VISMAYA: History & Philosophy of Physics

Category: optics

  • Optics – Fields, Size and Vector Calculus

    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.

  • Rayleigh – criticize and resurrect..

    Classic and Classical.. Rayleigh..

    Criticism and resurrection, Rayleigh style..

    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

  • Tiny value of the radiation pressure of sunlight on Earth

     

    • 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.

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  • Optical Momentum – Lectures

    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.

  • Intensity Interferometer – connection to coherence

    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,

    $$ \gamma_{12} = \frac{\left\langle U_1(t) U_2^\ast(t) \right\rangle}{\sqrt{\left\langle |U_1|^2 \right\rangle \left\langle |U_2|^2 \right\rangle}} $$

    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:

    $$ \left\langle I_1(t) \cdot I_2(t) \right\rangle $$

    where the enclosing brackets denote a time average.

    This correlation, measured in the intensity interferometer, is related to the degree of spatial coherence in the following way:

    $$ \left\langle I_1 I_2 \right\rangle = \left\langle I_1 \right\rangle \left\langle I_2 \right\rangle \left(1 + \left| \gamma_{12} \right|^2 \right) $$

    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:

    $$ \left\langle \Delta I_1 \Delta I_2 \right\rangle = \left\langle I_1 \right\rangle \left\langle I_2 \right\rangle \left| \gamma_{12} \right|^2 $$

    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.

    Reference:

    Dravins, Dainis. ‘Intensity Interferometry: Optical Imaging with Kilometer Baselines’. arXiv.Org, 12 July 2016. https://arxiv.org/abs/1607.03490

  • Born & Wolf to Mandel & Wolf

    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.

    This blog is part of my course blog on Quantum Optics.

    References:

    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.

    Mandel, Leonard, and Emil Wolf. Optical Coherence and Quantum Optics. 1st edn. Cambridge University Press, 1995. https://doi.org/10.1017/CBO9781139644105.

  • Raman Effect – The paper that announced it…

    Here I discuss the paper that announced the Raman effect to the world…

  • Quantum Optics course – thoughts and notes

    Jan 2026 – Apr 2026 – I am teaching a course on Quantum Optics. Below you will find some random thoughts and notes related to my reading. I will be updating the list as I go along the semester. You can add your comments below.

    Lectures:

    Pavan’s lectures on Quantum Optics (not the whole course)

    Some timelines for reference:

