NEW PATHS IN THE DEVELOPMENT OF THE THEORY OF LIGHT

(On S. I. Vavilov’s book The Microstructure of Light)

P. P. Feofilov

The centuries-long history of the development of the theory of light is the history of a struggle between opposing tendencies, generated by the internally contradictory nature of light and by the impossibility of creating a visual mechanical model of the light process. The instructive lessons of this history do not permit us to suppose that the synthesis of corpuscular and wave conceptions, formally carried out by modern physics, will not require a further reconsideration of views on the nature of light, or that new phenomena will not confront physicists with the necessity of changing not only individual propositions of the modern theory of light, but also its very essence.

In establishing the laws of the propagation of light, its reflection and refraction, and its action on matter, scientists could not help pondering questions concerning the nature of light; they could not help attempting to create a visual picture of the light process. And here the impeccably exact laws of optics, while remaining in themselves unquestionable, entered into insurmountable contradictions with one another.

For the ancient Greeks, who laid the foundations of geometrical optics, notions of visual rays issuing from the eyes were quite sufficient. Epicurus and Lucretius created equally fantastic, poetic conceptions of “films”—material images separating from objects and flying through space. In Aristotle’s idealistic philosophy, light lost the features of materiality with which the ancient atomists had endowed it, yet it remained connected with a ghostly medium. In the doctrine of the Stoics, during vision the eye brought the surrounding air into a state of tension, propagating in spherical waves with its center in the pupil of the eye. Although these primitive conjectures, as well as the mystical pronouncements of medieval scholars, are for the modern ...

physics only of historical interest, already in them one can discern the sources of the alternative corpuscle—wave, which confronted physicists in the period of the rapid development of optics that began in the seventeenth century. This development, initiated by Descartes, Grimaldi, Hooke, Huygens, Newton, and Lomonosov, proceeded under the sign of an acute struggle between corpuscular conceptions, which naturally entered into the general mechanical picture of the world, seemingly the only acceptable one, and wave theories, whose irrefutable argument was the discovery of the phenomena of interference and diffraction. Newton, without speaking definitely in favor of either theory of light, undoubtedly inclined toward corpuscles, although in his polemic with Hooke he also proposed a compromise hypothesis, still based on the same mechanical picture. The struggle became still more intense in the eighteenth and nineteenth centuries, when each new discovery forced one to lean to one side or the other. The blow dealt to corpuscular theory by the interference experiments of Young and Fresnel, and the impossibility of a consistent development of mechanical wave conceptions given the unproven existence of the ether, led to the conviction that attempts to create a purely mechanical theory of light were futile. The possibility of constructing a wave theory of light that had no need of a material medium was found in electrodynamics, which enabled Maxwell to develop the electromagnetic theory of the light process. With renewed sharpness the struggle between wave and corpuscular conceptions proceeded in our century in connection with the creation of quantum theory, which required discontinuity of the light flux.

In our time no one doubts the impossibility of constructing an exhaustive theory of light on the basis of only wave or only corpuscular conceptions. Attempts are already being made to create a unified theory of light based on quantum electrodynamics. However, this theory has an excessively abstract and formal character and, despite sufficient generality and mathematical justification, cannot satisfy the physicist seeking to concretize conceptions. For the experimental physicist, who creates a picture of a phenomenon above all on the basis of experience, the path of deep analysis and interpretation of individual phenomena is much closer: phenomena in which one or another aspect of the nature of light appears, phenomena in which the contradictoriness of this nature is revealed, phenomena in which the unity of the contradictory properties of light is discovered.

This path may appear not as direct as the path of creating a unified theory, one at least formally uniting the established conceptions of the nature of light; nevertheless it is no less fruitful and is entirely necessary for deepening and concretizing our conceptions of light. This path makes it possible to discover-

NEW PATHS IN THE DEVELOPMENT OF THE THEORY OF LIGHT

to reveal in optical phenomena aspects which had either remained unnoticed or proved simply unexpected. A profound analysis of the phenomena of optics makes it possible not only to understand in a new way the general scientific significance of individual facts, long known or having become the property of science only in recent years, but also to outline new paths in the development of the theory of light*).

A brilliant example of such an analysis was given in his last book, The Microstructure of Light, by the great Soviet scientist Academician S. I. Vavilov. This book, together with the unsurpassed model of popularization of science—the book The Eye and the Sun—was awarded in 1952 the Stalin Prize, First Class.

It will be no exaggeration to say that in this book, which generalizes on the basis of materialist dialectics the results of many years of research by S. I. Vavilov and his collaborators on various questions of physical optics, the foundations are laid and the paths indicated for the development of an entirely new direction in the theory of light.

It is no accident that the first of the three parts of the book is devoted to the presentation of data relating to the corpuscular aspect of optics, the second to phenomena in which the wave properties of light are most distinctly manifested—the second side of its contradictory nature—and in the third part a synthetic picture is given of certain peculiar cases of the interaction of light and matter, these two forms of manifestation of matter which it had long been customary to oppose to one another.

This dialectical principle of the construction of the book, suggested by the entire history of the development of optics, is extremely characteristic of S. I. Vavilov, a distinctive feature of whose scientific creativity was the striving for philosophical analysis, generalization, and substantiation of the results obtained by science. This striving manifested itself also in S. I. Vavilov’s own scientific investigations: possessing the rare gift of choosing, among the multitude of problems of contemporary physics, the most fundamental and principled ones, and, finding original and keen-witted solutions to them, of indicating the paths and prospects for the development of whole directions. However deceptively simple the problems that he posed and solved sometimes seemed, behind them there was always concealed a profound thought, leading to consequences and generalizations striking in their breadth.

