- Email: [email protected]
Optics communications special issue “electromagnetic coherence and polarization”
Optics Communications 283 (2010) 4423–4426
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Editorial overview
Optics communications special issue “electromagnetic coherence and polarization” With the rapid progress in areas such as near-field optics and microand nano-photonics, it has become increasingly important to treat the electromagnetic field and its fluctuations in full vector description. This has led to a reassessment of the foundations of coherence and polarization in random electromagnetic fields and paved the way towards many novel phenomena and useful applications both in classical and quantum contexts. In particular, in recent years the focus has been on the degree of polarization in electric fields that contain all three components, such as optical near fields or focused electromagnetic waves, and the degree of coherence in vector-valued (two- or threedimensional) electromagnetic fields. A workshop on partial electromagnetic coherence and 3D polarization was held in Koli in Finland on 24–27 May 2009 [1] and many contributions related to that workshop are contained in this special issue. However, the focus issue at hand has a broader scope. Indeed, a general call of manuscripts on electromagnetic coherence and polarization was issued and several excellent reports on a variety of manifestations and applications of coherence and polarization in optical fields are included in this issue. These applications range from the polarimetry of rough objects and biological tissue to the coherence control of logic gates and involve classical and quantum notions in linear and nonlinear regimes. Classical coherence and polarization are related to the notion of statistical similarity and this relationship is explored in the opening paper of this focus issue by Emil Wolf. The polarimetry of 3D electromagnetic wave fields in terms of two characteristic parameters is assessed by José J. Gil and Ignatio San José. In quantum theory additional constraints, such as commutation and entanglement, arise and lead to new phenomena. Alfredo Luis studies the accuracy of interferometric measurements with certain quantum states of light, while Gunnar Björk et al. analyze different proposals for the degree of polarization of quantum fields. The various measures of coherence, polarization, purity, entropy, entanglement, etc. and their interpretations and implications within the classical and quantum contexts of light, are still of considerable interest. In recent years it has become clear that the spectrum, polarization, and coherence of light change on radiation and upon propagation. The effects of diffraction on the classic Stokes theorem of splitting a beam into its polarized and unpolarized constituents have also been addressed. In the paper by Jani Tervo et al. the validity of the Stokes decomposition is analyzed in a single plane across a spatially variant random beam. Jari Lindberg et al. consider the relationship of the coherence and polarization properties of a true stochastic current source and the far field it generates. This work bridges directly the source and its far field, whereas Jonathan Petrucelli et al. model the propagation of electromagnetic waves throughout the space using discrete basis functions and Wigner functions for non-paraxial fields. Under certain specific conditions the properties of the field, such as the Stokes representation, intrinsic degrees of coherence, and maximum attainable visibility, remain invariant on 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.04.069
propagation; a family of such fields, which further are transversally position-independent, is introduced by Rosario Martínez-Herrero and Pedro M. Mejías. Both the traditional and the two-point Stokes parameters associated with partially coherent pulsed beams are studied by Chaoliang Ding et al. in which, as in many other papers in this issue, the so-called Gaussian Schell-model (GSM) is used as a method for illustrative examples. The cross-spectral density matrix, and to a lesser degree the polarization matrix, must in general satisfy mathematically stringent conditions. Hence the questions of feasibility and actual realization of beams of desired type are of importance. Radially and azimuthally polarized beams are widely used examples of polarization states. Tomohiro Shirai gives a physical interpretation of a superposition method for synthesizing genuine cross-spectral density matrices for electromagnetic beams. Victoria Ramírez-Sánchez et al., on the other hand, report on an experimental procedure for the synthesis of partially coherent beams with propagation-invariant polarization patterns. Measured results are consistent with the theoretical predictions. Andrey Ostrovsky et al. discuss two alternative approaches to produce electromagnetic sources with desired values for the degree of polarization and the transverse coherence width; one is based on free-space propagation and the other on the use of random phase screen. It should be emphasized, though, that the synthesis methods depend on which characteristic measures are adopted for the description of the coherence and polarization properties of the fluctuating electromagnetic fields. The focus issue also contains numerous excellent contributions on the effects of material properties, various applications of random electromagnetic beams, and implementations of photonic devices. Vassilios Yannopapas explores the role of non-local spatial dispersion in thermal fluctuational electrodynamics of a metallic sphere and shows that the main effect is a blue shift of the spectrum of the degree of polarization. Mohsen Ben Alouani Choubani et al. present a method for solving Hill's equation in one-dimensional photonic bandgap structures with arbitrary longitudinal permittivity profiles. The spectral shifts of electromagnetic GSM beams in Gaussian cavities in various conditions are studied by Yangjian Cai et al. by means of a recently developed tensor method. A similar technique is used by Serkan Sahin et al. to model active bistatic LIDAR system for detection of semi-rough objects embedded within atmospheric turbulence. An entirely different approach to assess scattering of randomly rough small particles, based on a linear regression of the Stokes parameters, is discussed by Karine Chamaillard et al. and a physical interpretation of the simulation results is put forward in terms of the coherence (or density) matrix formalism. Interesting grouptheoretical techniques are employed by Félix Fanjul-Vélez et al. in the polarimetric imaging of biological tissue phantoms in weak and strong scattering, both in Rayleigh and Mie regimes, including including effects of anisotropy. A polarization beam splitter with high extinction ratio and diffraction efficiency, based on subwavelength dielectric grating, has
4424
Editorial overview
