Abstract

The results of numerical simulation of inelastic scattering by microspheres with the use of a dipole model are presented. The formulas that are derived speed up the computation, thereby permitting larger-sized microspheres to be studied. The angular scattering cross section and depolarization are calculated for a wide range of size parameters as well as for different orientations of incident wave polarization. Calculations performed with small incremental changes in size permit the influence of morphology-dependent resonance (MDR) on the power and angular distribution of scattered radiation to be studied. TM and TE types of MDR produce enhanced scattering of the incident wave with vertical and horizontal polarization; the corresponding shape of the phase function becomes oscillatory. Special attention is paid to the simulation of backward scattering by water droplets, which is important for Raman lidar applications.

© 2002 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2002 (2)

M. A. Stowers, S. K. Friedlander, “Chemical characterization of flowing polydisperse aerosols by Raman spectroscopy,” Aerosol Sci. Technol. 36, 48–61 (2002).
[CrossRef]

Y. L. Pan, S. C. Hill, J. P. Wolf, S. Holler, R. K. Chang, J. R. Bottiger, “Backward-enhanced fluorescence from clusters of microspheres and particles of tryptophan,” Appl. Opt. 41, 2994–2999 (2002).
[CrossRef] [PubMed]

2001 (3)

2000 (3)

S. C. Hill, Y.-L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
[CrossRef] [PubMed]

P. H. Kaye, J. E. Barton, E. Hirst, J. M. Clark, “Simultaneous light scattering and intrinsic fluorescence measurement for the classification of airborne particles,” Appl. Opt. 39, 3738–3745 (2000).
[CrossRef]

I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, 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 (2)

N. Velesco, G. Shweiger, “Geometrical optics calculation of inelastic scattering on large particles,” Appl. Opt. 38, 1046–1052 (1999).
[CrossRef]

D. N. Whiteman, S. H. Melfi, “Cloud liquid water, mean droplet radius, and number density measurements using a Raman lidar,” J. Geophys. Res. 104, 31,411–31,419 (1999).
[CrossRef]

1998 (4)

R. Vehring, “Linear Raman spectroscopy on aqueous aerosols: influence of nonlinear effects on detection limits,” J. Aerosol. Sci. 29, 65–79 (1998).
[CrossRef]

R. Vehring, C. L. Aardahl, G. Schweiger, E. J. Davis, “The characterization of fine particles originating from an uncharged aerosol: size dependence and detection limits for Raman analysis,” J. Aerosol. Sci. 29, 1045–1061 (1998).

J. Popp, M. Lankers, M. Trunk, I. Hartmann, E. Urlaub, W. Kiefer, “High-precision determination of size, refractive index, and dispersion of single microparticles from morphology-dependent resonances in optical processes,” Appl. Spectrosc. 52, 284–291 (1998).
[CrossRef]

J. Musick, J. Popp, M. Trunck, W. Kiefer, “Investigations of radical polymerization and copolymerization reactions in optically levitated microdroplets by simultaneous Raman spectroscopy, Mie scattering, and radiation pressure measurements,” Appl. Spectrosc. 52, 692–701 (1998).
[CrossRef]

1997 (1)

1996 (2)

1995 (2)

1994 (2)

H. B. Lin, A. J. Campillo, “cw nonlinear optics in droplet microcavities displaying enhanced gain,” Phys. Rev. Lett. 73, 2440–2443 (1994).
[CrossRef] [PubMed]

L. G. Guimaraes, H. M. Nussenzveig, “Uniform approximation of Mie resonances,” J. Mod. Opt. 41, 625–647 (1994).
[CrossRef]

1992 (2)

1991 (3)

1990 (1)

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

1989 (1)

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

1988 (1)

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

1985 (2)

1984 (3)

1983 (1)

1979 (2)

1978 (2)

1976 (2)

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

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

1974 (1)

J. R. Scherer, M. K. Go, S. Kint, “Raman spectra and structure of water from -10 to 90°,” J. Phys. Chem. 78, 1304–1313 (1974).
[CrossRef]

1973 (1)

K. Cunningham, P. A. Lyons, “Depolarization ratio studies on liquid water,” J. Chem. Phys. 59, 2132–2139 (1973).
[CrossRef]

Aardahl, C. L.

R. Vehring, C. L. Aardahl, G. Schweiger, E. J. Davis, “The characterization of fine particles originating from an uncharged aerosol: size dependence and detection limits for Raman analysis,” J. Aerosol. Sci. 29, 1045–1061 (1998).