*) It would be naïve to think that this path presupposes the possibility of creating an exhaustive visual picture of the light process. Such an attempt, which in the final analysis amounts to an attempt to revive the mechanical theory of light, is obviously doomed to failure. Fighting against excessive formalism in many theoretical constructions, S. I. Vavilov always highly valued the role of the mathematical hypothesis as a method of investigation. At the same time, however, there is a fully legitimate striving to give, to the extent that this is possible, a concrete-physical, visual meaning to mathematical constructions.

The division of the book into three parts is by no means a mechanical division into three groups of phenomena unconnected with one another. In a number of places in the book the interpenetration of the contradictory properties of light is clearly shown, and the specially designed experiments vividly demonstrate the inseparable unity of these properties.

The main idea of the book is that the customary concepts of optics, which characterize light sources and light fluxes by their energies, spectrum, and state of polarization, prove insufficient when one passes to vanishingly small powers of light fluxes, when considering elementary emitting systems and the development of the emission process in time. The peculiar phenomena observed here fall outside the circle of ordinary optics, forming a specific domain of the optics of elementary processes—“micro-optics,” which differs from ordinary optics—“macro-optics,” in the apt expression of S. I. Vavilov, in certain respects in the same way as the molecular theory of matter differs from thermodynamics.

In contrast to macro-optics, the history of whose development goes back centuries, micro-optics is the fruit of the latest advances in physics, and its development was impossible without quantum theory, without a profound penetration into the world of microphenomena so characteristic of modern physics. Individual “micro-optical” phenomena have, of course, been known since ancient times; however, as a field of knowledge micro-optics is only beginning to take shape, and the Studies and Essays of S. I. Vavilov mark out the paths of its development. These paths consist in the study of manifestations of the discontinuous, quantum structure of a light flux at extremely small powers; in the study of the “microscopic” mechanism of interference phenomena; in the study of elementary acts of emission and absorption of light in phenomena unknown to macro-optics, which testify to the impossibility of considering elementary light sources in isolation from the medium in which they are found.

A unified micro-optical approach to the analysis of individual phenomena makes it possible to comprehend their place in the general system of knowledge in a new way and to indicate new paths for the development of optics, opening up in connection with the general development of modern physics.

The Microstructure of Light is valuable not only because it outlines the range of questions constituting a new direction in the development of the doctrine of light. This book is the result of many years of scientific creativity by a major scholar, and in reading it one can trace how large problems grow out of small, seemingly modest tasks; how facts that seemed scattered receive a natural generalization; and to what unexpected and important consequences a new approach to long-known and even

“trivial” phenomena. The book gives examples of originally conceived and cleverly executed experiments, teaches one to pose profound problems and to find simple solutions to them. At the same time, S. I. Vavilov’s book, through a number of brilliant examples of analysis of the data of physical experiment from the standpoint of materialist dialectics, teaches the creative application of the propositions of Marxist-Leninist philosophy to the phenomena of nature.

1. QUANTUM FLUCTUATIONS OF THE LIGHT FLUX — THE CORPUSCULAR ASPECT OF MICRO-OPTICS

In modern physics there are hardly any experiments that reveal the quantum nature of light with such vividness, with such obviousness (in the literal sense of the word), as S. I. Vavilov’s experiments on the visual observation of quantum fluctuations of the light flux.

The disorder of the microstructure of the light flux, caused by the statistical character of the processes of emission and by the quantum, discontinuous nature of light, inevitably leads to the existence of statistical deviations from average values (fluctuations) both of the intensity of the light flux and of its other properties (polarization, spectral composition, etc.). These fluctuations are determined, on the one hand, by the disorder of the molecular motions of the luminous medium (“classical” fluctuations) and, on the other hand, by the discreteness and spontaneous independence of the acts of emission of individual quanta of light (“quantum” fluctuations). Whereas classical fluctuations can be detected only in light fluxes emitted by sources possessing a very high temperature (\(\simeq 30\,000^\circ\) and above), quantum fluctuations must, naturally, be observed for any light fluxes, provided that the average power of these fluxes is sufficiently small.

For the observation of such weak light fluxes, receivers of radiant energy are needed that surpass in their sensitivity and stability the best modern photoelectric devices. Such a receiver proved to be the human eye, whose remarkable properties, which have repeatedly rendered invaluable services to science, make it possible to detect light fluxes of such small average power that in them fluctuations due to the quantum structure of light become perceptible.

The retina of the human eye can perceive extremely small portions of light energy, consisting of only a few tens of quanta; moreover, the minimum (threshold) number of quanta capable of producing a visual sensation proves to be sufficiently

determined for the given observer. Thus, an eye observing weak light flashes, the mean value of the luminous flux in which is close to this threshold value, will perceive those of them whose brightness, owing to the statistical character of the radiation, exceeds the threshold brightness, and will not notice those whose brightness is below this threshold. The corresponding statistical processing of the data on the number of registered and missed flashes at different mean values of the luminous flux makes it possible to determine the average number of photons producing a minimal visual sensation, and to compare the theoretically expected fluctuations with those observed experimentally.

