We present a quantum treatment of polarization of optical beams and discuss some properties of beams of any state of polarization. The analysis is based on quantum-mechanical interpretation of a canonical experiment that is used to elucidate polarization properties of stochastic fields in classical optics. Our work shows how to apply some ideas and techniques, commonly used in the classical theory, for fields that cannot be treated classically.
We present a quantum treatment of polarization of optical beams and discuss some properties of beams of any state of polarization. The analysis is based on quantum-mechanical interpretation of a canonical experiment that is used to elucidate polarization properties of stochastic fields in classical optics. Our work shows how to apply some ideas and techniques, commonly used in the classical theory, for fields that cannot be treated classically.
In the paper a quantum description of an effective state of polarization for an electromagnetic field containing variously polarized photons is presented. The discussion of the problem includes the quantum character of a single photon, comparison with a classical field, matrix description of photon polarization and physical interpretation of the representation of a density operator that represents photons in a statistical ensemble. Full text: PDF References: R.J. Glauber, Quantum Theory of Optical Coherence (Wiley-VCH 2007). C.C. Gerry, P.L. Knight, Introductory Quantum Optics (Cambrige Univeristy Press 2005) R.J. Glauber, New Techn. Ideas Quant. Measur. Theory 480, 336 (1986). L. Michalik, J. Jasinski, P.L. Makowski, A.W. Domanski,Problem of degree of polarization for photons, Proc. SPIE 7745, 77450K (2010). [CrossRef] T. Tudor, A. Gheondea, Pauli algebraic forms of normal and nonnormal operators, Jour. Opt. Soc. Am. A 24, 204 (2007). [CrossRef]
In the paper a quantum description of an effective state of polarization for an electromagnetic field containing variously polarized photons is presented. The discussion of the problem includes the quantum character of a single photon, comparison with a classical field, matrix description of photon polarization and physical interpretation of the Pauli representation of a density operator that represents photons in a statistical ensemble. Full text: PDF References: R.J. Glauber, Quantum Theory of Optical Coherence (Wiley-VCH 2007). C.C. Gerry, P.L. Knight, Introductory Quantum Optics (Cambrige Univeristy Press 2005) R.J. Glauber, New Techn. Ideas Quant. Measur. Theory 480, 336 (1986). L. Michalik, J. Jasinski, P.L. Makowski, A.W. Domanski,"Problem of degree of polarization for photons", Proc. SPIE 7745, 77450K (2010). [CrossRef] T. Tudor, A. Gheondea, "Pauli algebraic forms of normal and nonnormal operators", Jour. Opt. Soc. Am. A 24, 204 (2007). [CrossRef]
The theory of optical birefringence is discussed from the point of view of the scattering of polarized photons by molecules using the framework of formal scattering theory and quantum electrodynamics. In Part One, those features from noncovariant quantum electrodynamics relevant to the molecular scattering of photons are reviewed. Chapter One contains an outline of classical electrodynamics in the Coulomb gauge, including the Stokes parameter and density matrix formulations of polarization. Chapter Two deals with the quantization of the radiation field, and the occupation number representation is defined. The quantum mechanical description of polarized light is outlined in Chapter Three: operator equivalents of the density matrix and Stokes parameters are invoked, the parameters themselves being obtained from the expectation values of the Stokes operators with the state vector of the photon. The Stokes parameter and density matrix are then applied to the polarization of a general beam containing an arbitrary number of photons, and some new methods are developed. The interaction of the electromagnetic field with bound electrons is formulated in Chapter Four in terms of a canonically transformed interaction Hamiltonian in which the multipole terms are explicit. Since each term is then gauge-invariant, this Hamiltonian is particularly suited to the application of diagrammatic perturbation theory which follows from the iteration of the scattering matrix in the interaction representation (Chapter Five). Also the extension of the theory to multiphoton processes is facilitated "because the field strength is explicit in the transformed Hamiltonian. The S-matrix connects the initial and final asymptotic states of the scattering system, and in Chapter Six the state vector and density operator of the scattered photon beam are obtained from those of the incident beam. Part Two contains the application of the above methods to a variety of linear and nonlinear optical birefringence effects in the absence or presence of external fields. In Chapter