Effects of Spatial Coherence on the Angular Distribution of Radiant Intensity Generated by Scattering on a Sphere

Abstract

In the analysis of light scattering on a sphere it is implicitly assumed that the incident field is spatially fully coherent. However, under usual circumstances the field is partially coherent. We generalize the partial waves expansion method to this situation and examine the influence of the degree of coherence of the incident field on the radiant intensity of the scattered field in the far zone. We show that when the coherence length of the incident field is comparable to, or is smaller than, the radius of the sphere, the angular distribution of the radiant intensity depends strongly on the degree of coherence. The results have implications, for example, for scattering in the atmosphere and colloidal suspensions. DOI: 10.1103/PhysRevLett.104.173902 PACS numbers: 42.25.Fx, 42.25.Kb In the usual description of light scattering by a homogeneous sphere (the scalar analogue of the well-known Mie scattering) it is generally assumed that the incident field is spatially fully coherent [1][2][3][4][5]. In practice, this assumption is not always justified. Examples are fields generated by multimode lasers, and fields that have passed through a random medium such as the turbulent atmosphere. Hardly any studies have been devoted to this more general case (see, however, [6]). The extinguished power due to scattering of random fields on a random medium has been analyzed in [7,8], and certain reciprocity relations for cases of this kind were derived in [9]. The extinguished power from scattering a random field on deterministic media was discussed in [10,11]. However, the influence of the state of coherence of the incident field on the angular distribution of the scattered field seems to have been studied only in two publications [12,13].In this Letter we analyze the scattering of a wide class of beams of any state of coherence on a homogeneous spherical scatterer, namely, beams of the well-known Gaussian Schell-model class (see [14], Sec. 5.6.4). We present numerical examples that show how the effective spectral coherence length (i.e., the coherence length at a fixed frequency) of the incident beam affects the angular distribution of the radiant intensity of the scattered field.Let us first consider a plane, monochromatic scalar wave of unit amplitude, propagating in a direction specified by a real unit vector u 0 , incident on a deterministic, spherical scatterer occupying a volume V (see Fig. 1 whereHere r denotes the position vector of a point in space, t the time, and ! the angular frequency. Also, k ¼ !=c ¼ 2 = is the wave number, c being the speed of light in vacuum and denotes the wavelength. The timeindependent part Uðr; !Þ of the total field that results from scattering of the plane wave on a sphere may be expressed as the sum of the incident field U ðiÞ ðr; !Þ and the scattered field U ðsÞ ðr; !Þ, viz., Uðr; !Þ ¼ U ðiÞ ðr; !Þ þ U ðsÞ ðr; !Þ:The scattered field in the far-zone of the scatterer, at an observation point r ¼ ru (u 2 ¼ 1) is given by the asymptotic formula

Coherence effects in Mie scattering

“…(12) in the analysis of scattering of a Gaussian Schell-model beam by a sphere. In the analysis of scattering phenomena, one usually normalizes the scattered power by that of the incident field.…”

“…Examples of partially coherent fields include those generated by multimode lasers and beams that have passed through a random medium, e.g., the turbulent atmosphere. Such more general situations have only recently begun to attract attention [6][7][8][9][10][11][12][13].…”

“…In a previous study [12] the theory of Mie scattering has been generalized to include fields that are spatially partially coherent. In the present paper we use this formalism to study the scattering of partially coherent light (specifically, scattering of Gaussian Schell-model beams) by deterministic, spherical particles.…”

Experimentally generating any desired partially coherent Schell-model source using phase-only control

“…For example, numerous published articles exist predicting the polarization, coherence, and beam shape of partially coherent light after propagating through free space and random media [1][2][3][4][5][6][7][8][9][10] or scattering from deterministic and random objects/media. [11][12][13][14][15][16][17][18][19][20][21] Much work has also been performed exploiting coherence to control beam shape [22][23][24][25][26][27][28][29][30] and even as an encoding scheme for holography. 31 Excellent reviews and more in-depth discussions of these topics can be found in Refs.…”

Topological reactions of correlation functions in partially coherent electromagnetic beams

“…As we will show, a rich variety of topological reactions occurs on propagation of these partially coherent, electromagnetic GSM beams. The observation that different cross sections of a GSM beam have different coherence properties, has profound implications for their use in scattering [37] and interference experiments [17].…”