Behind the modest lines of the book setting forth the results of the observations lies the enormous work of the collective of S. I. Vavilov’s collaborators, who accumulated, by means of laborious and painstaking measurements, the experimental data necessary for statistical processing. The results of the experiments showed that the observed fluctuations correspond to those which should be expected on the basis of ideas about the quantum structure of the luminous flux. The quantum nature of light was successfully observed “with one’s own eyes”!

The significance of S. I. Vavilov’s experiments on the visual observation of quantum fluctuations is by no means limited to the vividness with which they demonstrate the quantum structure of the luminous flux.

Already at the very beginning of the investigations their significance for problems of the physics and physiology of the visual process began to become clear. The method of quantum fluctuations made it possible to determine the spectral sensitivity of the retina of the eye as such, independently of the absorption of light in the ocular media located in front of it.

The presence of a second maximum of the retina’s sensitivity in the ultraviolet part of the spectrum, discovered in these experiments, was later confirmed by observations of the spectral sensitivity of an eye deprived of its crystalline lens.

The study of quantum fluctuations of light by the visual method also made it possible to obtain new data for solving complex questions concerning the coefficient of utilization by the eye of the light energy incident upon it, the interaction of rods and cones under threshold-sensitivity conditions, the photochemical processes in the retina, and other subtle questions of the physiology of vision.

Quite recently it has begun to become clear that quantum fluctuations of the luminous flux may affect visual functions even at relatively high brightnesses. A number of basic physiological regularities of the visual process can be derived from fluctuation concepts. One may hope that the joint efforts of physicists, physiologists, and lighting engineers, based on the development of S. I. Vavilov’s ideas, will bring...

NEW PATHS IN THE DEVELOPMENT OF THE THEORY OF LIGHT

lead to the creation of an entirely new fluctuation theory of vision*).

The method of fluctuations has great cognitive significance not only for the physiology of vision, but also for the physics of the light process, making it possible with particular clarity to reveal the corpuscular-wave duality of light phenomena. This gnoseological significance of the fluctuation method is convincingly attested by S. I. Vavilov’s experiments on the observation of fluctuations of coherent beams, fluctuations of polarization, and the statistical structure of the interference field.

The corpuscular theory encounters insurmountable difficulties when attempts are made to interpret the phenomena of interference of coherent beams of extremely low intensity. The wave theory, as is known, has no difficulty in passing to light fluxes of arbitrarily small intensity. In the experiments of S. I. Vavilov, who observed fluctuations in two coherent beams obtained in the usual way by splitting a primary beam, it was established that fluctuations in both beams occur quite independently of one another. This circumstance shows that the consistent application of wave conceptions also suffers collapse, and that the path toward creating a unified picture of the phenomenon lies through a synthesis of corpuscular and wave conceptions.

Adjacent to these experiments are the experiments investigating the statistical structure of the interference field at vanishingly small intensities of light beams. From the point of view of purely corpuscular theories, one would have expected that at such intensities the interference pattern would disappear, since a light quantum that had passed through one of the slits of the interferometer would not have a partner that had passed through the second slit. Experiment showed that, whereas regular fluctuations are observed in the bright interference fringes, the dark fringes continue to remain dark even at vanishingly small powers of the light flux. Thus, in the micropicture of the interference process, a certain regularity is manifested, expressed in the fact that the statistics are played out only in the bright fringes. When one of the beams is screened, the interference pattern disappeared, and fluctuations in separate parts of the field occurred independently.

*) S. I. Vavilov’s works on the visual observation of quantum fluctuations elicited a number of works by foreign authors, in essence merely repeating his results. Some of these authors (including the well-known American optician Gecht and others) at first tried to ignore, and then quite groundlessly to criticize, the works of S. I. Vavilov. On the pages of his book S. I. Vavilov shows the untenability of this criticism and resolutely protests against “such treatment of the works of other authors, which is unusual in normal scientific publications.”

In exactly the same way, the fluctuations in two mutually perpendicular light beams obtained by splitting a beam of natural light with a Wollaston prism proved to be independent. These experiments show that natural light, at sufficiently low intensities, is polarized at every instant in a different way, i.e. possesses fluctuations of the state of polarization.

The generalization of the results of these experiments led S. I. Vavilov to formulate a general fluctuation principle: “each light beam, isolated by any means whatever, at sufficiently low power exhibits fluctuations of intensity, occurring quite independently and autonomously from oscillations in any other beam.”

The contradictory nature of the light process is revealed in all these experiments with complete obviousness. Demonstrating the futility of the metaphysical separation of the corpuscular and wave properties of matter and proving the organic fusion of these properties and their mutual interpenetration, the experiments of S. I. Vavilov can serve as a brilliant illustration of one of the basic propositions of dialectical materialism.

We have already said that, in a light flux emitted by a source of sufficiently high temperature \((>30\,000^\circ)\), alongside quantum fluctuations, “classical” fluctuations, determined by the properties of the source, must be detected. The paths for the development of investigations of classical fluctuations were only indicated by S. I. Vavilov, who pointed out that their observation may, at least in principle, make it possible to measure the temperature of very hot stars.

Developing this thought of S. I. Vavilov, one may assert that two light fluxes indistinguishable from the point of view of macro-optics, i.e. possessing identical intensity, spectrum, and polarization, but obtained one from a high-temperature source and the other from a low-temperature source (the spectral composition can be equalized, for example, with the aid of a light filter), must differ in the character and magnitude of their fluctuations. In the first beam (if the temperature of the source sending out this beam is sufficiently high), classical fluctuations as well as quantum fluctuations must be observed.

