Abstract

In this paper, we have investigated the main properties of the Raman and fluorescent matrix of scattering by microspheres using the matrix scattering formalism. The coherent and incoherent inelastic scattering of incident light by a microsphere is described by the Stokes parameters. We demonstrate the main symmetry properties of the coherent and incoherent Raman and fluorescent scattering matrices. Numerical results are presented to illustrate the Raman scattering efficiency, cross-phase coefficient, and some other parameters of scattering by microspheres.

© 2011 Optical Society of America

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2010

M. Putkiranta, A. Manninen, A. Rostedt, J. Saarela, T. Sorvajärvi, M. Marjamäki, R. Hernberg, and J. Keskinen, “Fluorescence properties of biochemicals in dry NaCl composite aerosol particles and in solutions,” Appl. Phys. B 99, 841–851 (2010).
[CrossRef]

D. Kim, I. Song, H. D. Cheong, Y. Kim, S. Baik, and J. Lee, “Spectrum characteristics of multichannel water Raman LIDAR signals and principal component analysis,” Opt. Rev. 17, 84–89 (2010).
[CrossRef]

A. Braeuer, S. Dowy, and A. Leipertz, “Simultaneous Raman and elastic light scattering imaging for particle formation investigation,” Opt. Lett. 35, 2553–2555 (2010).
[CrossRef] [PubMed]

Y. E. Geints, A. M. Kabanov, G. G. Matvienko, V. K. Oshlakov, A. A. Zemlyanov, S. S. Golik, and O. A. Bukin, “Broadband emission spectrum dynamics of large water droplets exposed to intense ultrashort laser radiation,” Opt. Lett. 35, 2717–2719 (2010).
[CrossRef] [PubMed]

S.-H. Park, Y.-G. Kim, D.-H. Kim, H.-D. Cheong, W.-S. Choi, and J.-I. Lee, “Selecting characteristic Raman wavelengths to distinguish liquid water, water vapor, and ice water,” J. Opt. Soc. Korea 14, 209–214 (2010).
[CrossRef]

C.-B. Xie, J. Zhou, N. Sugimoto, and Z.-F. Wang, “Aerosol observation with Raman LIDAR in Beijing, China,” J. Opt. Soc. Korea 14, 215–220 (2010).
[CrossRef]

B. Moody, C. M. Haslauer, E. Kirk, A. Kannan, E. G. Loboa, and G. S. McCarty, “In situ monitoring of adipogenesis with human-adipose-derived stem cells using surface-enhanced Raman spectroscopy,” Appl. Spectrosc. 64, 1227–1233 (2010).
[CrossRef] [PubMed]

2009

2008

2007

2006

2005

2004

2003

2002

2001

S. C. Hill, R. G. Pinnick, S. Niles, N. F. Fell, Y.-L. Pan, J. Bottiger, B. V. Bronk, S. Holler, and R. K. Chang, “Fluorescence from airborne microparticles: dependence on size, concentration of fluorophores, and illumination intensity,” Appl. Opt. 40, 3005–3013 (2001).
[CrossRef]

V. V. Datsyuk and I. A. Izmailov, “Optics of microdroplets,” Phys. Usp. 44, 1061–1073 (2001).
[CrossRef]

I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, and J. M. Lee, “Study of atmospheric water in gaseous and liquid state by using combined elastic–Raman depolarization lidar,” Appl. Phys. B 73, 739–744 (2001).
[CrossRef]

2000

I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, and J. M. Lee, “Raman lidar for the study of liquid water and water vapor in troposphere,” Appl. Phys. B 71, 113–117(2000).
[CrossRef]

1999

D. N. Whiteman and S. H. Melfi, “Cloud liquid water, mean droplet radius, and number density measurements using a Raman lidar,” J. Geophys. Res. 104, 31411–31419(1999).
[CrossRef]

1997

1996

1994

1992

1990

G. Schweiger, “Raman scattering on single aerosol particles and on flowing aerosols: a review,” J. Aerosol Sci. 21, 483–509(1990).
[CrossRef]

1988

H. Chew, “Total fluorescent scattering cross section,” Phys. Rev. A 37, 4107–4110 (1988).
[CrossRef] [PubMed]

1983

1981

H. C. van der Hulst, Light Scattering by Small Particles(Dover, 1981).

1980

1979

1978

1976

H. Chew, M. Kerker, and P. J. McNulty, “Raman and fluorescent scattering by molecules embedded in concentric spheres,” J. Opt. Soc. Am. 66, 440–444 (1976).
[CrossRef]

H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[CrossRef]

Ahmed, S.