been designed at UV frequencies (193 nm) in GuoGuo Kang et al. for use in high-definition (immersion) lithography. Improved chromatic correction for gypsum-based achromatic wave plates throughout the visible region is proposed by Mohamed A. Emam-Ismail through the inclusion of another layer of suitable (apochromatic) birefringent material. An enhanced digital signal processing method is suggested in Hai Zhu et al. for polarization division multiplexing in optical coherent receivers. Finally, Jian Qi Shen addresses the realization of photonic logic-gate devices and examines the quantum interference effects in a doublecontrol (Y-configuration) atomic system. The diversity of the research contributions in this focus issue demonstrates that beyond the foundations of electromagnetic coherence and polarization, also their utilization in classical, quantum, and non-linear optical systems attracts widely increasing attention. With applications such as Raman amplifiers, super-continuum radiation, coherent optical control, nano-photonics, and quantum entanglement, to name just a few, the scope of the implementations of coherence and polarization phenomena is likely to grow rapidly. The guest editors thank the staff of the Optics Communications offices in Osaka and Ulm, especially Kathy and Wolfgang Schleich, for their tireless assistance throughout the preparation of this focus issue. The invaluable help of all the reviewers is also gratefully acknowledged. Appendix A Papers I. Foundations of coherence and polarization I.1. E. Wolf, “Statistical similarity as a unifying concept of the theories of coherence and polarization of light” Abstract: It is shown that the concept of statistical similarity of light vibrations introduced in recent years provides a new insight into the physical meaning of coherence and of polarization of light and reveals a close analogy between the two phenomena. I.2. J.J. Gil and I.S. José, “3D polarimetric purity” Abstract: From our previous definition of the indices of polarimetric purity for 3D light beams [J.J. Gil, J.M. Correas, P.A. Melero and C. Ferreira, Monogr. Semin. Mat. G. de Galdeano 31, 161 (2004)], an analysis of their geometric and physical interpretation is presented. It is found that, in agreement with previous results, the first parameter is a measure of the degree of polarization, whereas the second parameter (called the degree of directionality) is a measure of the mean angular aperture of the direction of propagation of the corresponding light beam. This pair of invariant, non-dimensional, indices of polarimetric purity contains complete information about the polarimetric purity of a light beam. The overall degree of polarimetric purity is obtained as a weighted quadratic average of the degree of polarization and the degree of directionality. I.3. A. Luis, “Coherence and the statistics of the phase difference between partially polarized electromagnetic waves” Abstract: Coherence between two vectorial harmonic light vibrations is analyzed in terms of the statistics of their phase difference. This provides a natural and simple extension of second-order coherence to cover more complicate situations. In particular this assigns large coherence to quantum light states providing the most accurate interferometric measurements allowed by the quantum theory, even if they are incoherent according to the standard second-order approach. I.4. G. Björk, J. Söderholm, L.L. Sánchez-Soto, A.B. Klimov, I. Ghiu, P. Marian, and T.A. Marian, “Quantum degrees of polarization”
Abstract: We discuss different proposals for the degree of polarization of quantum fields. We show that the simplest approach, namely making a direct analogy with the classical description via the Stokes operators, produces unsatisfactory results. Still, we argue that these operators and their properties should be basic for any measure of polarization. We compare alternative quantum degrees and put forth that they order various states differently. This is to be expected, since every measure, although rooted in the Stokes operators, captures only certain characteristics. Therefore, it is likely that several quantum degrees of polarization will coexist, each one having its specific domain of usefulness. II. Coherence and polarization in radiation and propagation II.1. J. Tervo, J. Turunen, and G. Gori, “Impossibility of Stokes decomposition for a class of light beams” Abstract: Decomposition throughout all space of a typical light beam into the sum of a completely polarized and a completely unpolarized beam (Stokes decomposition) seems to be rather the exception than the rule. However, it is known that such decomposition can often be made across a certain plane, although it may lose validity upon propagation. Then, one may guess that, for any light beam, there exists at least one plane where the Stokes decomposition can be performed. Without adopting any particular model for polarized and unpolarized beams, we present a class of beams for which no such plane can exist. II.2. J. Lindberg, T. Setälä, M. Kaivola, and A.T. Friberg, “Coherence and polarization properties of a three-dimensional, primary, quasihomogeneous, and isotropic source and its far field” Abstract: We study the spatial coherence properties of a threedimensional, primary, quasihomogeneous, and isotropic source and the far field that it generates. We assess the spectrum, degree of polarization, electromagnetic degree of coherence, and effective degree of coherence of the source and of the far field. We also demonstrate the formalism for a spherical Gaussian Schell-model current source. The polarization properties of light are fully accounted for in the analysis, and it is found that certain results pertaining to scalar coherence theory are reproduced also within the electromagnetic treatment. II.3. J. Petrucelli, N.J. Moore, and M.A. Alonso, “Two methods for modeling the propagation of the coherence and polarization properties of nonparaxial fields” Abstract: The propagation of nonparaxial, partially coherent fields may be modeled in many ways. The standard techniques of Huygenstype propagation integrals or plane wave decompositions require quadruple oscillatory integrals that carry a significant computational cost. Two alternative, computationally efficient methods for such modeling are presented here. One uses a discrete nonparaxial basis expansion of the field, while the other uses Wigner functions for nonparaxial fields. Two possible nonparaxial generalizations of Gaussian Schell-model beams are presented and used to demonstrate the utility of the methods by computing the spatial distribution of several recently proposed definitions of the degree of polarization of a nonparaxial field. II.4. read R. Martínez-Herrero and P.M. Mejías, “On the propagation of random electromagnetic fields with position-independent stochastic behavior” Abstract: A certain kind of vectorial fields with position-independent stochastic behaviour is introduced, for which several main
Editorial overview
features are preserved upon free propagation. For this set of random electromagnetic fields, it is shown that the uniform degree of polarization, the maximum attainable visibility in a Young experiment, and the expansion of the cross-spectral density tensor as the sum of totally polarized and unpolarized terms are properties that apply for any propagation distance. An elementary example is also shown. II.5. C. Ding, Z. Zhao, L. Pan, and B. Lü, “Generalized Stokes parameters of stochastic spatially and spectrally coherent electromagnetic pulsed beams” Abstract: The analytical expressions for the generalized (twopoint) Stokes parameters of stochastic electromagnetic Gaussian Schell-model pulsed (GSMP) beams propagating in free space are obtained. The changes in the spectral Stokes parameters in free-space propagation are studied. The dependence of on-axis and transverse spectral Stokes parameters of stochastic electromagnetic GSMP beams on the pulse parameters including pulse duration and temporal coherence length is stressed and illustrated numerically. The results are interpreted physically.
