Unified Theory Of Coherence Research Articles

Condition of Keeping Polarization Property Unchanged in the Circle Polarization Shift Keying System

To improve the performance of the free-space optical (FSO) system, we recently proposed circle polarization shift keying (CPolSK). In the CPolSK system, it is important to study the condition of keeping the polarization properties unchanged in the turbulent atmosphere. Based on the unified theory of coherence and polarization, three formulas are derived to describe the condition of keeping the polarization degree invariant for the Gaussian–Schell model (GSM) beam. The third formula includes all the polarization states. Consequently, it is defined as the condition of polarization invariance in CPolSK systems. If this condition is satisfied, the two parameters of the polarization ellipse will remain the values of the source during the propagation. Several GSM beams with different parameters are numerically calculated to verify the conditions. This result is helpful in designing the transmitter of the polarization modulation system.

Spectral and polarization properties of stochastic electromagnetic beams propagating in gain or absorbing media

Based on the generalized Huygens–Fresnel diffraction principle and on the unified theory of coherence and polarization of light, the analytical expressions for the cross-spectral density matrix of a class of stochastic electromagnetic beams in linear, deterministic media with gain or absorption, in which the wave number is generally complex, has been derived. In particular, through numerical examples based on our analytical formulas the behavior of the spectral density, and of the degree of polarization of the Electromagnetic Gaussian Schell-model is analyzed. It is demonstrated how these statistical properties of the beam propagating in such media depend on the properties of the source and on the wave number of the medium. Numerical examples relate to two model sources: with uncorrelated and partially correlated mutually orthogonal transverse components of the electric field. The results will impact potential applications involving natural absorbing media, such as oceanic waters, and man-made media such as active lasers, for instance.

Condition for Gaussian Schell-model beam to maintain the state of polarization on the propagation in free space

In the free space optical communication system with circle polarization shift keying (CPolSK) modulation, the changes of polarization state of light beam have significant influence on the system performance. Keeping the state of polarization (SOP) unchanged on propagation can reduce the bit error rate. Based on the unified theory of coherence and polarization, we derive the sufficient condition for Gaussian Schell-model (GSM) beam to keep the SOP unchanged. We found that when the three spectral correlation widths (delta(xx), delta(yy) and delta(xy)) equal to each other and sigma(x) = sigma(y), the GSM beam maintains the SOP on propagation. This conclusion can be helpful for the design of the transmitter in the CPolSK system.

Characterization of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams

The unified theory of coherence and polarization proposed by Wolf is extended from stochastic stationary electromagnetic beams to stochastic spatially and spectrally partially coherent electromagnetic pulsed beams. Taking the stochastic electromagnetic Gaussian Schell-model pulsed (GSMP) beam as a typical example of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams, the expressions for the spectral density, spectral degree of polarization and spectral degree of coherence of stochastic electromagnetic GSMP beams propagating in free space are derived. Some special cases are analyzed. The illustrative examples are given and the results are interpreted physically.

Propagation properties of partially coherent radially polarized beam in a turbulent atmosphere

Based on the Huygens–Fresnel principle and the unified theory of coherence and polarization of partially coherent beams, we investigate the propagation characteristics of a partially coherent radially polarized doughnut (PCRPD) beam in a turbulent atmosphere. It is found that, after propagating through a turbulent atmosphere, the doughnut beam spot is changed into a circular Gaussian beam. Moreover, the degree of coherence, the degree of polarization and the degree of cross-polarization of the beam will change on propagation, and this change is dependent upon the degree of coherence of the source and atmospheric turbulence.

Free-space propagation of the spectral degree of cross-polarization of stochastic electromagnetic beams

Based on the unified theory of coherence and polarization and the extended Huygens–Fresnel integral the free-space evolution of the recently introduced spectral degree of cross-polarization of a stochastic electromagnetic beam is studied. Unlike the spectral degree of coherence, the degree of cross-polarization is unbounded and exhibits non-monotonic changes with growing propagation distance and growing radial distance from the center of the beam, at fixed transverse cross-sections. Our numerical results pertain to the electromagnetic Gaussian Schell-model beams. We derive expressions for the cross-spectral density matrix of the EGSM beam for arbitrary transverse and longitudinal positions. The results show that the behavior of the degree of cross-polarization on propagation is determined by all of the parameters of the source radiating the beam. At sufficiently large distances from the source, the degree of cross-polarization stabilizes for all points within the beam independently of their radial positions.

Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams

Electromagnetic Gaussian Schell-model (EGSM) beam with twist phase (i.e., twisted EGSM beam) is introduced as an extension of its scalar version based on the unified theory of coherence and polarization. We show how analytical paraxial propagation formulae of isotropic and anisotropic EGSM beams passing through a general astigmatic ABCD optical system can be modified in the presence of the twist phase. Numerical examples demonstrate that the twist phase affects the spectral density, the state of coherence, and the degree of polarization of EGSM beams on propagation.