Acker, W. P.

Armstrong, R. L.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

Barnes, M. D.

Barton, J. E.

Benner, R. E.

Biswas, A.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

Bottiger, J.

Bottiger, J. R.

Bronk, B. V.

Campillo, A. J.

J. D. Eversole, H. B. Lin, A. J. Campillo, “Input-output resonance correlation in laser induced emission from microdroplets,” J. Opt. Soc. Am. B 12, 287–296 (1995).
[CrossRef]

H. B. Lin, A. J. Campillo, “cw nonlinear optics in droplet microcavities displaying enhanced gain,” Phys. Rev. Lett. 73, 2440–2443 (1994).
[CrossRef] [PubMed]

Cha, H. K.

I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, 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, 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.

Chen, G.

Chew, H.

Choi, S. C.

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

Clark, J. M.

Conwell, P. R.

Cooke, D. D.

Cunningham, K.

K. Cunningham, P. A. Lyons, “Depolarization ratio studies on liquid water,” J. Chem. Phys. 59, 2132–2139 (1973).
[CrossRef]

Davis, E. J.

R. Vehring, C. L. Aardahl, G. Schweiger, E. J. Davis, “The characterization of fine particles originating from an uncharged aerosol: size dependence and detection limits for Raman analysis,” J. Aerosol. Sci. 29, 1045–1061 (1998).

Druger, S. D.

Evans, K. D.

Eversole, J. D.

Fell, N. F.

Fenn, J. B.

Ferrare, R.

Ferrare, R. A.

Friedlander, S. K.

M. A. Stowers, S. K. Friedlander, “Chemical characterization of flowing polydisperse aerosols by Raman spectroscopy,” Aerosol Sci. Technol. 36, 48–61 (2002).
[CrossRef]

Fung, K. H.

Go, M. K.

J. R. Scherer, M. K. Go, S. Kint, “Raman spectra and structure of water from -10 to 90°,” J. Phys. Chem. 78, 1304–1313 (1974).
[CrossRef]

Griaznov, V.

V. Griaznov, I. Veselovskii, A. Kolgotin, D. N. Whiteman, “Angle- and size-dependent characteristics of incoherent Raman and fluorescent scattering by microspheres. 1. General expressions,” Appl. Opt. (to be published).

Guimaraes, L. G.

L. G. Guimaraes, H. M. Nussenzveig, “Uniform approximation of Mie resonances,” J. Mod. Opt. 41, 625–647 (1994).
[CrossRef]

Hartmann, I.

Hill, S. C.

Y. L. Pan, S. C. Hill, J. P. Wolf, S. Holler, R. K. Chang, J. R. Bottiger, “Backward-enhanced fluorescence from clusters of microspheres and particles of tryptophan,” Appl. Opt. 41, 2994–2999 (2002).
[CrossRef] [PubMed]

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

S. C. Hill, Y.-L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
[CrossRef] [PubMed]

S. C. Hill, H. I. Saleheen, M. D. Barnes, W. B. Whitten, “Modeling fluorescence collection from single molecules in microspheres: effects of position, orientation, and frequency,” Appl. Opt. 35, 6278–6288 (1996).
[CrossRef] [PubMed]

G. Chen, W. P. Acker, R. K. Chang, S. C. Hill, “Fine structures in the angular distribution of stimulated Raman scattering from single droplets,” Opt. Lett. 16, 117–119 (1991).
[CrossRef] [PubMed]

S. C. Hill, C. K. Rushforth, R. E. Benner, P. R. Conwell, “Sizing dielectric spheres and cylinders by aligning measured and computed resonance locations — algorithm for multiple orders,” Appl. Opt. 24, 2380–2390 (1985).
[CrossRef] [PubMed]

S. C. Hill, R. E. Benner, C. K. Rushfort, P. R. Conwell, “Structural resonances observed in the fluorescence emission from small spheres on substrates,” Appl. Opt. 23, 1680–1683 (1984).
[CrossRef] [PubMed]

Hirst, E.

Hodges, J. T.

Holler, S.

Kaiser, T.

Kaye, P. H.

Kerker, M.

Kiefer, W.

Kifer, W.

Kim, D. H.

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

Kint, S.

J. R. Scherer, M. K. Go, S. Kint, “Raman spectra and structure of water from -10 to 90°,” J. Phys. Chem. 78, 1304–1313 (1974).
[CrossRef]

Kolgotin, A.

