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 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.
Statistical ensemble formalism of Kim, Mandel and Wolf (J. Opt. Soc. Am. A 4, 433 (1987)) offers a realistic model for characterizing the effect of stochastic non-image forming optical media on the state of polarization of transmittedlight. With suitable choice of the Jones ensemble, various Mueller transformations - some of which have been unknown so far - are deduced. It is observed that the ensemble approach is formally identical to the positive operator valued measures (POVM) on the quantum density matrix. This observation, in combination with the recent suggestion by Ahnert and Payne (Phys. Rev. A 71, 012330, (2005)) - in the context of generalized quantum measurement on single photon polarization states - that linear optics elements can be employed in setting up all possible POVMs, enables us to propose a way of realizing different types of Mueller devices.
Abstract A general approach to the discussion of optical birefringence phenomena is presented. It is based on the S-matrix approach to photon scattering in a nonrelativistic quantum field theoretical formalism and the Stokes operator description of polarization. The use of a canonically transformed interaction Hamiltonian in combination with diagrammatic perturbation theory enables the response of a system to electromagnetic radiation to be calculated in a straightforward and consistent manner to any order in the perturbation, and the effect of static fields is included easily. As an illustration, the angle of rotation of a beam of plane-polarized light by a solution of optically active molecules is calculated and the intensity dependence of the angle determined. The latter phenomenon should become apparent at high photon flux densities particularly when ω, the frequency of the incident light, or 2ω are similar to electronic excitation frequencies in the optically active molecules.
We discuss the propagation of a short laser pulse in an autoionizing medium with double Fano structure. By solving the coupled equations for atoms and fields simultaneously, we can consider the influence of double Fano structure on the pulse laser in the transmission process. Full Text: PDF References A. Raczyński, M. Rzepecka, J. Zaremba, and S. Zielińska-Kaniasty, "Electromagnetically induced transparency and light slowdown for Λ-like systems with a structured continuum", Opt. Commun. 266, 552 (2006). CrossRef T. Bui Dinh, W. Leoński, V. Cao Long and J. Perina Jr, "Electromagnetically induced transparency for a double Fano-profile system", Eur. Phys. J. D, 68 (2014) CrossRef T. Bui Dinh, W. Leoński, V. Cao Long and J. Perina Jr, "Electromagnetically induced transparency in systems with degenerate autoionizing levels in Λ-configuration", Optica Applicata 43, 471 (2013). CrossRef Cao Long Van, Structured continuum in various optical phenomena, in Physics and applications I: Quantum Optics" Ed. Wiesław Leoński, University of Zielona Góra Press, p.195 (2012). DirectLink M. Shapiro, "Electromagnetically induced transparency with structured multicontinua", Phys.Rev.A 75, 013424 (2007). CrossRef E. Paspalakis, P.L. Knight, "Population transfer via an autoionizing state with temporally delayed chirped laser pulses", J. Phys. B 31, 2753 (1998). CrossRef S.Y. Zhu and E.E. Fill, "Nonlinear theory of lasers without inversion with two upper lasing levels", Phys. Rev. A 42, 5684 (1990). CrossRef S. E. Harris, "Lasers without inversion: Interference of lifetime-broadened resonances", Phys. Rev. A 62, 1033 (1989). CrossRef E. Paspalakis, N. J. Kylstra, and P. L. Knight, "Propagation dynamics in an autoionization medium", Phys. Rev. A 60, 642 (1999). CrossRef W. Leoński, R. Tanaś and S. Kielich, "Laser-induced autoionization from a double Fano system", J. Opt. Am. B 4, 72 (1987). CrossRef