use in radio astronomy”. As the authors claimed in their paper: “The principle of the instrument is based upon the correlation between the rectified outputs of two independent receivers at each end of a baseline, and it is shown that the cross-correlation coefficient between these outputs is proportional to the square of the amplitude of the Fourier transform of the intensity distribution across the source.”(Brown and Twiss, 1954)
First, they tested their technique in a laboratory situation and followed it up with a measurement of the diameter of Sirius. Their technique was a game-changer in measuring the diameter of bright stars.
As the intensity interferometers were being developed, the laser was realized in the early 1960s. Unlike conventional light sources, laser light is coherent, and this brings in unique features that can be used to understand the nature of light. In the context of laser optics, intensity interferometers had immediate utility in studying coherence through correlation measurement. It was logical to combine lasers with intensity interferometers and study the correlation. This combination is what led to the discovery of some fascinating aspects of quantum properties of light, including anti-bunching.
If the book by Born and Wolf is considered a classic on the electromagnetic theory of light, the quantum extrapolation is the book by Leonard Mandel and Emil Wolf titled Optical Coherence and Quantum Optics.
This book discusses the interface of statistical optics, optical coherence, and quantum optics. The core argument of the book starts with probability theory and its connection to fluctuations of light and builds optical coherence, polarization, and eventually quantum optical effects of light. It is a well-written treatise on light with a flavor of experiments (Mandel did some pioneering experiments in quantum optics) and theoretical explanation (a hallmark of Wolf).
In the preface of the book, they bring together the importance of intensity interferometers and the discovery of lasers and explain how and why it led to a deeper understanding of quantum optics:
“Prior to the development of the first lasers in the 1960s, optical coherence was not a subject with which many scientists had much acquaintance, even though early contributions to the field were made by several distinguished physicists, including Max von Laue, Erwin Schrodinger and Frits Zernike. However, the situation changed once it was realized that the remarkable properties of laser light depended on its coherence. An earlier development that also triggered interest in optical coherence was a series of important experiments by Hanbury Brown and Twiss in the 1950s, showing that correlations between the fluctuations of mutually coherent beams of thermal light could be measured by photoelectric correlation and two-photon coincidence counting experiments. The interpretation of these experiments was, however, surrounded by controversy, which emphasized the need for understanding the coherence properties of light and their effect on the interaction between light and matter.” (Mandel and Wolf, 1995, p. 1)
This further led to a series of studies on light-matter interaction from a coherence perspective, and included analysis of the fluctuation of light by understanding the randomness and the associated statistics of the fluctuations. Mandel, Wolf, Glauber, E.C.G. Surdarshan and many others across the world laid the foundation and connection between optical coherence and quantum optics. What started as a technical development in radio astronomy turned out to be a vital tool in quantum optics.
Brown, R. Hanbury, and R. Q. Twiss. ‘LXXIV. A New Type of Interferometer for Use in Radio Astronomy’. Philosophical Magazine 45, no. 366 (1954): 663–82. https://doi.org/10.1080/14786440708520475.
Brown, R. Hanbury, and R. Q. Twiss. ‘Correlation between Photons in Two Coherent Beams of Light’. Nature 177, no. 4497 (1956): 27–29. https://doi.org/10.1038/177027a0.
Hanbury Brown, R., and R. Q. Twiss. ‘A Test of a New Type of Stellar Interferometer on Sirius’. Nature 178, no. 4541 (1956): 1046–48. https://doi.org/10.1038/1781046a0.
Perhaps, an anonymous feedback on your teaching is one of them….
“very well taught course at a well defined pace. The interesting way various different aspects and fields in Optics was introduced was fascinating, made us so very keen on knowing more! The mind maps at the beginning of every topic, the indexes professor made was a great way to keep the bigger picture in mind and helped us glide through it. The assignment was also a great way to make us go through materials without feeling it it be imposing, rather finding it more interesting! Thank you so much Sir for this amazing course, the enthusiastic way in which you taught, all the great conversations you engaged in with us, and opened our eyes to explore so much more in this field! thank you!!“
I had a diverse class (BS-Physics majors, MS Quantum Tech, iPhD) with 110+ students, and I am glad a lot of students enjoyed the course this time. I am a bit overwhelmed by the positive feedback I received on my teaching methods. For sure, I learnt about the subject as much as they did.
And as I always say: there is more to learn…for all of us..
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