4425
polarization modulation by a random phase screen. The dependence of the results on the employed definition of electromagnetic coherence is discussed. IV. Materials, applications, and devices IV.1. V. Yannopapas, “Effect of material spatial dispersion in the degree of polarization of thermal radiation emitted by a spherical source” Abstract: The influence of material spatial dispersion in the degree of polarization emitted by a metallic sphere is studied by means of fluctuational electrodynamics. The corresponding cross-spectral correlation functions of the electric field are calculated on a basis of a non-local scattering T-matrix for a spherical scatterer and for nonlocal electric functions for the metal such as those provided by the hydrodynamic model and the Lindhard theory. It is shown that the main effect of the material spatial dispersion is a blue shift of the spectra of the degree of polarization which, however, diminishes as the sphere size increases. Also, at the bulk plasma frequency, a local maximum of the degree of polarization emerges as a result of the excitation of bulk plasmons which is not evident when a local dielectric function is assumed.
III. Synthesis of special coherence and polarization properties III.1. T. Shirai, “Interpretation of the recipe for synthesizing genuine cross-spectral density matrices” Abstract: A physical interpretation of the recipe for synthesizing genuine 2 × 2 cross-spectral density matrices that characterize stochastic electromagnetic sources and beams is described. In this interpretation, the synthesized field is regarded as an incoherent superposition of spatially coherent fields originating from a partially polarized, spatially incoherent virtual source. The coherence and the polarization properties of the synthesized field are also examined in view of this interpretation. As a result, we found that the spectral degree of coherence and that of polarization of the synthesized field are generally different from those of the virtual source by the effect of the superposition. We also found, however, that there are some situations in which the spectral degree of polarization of the synthesized field remains unchanged even though the superposition takes place. III.2. V. Ramírez-Sánchez, G. Piguero, and M. Santarsiero, “Synthesis and characterization of partially coherent beams with propagation-invariant transverse polarization pattern” Abstract: Partially coherent beams, whose transverse polarization pattern remains invariant upon paraxial propagation, are synthesized and characterized. Synthesis is performed by imposing a spirallike polarization profile to an axially symmetric partially coherent light source. Irradiance and polarization profiles of the propagated beam are detected at different transverse planes, both in the near and in the far zone, and are compared with the theoretical ones. Furthermore, global parameters, measuring the circular, radial and azimuthal polarization contents across the beam profile, are used to characterize the generated beam from a global point of view. III.3. A.S. Ostrovsky, M.A. Olvera, C. Rickenstorff, G. MartínezNiconoff, and V. Arrizón, “Generation of a secondary electromagnetic source with desired statistical properties” Abstract: Two alternative techniques for generating a secondary electromagnetic source with the desired degree of polarization and transverse coherence length are proposed and compared. The first technique is based on the changes of coherence and polarization on propagation, while the second one makes use of the coherence and
IV.2. M. Choubani, F. Choubani, A. Gharsallah, J. David, and N.E. Mastorakis, “Analysis and design of electromagnetic band gap structures with stratified and inhomogeneous media” Abstract: In this study, a generalized and easy to use method based on Hill's equation and chain matrix concept is used to analyze the electromagnetic wave propagation in stratified dielectric and inhomogeneous media with arbitrary profiles. Numerical simulations are performed to compute the reflection and transmission of several electromagnetic bandgap (EBG) structures for various permittivity profiles, and given polarization as well as incidence angles of driving fields. Multilayer structures are analyzed and optimized to enhance their selectivity performances obtained results agree excellently well with other published data. IV.3. Y. Cai, M. Yao, and O. Korotkova, “Spectral shift of a stochastic electromagnetic Gaussian Schell-model beam in a Gaussian cavity” Abstract: Spectral changes of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam interacting with a Gaussian cavity are investigated. It is shown that the spectral shift is mainly determined by the degree of polarization of the initial beam and by the parameters of the cavity. Generically the blue shift occurs at on-axis points, while the red shift can occur at off-axis points. The condition under which the relative spectral shift is independent of the degree of polarization of the initial beam is analyzed. IV.4. S. Sahin, Z. Tong, and O. Korotkova, “Sensing of semi-rough targets embedded in atmospheric turbulence by means of stochastic electromagnetic beams” Abstract: An active bistatic LIDAR system operating through atmospheric turbulence is considered. Illumination field is assumed to be an electromagnetic Gaussian–Schell-model beam. Target surface is modeled as a combination of isotropic phase screen governed by Gaussian statistics, to account for its roughness, and a Gaussian lens to account for its size and radius of curvature. With the help of a recently developed tensor method for propagation of stochastic electromagnetic beams through ABCD systems and random media we examine the evolution of states of coherence and polarization of the beam. In the case of unresolved flat (planar) target we show that by comparing coherence and polarization properties of the illumination beam and of the return beam it is possible to predict the typical roughness of the target surface.