Althausen, D.

Ansmann, A.

Baik, S.

D. Kim, I. Song, H. D. Cheong, Y. Kim, S. Baik, and J. Lee, “Spectrum characteristics of multichannel water Raman LIDAR signals and principal component analysis,” Opt. Rev. 17, 84–89 (2010).
[CrossRef]

Baumgart, R.

Behrendt, A.

Berger, A. J.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Bottiger, J.

Braeuer, A.

Bronk, B. V.

Bukin, O. A.

Byrn, S. R.

Cha, H.

Cha, H. K.

I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, and J. M. Lee, “Study of atmospheric water in gaseous and liquid state by using combined elastic–Raman depolarization lidar,” Appl. Phys. B 73, 739–744 (2001).
[CrossRef]

I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, and J. M. Lee, “Raman lidar for the study of liquid water and water vapor in troposphere,” Appl. Phys. B 71, 113–117(2000).
[CrossRef]

Chang, R. K.

Chaw, S.

Cheong, H. D.

D. Kim, I. Song, H. D. Cheong, Y. Kim, S. Baik, and J. Lee, “Spectrum characteristics of multichannel water Raman LIDAR signals and principal component analysis,” Opt. Rev. 17, 84–89 (2010).
[CrossRef]

Cheong, H.-D.

Chew, H.

Choi, S. C.

I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, and J. M. Lee, “Study of atmospheric water in gaseous and liquid state by using combined elastic–Raman depolarization lidar,” Appl. Phys. B 73, 739–744 (2001).
[CrossRef]

I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, and J. M. Lee, “Raman lidar for the study of liquid water and water vapor in troposphere,” Appl. Phys. B 71, 113–117(2000).
[CrossRef]

Choi, W.-S.

Cooke, D. D.

Datsyuk, V. V.

V. V. Datsyuk and I. A. Izmailov, “Optics of microdroplets,” Phys. Usp. 44, 1061–1073 (2001).
[CrossRef]

Davis, E. J.

Dowy, S.

Druger, S. D.

Engelmann, R.

Esmonde-White, K. A.

Evans, K. D.

Fell, N. F.

Ferrare, R.

Ferrare, R. A.

Geints, Y. E.

Golik, S. S.

Griaznov, V.

Grieken, R. V.

Gross, B.

Haslauer, C. M.

Hernberg, R.

M. Putkiranta, A. Manninen, A. Rostedt, J. Saarela, T. Sorvajärvi, M. Marjamäki, R. Hernberg, and J. Keskinen, “Fluorescence properties of biochemicals in dry NaCl composite aerosol particles and in solutions,” Appl. Phys. B 99, 841–851 (2010).
[CrossRef]

A. Manninen, M. Putkiranta, A. Rostedt, J. Saarela, T. Laurila, M. Marjamäki, J. Keskinen, and R. Hernberg, “Instrumentation for measuring fluorescence cross sections from airborne microsized particles,” Appl. Opt. 47, 110–115 (2008).
[CrossRef] [PubMed]

Hill, S. C.

Holler, S.

Hu, M.

Hu, Y.

Huang, H. C.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Iarlori, M.

Izmailov, I. A.

V. V. Datsyuk and I. A. Izmailov, “Optics of microdroplets,” Phys. Usp. 44, 1061–1073 (2001).
[CrossRef]

Kabanov, A. M.

Kannan, A.

Kerker, M.

Keskinen, J.

M. Putkiranta, A. Manninen, A. Rostedt, J. Saarela, T. Sorvajärvi, M. Marjamäki, R. Hernberg, and J. Keskinen, “Fluorescence properties of biochemicals in dry NaCl composite aerosol particles and in solutions,” Appl. Phys. B 99, 841–851 (2010).
[CrossRef]

A. Manninen, M. Putkiranta, A. Rostedt, J. Saarela, T. Laurila, M. Marjamäki, J. Keskinen, and R. Hernberg, “Instrumentation for measuring fluorescence cross sections from airborne microsized particles,” Appl. Opt. 47, 110–115 (2008).
[CrossRef] [PubMed]

Kim, D.