V. Griaznov, I. Veselovskii, A. Kolgotin, D. N. Whiteman, “Angle- and size-dependent characteristics of incoherent Raman and fluorescent scattering by microspheres. 1. General expressions,” Appl. Opt. (to be published).

Kratohvil, J. P.

Lankers, M.

Latifi, H.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

Lee, E.-H.

Lee, J. M.

I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, 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, 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, M.-P.

Li, J.

Lin, H. B.

J. D. Eversole, H. B. Lin, A. J. Campillo, “Input-output resonance correlation in laser induced emission from microdroplets,” J. Opt. Soc. Am. B 12, 287–296 (1995).
[CrossRef]

H. B. Lin, A. J. Campillo, “cw nonlinear optics in droplet microcavities displaying enhanced gain,” Phys. Rev. Lett. 73, 2440–2443 (1994).
[CrossRef] [PubMed]

Long, M. B.

Lyons, P. A.

K. Cunningham, P. A. Lyons, “Depolarization ratio studies on liquid water,” J. Chem. Phys. 59, 2132–2139 (1973).
[CrossRef]

McNulty, P. J.

Melfi, S. H.

Musick, J.

Niles, S.

Nussenzveig, H. M.

L. G. Guimaraes, H. M. Nussenzveig, “Uniform approximation of Mie resonances,” J. Mod. Opt. 41, 625–647 (1994).
[CrossRef]

Pan, Y. L.

Pan, Y.-L.

S. C. Hill, Y.-L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
[CrossRef] [PubMed]

Pastel, R.

Pinnick, R. G.

Popp, J.

Roll, G.

Rushfort, C. K.

Rushforth, C. K.

Saleheen, H. I.

Schaschek, K.

Scherer, J. R.

J. R. Scherer, M. K. Go, S. Kint, “Raman spectra and structure of water from -10 to 90°,” J. Phys. Chem. 78, 1304–1313 (1974).
[CrossRef]

Schweiger, G.

R. Vehring, C. L. Aardahl, G. Schweiger, E. J. Davis, “The characterization of fine particles originating from an uncharged aerosol: size dependence and detection limits for Raman analysis,” J. Aerosol. Sci. 29, 1045–1061 (1998).

Schwemmer, G.

Sculley, M.

Shweiger, G.

Stowers, M. A.

M. A. Stowers, S. K. Friedlander, “Chemical characterization of flowing polydisperse aerosols by Raman spectroscopy,” Aerosol Sci. Technol. 36, 48–61 (2002).
[CrossRef]

Struthers, A.

Tang, I. N.

Thurn, R.

Trunck, M.

Trunk, M.

Tzeng, H.-M.

Urlaub, E.

Vehring, R.

R. Vehring, “Linear Raman spectroscopy on aqueous aerosols: influence of nonlinear effects on detection limits,” J. Aerosol. Sci. 29, 65–79 (1998).
[CrossRef]

R. Vehring, C. L. Aardahl, G. Schweiger, E. J. Davis, “The characterization of fine particles originating from an uncharged aerosol: size dependence and detection limits for Raman analysis,” J. Aerosol. Sci. 29, 1045–1061 (1998).

Velesco, N.

Veselovskii, I.

V. Griaznov, I. Veselovskii, A. Kolgotin, D. N. Whiteman, “Angle- and size-dependent characteristics of incoherent Raman and fluorescent scattering by microspheres. 1. General expressions,” Appl. Opt. (to be published).

Veselovskii, I. A.

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

Wall, K. F.

Whiteman, D.

Whiteman, D. N.

D. N. Whiteman, S. H. Melfi, “Cloud liquid water, mean droplet radius, and number density measurements using a Raman lidar,” J. Geophys. Res. 104, 31,411–31,419 (1999).
[CrossRef]

D. N. Whiteman, S. H. Melfi, R. A. Ferrare, “Raman lidar system for measurement of water vapor and aerosols in the Earth’s atmosphere,” Appl. Opt. 31, 3068–3082 (1992).
[CrossRef] [PubMed]

V. Griaznov, I. Veselovskii, A. Kolgotin, D. N. Whiteman, “Angle- and size-dependent characteristics of incoherent Raman and fluorescent scattering by microspheres. 1. General expressions,” Appl. Opt. (to be published).

Whitten, W. B.

Wolf, J. P.