4426
Editorial overview
IV.5. K. Chamaillard, A.T. Friberg, and C. Dainty, “Coherency matrix description for statistical linear regression of Stokes parameters in rough small-particle scattering” Abstract: A statistical analysis of the Stokes parameters in light scattering by randomly rough small particles shows a linear regression law between the squares of the first two components Is and Qs of the Stokes vector. While the coefficients of this linear regression contain physical characteristics of the particles, they cannot be directly interpreted in terms of the degree of polarization of the scattered field. We propose an interpretation of this relationship between the Stokes parameters on the basis of the general coherence-density matrix formalism. The link between the statistical regression results and the polarization properties of the stochastic scattered components of the field is established through the coherency matrix elements. IV.6. F. Fanjul-Vélez, N. Ortega-Quijano, and J.L. Arce-Diego, “Polarimetry group theory analysis in biological tissue phantoms by Mueller coherency matrix” Abstract: The characterization of biological tissues by optical techniques provides several advantages over other techniques. Optical techniques enable to perform high resolution and contrast imaging, in a non-invasive way and with no-contact. Biological tissues are turbid media that strongly scatter light. The ultrastructure of some tissues makes them present a certain degree of anisotropy. Both scattering and anisotropy affect light polarization. Some pathologies alter these characteristics of the tissue. As a consequence polarized light can be used to extract additional information and achieve a better diagnosis. In this work, group theory is applied to analyze the polarization behavior of several samples. Firstly, the Mueller matrix for each sample is measured. Then, the Mueller coherency matrix is obtained by means of the SU(4)-O+(6) homomorphism. Finally, the target decomposition theorem is applied by analyzing the eigenvalues and eigenvectors, and subsequently the different polarimetric effects are separated. In this way, the contrast of tissue imaging can be increased. This analysis is applied to biological tissue phantoms, which consisted on glucose suspensions of polystyrene spheres with different scatterer concentrations. Their behavior can be modeled by means of single or multiple scattering depending on the concentration, either in the Rayleigh or Mie regimes. The same procedure could be used in a wide range of applications, like the study of cancerous cells that grow without control in cell cultures, or erythrocytes monitoring in anemia. The technique also has a great potential to be applied in polarization sensitive optical coherence tomography (PS-OCT). IV.7. G. Kang, Q. Tan, and G. Jin, “Polarization-selective subwavelength grating used with 193 nm light” Abstract: Hyper-NA ArF (193 nm) immersion lithography is one of the most potential technologies to achieve 32 nm critical dimension node. At the corresponding large angles in the photoresist, control of polarization becomes necessary. A polarization beam splitter (PBS) based on a subwavelength dielectric grating has been designed for use with 193 nm light. The polarization-selective property of such grating is explained by the mechanism of modes interference. The designed grating working as a 1 × 2 beam splitter can transmit TM wave (∼90%) to the zeroth order with extinction ratio of 753, and it diffracts TE wave (∼ 80%) to the -1st order with extinction ratio of 300. IV.8. M.A. Emam-Ismail, “Retardation calculation for achromatic and apochromatic quarter and half wave plates of gypsum based birefringent crystal”
and quarter wave retarders made from gypsum birefringent crystal combined with KDP, ADP, MgF2, sapphire and calcite birefringent crystals of properly thicknesses. For such achromatic wave plate, the residual variation percentages of the retardation as a function of wavelength for gypsum/KDP, gypsum/ADP, gypsum/MgF2, gypsum/ sapphire and gypsum/calcite are found to be ±1.7%, ±3%, ±12.2%, ±12.0% and ±7.2%, respectively. To reduce the spectral variation of retardation, a third layer (apochromatic) of birefringent material is added to the aforementioned two layers combination. The apochromatic wave plate consists of gypsum/KDP/quartz, gypsum/ADP/quartz, MgF2/ ADP/gypsum, MgF2/KDP/gypsum and gypsum/sapphire/MgF2 with the calculated spectral residual variation percentages of retardation are found to be ±0.27, ±0.33, ±0.3, ±0.17 and ±0.45, respectively. IV.9. H. Zhu, X. Chen, and W. Zhou, “An improvement on constant modulus algorithm for polarization demultiplexing in optical coherent receivers” Abstract: In order to solve the problem of ill-convergence for constant modulus algorithm (CMA) in polarization division multiplexing system with optical coherent receivers, a modified constant modulus algorithm based on BER aiding to control initial tap setup, called as BER-Aiding CMA (BA-CMA), is proposed in this paper. By analyzing the principle of CMA for adaptive digital equalization and polarization demultiplexing, the convergence behavior leading undesirable result is investigated and therefore BA-CMA is proposed. Simulation results show that the proposed algorithm can overcome the undesirable convergence effectively and keep inherent advantages of CMA at the same time. IV.10. J.Q. Shen, “Coherence control for photonic logic gates via Yconfiguration double-control quantum interferences” Abstract: Destructive and constructive quantum interferences exhibited in a four-level Y-configuration double-control atomic system are suggested. It is shown that the probe transition (driven by the probe field) can be manipulated by the quantum interferences between two control transitions (driven by the control fields) of the four-level system. The atomic vapor is opaque (or transparent) to the probe field if the destructive (or constructive) quantum interference between the control transitions emerges. The optically sensitive responses due to double-control quantum interferences can be utilized to realize some quantum optical and photonic devices such as the logic-gate devices, e.g., the NOT, OR, NOR and EXNOR gates. Reference [1] A.T. Friberg, J. Turunen, J. Tervo (Eds.), Proceedings of Koli Workshop on Electromagnetic Coherence and 3D Polarization, University of Joensuu, Finland, 2009.