Thus, the magnitude of the fluctuations may be regarded as a new characteristic of a light flux.

2. LIMITS OF VALIDITY OF THE SUPERPOSITION PRINCIPLE. “NONLINEARITY” IN OPTICS

The principle of complete superposition of energy at all points of space in which light beams coming from different sources intersect was regarded as self-evident in all classical optical theories. The linearity of the equations following from this principle was

...of optics seemed to be its unshakable foundation. Descartes, Newton, Huygens, and Lomonosov, in all their theoretical constructions, proceeded from the indubitability of the superposition principle. Nonobservance of this principle would have had to lead to a violation of the independent passage of a light beam through a space in which other light beams propagate, and to produce the phenomenon of “self-scattering” of light. It is not without interest to note that, in the absence of such “self-scattering,” Lomonosov saw a convincing argument against the corpuscular theory of light, according to which, when powerful light beams crossed, there ought to occur “interference in the rays.” The defenders of the corpuscular theory sought a way out in the supposition of the extreme smallness of the light corpuscles.

The discovery of the quantum character of light phenomena compelled the question of the superposition principle and of the linearity of the equations of optics to be raised once again. In a number of works attempts were made to detect “self-scattering” of light, attempts that invariably gave a negative result. However, the limits of the empirical accuracy of the superposition principle remained sufficiently indefinite. The boldly conceived experiments of S. I. Vavilov, carried out by him as early as the 1920s, showed that these limits are extraordinarily broad in space devoid of matter. Having convinced himself of the futility of attempts to establish the limits of fulfillment of the superposition principle under terrestrial experimental conditions, S. I. Vavilov made an estimate of these limits from the brightness of the solar corona, observed in a space in which light beams of enormous intensity intersect. It turned out that even if the entire solar corona is attributed to “self-scattering” of light, the effective transverse cross section of a quantum proves to be extraordinarily small—only about \(10^{-40}\ \mathrm{cm}^{2}\). Although the modern theory of light, formally uniting corpuscular and wave representations, while admitting in principle the possibility of a violation of linearity in vacuum*), gives for the transverse cross section of quanta a value 30 orders of magnitude (!) smaller than this, the experiments and considerations of S. I. Vavilov have not lost their significance to this day.

If the limits of applicability of the superposition principle in space devoid of matter lie far beyond experimental possibilities, then, in the propagation of light in matter, the quantum character of microscopic processes can lead to a very substantial violation of “linearity.”

As early as 1920, in the period of the formation of quantum theory, S. I. Vavilov published the results of experiments testing the independence

*) These violations of linearity are due to the possibility of the formation, from a “hard” photon, of an electron–positron pair.

of the absorption coefficient of a substance on the intensity of the light passing through the substance. These experiments were carried out over record-wide ranges—the light intensity was varied by a factor of \(10^{20}\)—and showed that the absorption coefficient does not depend on the intensity of the light. At the present time this result may seem trivial; however, in its day it proved fatal for the hypothesis of the continuous character of absorption and the quantum character of radiation, a hypothesis advanced by the creator of the theory of quanta, M. Planck. This hypothesis led to the conclusion that absorption should increase strongly in the region of extremely low light intensities, and the absence of such an increase, discovered in the experiments of S. I. Vavilov, testified that absorption too has a quantum character. Planck’s attempt to reconcile wave and corpuscular conceptions in so primitive a manner proved untenable.

The quantum character of the processes of absorption and emission and the finite duration of molecules’ residence in excited states make it necessary to expect deviations from “linearity” in another limiting case—at very high intensities of the transmitted light. In the experiments of S. I. Vavilov these deviations were not observed, since the duration of the excited state of the dye molecules with which the experiments were performed did not exceed \(10^{-8}\) sec. With such short durations, the number of excited molecules—whose absorption spectrum, obviously, must differ from the absorption spectrum of unexcited molecules—amounted, even at the highest intensities used, to only a negligible fraction of the total number of molecules. However, already in the case of uranium glass, for which the duration of excited states has a value of the order of \(10^{-4}\) sec, S. I. Vavilov and V. L. Levshin succeeded in observing deviations from “linearity,” expressed in a decrease of the absorbing power under very intense transmitted light. In the so-called phosphors, which have durations of excited states of the order of seconds and more, significant violations of “linearity” can readily be observed already at comparatively low intensities; moreover, in a number of cases these violations are so large that they can serve as the basis for special “absolute photometers.” The “nonlinear” photometer constructed in its day on the idea of S. I. Vavilov may be regarded as the first realization of a new and original principle of photometry.

The violation of “linearity,” which constitutes one of the fundamental principles of ordinary optics, made it possible for S. I. Vavilov to pose the problem and outline the paths for the development of a new direction—“nonlinear” optics, which critically examines the constancy of such characteristics of a substance as absorption, dispersion, double

birefringence, dichroism, etc. Despite the fact that one constantly has to deal with “nonlinear” optics both in solving problems of astrophysics, when the question concerns the colossal density of light energy inside stars, and in the modest conditions of the laboratory in the study of luminescence phenomena, a rigorous mathematical apparatus for solving “nonlinear” optical problems is still lacking. And S. I. Vavilov sets physicists the task of creating such an apparatus.

3. THE WAVE ASPECT OF MICRO-OPTICS

a) Micro-optical consideration of general problems of interference

In the second part of the book S. I. Vavilov has realized a possibility, not obvious at first sight, of a micro-optical investigation of phenomena determined by the wave properties of light and, first and foremost, of interference phenomena. An original concrete-physical, rather than formal-mathematical, approach to the consideration of interference phenomena enabled S. I. Vavilov to say a new word in this classical field of optics.

