Far-zone behaviors of scattering-induced statistical properties of partially polarized spatially and spectrally partially coherent electromagnetic pulsed beam

doi:10.1088/1674-1056/ab9de7

Abstract

In this study, we explore the far-zero behaviors of a scattered partially polarized spatially and spectrally partially coherent electromagnetic pulsed beam irradiating on a deterministic medium. The analytical formula for the cross-spectral density matrix elements of this beam in the spherical coordinate system is derived. Within the framework of the first-order Born approximation, the effects of the scattering angle θ, the source parameters (i.e., the pulse duration T₀ and the temporal coherence length T_cxx), and the scatterer parameter (i.e., the effective width of the medium σ_R) on the spectral density, the spectral shift, the spectral degree of polarization, and the degree of spectral coherence of the scattered source in the far-zero field are studied numerically and comparatively. Our work improves the scattering theory of stochastic electromagnetic beams and it may be useful for the applications involving the interaction between incident light waves and scattering media.

Keywords: scattering partially polarized spatially and spectrally partially coherent electromagnetic pulsed beam statistical properties deterministic medium

Received: 08 March 2020
Revised: 22 April 2020
Accepted manuscript online: 18 June 2020

PACS:	42.25.Fx	(Diffraction and scattering)
	42.25.Ja	(Polarization)
	42.25.Kb	(Coherence)

Corresponding Authors: ^†Corresponding author. E-mail: minggao1964@163.com

About author:

†Corresponding author. E-mail: minggao1964@163.com

* Project supported by the National Natural Science Foundation of China (Grant No. 11504286), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2019JM-470), the Fund from the International Technology Collaborative Center for Advanced Optical Manufacturing and Optoelectronic Measurement, and the Science Fund from the Shaanxi Provincial Key Laboratory of Photoelectric Measurement and Instrument Technology.

Cite this article:

Yan Li(李艳), Ming Gao(高明)†, Hong Lv(吕宏), Li-Guo Wang(王利国), and Shen-He Ren(任神河) Far-zone behaviors of scattering-induced statistical properties of partially polarized spatially and spectrally partially coherent electromagnetic pulsed beam 2020 Chin. Phys. B 29 104201

Fig. 1.

Illustration of symbols relating to incident partially polarized spatially and spectrally partially coherent electromagnetic pulsed source irradiating on deterministic scattering medium in spherical coordinate system.

Parameter	Simulation value	Unit
Wavelength λ₀	632.8	nm
Beam width w₀	5	mm
Pulse duration T₀	5	fs
Spatial coherence width δ_αβ	δ_xx = 1, δ_yy = 0.5 δ_xx, δ_xy = δ_yx = 1.5 δ_xx	mm
Temporal coherence width of the pulse T_cαβ	T_cxx = 5, T_cyy = 0.5 T_cxx, T_cxy = T_cyx = 1.5 T_cxx	fs
Average amplitudes A_α	A_x = 1.5, A_y = 1	/
Correlation coefficient B_αβ	B_xx = B_yy = 1, $B_{x y} = B_{y x}^{*} = 0.3 \exp (i π / 3)$	/
Effective width of the medium σ_R	1.0 λ₀	nm
Observation azimuth φ	0	rad
Angular frequency ω	ω₀ = 3.0 × 10¹⁵, ω = 1.1 ω₀, ω₁ = 1.05 ω₀, ω₂ = 0.95ω₀	rad/s

Table 1.

Simulation parameters.

Fig. 2.

Contour graphs of normalized spectral intensity of scattered partially polarized spatially and spectrally partially coherent EGSMP beam for different values of σ_R as a function of θ and [(a1)–(a4)] φ, [(b1)–(b4)] T₀, and [(c1)–(c4)] T_cxx.

Fig. 3.

Comparison between incident field and scattered field with respect to the normalized spectral intensity versus relative spectral shift (ω – ω₀)/ω₀ for different values of (a) θ, (b) σ_R, (c) T₀, and (d) T_cxx, with [(a) and (b)] S₀ denoting incident normalized spectral intensity, [(c) and (d)] numbers 1 and 2 representing incident normalized spectral intensity, and 3 and 4 referring to scattered normalized spectral intensity.

Fig. 4.

Behaviors of the spectral DOP of scattered partially polarized spatially and spectrally partially coherent EGSMP beam versus relative spectral shift (ω – ω₀)/ω₀ for different values of (a1, a2) θ, (b1, b2) σ_R, (c1, c2) T₀, and (d1, d2) T_cxx, with [(a1)–(d1)] B_xy = B_yx = 0, and [(a2)–(d2)] $B_{x y} = B_{y x}^{*} = 0.3 \times \exp (i π / 3)$ .

Fig. 5.

Behaviors of spectral DOP of both incident and scattered partially polarized spatially and spectrally partially coherent EGSMP beam versus scattering angle θ for different values of [(a1),(a2)] T₀ and [(b1), (b2)] T_cxx, with [(a1), (b1)] B_xy = B_yx = 0, [(a2), (b2)] $B_{x y} = B_{y x}^{*} = 0.3 \times \exp (i π / 3)$ , numbers 1–3 denoting incident spectral DOP, and numbers 4–6 representing scattered spectral DOP.

Fig. 6.

Contour graphs of modulus of degree of spectral coherence of scattered partially polarized spatially and spectrally partially coherent EGSMP beam as a function of ω₁ and ω₂ for different values of θ, σ_R, T₀, and T_cxx.

Fig. 7.

Curves of modulus of degree of spectral coherence of scattered partially polarized spatially and spectrally partially coherent EGSMP beam versus (ω₁ – ω₂)/(ω₁ + ω₂) for different values of θ, σ_R, T₀, and T_cxx.

Fig. 8.

The 3D moduli of degree of spectral coherence distribution and corresponding cross line (φ = 0) of scattered partially polarized spatially and spectrally partially coherent EGSMP beam for different values of T₀, with numbers 1–3 denoting incident modulus of degree of spectral coherence, and numbers 4–6 referring to scattered modulus of degree of spectral coherence.

Fig. 9.

3D moduli of degree of spectral coherence distribution and corresponding cross line (φ = 0) of scattered partially polarized spatially and spectrally partially coherent EGSMP beam for different values of T_cxx, with numbers 1–3 denoting incident modulus of degree of spectral coherence, and numbers 4–6 referring to scattered modulus of degree of spectral coherence.

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Far-zone behaviors of scattering-induced statistical properties of partially polarized spatially and spectrally partially coherent electromagnetic pulsed beam

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