Ari T. Friberg Aalto University, Department of Applied Physics, Box 13500, FI-00076 Aalto, Finland University of Eastern Finland, Department of Physics and Mathematics, Box 111, FI-80101 Joensuu, Finland Royal Institute of Technology, Department of Microelectronics and Applied Physics, Electrum 229, SE-164 40 Kista, Sweden Corresponding author. E-mail address: ari.friberg@tkk.fi Jari Turunen University of Eastern Finland, Department of Physics and Mathematics, Box 111, FI-80101 Joensuu, Finland
19 April 2010 Abstract: In the present paper, we report a direct calculation of retardation for a visible region (λ = 0.4 μm to 0.7 μm) achromatic half
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Editorial overview
Optics communications special issue “electromagnetic coherence and polarization” With the rapid progress in areas such as near-field optics and microand nano-photonics, it has become increasingly important to treat the electromagnetic field and its fluctuations in full vector description. This has led to a reassessment of the foundations of coherence and polarization in random electromagnetic fields and paved the way towards many novel phenomena and useful applications both in classical and quantum contexts. In particular, in recent years the focus has been on the degree of polarization in electric fields that contain all three components, such as optical near fields or focused electromagnetic waves, and the degree of coherence in vector-valued (two- or threedimensional) electromagnetic fields. A workshop on partial electromagnetic coherence and 3D polarization was held in Koli in Finland on 24–27 May 2009 [1] and many contributions related to that workshop are contained in this special issue. However, the focus issue at hand has a broader scope. Indeed, a general call of manuscripts on electromagnetic coherence and polarization was issued and several excellent reports on a variety of manifestations and applications of coherence and polarization in optical fields are included in this issue. These applications range from the polarimetry of rough objects and biological tissue to the coherence control of logic gates and involve classical and quantum notions in linear and nonlinear regimes. Classical coherence and polarization are related to the notion of statistical similarity and this relationship is explored in the opening paper of this focus issue by Emil Wolf. The polarimetry of 3D electromagnetic wave fields in terms of two characteristic parameters is assessed by José J. Gil and Ignatio San José. In quantum theory additional constraints, such as commutation and entanglement, arise and lead to new phenomena. Alfredo Luis studies the accuracy of interferometric measurements with certain quantum states of light, while Gunnar Björk et al. analyze different proposals for the degree of polarization of quantum fields. The various measures of coherence, polarization, purity, entropy, entanglement, etc. and their interpretations and implications within the classical and quantum contexts of light, are still of considerable interest. In recent years it has become clear that the spectrum, polarization, and coherence of light change on radiation and upon propagation. The effects of diffraction on the classic Stokes theorem of splitting a beam into its polarized and unpolarized constituents have also been addressed. In the paper by Jani Tervo et al. the validity of the Stokes decomposition is analyzed in a single plane across a spatially variant random beam. Jari Lindberg et al. consider the relationship of the coherence and polarization properties of a true stochastic current source and the far field it generates. This work bridges directly the source and its far field, whereas Jonathan Petrucelli et al. model the propagation of electromagnetic waves throughout the space using discrete basis functions and Wigner functions for non-paraxial fields. Under certain specific conditions the properties of the field, such as the Stokes representation, intrinsic degrees of coherence, and maximum attainable visibility, remain invariant on 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.04.069
propagation; a family of such fields, which further are transversally position-independent, is introduced by Rosario Martínez-Herrero and Pedro M. Mejías. Both the traditional and the two-point Stokes parameters associated with partially coherent pulsed beams are studied by Chaoliang Ding et al. in which, as in many other papers in this issue, the so-called Gaussian Schell-model (GSM) is used as a method for illustrative examples. The cross-spectral density matrix, and to a lesser degree the polarization matrix, must in general satisfy mathematically stringent conditions. Hence the questions of feasibility and actual realization of beams of desired type are of importance. Radially and azimuthally polarized beams are widely used examples of polarization states. Tomohiro Shirai gives a physical interpretation of a superposition method for synthesizing genuine cross-spectral density matrices for electromagnetic beams. Victoria Ramírez-Sánchez et al., on the other hand, report on an experimental procedure for the synthesis of partially coherent beams with propagation-invariant polarization patterns. Measured results are consistent with the theoretical predictions. Andrey Ostrovsky et al. discuss two alternative approaches to produce electromagnetic sources with desired values for the degree of polarization and the transverse coherence width; one is based on free-space propagation and the other on the use of random phase screen. It should be emphasized, though, that the synthesis methods depend on which characteristic measures are adopted for the description of the coherence and polarization properties of the fluctuating electromagnetic fields. The focus issue also contains numerous excellent contributions on the effects of material properties, various applications of random electromagnetic beams, and implementations of photonic devices. Vassilios Yannopapas explores the role of non-local spatial dispersion in thermal fluctuational electrodynamics of a metallic sphere and shows that the main effect is a blue shift of the spectrum of the degree of polarization. Mohsen Ben Alouani Choubani et al. present a method for solving Hill's equation in one-dimensional photonic bandgap structures with arbitrary longitudinal permittivity profiles. The spectral shifts of electromagnetic GSM beams in Gaussian cavities in various conditions are studied by Yangjian Cai et al. by means of a recently developed tensor method. A similar technique is used by Serkan Sahin et al. to model active bistatic LIDAR system for detection of semi-rough objects embedded within atmospheric turbulence. An entirely different approach to assess scattering of randomly rough small particles, based on a linear regression of the Stokes parameters, is discussed by Karine Chamaillard et al. and a physical interpretation of the simulation results is put forward in terms of the coherence (or density) matrix formalism. Interesting grouptheoretical techniques are employed by Félix Fanjul-Vélez et al. in the polarimetric imaging of biological tissue phantoms in weak and strong scattering, both in Rayleigh and Mie regimes, including including effects of anisotropy. A polarization beam splitter with high extinction ratio and diffraction efficiency, based on subwavelength dielectric grating, has
4424
Editorial overview