In the classical consideration of interference phenomena it is customary to operate with waves infinitely extended in time and with infinitely small sources emitting isotropic spherical waves. These simplifications and restrictions become inadmissible in the transition to real elementary radiating systems with a finite duration of emission, to the real conditions of interference experiments with the inevitable limitation of light beams, i.e. in the transition to a microscopic consideration of interference problems.

In the masterly exposition of the foundations of the theory of interference given in The Microstructure of Light, what is extraordinarily characteristic of S. I. Vavilov is the striving to build arguments on concrete, tangible images. Thanks to this, the reader is compelled to ponder the details of the mechanism of interference phenomena that slip away in the usual exposition. Thus, here the question of the impossibility of realizing ideal monochromatic beams is considered in a completely new way; the general case of an interference pattern, arising as a combination of the interference of parallel and antiparallel waves and of a traveling wave that interferes with nothing, is considered in a new way. Very essential is the consideration carried out by S. I. Vavilov of the influence on the interference pattern of the sizes of the sources sending the interfering beams, as well as of the diffraction structure of the interference field, the necessity of taking which into account

follows from the unavoidable diaphragming of light beams in real interference experiments. The results obtained have a direct bearing on the theory of interference instruments.

Having posed the question of the coherence of light beams in a new way, S. I. Vavilov suggested that, in principle, coherent light beams can also be obtained from separate elementary sources, provided there is interaction between the sources. It is only necessary that the sources be situated sufficiently close to one another and that the average duration of the emission process considerably exceed the period of the light oscillations. This suggestion, based on the conception of the resonant interaction of sources, is most closely connected with the consequences of the combined consideration of the light source and the medium carried out in the third part of the book. The experiments conceived by S. I. Vavilov for the experimental verification of this suggestion still await their realization.

Remarkable in their simplicity and full of profound meaning are S. I. Vavilov’s experiments on observing the influence of a medium on interference phenomena. The results of these experiments, which at first glance seem paradoxical, make it possible to speak of a phenomenon, absurd from the usual point of view, of rotation of the plane of polarization of unpolarized light. If two coherent natural beams are made to interfere, and then a medium is introduced into the path of one of them—for example, a medium that rotates the plane of polarization of linearly polarized light by \(90^\circ\)—then the interference pattern disappears, although both beams still remain coherent and natural. This is connected with the fact that, for each elementary emission (photon, in the corpuscular interpretation), the planes of polarization of the rays that meet turn out to be rotated relative to one another by \(90^\circ\), which makes interference impossible. Thus interference makes it possible to reveal changes in the internal structure of a natural beam that are inaccessible to ordinary methods of light analysis based on observation of intensity, frequency, and state of polarization. An analogous experiment can be performed with a half-wave plate placed in the path of one of the interfering natural beams. The half-wave plate likewise leaves natural light natural, but introduces into it regular changes that can be detected by interferential comparison with another coherent natural beam that has not undergone such changes.

In these experiments of S. I. Vavilov, which deepen the concept of natural light, one may see a vivid example of the interpenetration of opposites: natural light is at the same time unpolarized and polarized.

The heuristic value of the micro-optical approach to interference phenomena is revealed especially clearly when considering the dependence of the character of the interference pattern on the nature of elementary emitters, and when studying the radiation of electrons propagating in a medium with a velocity exceeding the phase velocity of light.

b) Interference and the nature of elementary emitters

In the classical theory of interference, the question did not arise of the anisotropy of the light field of individual elementary emitters, or of the directionality of their radiation. It was not essential, since interference was always considered either between rays obtained by splitting a single light beam by means of reflection or refraction (Newton’s interference), or between rays propagating from a source at small angles (Fresnel interference).

It is not difficult to understand, however, that if these restrictions are removed and light beams issuing from an elementary source at wide angles are made to interfere, then the properties of the spatial anisotropy of the source will manifest themselves in the character of the interference pattern. As is known, elementary emitters of different multipolarity (electric and magnetic dipoles, quadrupoles, etc.) possess different spatial distributions of radiation and, consequently, must give different patterns in wide-angle interference. Although the observation of wide-angle interference had been carried out earlier*), before S. I. Vavilov no one paid attention to the possibility of using the results obtained to determine the multipolarity of elementary emitters.

Calculations of the character of the interference field at different angles between the interfering beams, carried out by S. I. Vavilov, showed that the visibility of the interference fringes and the degree of their polarization are qualitatively different for sources constructed from different elementary emitters. Thus, analysis of the interference pattern makes it possible to reveal characteristic microstructural features of elementary emitters. This result demonstrates the possibilities of interference as a method of investigation. The directionality of elementary radiation is usually not taken into account, since the chaotic distribution of emitters in real sources averages out the pattern; however,

*) Schrödinger’s experiments on wide-angle interference, carried out by him in 1920, were intended to resolve the apparent contradiction between the omnidirectional radiation of classical oscillators and the directed trajectory of individual photons. At present, of course, such a formulation of the question is of only historical interest.

multipole microstructure of a light beam can be revealed in interference experiments.