D. Kim, I. Song, H. D. Cheong, Y. Kim, S. Baik, and J. Lee, “Spectrum characteristics of multichannel water Raman LIDAR signals and principal component analysis,” Opt. Rev. 17, 84–89 (2010).
[CrossRef]

D. Kim and H. Cha, “Suggestion for qualitative lidar identification of different types of aerosol using the two-wavelength rotational Raman and elastic lidar,” Opt. Lett. 31, 2915–2917 (2006).
[CrossRef] [PubMed]

Kim, D. H.

I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, and J. M. Lee, “Study of atmospheric water in gaseous and liquid state by using combined elastic–Raman depolarization lidar,” Appl. Phys. B 73, 739–744 (2001).
[CrossRef]

I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, and J. M. Lee, “Raman lidar for the study of liquid water and water vapor in troposphere,” Appl. Phys. B 71, 113–117(2000).
[CrossRef]

Kim, D.-H.

Kim, Y.

D. Kim, I. Song, H. D. Cheong, Y. Kim, S. Baik, and J. Lee, “Spectrum characteristics of multichannel water Raman LIDAR signals and principal component analysis,” Opt. Rev. 17, 84–89 (2010).
[CrossRef]

Kim, Y.-G.

Kirk, E.

Kolgotin, A.

Lange, S.

Laucks, M. L.

Laurila, T.

LeClair, S. V.

Lee, J.

D. Kim, I. Song, H. D. Cheong, Y. Kim, S. Baik, and J. Lee, “Spectrum characteristics of multichannel water Raman LIDAR signals and principal component analysis,” Opt. Rev. 17, 84–89 (2010).
[CrossRef]

Lee, J. M.

I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, and J. M. Lee, “Study of atmospheric water in gaseous and liquid state by using combined elastic–Raman depolarization lidar,” Appl. Phys. B 73, 739–744 (2001).
[CrossRef]

I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, and J. M. Lee, “Raman lidar for the study of liquid water and water vapor in troposphere,” Appl. Phys. B 71, 113–117(2000).
[CrossRef]

Lee, J.-I.

Leipertz, A.

Li, J.

Loboa, E. G.

Malinka, A. V.

Manninen, A.

M. Putkiranta, A. Manninen, A. Rostedt, J. Saarela, T. Sorvajärvi, M. Marjamäki, R. Hernberg, and J. Keskinen, “Fluorescence properties of biochemicals in dry NaCl composite aerosol particles and in solutions,” Appl. Phys. B 99, 841–851 (2010).
[CrossRef]

A. Manninen, M. Putkiranta, A. Rostedt, J. Saarela, T. Laurila, M. Marjamäki, J. Keskinen, and R. Hernberg, “Instrumentation for measuring fluorescence cross sections from airborne microsized particles,” Appl. Opt. 47, 110–115 (2008).
[CrossRef] [PubMed]

Marjamäki, M.

M. Putkiranta, A. Manninen, A. Rostedt, J. Saarela, T. Sorvajärvi, M. Marjamäki, R. Hernberg, and J. Keskinen, “Fluorescence properties of biochemicals in dry NaCl composite aerosol particles and in solutions,” Appl. Phys. B 99, 841–851 (2010).
[CrossRef]

A. Manninen, M. Putkiranta, A. Rostedt, J. Saarela, T. Laurila, M. Marjamäki, J. Keskinen, and R. Hernberg, “Instrumentation for measuring fluorescence cross sections from airborne microsized particles,” Appl. Opt. 47, 110–115 (2008).
[CrossRef] [PubMed]

Matvienko, G. G.

McCarty, G. S.

McNulty, P. J.

Melfi, S. H.

Moody, B.

Morris, M. D.

Moshary, F.

Müller, D.

Nakamura, T.

Niles, S.

Onishi, M.

Oshlakov, V. K.

Pan, Y.-L.

Park, S.-H.

Pendleton, J. D.

Pinnick, R. G.

Potgieter-Vermaak, S.

Putkiranta, M.

