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.
BORN AGAIN: Today I opened the google webpage and to my surprise found the doodle (picture above) celebrating birthday of Max Born. He was not only a great physicist who contributed immensely to quantum mechanics and other branches of physics (including optics), but also a mentor to many great physicists including Fermi, Heisenberg, Pauli, Wigner, Teller, Emil Wolf and many more.
Every student who has studied physics, is aware of quantum mechanical wavefunction (ψ). Given a quantum system and its environment (electron in an atom, for example), wavefunction is a fundamental quantity that one can compute, and forms the basis to understand the system in greater detail. When quantum mechanics was evolving in early 1900s, the question of how to physically interpret the meaning of wavefunction was at the forefront. It was Max Born who gave the statistical interpretation for the wavefunction, which later fetched him a Nobel prize in 1954.
Born identified the importance of interpretation of the wavefunction, and its connect to the realistic, observable parameter. To quote Born from his Nobel lecture :
“The problem was this: an harmonic oscillation not only has a frequency,
but also an intensity. For each transition in the array there must be
a corresponding intensity. The question is how to find this through the
considerations of correspondence? “
This quest set forth an intense programme in physics and motivated people like Heisenberg, Schrodinger, Bohr, and Einstein to find an answer. Interestingly, Born’s work was heavily inspired by Einstein’s work. To quote Born from his Nobel lecture:
“But the decisive step was again taken by Einstein who, by a fresh
derivation of Planck’s radiation formula, made it transparently clear that the
classical concept of intensity of radiation must be replaced by the statistical
concept of transition probability.”
Further, he adds
“Again an idea of Einstein’s gave me the lead. He had tried to make the duality of particles light quanta or photons – and waves comprehensible by interpreting the square of the optical wave amplitudes as probability density for the occurrence of photons. This concept could at once be carried over to the ψ-function: |ψ|^2 ought to represent the probability density for electrons (or other particles).”
Reading Born’s Nobel lecture, two things struck me : first was that science is never done in isolation. Every single idea is inspired by another idea. Second, physical optics has a major influence on interpretation of quantum mechanics. Max Born was no stranger to optics. In fact, he was one of the pioneers of classical optics, and I am not surprised that he could make some vital connections between physical optics and quantum mechanics.
My personal copy…..standing tall and heavy :)
THE BOOK: This brings me to the most famous book written in optics(see picture above) by none other than Max Born and Emil Wolf (Emil Wolf was the last research assistant of Max Born, and a well know optical physicist) The book is titled “Principles of Optics”, but in optics community we call it “Born and Wolf”. The first edition of this book appeared in 1959, and has never gone out of print. Currently, it is in its 7th edition and is 951 pages thick !
As described in the preface (first edition of Born and Wolf), several people urged Born to translate his 1933 book: “Optik” from german to english. By 1950s, optics had evolved and had made inroads into atomic physics, molecular spectroscopy, solid-state physics and various other branches of science and technology. So, they had to write the book from scratch taking new ideas into consideration.
“Born and Wolf” explains optical phenomenon through the eyes of Maxwell’s theory, and has become the foundation on which various aspects of classical optics can be studied in a mathematically rigorous fashion. In fact, it also lays foundation to various quantum optical phenomenon including coherence and correlation functions, on which Emil Wolf’s contribution has been immense.
For me, chapter 13 on “Scattering from homogeneous media” is the highlight of this book. It starts with elements of scalar theory of scattering by expaining the first-order Born approximation followed by discussion on scattering from periodic potential. The best part is the discussion on multiple scattering, which in a sense lays the foundation to study various important optical phenomenon including diffraction tomography and optical cross-section theorem (or more famously known as Optical theorem). Also, the 13th chapter has a very interesting discussion on concept of far-field and its connection to scattering of electromagnetic waves.
Actually, the book is very well known for its treatment on diffraction theory and image formation. It gives a very strong footing to attack problems in imaging, aberration and inteferometry using Maxwell’s equation and related boundary condition. It also, highlights optics of metals, which has now transformed and evolved into a sub-field of optics and photonics – plasmonics.