S. I. Vavilov’s unfailing interest in finding experimental possibilities for investigating the multipole nature of elementary emitting and absorbing systems also led him to another original method, likewise based on the anisotropy of the spatial distribution of radiation, i.e. likewise essentially belonging to micro-optics. This method, which makes it possible to determine simultaneously the nature of both the emitting and the absorbing systems of luminescent objects, consists in studying the dependence of the polarization of luminescence light on the direction of observation and on the position of the electric vector of the exciting light. The spatial distribution of polarization proves to be specific for emitters of various types and makes it possible to determine their nature.

In considering S. I. Vavilov’s work in the field of quantum fluctuations, we indicated that to the usual characteristics of a light flux—intensity, spectrum, polarization, and direction—a new characteristic may be added: the magnitude of the fluctuations of the light flux.

S. I. Vavilov’s works in the field of seeking methods for the experimental study of the nature of elementary emitters in complex molecular systems lead to a new enrichment of the concept of the light flux. To the indicated characteristics of the light flux one more essential characteristic must be added—the nature of the elementary emitters of the light beam. The methods developed by S. I. Vavilov continue to this day to remain the only means for the experimental determination of this characteristic for radiations with a continuous spectrum.

c) The Vavilov–Cherenkov phenomenon. The optics of “superluminal” velocities

In 1933 P. A. Cherenkov, working under the direction of S. I. Vavilov, investigated the universal visible glow of pure liquids under the action of the γ-rays of radium. Analysis of the peculiar properties of this glow led S. I. Vavilov to the conclusion that here we are dealing with a new kind of radiation. Further investigations showed that this radiation accompanies the propagation of electrons in a medium with a velocity exceeding the phase velocity of light.

The path by which S. I. Vavilov arrived at the conclusion that the observed glow was not, as might have seemed at first glance, ordinary γ-luminescence is very instructive and essential for the analysis of scientific creativity.

S. I. Vavilov, and therefore it is necessary to dwell on it in somewhat greater detail.

An example of how consistently and logically irreproachably S. I. Vavilov developed his ideas about individual physical concepts and quantities may be provided by the duration of excited states of molecules.

In the theory of polarized luminescence developed by S. I. Vavilov as early as the 1920s, an important role was played by the idea of the finiteness of the time spent by molecules in the excited state, allowing the molecules to lose their initially arising orientation, as a result of which the emission becomes depolarized. Later the idea of the duration of excited states was introduced into the theory of quenching of luminescence, developed by S. I. Vavilov and his collaborators. In this theory the probability of quenching was directly connected with the duration, which served as the basic criterion in classifying types of quenching. Through the duration of luminescence it proved possible to connect depolarization with quenching. In these basic luminescent processes, determined by the duration of excited states, the interaction of individual molecules of the luminescing substance does not participate. But the transfer of the basic ideas about the kinetics of processes developing in time allowed S. I. Vavilov in the 1940s to develop the theory of the influence of concentration on luminescence, which will be discussed below (§ 4). Here it is important to emphasize that at the foundation of this theory lies the idea of the finiteness of the time spent by molecules in the excited state.

A consistent analysis of the role of the duration of the excited state of luminescing molecules led S. I. Vavilov in 1944 to the necessity of introducing the idea of the finite duration of the excited state into the very definition of the concept of luminescence. The classical definition of luminescence as a nonequilibrium process of radiation, given earlier by Wiedemann, required limitations in order that it might be brought into correspondence with the ideas about luminescence actually used in physics. Wiedemann’s definition suffered from excessive breadth, including such phenomena non-luminescent in the generally accepted sense as all possible kinds of scattering, reflection, bremsstrahlung, etc. To distinguish them from luminescence an additional criterion was necessary. Nonequilibrium radiation, in contrast to equilibrium thermal radiation, always bears the characteristic features of the radiating body or of the cause that produced the radiation, which are reflected in the spectrum, intensity, polarization, spatial anisotropy and, finally, in the duration of the emission. Having analyzed the whole diversity of nonequilibrium radia-

tions and their properties, S. I. Vavilov came to the conclusion that only duration can serve as an unambiguous criterion for distinguishing luminescence from all other types of nonequilibrium radiation. This enabled him to give the well-known, impeccably strict definition of luminescence.

The consistent application of the criterion of duration as a basis for classifying types of glow enabled S. I. Vavilov to suspect that the glow observed by P. A. Cherenkov did not belong to the class of luminescent processes. Indeed, it was subject neither to quenching nor to depolarization, i.e., it did not possess a finite duration. Soon new and unexpected properties of the glow were discovered: its spatial directionality, a peculiar state of polarization, and susceptibility to the influence of a magnetic field. As a result, a new phenomenon was discovered: radiation emitted by electrons moving with a velocity exceeding the phase velocity of light in the medium—a phenomenon revealing new, unforeseen possibilities for the optics of sources moving in a material medium with superluminal velocities*).

A micro-optical analysis of the structure of the interference field of light waves that arise when a superfast electron passes through a medium makes it possible to give an elementary theory of the Vavilov–Cherenkov radiation, explaining the peculiar character of the directionality of this radiation. As is known, when light or electrons propagate in a homogeneous medium, no light is emitted to the sides, despite the fact that every point of the trajectory of a photon or electron may be regarded as the center of spherical waves. This is connected with the interference of the waves, which leads to the mutual annihilation of disturbances at all points of space except those lying on the trajectory. The situation is different when the electrons have “superluminal” velocity. In this case, as a result of interference, all rays will be extinguished except those rays that form with the electron trajectory a definite angle depending on the electron velocity. As a result, in accordance with experiment, the radiation will be directed along a cone.