M. Putkiranta, A. Manninen, A. Rostedt, J. Saarela, T. Sorvajärvi, M. Marjamäki, R. Hernberg, and J. Keskinen, “Fluorescence properties of biochemicals in dry NaCl composite aerosol particles and in solutions,” Appl. Phys. B 99, 841–851 (2010).
[CrossRef]

A. Manninen, M. Putkiranta, A. Rostedt, J. Saarela, T. Laurila, M. Marjamäki, J. Keskinen, and R. Hernberg, “Instrumentation for measuring fluorescence cross sections from airborne microsized particles,” Appl. Opt. 47, 110–115 (2008).
[CrossRef] [PubMed]

Rizi, V.

Rocci, G.

Roessler, B. J.

Rostedt, A.

M. Putkiranta, A. Manninen, A. Rostedt, J. Saarela, T. Sorvajärvi, M. Marjamäki, R. Hernberg, and J. Keskinen, “Fluorescence properties of biochemicals in dry NaCl composite aerosol particles and in solutions,” Appl. Phys. B 99, 841–851 (2010).
[CrossRef]

A. Manninen, M. Putkiranta, A. Rostedt, J. Saarela, T. Laurila, M. Marjamäki, J. Keskinen, and R. Hernberg, “Instrumentation for measuring fluorescence cross sections from airborne microsized particles,” Appl. Opt. 47, 110–115 (2008).
[CrossRef] [PubMed]

Saarela, J.

M. Putkiranta, A. Manninen, A. Rostedt, J. Saarela, T. Sorvajärvi, M. Marjamäki, R. Hernberg, and J. Keskinen, “Fluorescence properties of biochemicals in dry NaCl composite aerosol particles and in solutions,” Appl. Phys. B 99, 841–851 (2010).
[CrossRef]

A. Manninen, M. Putkiranta, A. Rostedt, J. Saarela, T. Laurila, M. Marjamäki, J. Keskinen, and R. Hernberg, “Instrumentation for measuring fluorescence cross sections from airborne microsized particles,” Appl. Opt. 47, 110–115 (2008).
[CrossRef] [PubMed]

Schulte, J.

Schweiger, G.

Schwemmer, G.

Sculley, M.

Smith, Z. J.

Song, I.

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[CrossRef]

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[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Raman scattering efficiency σ / σ 0 versus the size parameter of spheres for inelastic coherent and incoherent scattering. The relative refractive index is M = 1.3435 , the relative frequency shift is p = 1.137 , and the step of the size parameter is 0.5.

Fig. 2
Fig. 2

Contour plot of the phase function σ ( θ ) / σ versus the scattering angle and the size parameter for coherent scattering into the forward hemisphere. Values of the phase function are shown in gray scale. The relative refractive index is M = 1.3435 , the relative frequency shift is p = 1.137 , and the step of the size parameter is 0.5.

Fig. 3
Fig. 3

Same as in Fig. 2, but for coherent scattering into the backward hemisphere.

Fig. 4
Fig. 4

Contour plot of the cross-phase coefficient ( R 44 R 33 ) / R 11 versus the scattering angle and the size parameter for incoherent scattering in gray scale. The relative refractive index is M = 1.3435 , the relative frequency shift is p = 1.137 , and the step of the size parameter is 0.5.

Fig. 5
Fig. 5

Ratio R 34 / R 11 versus the scattering angle and the size parameter for coherent scattering in gray scale. The relative refractive index is M = 1.3435 , the relative frequency shift is p = 1.137 , and the step of the size parameter is 0.5.

Fig. 6
Fig. 6

Contour plot of the ratio R 34 / R 11 versus the scattering angle and the size parameter for incoherent scattering in gray scale. The relative refractive index is M = 1.3435 , the relative frequency shift is p = 1.137 , and the step of the size parameter is 0.5.

Fig. 7
Fig. 7

Ratio R 33 / R 11 versus the scattering angle and the size parameter for coherent scattering in gray scale. The relative refractive index is M = 1.3435 , the relative frequency shift is p = 1.137 , and the step of the size parameter is 0.5.

Fig. 8
Fig. 8

Contour plot of the ratio R 44 / R 11 versus the scattering angle and the size parameter for incoherent scattering in gray scale. The relative refractive index is M = 1.3435 , the relative frequency shift is p = 1.137 , and the step of the size parameter is 0.5.