    Interactive timeline – includes pre-quantum optics

    1. Anyone interested in physics should know a bit about renormalized QED and the efforts that went behind it… It still remains a benchmark of how experiments and theory work in elevating each other…
      • Hari Dass (erstwhile, IMSc) on FB made an interesting observation:it’s unfortunate that after all those and subsequent developments, a mystery is being built out of renormalisation..it was the price to pay for assuming, without any justification, that the microscopic description held to arbitrarily small distances..wilson,schwinger and even feynman have clarified that the right way to do physics is to start with an effective description with a cutoff, which can be fully quantum in nature, and keep extending it to higher and higher scales with the help of further data, as well as with better theoretical understanding..
    2. “The photon is the only particle that was known as a field before it was detected as a particle.” 
      • This is how Weinberg introduces the birth of quantum field theory. He further adds:  “Thus it is natural that the formalism of quantum field theory should have been developed in the first instance in connection with radiation and only later applied to other particles and fields.”Ref: S. Weinberg (in Quantum Theory of Fields, p.15,  1995)
        • Sudipta Sarkar (IIT G) made an interesting observation in facebook:
          • “In some sense, it did right! Dirac started QFT with the effort to quantise radiation! But formally, it is not easy to write down the quantum version of electrodynamics owing to gauge symmetry. It took quite a bit of time to understand how to manage a quantum theory with massless states!“
          • My reply: “indeed..the reconciliation of symmetry was a bottleneck. I am also amazed by the progress of thought, especially by Dirac, who took the harmonic oscillator problem and treated it the way he did. Historically, the question of quantization of particles was already an established programme, but to quantize the field was indeed a major challenge, and hence ‘second quantization’.“
          • The concept of creation and annihilation operators is an intriguing one because it brings in the thoughts from the commutation relationship that existed in classical physics and transfers that into quantum mechanics. This intellectual connection is mainly attributed to Dirac, and historically, this has been one of the most important connections to be made. The question of field quantization already existed in 1920s, but it is thanks to Dirac who really made this connection in a systematic and mathematically consistent way.
    3. In the context of the quantum harmonic oscillator model of electromagnetic radiation, the shift from canonical variables such as position and momentum to creation and annihilation operators is a fascinating one. Interestingly, this progression further leads to the so-called number operator. It is also a progression from Hermitian to non-Hermitian and again back to a Hermitian operator. In the process of understanding the number operators, one realizes that the ground-state results in the so-called zero-point energy. Taken further, the commutation of the number operator with the electric field of the electromagnetic radiation results in the number-amplitude uncertainty. This further gives an insight into why the field amplitude has a non-zero spread, even for the n = 0 state, and therefore results in the so-called vacuum fluctuations.
      • It can’t get more quantum than this…
    4. An essay on Quantum States in Argand Diagrams: https://historyofscience.in/2026/02/03/quantum-states-in-argand-diagrams-vacuum-coherent-and-squeezed/
    5. The word photon has an interesting and surprising origin – see this paper.
    6. Born & Wolf to Mandel & Wolf – a blog on a famous book and on the connection between radio astronomy and quantum optics.
    7. Intensity Interferometer – connection to coherence
    8. References related to Hong-Ou-Mandel experiments:
      • Original paper
        • Hong, C. K., Z. Y. Ou, and L. Mandel. ‘Measurement of Subpicosecond Time Intervals between Two Photons by Interference’. Physical Review Letters 59, no. 18 (1987): 2044–46. https://doi.org/10.1103/PhysRevLett.59.2044.
      • The references below discuss a few contemporary yet simple approaches toward the HOM experiment. 
        • DiBrita, Nicholas S., and Enrique J. Galvez. ‘An Easier-to-Align Hong–Ou–Mandel Interference Demonstration’. American Journal of Physics 91, no. 4 (2023): 307–15. https://doi.org/10.1119/5.0119906.
        • Bjurlin, Cyrus, and Theresa Chmiel. ‘A Versatile Hong–Ou–Mandel Interference Experiment in Optical Fiber for the Undergraduate Laboratory’. American Journal of Physics 93, no. 2 (2025): 180–86. https://doi.org/10.1119/5.0210869.

    Prof. Supradeepa from IISc made an important observation related to the non-Poissonian distribution and anti-bunching as follows: When I taught quantum optics earlier this semester, there was an interesting discussion with students which I had not had given thought previously. I have seen the terms anti-bunching and g2(0) < 1 sometimes interchanged. But the idea is that g2(0) < 1 is only non-poissonian while, the stronger condition that g2(0) < g2(\tau) is also needed to have anti-bunching. An easy to calculate example was fock states with |n> for n > 1. g2(tau) = 1-1/n, so these states are non-poissonian because g2(0)<1, but not anti-bunched.

    My reply: This is an important point, and Fox’s book has a small discussion related to this non-equivalence: sub-Poisson distribution and anti-bunching can overlap, but need not be the same. As you mentioned, g2(0) < 1 and g2(0) < g2(\tau) have to be satisfied. The criteria for a single-photon source are much stricter than those for a sub-Poisson light source. In my lecture, I do mention this as seen in the picture…

  • Teaching & Meaning

    What adds meaning to my academic work?

    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..

    Human interaction zindabad :-)

  • Quantum Optics – teaching in Jan 2026

    More than 22 years ago, I started my journey as a research student in theoretical physics – Quantum Electrodynamics (QED) + Radiative Transfer (MSc summer project at the Indian Institute of Astrophysics), and my special paper in the MSc final semester was QED. Later in my PhD, I branched into experiments on light scattering (Raman, Mie & Rayleigh).

    Over the years, QED and quantum optics have always been at the back of my mind while studying, researching and teaching.

    Come January, I will be teaching a course on Quantum Optics to MS(Quantum Tech), MS-PhDs, and 4th-year physics UGs

    I designed the first course on this topic at IISER Pune about a decade ago with the able inputs from Prof. Rajaram Nityananda, and I have taught the course a few times. Now, after a few years, I will teach it again.

    With the emergence of quantum sci & tech, there is a new impetus and excitement on this topic.

    Having said that, the foundations of the topic remain the same, and Quantum Optics has a wonderful history and philosophy associated with it…and where better to start than Dirac’s classic (see below).

    Look out for ‘quantum blogs’ in 2026…