The interference interpretation of the Vavilov–Cherenkov phenomenon leads to the conclusion (not yet verified experimentally) that if the layer of substance through which the electron passes is small in comparison with the wavelength, then the visible glow with its peculiar properties should arise also at electron velocities that do not reach the velocity of light.

*) It should be noted that the application of the duration criterion enabled S. I. Vavilov to prove that the glow observed in 1928 in India, interpreted by its authors as a new type of light scattering, is ordinary luminescence caused by insignificant impurities contained in the irradiated substance.

Expounding, alongside the interference interpretation, the elementary corpuscular theory of the radiation of fast electrons, S. I. Vavilov emphasizes that here the point is not a double explanation, but that “both interpretations merge into one in accordance with the dual corpuscular-wave nature of light.”

4. INTERACTION OF SOURCE AND MEDIUM

In ordinary optics it is assumed that, in order to solve problems concerning the propagation of light in a medium, it is sufficient to characterize the light source with respect to its intensity, spectrum, and state of polarization, and to specify constants characterizing the medium—its absorption and refraction indices and the magnitude of its optical activity. Such a macroscopic description, which ignores the interrelation of light sources and the medium, proves insufficient for explaining a number of phenomena, in particular certain phenomena in fluorescing solutions.

In contrast to this, microoptics proceeds from ideas about the source and the medium as a single, organically connected whole. In the third part of S. I. Vavilov’s book it is shown that such a dialectical approach to the consideration of physical problems makes it possible to draw a number of conclusions of fundamental significance and to discover a number of new phenomena unknown to ordinary optics.

a) Microoptics of an absorbing medium

The physical basis of the assumption of macrooptics concerning the possibility of considering the light source and the medium independently is the supposition that the distances between the radiating particles of a substance and the particles absorbing and scattering light considerably exceed the wavelength of the emitted light. In other words, macrooptics confines itself to processes taking place in the “wave zone.” Such a restriction proves impermissible when considering processes in media that simultaneously emit and absorb light, for example in macroscopic light sources or in luminescent media, where the emitting molecules are surrounded by other molecules (identical or foreign) capable of absorbing the emitted light. In this case it is necessary to abandon the idea of the separateness of the light source and the medium and to pass to a more general conception of the light source and the medium as a single, organically connected whole. In doing so one must take into account not only the “passive” role of remote absorbing particles, which weaken radiation already formed, but also the “active” participation of absorbing particles located near the radiating one in the formation

emission. This “active” role of the nearest absorbing particles manifests itself in the inductive resonance coupling into which they enter with the emitting particles. In the case of luminescent solutions, inductive resonance causes a change in the radiative capacity of the luminescing molecules and in the absorbing capacity of the nearest unexcited molecules. Thus, alongside the “trivial” macro-optical causes of changes in the intensity of light arising in an absorbing medium and passing through it, there must also be distinctive micro-optical causes.

The influence of emitting molecules on the absorptive capacity of neighboring unexcited molecules should manifest itself most strongly in the transition to extremely thin luminescing layers, and should be observed in the form of deviations from Bouguer’s law, which establishes the independence of the absorption coefficient from the thickness of the absorbing layer. Experiments to detect these deviations from Bouguer’s law, carried out by S. I. Vavilov with astonishing experimental virtuosity, showed (in accordance with expectation) an increase in absorption when molecules were brought closer together. This increase is small in magnitude, but it has very great fundamental significance—“it is as though it throws a bridge between ordinary optics with a separated light source and medium and the optics of an emitting and absorbing medium, when the concepts of source and medium are difficult to separate.”

b) Inductive resonance and energy migration

The presence of inductive resonance coupling between molecules in solutions leads to the fact that, when molecules approach one another sufficiently closely, i.e., at a sufficiently high concentration of the dissolved substance, the excitation energy acquired by a molecule as a result of absorption of a quantum of light becomes capable of being transferred from excited molecules to unexcited ones, in the same way “as the energy of coupled oscillating pendulums is alternately pumped from one pendulum to another.” The excitation energy can thus migrate from molecule to molecule, with the result that a number of peculiar phenomena may occur, in particular in luminescing solutions, where, as a result of energy migration, the molecule that has absorbed the light quantum and the molecule that emits its energy in the form of luminescence may prove to be spatially separated.

In luminescence it has long been known that an increase in the concentration of a dissolved luminescent substance affects all the principal characteristics of the glow—its spectrum, yield, polarization, and duration.

NEW PATHS IN THE DEVELOPMENT OF THE THEORY OF LIGHT

The explanation of some of these phenomena encountered no difficulties, since they are connected with the “trivial” influence of the absorption of luminescence light passing through an absorbing medium. However, a number of phenomena—in particular, the decrease in yield, degree of polarization, and duration of afterglow with increasing concentration—could not be fully explained by this “trivial” influence: the phenomena were also observed in thin layers, where the influence of reabsorption was excluded. Attempts to create physicochemical theories of the phenomenon were not crowned with success.

A consistent explanation of the influence of the coming together of molecules on the characteristics of luminescence was found as a result of bringing in ideas about the migration of excitation energy. These ideas entered the theory of luminescence through quantum mechanics, with its largely formal representation of the resonance of coupled systems. While qualitatively explaining the phenomena, theories based on quantum-mechanical considerations diverged decisively from experiment in attempts at quantitative calculation. S. I. Vavilov drew attention to the fact that, in essence, energy migration is a purely classical effect connected with the presence of inductive resonance between excited and unexcited molecules. Classical optics, however, did not take into account the possibility of the existence of this effect. Consciously renouncing an overly detailed specification of the character of the inductive interaction of molecules and concealing, behind empirical constants, the details of the mechanism of energy migration that were not amenable to deciphering, S. I. Vavilov developed an internally consistent phenomenological theory of the influence of concentration on the luminescence of solutions.