Seven, general equations are obtained for the polarization changes imposed on a forward scattered photon in terms of matrix elements of the reaction operator between plane polarized photon base states; whereas Chapter Eight extends this treatment to an n-photon beam, thereby encompassing the hyperpolarizability contributions to the polarization changes of the forward scattered beam. It is then demonstrated that the fundamental process in optical birefringence can be interpreted as an infinitesimal unitary transformation of the polarization spinor. Also the S-matrix approach to birefringence is compared with the methods used in crystal optics, and with the classical treatments of the scattering of polarized light by molecules. The general equations obtained for the polarization changes of the forward scattered beam are subsequently interpreted in the light of the physical circumstances appropriate to the bire- fringence effect of interest. In Chapters Nine, Ten, and Eleven, diagrammatic perturbation theory is used to obtain explicit expressions, in terms of molecular polarizability and rotation tensors, for the linear and nonlinear contributions to the polarization changes involved in natural optical activity, and in birefringence phenomena induced by static and optical electric and magnetic fields. The nonforward scattering of polarized photons by molecules is discussed in Part Three. General equations are calculated in Chapter Twelve for the azimuth, ellipticity, and depolarization ratio of the Rayleigh beam at any scattering angle and for any polarization of the incident beam. Explicit expressions in terms of molecular quantities are then obtained for the polarization at scattering angles of 90° and almost zero from both optically inactive and optically active molecules. It is demonstrated that a determination of the precise polarization state of the scattered beam can provide useful molecular information additional to that obtained from depolarization ratios alone. This is because the depolarization ratio depends on only the diagonal elements of the polarization density matrix and so does not convey all the information about the system. Raman scattering processes are contained in the formulation and the polarization of the Raman light at any scattering angle can be obtained. This is shown to be particularly useful for predicting the polarization of stimulated Raman light for any Raman-active liquid placed within a laser cavity. By extending the nonforward scattering formulation to incorporate multiphoton processes, equations are obtained in Chapter Thirteen for the ellipticity, azimuth, and depolarization ratio of the second harmonic wave at any scattering angle as a function of the incident polarization. Several specific situations are subsequently investigated. Finally, it is shown in Chapter Fourteen that the near-forw- ard Rayleigh and Raman scattering formulations provide an explanation for the observed polarization, as a function of the initial polarization, of the self-trapped filaments that arise from the self-focusing of an intense laser beam.
Conceptual and operational aspects of the description of the polarization of light in classical and quantum optics are discussed. Primary emphasis is placed on the concept of P -quasispin, which ensures an adequate analysis for arbitrary quantum light fields. In terms of this concept, the polarization density matrix, which is obtained by reduction of the total field density operator and which completely describes the polarization state of quantum radiation, as well as the operational (measured in polarization experiments) characteristics and the transformations of the polarization dynamics, are determined. Applications of the formalism developed to biphoton optics are discussed.
We analyze the behavior of light as it passes through systems composed of polarizing filters at different angular orientations. The analysis is initially conducted in the context of classical optics, using Malus's Law to calculate the transmitted intensity for the cases of two perpendicular filters (0° and 90°) and three filters (0°, 45°, and 90°). We then apply quantum mechanics to describe the phenomenon using state notation and the probabilistic interpretation of the projection of the polarization states of photons.
A quantum-mechanical description of the phase shifters, retarders, mirrors and beam splitters is given in the paper. The description is then applied on two types of states. On a coherent state, a classical-like state, and on a number state, hence the strict quantum state. The quantum description of a beam splitter can be found in the literature. However the description does not treat with the polarization concept. The paper is aimed to introduce quantum description of an arbitrary oriented retarder and give a description of a beam splitter which treats with the polarization.