been designed at UV frequencies (193 nm) in GuoGuo Kang et al. for use in high-definition (immersion) lithography. Improved chromatic correction for gypsum-based achromatic wave plates throughout the visible region is proposed by Mohamed A. Emam-Ismail through the inclusion of another layer of suitable (apochromatic) birefringent material. An enhanced digital signal processing method is suggested in Hai Zhu et al. for polarization division multiplexing in optical coherent receivers. Finally, Jian Qi Shen addresses the realization of photonic logic-gate devices and examines the quantum interference effects in a doublecontrol (Y-configuration) atomic system. The diversity of the research contributions in this focus issue demonstrates that beyond the foundations of electromagnetic coherence and polarization, also their utilization in classical, quantum, and non-linear optical systems attracts widely increasing attention. With applications such as Raman amplifiers, super-continuum radiation, coherent optical control, nano-photonics, and quantum entanglement, to name just a few, the scope of the implementations of coherence and polarization phenomena is likely to grow rapidly. The guest editors thank the staff of the Optics Communications offices in Osaka and Ulm, especially Kathy and Wolfgang Schleich, for their tireless assistance throughout the preparation of this focus issue. The invaluable help of all the reviewers is also gratefully acknowledged. Appendix A Papers I. Foundations of coherence and polarization I.1. E. Wolf, “Statistical similarity as a unifying concept of the theories of coherence and polarization of light” Abstract: It is shown that the concept of statistical similarity of light vibrations introduced in recent years provides a new insight into the physical meaning of coherence and of polarization of light and reveals a close analogy between the two phenomena. I.2. J.J. Gil and I.S. José, “3D polarimetric purity” Abstract: From our previous definition of the indices of polarimetric purity for 3D light beams [J.J. Gil, J.M. Correas, P.A. Melero and C. Ferreira, Monogr. Semin. Mat. G. de Galdeano 31, 161 (2004)], an analysis of their geometric and physical interpretation is presented. It is found that, in agreement with previous results, the first parameter is a measure of the degree of polarization, whereas the second parameter (called the degree of directionality) is a measure of the mean angular aperture of the direction of propagation of the corresponding light beam. This pair of invariant, non-dimensional, indices of polarimetric purity contains complete information about the polarimetric purity of a light beam. The overall degree of polarimetric purity is obtained as a weighted quadratic average of the degree of polarization and the degree of directionality. I.3. A. Luis, “Coherence and the statistics of the phase difference between partially polarized electromagnetic waves” Abstract: Coherence between two vectorial harmonic light vibrations is analyzed in terms of the statistics of their phase difference. This provides a natural and simple extension of second-order coherence to cover more complicate situations. In particular this assigns large coherence to quantum light states providing the most accurate interferometric measurements allowed by the quantum theory, even if they are incoherent according to the standard second-order approach. I.4. G. Björk, J. Söderholm, L.L. Sánchez-Soto, A.B. Klimov, I. Ghiu, P. Marian, and T.A. Marian, “Quantum degrees of polarization”
Abstract: We discuss different proposals for the degree of polarization of quantum fields. We show that the simplest approach, namely making a direct analogy with the classical description via the Stokes operators, produces unsatisfactory results. Still, we argue that these operators and their properties should be basic for any measure of polarization. We compare alternative quantum degrees and put forth that they order various states differently. This is to be expected, since every measure, although rooted in the Stokes operators, captures only certain characteristics. Therefore, it is likely that several quantum degrees of polarization will coexist, each one having its specific domain of usefulness. II. Coherence and polarization in radiation and propagation II.1. J. Tervo, J. Turunen, and G. Gori, “Impossibility of Stokes decomposition for a class of light beams” Abstract: Decomposition throughout all space of a typical light beam into the sum of a completely polarized and a completely unpolarized beam (Stokes decomposition) seems to be rather the exception than the rule. However, it is known that such decomposition can often be made across a certain plane, although it may lose validity upon propagation. Then, one may guess that, for any light beam, there exists at least one plane where the Stokes decomposition can be performed. Without adopting any particular model for polarized and unpolarized beams, we present a class of beams for which no such plane can exist. II.2. J. Lindberg, T. Setälä, M. Kaivola, and A.T. Friberg, “Coherence and polarization properties of a three-dimensional, primary, quasihomogeneous, and isotropic source and its far field” Abstract: We study the spatial coherence properties of a threedimensional, primary, quasihomogeneous, and isotropic source and the far field that it generates. We assess the spectrum, degree of polarization, electromagnetic degree of coherence, and effective degree of coherence of the source and of the far field. We also demonstrate the formalism for a spherical Gaussian Schell-model current source. The polarization properties of light are fully accounted for in the analysis, and it is found that certain results pertaining to scalar coherence theory are reproduced also within the electromagnetic treatment. II.3. J. Petrucelli, N.J. Moore, and M.A. Alonso, “Two methods for modeling the propagation of the coherence and polarization properties of nonparaxial fields” Abstract: The propagation of nonparaxial, partially coherent fields may be modeled in many ways. The standard techniques of Huygenstype propagation integrals or plane wave decompositions require quadruple oscillatory integrals that carry a significant computational cost. Two alternative, computationally efficient methods for such modeling are presented here. One uses a discrete nonparaxial basis expansion of the field, while the other uses Wigner functions for nonparaxial fields. Two possible nonparaxial generalizations of Gaussian Schell-model beams are presented and used to demonstrate the utility of the methods by computing the spatial distribution of several recently proposed definitions of the degree of polarization of a nonparaxial field. II.4. read R. Martínez-Herrero and P.M. Mejías, “On the propagation of random electromagnetic fields with position-independent stochastic behavior” Abstract: A certain kind of vectorial fields with position-independent stochastic behaviour is introduced, for which several main
Editorial overview
features are preserved upon free propagation. For this set of random electromagnetic fields, it is shown that the uniform degree of polarization, the maximum attainable visibility in a Young experiment, and the expansion of the cross-spectral density tensor as the sum of totally polarized and unpolarized terms are properties that apply for any propagation distance. An elementary example is also shown. II.5. C. Ding, Z. Zhao, L. Pan, and B. Lü, “Generalized Stokes parameters of stochastic spatially and spectrally coherent electromagnetic pulsed beams” Abstract: The analytical expressions for the generalized (twopoint) Stokes parameters of stochastic electromagnetic Gaussian Schell-model pulsed (GSMP) beams propagating in free space are obtained. The changes in the spectral Stokes parameters in free-space propagation are studied. The dependence of on-axis and transverse spectral Stokes parameters of stochastic electromagnetic GSMP beams on the pulse parameters including pulse duration and temporal coherence length is stressed and illustrated numerically. The results are interpreted physically.