Equations (31)

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E inc O X = E 0 e x exp ( i k 02 z ) ,
E inc O Y = E 0 e y exp ( i k 02 z ) ,
p ( r ) = α 1 E tra ( r )
E 2 θ 1 = exp ( i k 2 r ) k 2 r i , m ( i ) l + 1 i l ( l + 1 ) × [ c M 1 ( l , m ) 1 sin θ Y l m φ c E 1 ( l , m ) n 2 Y l m θ ] ,
E 2 φ 1 = exp ( i k 2 r ) k 2 r i , m ( i ) l + 1 i l ( l + 1 ) × [ c E 1 ( l , m ) n 2 1 sin θ Y l m φ + c M 1 ( l , m ) Y l m θ ] ,
( E θ sca E φ sca ) = exp ( i k 2 r ) i k 2 r ( S 2 1 S 3 1 S 4 1 S 1 1 ) ( E θ inc E φ inc ) ,
S 2 , 4 1 = i , m ( i ) l + 1 1 l ( l + 1 ) × [ c M 1 ( l , m ) 1 sin θ Y l m φ c E 1 ( l , m ) n 2 Y l m θ ] ,
S 1 , 3 1 = i , m ( i ) l + 1 1 l ( l + 1 ) × [ c E 1 ( l , m ) n 2 1 sin θ Y l m φ + c M 1 ( l , m ) Y l m θ ] .
E 2 θ 1 O X = E 0 exp ( i k 2 r ) i k 2 r S 2 1 ( r , θ , φ , θ , φ = 0 ) ,
E 2 φ 1 O X = E 0 exp ( i k 2 r ) i k 2 r S 4 1 ( r , θ , φ , θ , φ = 0 ) ,
E 2 θ 1 O Y = E 0 exp ( i k 2 r ) i k 2 r S 3 1 ( r , θ , φ , θ , φ = 0 ) ,
E 2 φ 1 O Y = E 0 exp ( i k 2 r ) i k 2 r S 1 1 ( r , θ , φ , θ , φ = 0 ) ,
E 2 θ 1 O X = H h , E 2 φ 1 O X = V h ,
E 2 θ 1 O Y = H v , E 2 φ 1 O Y = V v .
S ( θ ) = 0 a 0 π 0 2 π ρ S 1 ( r , θ , φ , θ , φ = 0 ) r 2 sin ϑ d r d θ d φ = ( S 2 0 0 S 1 ) ,
R ( θ ) = ( R 11 R 12 0 0 R 12 R 11 0 0 0 0 R 33 R 34 0 0 R 34 R 33 )
R ( θ ) = 0 a 0 π 0 2 π ρ R 1 ( r , θ , φ , θ , φ = 0 ) r 2 sin ϑ d r d θ d φ ,
R ( θ ) = ( R 11 R 12 0 0 R 21 R 22 0 0 0 0 R 33 R 34 0 0 R 43 R 44 )
R ( 0 ) = ( R 11 0 0 0 0 R 22 0 0 0 0 R 22 0 0 0 0 R 44 ) .
R ( π ) = ( R 11 0 0 0 0 R 22 0 0 0 0 R 22 0 0 0 0 R 11 2 R 22 ) .
I sca = 1 k 2 2 r 2 R ( θ ) I inc ,
I = E I I E I I * + E E * ,
Q = E I I E I I * E E * ,
U = E I I E * + E I I * E ,
V = i ( E I I E * E I I * E ) .
σ = 2 π 0 π σ ( θ ) sin θ d θ .
S 1 ( θ ) = 9 b 1 ( cos θ 0 0 1 ) ,
b 1 = i k 3 μ 1 α 1 ( M 2 + 2 ) 2 .
R ( θ ) = 81 ( υ ρ ) 2 | b 1 | 2 R 0 ( θ ) ,
R ( θ ) = 81 υ ρ | b 1 | 2 R 0 ( θ ) ,
R 0 ( θ ) = ( 1 2 ( 1 + cos 2 θ ) 1 2 ( cos 2 θ 1 ) 0 0 1 2 ( cos 2 θ 1 ) 1 2 ( 1 + cos 2 θ ) 0 0 0 0 cos θ 0 0 0 0 cos θ ) .

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