Origins of the book: The writing of this book has a historical context. Emil Wolf was a research assistant (post-doc) of Max Born and joined him after his Ph.D. He recollects his experiences with Born and about writing this book in an interesting article. Below is an interesting quote:
“Through Gabor I learned in 1950 that Born was thinking of preparing a
new book on optics, somewhat along the lines of his earlier German book
Optik, published in 1933, but modernized to include accounts of the more
important developments that had taken place in the nearly 20 years that
had gone by since then. At that time Born was the Tait Professor of Natural
Philosophy at the University of Edinburgh, a post he had held since 1936,
and in 1950 he was 67 years old, close to his retirement. He wanted to find
some scientists who specialized in modern optics and who would be willing
to collaborate with him in this project. Born approached Gabor for advice,
and at first it was planned that the book would be written jointly by him,
Gabor, and H. H. Hopkins. The book was to include a few contributed
sections on some specialized topics, and Gabor invited me to write a section
on diffraction theory of aberrations, a topic I was particularly interested in
at that time. Later it turned out that Hopkins felt he could not devote
adequate time to the project, and in October of 1950, Gabor, with Born’s
agreement, wrote to Linfoot and me asking if either of us, or both, would
be willing to take Hopkins’ place. After some lengthy negotiations it was
agreed that Born, Gabor, and I would co-author the book.”
Wolf writes about Born and his working style:
“In spite of his advanced age Born was very active and, as throughout all
his adult life, a prolific writer. He had a definite work routine. After coming
to his office he would dictate to his secretary answers to the letters that
arrived in large numbers almost daily. Afterward he would go to the adjacent
room where all his collaborators were seated around a large U-shaped
table. He would start at one end of it, stop opposite each person in turn,
and ask the same question: “What have you done since yesterday?” After
listening to the answer he would discuss the particular research activity and
make suggestions. Not everyone, however, was happy with this procedure.
I remember a physicist in this group who became visibly nervous each day
as Born approached to ask his usual question, and one day he told me that
he found the strain too much and that he would leave as soon as he could
find another position. He indeed did 80 a few months later. At first I too
was not entirely comfortable with Born’s question, since obviously when one
is doing research and writing there are sometimes periods of low productivity.
One day when Born stood opposite me at the U-shaped table and asked,
“Wolf, what have you done since yesterday?” I said simply, “Nothing!” Born
seemed a bit startled, but he did not complain and just moved on to the next
person, asking the same kind of question again.”
Wolf also gives an account of why Gabor pulled-out, and how Wolf had to play an unexpected, but vital role in writing this book:
“…..Gabor soon found it difficult to devote the necessary time to the project, and it was mutually agreed that he would not be a co-author after all, but would just
contribute a section on electron optics. So in the end it became my task to
do most of the actual writing. Fortunately I was rather young then, and so
I had the energy needed for what turned out to be a very large project. I
was in fact 40 years younger than Born. This large age gap is undoubtedIy
responsible for a question I am sometimes asked, whether I am a son of the
Emil Wolf who co-authored Principles of Optics with Max Born!”
Wolf also praises Born’s open-mindness to various branch of physics:
“Optics in those days-remember we are talking about optics in pre-laser
days-was not a subject that most physicists would consider exciting; in fact,
relatively little advanced optics was taught at universities in those days. The fashion then was nuclear physics, particle physics, high energy physics, and
solid state physics. Born was quite different in this respect from most of his
colleagues. To him all physics was important, and rather than distinguish
between “fashionable” and “unfashionable” physics he would only distinguish
between good and bad physics research.”
Emil Wolf is now 95 years old, and is still a very active researcher. His recent paper was in 2016 on partially coherent sources and their scattering from a crystal. Wolf’s books are classics in optics, and continues to raise probing questions and important connections in sub-branches of optics.
In an essence, great science books are written with love and passion to communicate the excitement of science. Born and Wolf certainly does that, and continues to inspire us to learn optics from the masters themselves.
“The work for which the Nobel Prize has been awarded to me is of a kind which has no immediate effect on human life and activity, but rather on human thinking. But indirectly it had a considerable influence not only in physics but in other fields of human endeavour.
This transformation of thinking in which I have taken part is however a real child of science, not of philosophy: it was not the result of speculation, but forced upon us by the observed properties of Nature.”
Max Born and Emil Wolf, your work and your books have transformed our thinking, and the way we see light and matter. Thank You !