4425
polarization modulation by a random phase screen. The dependence of the results on the employed definition of electromagnetic coherence is discussed. IV. Materials, applications, and devices IV.1. V. Yannopapas, “Effect of material spatial dispersion in the degree of polarization of thermal radiation emitted by a spherical source” Abstract: The influence of material spatial dispersion in the degree of polarization emitted by a metallic sphere is studied by means of fluctuational electrodynamics. The corresponding cross-spectral correlation functions of the electric field are calculated on a basis of a non-local scattering T-matrix for a spherical scatterer and for nonlocal electric functions for the metal such as those provided by the hydrodynamic model and the Lindhard theory. It is shown that the main effect of the material spatial dispersion is a blue shift of the spectra of the degree of polarization which, however, diminishes as the sphere size increases. Also, at the bulk plasma frequency, a local maximum of the degree of polarization emerges as a result of the excitation of bulk plasmons which is not evident when a local dielectric function is assumed.
III. Synthesis of special coherence and polarization properties III.1. T. Shirai, “Interpretation of the recipe for synthesizing genuine cross-spectral density matrices” Abstract: A physical interpretation of the recipe for synthesizing genuine 2 × 2 cross-spectral density matrices that characterize stochastic electromagnetic sources and beams is described. In this interpretation, the synthesized field is regarded as an incoherent superposition of spatially coherent fields originating from a partially polarized, spatially incoherent virtual source. The coherence and the polarization properties of the synthesized field are also examined in view of this interpretation. As a result, we found that the spectral degree of coherence and that of polarization of the synthesized field are generally different from those of the virtual source by the effect of the superposition. We also found, however, that there are some situations in which the spectral degree of polarization of the synthesized field remains unchanged even though the superposition takes place. III.2. V. Ramírez-Sánchez, G. Piguero, and M. Santarsiero, “Synthesis and characterization of partially coherent beams with propagation-invariant transverse polarization pattern” Abstract: Partially coherent beams, whose transverse polarization pattern remains invariant upon paraxial propagation, are synthesized and characterized. Synthesis is performed by imposing a spirallike polarization profile to an axially symmetric partially coherent light source. Irradiance and polarization profiles of the propagated beam are detected at different transverse planes, both in the near and in the far zone, and are compared with the theoretical ones. Furthermore, global parameters, measuring the circular, radial and azimuthal polarization contents across the beam profile, are used to characterize the generated beam from a global point of view. III.3. A.S. Ostrovsky, M.A. Olvera, C. Rickenstorff, G. MartínezNiconoff, and V. Arrizón, “Generation of a secondary electromagnetic source with desired statistical properties” Abstract: Two alternative techniques for generating a secondary electromagnetic source with the desired degree of polarization and transverse coherence length are proposed and compared. The first technique is based on the changes of coherence and polarization on propagation, while the second one makes use of the coherence and
IV.2. M. Choubani, F. Choubani, A. Gharsallah, J. David, and N.E. Mastorakis, “Analysis and design of electromagnetic band gap structures with stratified and inhomogeneous media” Abstract: In this study, a generalized and easy to use method based on Hill's equation and chain matrix concept is used to analyze the electromagnetic wave propagation in stratified dielectric and inhomogeneous media with arbitrary profiles. Numerical simulations are performed to compute the reflection and transmission of several electromagnetic bandgap (EBG) structures for various permittivity profiles, and given polarization as well as incidence angles of driving fields. Multilayer structures are analyzed and optimized to enhance their selectivity performances obtained results agree excellently well with other published data. IV.3. Y. Cai, M. Yao, and O. Korotkova, “Spectral shift of a stochastic electromagnetic Gaussian Schell-model beam in a Gaussian cavity” Abstract: Spectral changes of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam interacting with a Gaussian cavity are investigated. It is shown that the spectral shift is mainly determined by the degree of polarization of the initial beam and by the parameters of the cavity. Generically the blue shift occurs at on-axis points, while the red shift can occur at off-axis points. The condition under which the relative spectral shift is independent of the degree of polarization of the initial beam is analyzed. IV.4. S. Sahin, Z. Tong, and O. Korotkova, “Sensing of semi-rough targets embedded in atmospheric turbulence by means of stochastic electromagnetic beams” Abstract: An active bistatic LIDAR system operating through atmospheric turbulence is considered. Illumination field is assumed to be an electromagnetic Gaussian–Schell-model beam. Target surface is modeled as a combination of isotropic phase screen governed by Gaussian statistics, to account for its roughness, and a Gaussian lens to account for its size and radius of curvature. With the help of a recently developed tensor method for propagation of stochastic electromagnetic beams through ABCD systems and random media we examine the evolution of states of coherence and polarization of the beam. In the case of unresolved flat (planar) target we show that by comparing coherence and polarization properties of the illumination beam and of the return beam it is possible to predict the typical roughness of the target surface.