As a result of energy migration in an isotropic medium with chaotically arranged molecules of the luminescent substance, the initially existing partial orientation of excited molecules (caused by the anisotropy of individual molecules and by the inevitable anisotropy of the exciting beam of light) will gradually be lost. As a result, the degree of polarization of the luminescence must decrease as the migration process develops, i.e. as the concentration of the luminescent substance increases. In the course of migration, the excitation energy may fall upon a molecule incapable of emission, as a result of which the luminescence is quenched. The probability of such quenching, too, must evidently grow with increasing concentration. The reduction of the mean duration of the excited state as the concentration of the luminescent substance increases is explained just as naturally.

The formulas obtained by S. I. Vavilov on the basis of these ideas about the processes occurring during energy migration

excitation in luminescent solutions, are in complete agreement with the experimental data.

The theory developed by S. I. Vavilov is a very convincing example of the necessity of rational limitation in the formulation of a physical problem—a limitation determined by the state of our knowledge of the details of the processes under study. Alien to the formalism of the theory of quantum-mechanical resonance, it creates clear representations of the processes connected with the manifestation of energy migration, while at a certain stage refraining from their further concretization.

S. I. Vavilov’s theory not only explains all known facts determined by the influence of concentration on luminescence, but also makes it possible to predict new phenomena. Thus, for example, the phenomenon of an increase in depolarization as the glow decays was predicted, connected with the fact that the energy emitted at later stages of the glow has greater chances of undergoing migration, which, as we have seen, leads to depolarization of the glow.

This phenomenon was indeed discovered in a number of objects of different nature.

Having developed the theory of concentration phenomena on the basis of data obtained in the study of luminescent solutions, where inductive resonance takes place between chemically identical molecules, S. I. Vavilov showed experimentally that identity of molecules is by no means obligatory for inductive resonance. Excitation energy can also migrate between heterogeneous molecules; what is essential is only the overlap of the emission spectrum of the excited molecule with the absorption spectrum of the unexcited one. This overlap testifies to the presence of common frequencies in the molecules, i.e. to the fulfillment of the necessary condition for the possibility of resonance interaction.

If the molecules of the second substance present in the solution are not capable of luminescence, then resonant transfer of energy to these molecules from the primarily excited molecules of the luminescent substance will inevitably be accompanied by quenching.

The micro-optical approach to this remarkable manifestation of the interaction of a source and the surrounding medium makes it possible to regard the quenching of luminescence by foreign absorbing substances as absorption of light that increases extremely strongly at small distances from the source.

If, however, the molecules of the second substance are also capable of luminescing, then, as a result of the migration of energy to these molecules, emission by the molecules of both substances will be observed in the luminescence of the solution (which can be detected without difficulty,

if their spectra are different), despite the fact that the exciting light is absorbed by only one of them. S. I. Vavilov did not have time to include in his book the results of experiments carried out under his direction, in which it was established that such sensitized luminescence as the result of resonant migration of energy does indeed occur.

The whole complex of questions considered by S. I. Vavilov in connection with the study of the process of emission in an absorbing medium shows the fruitfulness of such an approach, in which the sources and the medium are regarded not as separate elements of an optical process, but as inseparably connected, interacting with and conditioning one another.

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The questions touched upon in The Microstructure of Light do not, of course, exhaust the field of micro-optics as the optics of elementary processes. However, the main features of this new direction in optics, which arose in connection with the penetration of modern physics into the world of microphenomena, are outlined in it quite clearly.

The new prospects for the development of the study of light traced by S. I. Vavilov must be studied thoroughly and deeply. The fruitfulness of many of the paths he indicated is evident even now.

Along with a unified “micro-optical” analysis of already solved problems of optics, along with the presentation of his own scientific results, S. I. Vavilov sets forth in his book a number of most important fundamental problems: the need for a deeper, non-mechanical unification of the electromagnetic theory of light with quantum facts and concepts; the need for a concrete physical interpretation of the fundamental phenomenon of the formation of an electron–positron pair from a \(\gamma\)-photon; the need to overcome the formalism and the “irreducibility” of the classical doctrine of the electromagnetic field itself; and a number of other problems that in essence belong to micro-optics. It is very characteristic that a large part of these problems is connected with overcoming the formalism that is, to a considerable extent, inherent in many works on theoretical physics—a formalism that S. I. Vavilov considered inadmissible.

The abstract character of many constructions of modern physics requires an especially close union of theory and experiment. In this respect The Microstructure of Light is a brilliant example, showing, on the one hand, what clear and tangible meaning the most seemingly complex and abstract constructions of theory can acquire, and, on the other hand, what

deep theoretical generalizations can be made on the basis of what would seem to be the simplest experiments.

There is no doubt that many of the ideas expressed in S. I. Vavilov’s book will become the subject of special investigations. Generations of opticians will be educated on the remarkable book of this outstanding scientist-materialist; from it they will learn boldness and profundity in the formulation of experiments, the ability to generalize observed facts by considering them dialectically in their interconnection with a broad range of phenomena, the ability to draw far-reaching conclusions and to blaze new paths in science.