Optoelectronic functional materials are divided into two categories as electronic functional material and photonic functional material. And the comparison of the two materials exhibits that the theory of electronic functional material, solid-state quantum mechanics, has developed quite ripe, but the theory of photonic functional material is still in the classical stage or quasi-classical stage. While today, photonic functional material has gradually developed into microscopic field, the deficiency of quantum mechanics in its theory has confined the development of photonic functional material. The optical theory in this paper is different from the traditional optical theory that originates from wave optics, but originates from ray optics and introduces quantum mechanics into ray optics, thus sets up the formula of ray optics quantum mechanics. The conclusion exhibits great symmetry between ray optics quantum mechanics and solid-state quantum mechanics. Nonrelativistic ray optics quantum mechanics is set up on the condition that light is confined near the axis. This paper introduces the construction of ray optics quantum mechanics concisely, and its main equations as well.
Optoelectronic functional materials are divided into two categories as electronic functional material and photonic functional material. And the comparison of the two materials exhibits that the theory of electronic functional material, solid-state quantum mechanics, has developed quite ripe, but the theory of photonic functional material is still in the classical stage or quasi-classical stage. While today, photonic functional material has gradually developed into microscopic field, the deficiency of quantum mechanics in its theory has confined the development of photonic functional material. The optical theory in this paper is different from the traditional optical theory that originates from wave optics, but originates from ray optics and introduces quantum mechanics into ray optics, thus sets up the formula of ray optics quantum mechanics. The conclusion exhibits great symmetry between ray optics quantum mechanics and solid-state quantum mechanics. Nonrelativistic ray optics quantum mechanics is set up on the condition that light is confined near the axis. This paper introduces the construction of ray optics quantum mechanics concisely, and its main equations as well.
Let us return from optics to mechanics and explore the analogy to its fullest extent. In optics the old system of mechanics corresponds to intellectually operating with isolated mutually independent light rays. The new undulatory mechanics corresponds to the wave theory of light . Erwin Schrödinger, Nobel lecture , 1933 In this chapter we shall see that electromagnetic waves and electrons feature a number of common properties under conditions of spatial confinement. Simple and familiar problems from introductory quantum mechanics and textbook wave optics are recalled in this chapter to emphasize the basic features of waves in spatially inhomogeneous media. Herewith we make a first step towards understanding the properties of electrons and electromagnetic waves in nanostructures and notice that these properties in many instances are counterparts. Different formulas and statements of this chapter can be found in handbooks on quantum mechanics and wave optics. A few textbooks on quantum mechanics do consider analogies of propagation and reflection phenomena in wave optics with those in wave mechanics. Isomorphism of the Schrödinger and Helmholtz equations In Chapter 2 we discussed that an electron in quantum mechanics is described by the wave function, the square of its absolute value giving the probability of finding an electron at a specific point in space. This function satisfies the Schrödinger equation (2.56) which is the second-order differential equation with respect to space and the first-order differential equation with respect to time.
The similarities between quantum mechanics and paraxial optics were already well-known to the founding fathers of quantum mechanics; indeed knowledge of paraxial optics partly informed quantum mechanics as a wave theory. Likewise quantum mechanical methods have been employed to better understand optics, for example, to determine which optical transformations are in principle realisable and which not. Recently the notion of classical entanglement has been mooted, ushering in a new avenue to explore, perhaps bridging the classical-quantum divide. These developments have raised questions as to which quantum tasks could be implemented with classical light, taking advantage of the wealth of four centuries of experience in optics. In this article we review the similarities as well as differences between optics and quantum mechanics, providing a quantum notation for classical light. We review the evidence for cross-fertilisation between quantum mechanics and classical optics, in particular considering the issue of classical entanglement and its exploitation for quantum tasks. Our work provides a concise theoretical framework punctuated with relevant examples, and critically assesses the current state of the field and its limits.
When rewritten in an appropriate manner, the microscopic Maxwell-Lorentz equations appear as a wavemechanical theory for photons, and their quantum physical interaction with matter. A natural extension leads from photon wave mechanics to quantum electrodynamics (QED). In its modern formulation photon wave mechanics has given us valuable new insight in subjects such as spatial photon localization, near-field photon dynamics, transverse photon mass, photon eikonal theory, photon tunneling, and rim-zone electrodynamics. The present review is based on my plenary lecture at the SPIE-Europe 2009 Optics and Optoelectronics International Symposium in Prague.
This chapter describes the formation, development, and major subjects of nonlinear optics and photonics. The semiclassical theory treats the light as a classical electromagnetic field governed by Maxwell equations, while the optical medium is a molecular system governed by quantum mechanics; the key parameters for this theory are various-order nonlinear susceptibilities. The quantum theory of radiation treats light as an ensemble of photons and the medium as a molecular system, both of which are described by quantum mechanics, and the key aspect is the concept of the so-called intermediate state represented by a virtual energy state level. The semiclassical theory gives a concise quantitative description of various nonlinear multi-wave mixing effects as well as those nonlinear processes related to the induced refractive-index changes. In contrast, the quantum theory of radiation can provide a conceptual interpretation for almost all known nonlinear optical effects and phenomena.
Light in media The backbone of theoretical quantum optics is the quantum field theory of light, the quantum theory of the electromagnetic field. Quantum electrodynamics becomes surprisingly complicated if one insists on formulating it in a relativistically and gauge-invariant form, as one surely should do in elementary particle physics. Moreover, in quantum optics, we are concerned with light quanta in materials such as glass, with quantum electromagnetism in media, which is even more complicated. To cut a long story short, here we follow a minimalistic approach where we develop the essentials of quantum electrodynamics with as little technical effort as possible, sailing around the cliffs of relativistic quantum field theories. We do not assume any prior knowledge of classical field theory; we only borrow a few ideas from classical electromagnetism (Jackson, 1998). Complications and problems still remain, but hopefully these are mostly no longer formal difficulties, but rather conceptual problems of the quantum nature of light. As Dr Samuel Johnson said on poetry “We all know what light is; but it is not easy to tell what it is. ” Maxwell's equations What is light? Light is a quantum object - we describe its properties by quantum observables, Hermitian operators, and its state by a state vector | ψ _ or density matrix ρ . We use the Heisenberg picture of quantum mechanics where the operators evolve in time, but the quantum state does not change.
This chapter begins with a brief outline of some of the key motivations for considering a quantum theory: the early attempts to determine the spectral distribution of energy density of black bodies; stability of atoms and molecules; specific heats of solids; interference and diffraction of light beams; polarization of photons. The experimental foundations of wave mechanics are then presented in detail, but in a logical order quite different from its historical development: photo-emission of electrons by metallic surfaces, X- and γ-ray scattering from gases, liquids and solids, interference experiments, atomic spectra and the Bohr hypotheses, the experiment of Franck and Hertz, the Bragg experiment, diffraction of electrons by a crystal of nickel (Davisson and Germer), and measurements of position and velocity of an electron. The need for a quantum theory In the second half of the nineteenth century it seemed that the laws of classical mechanics, developed by the genius of Newton, Lagrange, Hamilton, Jacobi and Poincaré, the Maxwell theory of electromagnetic phenomena and the laws of classical statistical mechanics could account for all known physical phenomena. Still, it became gradually clear, after several decades of experimental and theoretical work, that one has to formulate a new kind of mechanics, which reduces to classical mechanics in a suitable limit, and makes it possible to obtain a consistent description of phenomena that cannot be understood within the classical framework. It is now appropriate to present a brief outline of this new class of phenomena, the systematic investigation of which is the object of the following sections and of chapters 4 and 14.