4426
Editorial overview
IV.5. K. Chamaillard, A.T. Friberg, and C. Dainty, “Coherency matrix description for statistical linear regression of Stokes parameters in rough small-particle scattering” Abstract: A statistical analysis of the Stokes parameters in light scattering by randomly rough small particles shows a linear regression law between the squares of the first two components Is and Qs of the Stokes vector. While the coefficients of this linear regression contain physical characteristics of the particles, they cannot be directly interpreted in terms of the degree of polarization of the scattered field. We propose an interpretation of this relationship between the Stokes parameters on the basis of the general coherence-density matrix formalism. The link between the statistical regression results and the polarization properties of the stochastic scattered components of the field is established through the coherency matrix elements. IV.6. F. Fanjul-Vélez, N. Ortega-Quijano, and J.L. Arce-Diego, “Polarimetry group theory analysis in biological tissue phantoms by Mueller coherency matrix” Abstract: The characterization of biological tissues by optical techniques provides several advantages over other techniques. Optical techniques enable to perform high resolution and contrast imaging, in a non-invasive way and with no-contact. Biological tissues are turbid media that strongly scatter light. The ultrastructure of some tissues makes them present a certain degree of anisotropy. Both scattering and anisotropy affect light polarization. Some pathologies alter these characteristics of the tissue. As a consequence polarized light can be used to extract additional information and achieve a better diagnosis. In this work, group theory is applied to analyze the polarization behavior of several samples. Firstly, the Mueller matrix for each sample is measured. Then, the Mueller coherency matrix is obtained by means of the SU(4)-O+(6) homomorphism. Finally, the target decomposition theorem is applied by analyzing the eigenvalues and eigenvectors, and subsequently the different polarimetric effects are separated. In this way, the contrast of tissue imaging can be increased. This analysis is applied to biological tissue phantoms, which consisted on glucose suspensions of polystyrene spheres with different scatterer concentrations. Their behavior can be modeled by means of single or multiple scattering depending on the concentration, either in the Rayleigh or Mie regimes. The same procedure could be used in a wide range of applications, like the study of cancerous cells that grow without control in cell cultures, or erythrocytes monitoring in anemia. The technique also has a great potential to be applied in polarization sensitive optical coherence tomography (PS-OCT). IV.7. G. Kang, Q. Tan, and G. Jin, “Polarization-selective subwavelength grating used with 193 nm light” Abstract: Hyper-NA ArF (193 nm) immersion lithography is one of the most potential technologies to achieve 32 nm critical dimension node. At the corresponding large angles in the photoresist, control of polarization becomes necessary. A polarization beam splitter (PBS) based on a subwavelength dielectric grating has been designed for use with 193 nm light. The polarization-selective property of such grating is explained by the mechanism of modes interference. The designed grating working as a 1 × 2 beam splitter can transmit TM wave (∼90%) to the zeroth order with extinction ratio of 753, and it diffracts TE wave (∼ 80%) to the -1st order with extinction ratio of 300. IV.8. M.A. Emam-Ismail, “Retardation calculation for achromatic and apochromatic quarter and half wave plates of gypsum based birefringent crystal”
and quarter wave retarders made from gypsum birefringent crystal combined with KDP, ADP, MgF2, sapphire and calcite birefringent crystals of properly thicknesses. For such achromatic wave plate, the residual variation percentages of the retardation as a function of wavelength for gypsum/KDP, gypsum/ADP, gypsum/MgF2, gypsum/ sapphire and gypsum/calcite are found to be ±1.7%, ±3%, ±12.2%, ±12.0% and ±7.2%, respectively. To reduce the spectral variation of retardation, a third layer (apochromatic) of birefringent material is added to the aforementioned two layers combination. The apochromatic wave plate consists of gypsum/KDP/quartz, gypsum/ADP/quartz, MgF2/ ADP/gypsum, MgF2/KDP/gypsum and gypsum/sapphire/MgF2 with the calculated spectral residual variation percentages of retardation are found to be ±0.27, ±0.33, ±0.3, ±0.17 and ±0.45, respectively. IV.9. H. Zhu, X. Chen, and W. Zhou, “An improvement on constant modulus algorithm for polarization demultiplexing in optical coherent receivers” Abstract: In order to solve the problem of ill-convergence for constant modulus algorithm (CMA) in polarization division multiplexing system with optical coherent receivers, a modified constant modulus algorithm based on BER aiding to control initial tap setup, called as BER-Aiding CMA (BA-CMA), is proposed in this paper. By analyzing the principle of CMA for adaptive digital equalization and polarization demultiplexing, the convergence behavior leading undesirable result is investigated and therefore BA-CMA is proposed. Simulation results show that the proposed algorithm can overcome the undesirable convergence effectively and keep inherent advantages of CMA at the same time. IV.10. J.Q. Shen, “Coherence control for photonic logic gates via Yconfiguration double-control quantum interferences” Abstract: Destructive and constructive quantum interferences exhibited in a four-level Y-configuration double-control atomic system are suggested. It is shown that the probe transition (driven by the probe field) can be manipulated by the quantum interferences between two control transitions (driven by the control fields) of the four-level system. The atomic vapor is opaque (or transparent) to the probe field if the destructive (or constructive) quantum interference between the control transitions emerges. The optically sensitive responses due to double-control quantum interferences can be utilized to realize some quantum optical and photonic devices such as the logic-gate devices, e.g., the NOT, OR, NOR and EXNOR gates. Reference [1] A.T. Friberg, J. Turunen, J. Tervo (Eds.), Proceedings of Koli Workshop on Electromagnetic Coherence and 3D Polarization, University of Joensuu, Finland, 2009.
Ari T. Friberg Aalto University, Department of Applied Physics, Box 13500, FI-00076 Aalto, Finland University of Eastern Finland, Department of Physics and Mathematics, Box 111, FI-80101 Joensuu, Finland Royal Institute of Technology, Department of Microelectronics and Applied Physics, Electrum 229, SE-164 40 Kista, Sweden Corresponding author. E-mail address: ari.friberg@tkk.fi Jari Turunen University of Eastern Finland, Department of Physics and Mathematics, Box 111, FI-80101 Joensuu, Finland
19 April 2010 Abstract: In the present paper, we report a direct calculation of retardation for a visible region (λ = 0.4 μm to 0.7 μm) achromatic half