Tag: optics

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.

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 :-)

Random Walks in Polarization

I have been teaching polarization of light in my optics class. In there, I introduced them to matrix representation of polarization states. One of the standard references that I use for explanation is a 1954 paper in American J. Physics, by McMaster titled: “Polarization and the Stokes Parameters.”

While skimming through the pdf of the journal paper, I found an excerpt from a 1954 book, which quotes Fresnel writing to Thomas Young:

Further, I knew from the past that S. Chandrasekhar (astrophysicist) had a role in rejuvenating Stokes vector formalism in radiative transfer. Below is his description from AIP oral history archives (May 1977):

” I started the sequence of papers, and almost at the time I started it, I read the paper by Wick in which he had used the method of discrete coordinates,* and I realized at once that that method can be used in a large scale way for solving all problems. So that went on. I have always said and felt that the five years in which I worked on radiative transfer [1944 – 49] is the happiest period of my scientific life. I started on it with no idea that one paper would lead to another, which would lead to another, which would lead to another and soon for some 24 papers — and the whole subject moved with its own momentum.” (emphasis added)

He further states how he rediscovered Stokes polarization vector formalism:

“All this had a momentum of it own. Then suddenly I realized one had to put polarization in; the problems of characterizing polarized light — my rediscovery of Stokes original paper, writing on Stokes parameters and calling them Stokes parameters for the first time“

Chandra further adds that the Stokes formalism was almost forgotten for 50 years, and he had a role in resurrecting it.

Next, there was some noise on social media where some one questioned the utility of matrix multiplication. For them, below is a wonderful review article by McMaster (again), to explore from polarization viewpoint, and realize the power of non-commutative matrix algebra:

Finally, the original paper by Stokes on his formalism, which is hard to find (thanks to paywall). But, classic papers are hard to suppress, and I found the full paper on internet archives.

Below is a snapshot:

Enjoy your random walk !

Pursuit of Radiance – musical & philosophical

What happens when Carnatic music, eastern and western philosophy and optics come together?

Well….if you ask my friend Karthik Raveendran, who is a Carnatic vocalist and a physicist, he will say Kānthimathīm – which is his musical video perspective on ‘Pursuit of Radiance’.

Below I post his spectacular art, which includes his music and philosophical thoughts on the mentioned topics. All this visualized through Indian architecture, Finnish lakes and auroras over its sky.

He has been very kind to acknowledge me in his video for my minor input on scientific philosophy. I am truly honored.

Do watch+listen (~ 14 min)

Liquid Crystal Droplets + Plasmonic nanoparticle clusters

A droplet of liquid can act as an optical resonator. One can create a droplet of a liquid crystal and utilize its optical and topological properties. In recent times, liquid crystal droplets have emerged as a ‘soft photonic element’ in topological optics and photonics. Studying their optical behaviour in a controlled environment is a contemporary research problem.

In this context, we have an arXiv preprint on liquid crystal droplets and their reversible coupling to a small assembly of nanoparticles on a glass surface (see video).

Specifically, we ask: What happens to the modes of light inside the droplet due to such an interaction?

Thanks to the efforts of Sumant Pandey, we experimentally demonstrate the utility of optical tweezers to proximally couple (and decouple) nematic liquid crystal droplets to gold nanoparticle clusters, and record whispering gallery modes in coupled and decoupled states. We observe tuning of sharp resonant modes.
For more details, see the preprint: https://arxiv.org/abs/2509.10126v1

Art and Chu – in Bell labs

Steven Chu and Arthur Ashkin in 1986, in front of the apparatus shortly after the first optical trapping experiment was completed. Image from Chu’s Nobel lecture.

Steven Chu’s Nobel lecture has some gems. Below, he shares his experience of working with Arthur Ashkin.

“In 1986, the world was excited about atom trapping. During this time, Art Ashkin began to use optical tweezers to trap micron sized particles. While experimenting with colloidal tobacco mosaic viruses, he noticed tiny, translucent objects in his sample. Rushing into my lab, he excitedly proclaimed that he had ‘discovered Life’. I went into his lab, half thinking that the excitement of the last few years had finally gotten the better of him. In his lab was a microscope objective focusing an argon laser beam into a petri dish of water. Off to the side was an old Edmund Scientific microscope. Squinting into the microscope, I saw my eye lashes. Squinting harder, I occasionally saw some translucent objects. Many of these objects were ‘floaters’, debris in my vitreous humor that could be moved by blinking my eyes. Art assured me that there were other objects there that would not move when I blinked my eyes. Sure enough, there were objects in the water that could be trapped and would swim away if the light were turned off. Art had discovered bugs in his apparatus, but these were real bugs, bacteria that had eventually grown in his sample beads and water.”

Chu won the physics Nobel in 1997, and Ashkin won the same in 2018. Ashkin was the pioneer of optical trapping and tweezers, and applied it to a variety of problems, including the manipulation of biological matter. Chu harnessed the momentum of light to trap and cool atoms. Both started their work and collaborated at Bell Labs. Chu moved to Stanford, whereas Ashkin stayed back. Bell Labs was a remarkable place in the 1980s, as Chu describes in his lecture :

“Bell Labs was a researcher’s paradise. Our management supplied us with funding, shielded us from bureaucracy, and urged us to do the best science possible. The cramped labs and office cubicles forced us to rub shoulders with each other. Animated discussions frequently interrupted seminars and casual conversations in the cafeteria would sometimes mark the beginning of a new collaboration.”

Can the world afford to have another Bell Labs in 2025? Can it recreate the magic?

Real is imaginary and vice versa

This week in my optics class, I have been teaching Kramers-Kronig (KK) relations of electric susceptibility. It is fascinating to see the causality argument emerge from the relationship between the real and imaginary parts of the complex susceptibility. Whereas the time domain explanation is relatively easier to appreciate (that dissipation follows perturbation in time), for me, the frequency domain implication in KK relation is fascinating: the fact that information about the real part of the function at all frequencies can give you insight into the imaginary part at any given frequency (and vice versa) makes it such a powerful mathematical and physical tool. For example, by knowing the absorption spectrum of a medium, you can find out the refractive index of a medium at a particular frequency that is not easily accessible in experiments.

Two inferences I draw:

1) Complex analysis combined with differential calculus is one of the most beautiful and powerful mathematical tools invented, and exploring its application in experimental scenarios has made physics intriguing, useful, and profound.

2) The KK relationship shows how causality and the structure of matter are connected to each other, and by studying them, one will be able to extrapolate the idea beyond the problem at hand and apply it to a different context in physics. It just shows how ideas hop from one domain to another and how mathematics plays a critical role in intellectual arbitrage.

Real is imaginary and vice versa. Complex numbers zindabad!