Formulations for second and higher harmonic frequency up & down conversions, as well as multi photon processes directly assume summability and divisibility of photons. Quantum mechanical (QM) interpretations are completely congruent with these assumptions. However, for linear optical phenomena (interference, diffraction, refraction, material dispersion, spectral dispersion, etc.), we have a profound dichotomy. Most optical engineers innovate and analyze all optical instruments by propagating pure classical electromagnetic (EM) fields using Maxwell's equations and gives only 'lip-service' to the concept "indivisible light quanta". Further, irrespective of linearity or nonlinearity of the phenomena, the final results are always registered through some photo-electric or photo-chemical effects. This is mathematically well modeled by a quadratic action (energy absorption) relation. Since QM does not preclude divisibility or summability of photons in nonlinear & multi-photon effects, it cannot have any foundational reason against these same possibilities in linear optical phenomena. It implies that we must carefully revisit the fundamental roots behind all lightmatter interaction processes and understand the common origin of "graininess" and "discreteness' of light energy.
Formulations for second and higher harmonic frequency up & down conversions, as well as multi photon processes directly assume summability and divisibility of photons. Quantum mechanical (QM) interpretations are completely congruent with these assumptions. However, for linear optical phenomena (interference, diffraction, refraction, material dispersion, spectral dispersion, etc.), we have a profound dichotomy. Most optical engineers innovate and analyze all optical instruments by propagating pure classical electromagnetic (EM) fields using Maxwell's equations and gives only 'lip-service' to the concept "indivisible light quanta". Further, irrespective of linearity or nonlinearity of the phenomena, the final results are always registered through some photo-electric or photo-chemical effects. This is mathematically well modeled by a quadratic action (energy absorption) relation. Since QM does not preclude divisibility or summability of photons in nonlinear & multi-photon effects, it cannot have any foundational reason against these same possibilities in linear optical phenomena. It implies that we must carefully revisit the fundamental roots behind all lightmatter interaction processes and understand the common origin of "graininess" and "discreteness' of light energy.
As low light detection technologies are advancing, novel experiments like single molecule spectroscopy, quantum computation, quantum encryption are proliferating. Quantum mechanical detectors can produce only discrete "clicks" at different rates based on the propagating field energy through them, irrespective of whether the photons are divisible or indivisible packets of energy. This is because electrons are quantized elementary particles and they are always bound in quantized energy levels in different quantum systems. Highly successful quantum formalism is not capable of providing the microscopic picture of the processes undergoing during QM interactions; that is left to human imaginations allowing for sustained controversies and mis-interpretations. This paper underscores the paradoxes that arise with the assumption that photons are indivisible elementary particles based on the obvious but generally ignored fact that EM fields do not operate on (interfere with) each other. Then we propose that atomic or molecular emissions emerge and propagate out as space and time finite classical wave packets. We also suggest experiments to validate that the amplitude of a photon wave packet can be split and combined by classical optical components using the specific example of an N-slit grating.
The intention of this paper is to underscore that to understand fundamentally new properties of light beams, we must first find the limits of semi classical model to explain optical interference phenomena. We claim that we have not yet reached that limit. Careful analysis of the processes behind detecting fringes indicate that the effect of superposition of multiple optical beams can become manifest only through the mediation of the detecting dipoles. Since the detectors are quantum mechanical, (i) the observed effects are different for different detectors for the same superposed light beams, and further, (ii) they are only capable of registering discrete number of "clicks", whose rate will vary with the incident intensity. A reduced rate of "clicks" at very low intensity does not prove that light consists of indivisible packets of energy. We have also experimentally demonstrated that (i) neither Fourier synthesis, nor, (ii) Fourier decomposition actually model the behavior of EM fields under all possible circumstances. Superposed light beams of different frequencies do not synthesize a new average optical frequency. A pure amplitude modulated pulse does not contain any of the mathematical, Fourier analyzed frequencies. The QED definition of photon being a Fourier mode in the vacuum, it necessarily becomes non-local. Since we have demonstrated that the Fourier theorem has various limitations in classical physics, its indiscriminate use in quantum mechanics should also be critically reviewed.