Aerosol Sci. Technol. (1)

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[CrossRef]

S. C. Hill, R. G. Pinnick, S. Niles, N. F. Fell, Y. L. Pan, J. Bottiger, B. V. Bronk, S. Holler, R. K. Chang, “Fluorescence from airborne microparticles: dependence on size, concentration of fluorophores, and illumination intensity,” Appl. Opt. 40, 3005–3013 (2001).
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R. Thurn, W. Kiefer, “Structural resonances observed in the Raman spectra of optically levitated liquid droplets,” Appl. Opt. 24, 1515–1519 (1985).
[CrossRef] [PubMed]

J. Popp, M. Lankers, K. Schaschek, W. Kifer, J. T. Hodges, “Observation of sudden temperature jumps in optically levitated microdroplets due to morphology-dependent input resonances,” Appl. Opt. 34, 2380–2386 (1995).
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T. Kaiser, G. Roll, G. Shweiger, “Investigation of coated droplets in an optical trap: Raman-scattering, elastic-light-scattering and evaporation characteristics,” Appl. Opt. 35, 5918–5924 (1996).
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Appl. Phys. B (2)

I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, J. M. Lee, “Raman lidar for the study of liquid water and water vapor in troposphere,” Appl. Phys. B 71, 113–117 (2000).
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I. A. Veselovskii, H. K. Cha, D. H. Kim, S. C. Choi, 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).
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Appl. Spectrosc. (4)

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J. Chem. Phys. (1)

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J. Geophys. Res. (1)

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J. Mod. Opt. (1)

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[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (2)

J. Phys. Chem. (1)

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[CrossRef]

Opt. Lett. (2)

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[CrossRef]

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Phys. Rev. Lett. (2)

S. C. Hill, Y.-L. Pan, S. Holler, R. K. Chang, “Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities,” Phys. Rev. Lett. 85, 54–57 (2000).
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Other (1)

V. Griaznov, I. Veselovskii, A. Kolgotin, D. N. Whiteman, “Angle- and size-dependent characteristics of incoherent Raman and fluorescent scattering by microspheres. 1. General expressions,” Appl. Opt. (to be published).

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Figures (9)

Fig. 1
Fig. 1

Comparison of angular distribution of scattered field components for incoherent Raman and Mie scattering. The calculations were performed for size x = 20; angular step Δθ = 2°; refractive index n 1 = 1.5; and ratio λ/λ0 = 1.196.

Fig. 2
Fig. 2

Components H H and V V and their depolarizations V H /H H and H V /V V as functions of scattering angle for sizes x = 0.2, 1, 2, 15, 20. Refractive index, n 1 = 1.5; λ/λ0 = 1.196.

Fig. 3
Fig. 3

Normalized components V v and H H versus size at scattering angles 180° and 90°. Calculations were performed for n 1 = 1.5 and n = 1.33 in steps of Δx = 0.005. The results are smoothed over interval Δx sm = 0.05.

Fig. 4
Fig. 4

Depolarization of components V V and H H for scattering at 90° and 180° angles. Calculations were performed for n 1 = 1.5 and n = 1.33 in steps of Δx = .005. The results are smoothed over interval Δx sm = 0.05.

Fig. 5
Fig. 5

Normalized volume-averaged source function, inelastic backscattering, and depolarization, all relative to input size parameter. Refractive index, n 1 = 1.33; wavelength shift, λ/λ0 = 1.1; calculation increment, Δx = 0.0001.

Fig. 6
Fig. 6

Normalized inelastic scattering at (a) 180° and 90° observation angles for (b) vertical and (c) horizontal orientation of incident wave polarization. Refractive index, n 1 = 1.33; wavelength shift, λ/λ0 = 1.1; calculation increment, Δx = 0.0001.

Fig. 7
Fig. 7

Depolarization of radiation scattered at 90° for (a) vertical and (b) horizontal orientation of incident wave polarization. Refractive index, n 1 = 1.33; wavelength shift, λ/λ0 = 1.1; calculation increment, Δx = 0.0001.

Fig. 8
Fig. 8

Angular distribution of components V V and H H for the input size parameters that correspond to the (a) out-of-resonance value and to resonances (b) TM1 71 and (c) TE2 67. Calculations were performed in angular increments of Δθ = 0.5°, and n 1 = 1.33.

Fig. 9
Fig. 9

Dependence of normalized Raman backscatter and depolarization on input size parameter. Calculations were performed in steps of Δx = 0.05 for refractive index n 1 = 1.33, θ = 180°, and λ/λ0 = 1.1. The results for depolarization are smoothed over interval Δx av = 0.5.

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