Spectral changes of polychromatic stochastic electromagnetic vortex beams propagating through turbulent atmosphere

The unified theory of coherence and polarization and the propagation law of 2 × 2 cross-spectral density are employed to investigate spectral changes of the polychromatic stochastic electromagnetic vortex beam propagating in turbulent atmosphere. It is shown that the spectral changes of a polychromatic stochastic electromagnetic vortex beam in turbulent atmosphere differ from those of the beam without vortex. Specially, the on-axis relative spectral shifts exhibit not only blue-shift, but also red-shift. It is also shown that the topological charge, the correlation length and the refractive index structure constant influence the spectral changes of polychromatic stochastic electromagnetic vortex beams in a turbulent atmosphere.

Changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian beams in turbulence

The unified theory of coherence and polarization is applied to an investigation of the changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic Hermite–Gaussian (EHG) beams propagating through atmospheric turbulence. Based on the extended Huygens–Fresnel principle, the 2×2 electric cross-spectral density matrix of partially coherent EHG beams in turbulence is expressed analytically by using a quadratic approximation of Rytov's phase structure function. The analytical expressions for the degree of polarization, the degree of coherence and the spectrum of partially coherent EHG beams in turbulence are derived, and the corresponding analytical results of electromagnetic Gaussian Schell-model (EGSM) beams can be obtained when the order number of the Hermite polynomial is zero. Some interesting results are obtained, which are illustrated by using numerical examples.

Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere

The polychromatic partially coherent electromagnetic Cosh–Gaussian (EChG) beam is introduced and taken as a typical example of polychromatic partially coherent electromagnetic beams. Based on the unified theory of coherence and polarization, the expressions for the spectrum and the degree of polarization of polychromatic partially coherent EChG beams in the turbulent atmosphere are derived, and the conditions for keeping polarization invariance and for determining the position where the degree of polarization becomes zero along the propagation path are also given. It is shown that the normalized spectrum is close to the normalized source spectrum due to turbulence. The reasonable physical explanation of spectral shift is given. On the other hand, the bandwidth does not affect the degree of polarization, and the degree of polarization tends to the value at the source plane due to turbulence in the long-propagation distance limit. The spectrum and polarization of polychromatic electromagnetic Gaussian Schell-model (EGSM) beams and electromagnetic Gaussian (EG) beams in turbulence are treated as special cases of polychromatic partially coherent EChG beams.

Coherence and polarization properties of electromagnetic laser modes

Abstract A recently formulated mode representation of stochastic electromagnetic fields, based on a unified theory of coherence and polarization is applied to determine the transverse laser resonator modes in any rotationally symmetric cavity. It is found that the electromagnetic modes can be expressed in a simple way in terms of the classic Fox–Li modes of the monochromatic scalar theory; and that, if there is no degeneracy, each mode is completely spatially coherent and its degree of polarization is the same at each point of the cavity mirror.

Changes of polarization of light beams on propagation through tissue

The values of the degree of polarization and the coherence of the light beam are of great importance in many areas. In this paper, we study the effects of tissue turbulence on the degree of polarization of a partially coherent electromagnetic beam. Based on the unified theory of coherence and polarization for random electromagnetic beams and the spectral density of the index of refraction fluctuations of tissue, we have established the detailed formula for calculating the change of the degree of polarization of the beam when propagating through tissue. Compared with the light propagation through atmosphere, the result shows that although the propagation distance in tissue imaging is very short, the degree of polarization of the beam may change greatly. An example was given which clearly shows the effect of the correction properties and the tissue turbulence on the degree of polarization of the light beam propagating within the tissue.

Polarization properties of a class of electromagnetic Gaussian Schell-model beams which have the same far-zone intensity distribution as a fully coherent laser beam

The polarization properties of an electromagnetic Gaussian Schell-model beam propagating in free space are examined on the basis of the recently formulated unified theory of coherence and polarization. Specifically, we derive formulas for the orientation angle and the ellipticity of the polarization ellipse of the polarized portion of beams which are not necessarily isotropic in a well-defined sense. These formulas are generalizations of recently derived expressions for a class of isotropic beams. Conditions are also derived under which the polarization properties remain unchanged on propagation for electromagnetic Gaussian Schell-model beams which have the same far-zone intensity distribution as a fully coherent laser beam.

Polarization of a spatially fully coherent electromagnetic beam

Abstract Using a recently developed unified theory of coherence and polarization [E. Wolf, Phys. Lett., A312, 263–267 (2003)] it is shown that a spatially completely coherent random electromagnetic beam can have a degree of polarization P which may take on any value (0 ≤ P ≤ 1) at points in the beam. In particular the beam can be fully polarized at one point and completely unpolarized or partially polarized at another point. This result also holds for electromagnetic beams which are not completely spatially coherent.

Polarization of a spatially fully coherent electromagnetic beam

Using a recently developed unified theory of coherence and polarization [E. Wolf, Phys. Lett., A312, 263–267 (2003)] it is shown that a spatially completely coherent random electromagnetic beam can have a degree of polarization P which may take on any value (0 ≤ P ≤ 1) at points in the beam. In particular the beam can be fully polarized at one point and completely unpolarized or partially polarized at another point. This result also holds for electromagnetic beams which are not completely spatially coherent.

Polarization: Unified Theory of Coherence and Polarization

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text Emil Wolf, "Polarization: Unified Theory of Coherence and Polarization," Optics & Photonics News 14(12), 37-37 (2003) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article