Nonlinear optics is the study of the response of dielectric media to strong optical fields. The fields are sufficiently strong that the response of the medium is, as its name implies, nonlinear. That is, the polarization, which is the dipole moment per unit volume in the medium, is not a linear function of the applied electric field. In the equation for the polarization, there is a linear term, but, in addition, there are terms containing higher powers of the electric field. This leads to significant new types of behavior, one of the most notable being that frequencies different from that of the incident electromagnetic wave, such as harmonics or subharmonics, can be generated. Linear media do not change the frequency of light incident upon them. The first observation of a nonlinear optical effect was, in fact, second-harmonic generation – a laser beam entering a nonlinear medium produced a second beam at twice the frequency of the original. Another type of behavior that becomes possible in nonlinear media is that the index of refraction, rather than being a constant, is a function of the intensity of the light. For a light beam with a nonuniform intensity profile, this can lead to self-focusing of the beam. Most nonlinear optical effects can be described using classical electromagnetic fields, and, in fact, the initial theory of nonlinear optics was formulated assuming the fields were classical. When the fields are quantized, however, a number of new effects emerge. Quantized fields are necessary if we want to describe fields that originate from spontaneous emission. For example, in a process known as spontaneous parametric down-conversion, a beam of light at one frequency, the pump, produces a beam at half the original frequency, the signal. This second beam is a result of spontaneous emission.
Introduction One of the most impressive accomplishments of wave optics is its success in providing a coherent and succinct description of the interactions between electromagnetic waves and matter (gases, solids, etc.). Maxwell's equations, which describe the propagation of light, and the Laplace–Lorentz equations, which describe the source terms of light, allow one to take into account the phenomena of refraction, diffusion, and diffraction of light by dense media. It is amazing – to say the least – that such a theory can account for the complex interactions of an electromagnetic wave with an immense ensemble of atoms (each approximated in terms of individual harmonic oscillators), by means of a simple optical index n op . Such an achievement is reminiscent and, indeed, on par with the level of concision achieved by the concept of effective mass in representing the interaction of a conduction electron with a crystalline lattice. In the description of all these effects, an electromagnetic wave with (angular) frequency ω forces free carriers into oscillatory motion at the same frequency, leading to radiative re-emission at this same frequency. This behaviour is a natural by-product of the linear equations we have employed up until now. In this chapter, we will see that non-linear media (i.e. materials whose response to external excitations contains non-linear terms), may by used to perform frequency conversion as evidenced, for example, by second harmonic light generation or optical parametric oscillations.
The behavior of light and its interaction with matter is certainly one of the most interesting phenomena of physics. It has puzzled thinkers and scientists in ancient Greece (Archimedes) and through the Middle Ages, at least since the times of Robert Grosseteste (1168–1235), right up to the theories of Galileo Galilei and Isaac Newton. The classical electromagnetic theory of light (see Tab. 13.1) was beautifully established in the second half of the nineteenth century with the Maxwell equations. Quantum optics is nothing other than the quantum theory of light. It finds its roots in Planck's discovery (1900) that the assumption of energy quantization for a harmonic oscillator allowed us to solve the black-body problem (see Subsec. 1.5.1). The successive early steps that led to the quantization of the electromagnetic field include Einstein's explanation of the photoelectric effect with the introduction of the quantum of light (see Subsec. 1.2.1) and the interpretation of atomic spectra (see Subsec. 1.5.4). Quantum optics is usually not covered by conventional textbooks on quantum mechanics. We include its discussion here for two main reasons: first, because it is a fundamental and advanced application of the basic framework of quantum mechanics, and, second, because in the last 30 years quantum optics has played (and is still playing) a major role in the advancement and understanding of quantum mechanics.
The 'graininess' in the energy content of light is reported in experiments ranging from the blackbody spectrum and photo-electric effect to revivals in the Jaynes-Cummings model. Laser shot noise and antibunching of correlations in resonance fluorescence signify a departure from continuous wave behavior for light. Such phenomena underlie the unique sense in which a photon is regarded as an indivisible particle, experimentally tied to the fact that a beam splitter does not split a single photon of a two-photon pair. We consider three arguments for indivisibility - quantization of energy, particle-like fluctuations, and which-way measurements. We argue that in each case, photon indivisibility is an inference based on energy conserving interactions where the detection mechanism involves countable electrons subject to space and bandwidth limitations. The indivisibility of the photon thus remains an open question, and one that we can use to probe the foundations of quantum electrodynamics.