Abstract

The EM field enhancement in the forward direction of a dielectric sphere was derived leading to high-energy density in a critical ring region where, experimentally, the nonlinear processes are observed for small liquid droplets.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. B. Snow, S.-X. Qian, R. K. Chang, “Stimulated Raman Scattering from Individual Water and Ethanol Droplets at Morphology-Dependent Resonances,” Opt. Lett. 10, 37–39 (1985).
    [CrossRef] [PubMed]
  2. S.-X. Qian, R. K. Chang, “Multiorder Stokes Emission from Micrometer-Size Droplets,” Phys. Rev. Lett. 56, 926–929 (1986).
    [CrossRef] [PubMed]
  3. P. Chylek, M. A. Jarzembski, N. Y. Chou, R. G. Pinnick, “Effect of Size and Material of Liquid Spherical Particles on Laser-Induced Breakdown,” Appl. Phys. Lett. 49, 1475–1477 (1986).
    [CrossRef]
  4. P. Chylek, M. A. Jarzembski, V. Srivastava, R. G. Pinnick, J. D. Pendleton, J. P. Cruncleton, “Effect of Spherical Particles on Laser-Induced Breakdown of Gases,” Appl. Opt. 26, 760–762 (1987).
    [CrossRef] [PubMed]
  5. R. G. Pinnick et al., “Aerosol-Induced Laser Breakdown Thresholds: Wavelength Dependence,” Appl. Opt. 27, 987–996 (1988).
    [CrossRef] [PubMed]
  6. R. K. Chang, J. H. Eickmans, W.-F. Hsieh, C. F. Wood, J.-Z. Zhang, J. Zheng, “Laser-Induced Breakdown in Large Transparent Water Droplets,” Appl. Opt. 27, 2377–2385 (1988).
    [CrossRef] [PubMed]
  7. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 204.

1988

1987

1986

S.-X. Qian, R. K. Chang, “Multiorder Stokes Emission from Micrometer-Size Droplets,” Phys. Rev. Lett. 56, 926–929 (1986).
[CrossRef] [PubMed]

P. Chylek, M. A. Jarzembski, N. Y. Chou, R. G. Pinnick, “Effect of Size and Material of Liquid Spherical Particles on Laser-Induced Breakdown,” Appl. Phys. Lett. 49, 1475–1477 (1986).
[CrossRef]

1985

Chang, R. K.

Chou, N. Y.

P. Chylek, M. A. Jarzembski, N. Y. Chou, R. G. Pinnick, “Effect of Size and Material of Liquid Spherical Particles on Laser-Induced Breakdown,” Appl. Phys. Lett. 49, 1475–1477 (1986).
[CrossRef]

Chylek, P.

P. Chylek, M. A. Jarzembski, V. Srivastava, R. G. Pinnick, J. D. Pendleton, J. P. Cruncleton, “Effect of Spherical Particles on Laser-Induced Breakdown of Gases,” Appl. Opt. 26, 760–762 (1987).
[CrossRef] [PubMed]

P. Chylek, M. A. Jarzembski, N. Y. Chou, R. G. Pinnick, “Effect of Size and Material of Liquid Spherical Particles on Laser-Induced Breakdown,” Appl. Phys. Lett. 49, 1475–1477 (1986).
[CrossRef]

Cruncleton, J. P.

Eickmans, J. H.

Hsieh, W.-F.

Jarzembski, M. A.

P. Chylek, M. A. Jarzembski, V. Srivastava, R. G. Pinnick, J. D. Pendleton, J. P. Cruncleton, “Effect of Spherical Particles on Laser-Induced Breakdown of Gases,” Appl. Opt. 26, 760–762 (1987).
[CrossRef] [PubMed]

P. Chylek, M. A. Jarzembski, N. Y. Chou, R. G. Pinnick, “Effect of Size and Material of Liquid Spherical Particles on Laser-Induced Breakdown,” Appl. Phys. Lett. 49, 1475–1477 (1986).
[CrossRef]

Pendleton, J. D.

Pinnick, R. G.

Qian, S.-X.

Snow, J. B.

Srivastava, V.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 204.

Wood, C. F.

Zhang, J.-Z.

Zheng, J.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Schematic of a sphere illuminated by an uniform electromagnetic field (a) creating a high energy density in the forward direction in the region at critical angle θc due to the refraction of rays around the critical incident angle ϕcϕi=1 [Eq. (2)]. (b) Part of the energy incident on the shaded ring region on the illuminated side of the sphere is reflected away. The transmitted energy is mapped into a smaller shaded ring region in the forward direction giving an enhancement of the fields S [Eqs. (8) and (12)]. (δϕ,δθ correspond to infinitesimal divisions; ϕii correspond to discrete divisions.)

Fig. 2
Fig. 2

Electromagnetic field enhancement S(m, ϕ) shown as a function of θ [Eq. (1)] for increasing the number of areal subdivisions of the sphere from (a) to (c) for a discrete case [Eq. (12)] and (d) for infinitesimal divisions [Eq. (8)]. Decreasing the fraction fi from 1.0 to infinitesimal δf increases the resolution showing the dramatic increase of field enhancement for the critical ring region located at the critical refracted angle θc.

Fig. 3
Fig. 3

Experimental setup (a) used to observe visually the critical ring located at the critical refracted angle θc; (b) an ∼120-μm diam water droplet showing SRS on the inner critical ring at θc, which has not been detected before, we believe. The SRS observed at the periphery of the droplet corresponds to the structural resonances.1,2,5

Fig. 4
Fig. 4

Interaction of a ∼120-μm diam water droplet and laser beam [same setup as shown in Fig. 3(a)] as a function of increasing laser power. In the forward direction of the droplet, the SRS occurs at regions of high electromagnetic field intensity on the well defined inner critical ring (a)–(d). At the breakdown threshold (e) and above the threshold (f), the breakdown originates from this ring. The SRS and the laser-induced breakdown is not observed along the axis of the droplet at the threshold levels.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

θ i = 180 ° 2 sin 1 [ 1 ( sin ϕ i / m ) 2 ] 1 / 2 ϕ i .
ϕ c = sin 1 [ ( 4 m 2 ) / 3 ] 1 / 2 ,
δ A = 2 π a 2 sin ϕ δ ϕ
δ A = 2 π a 2 sin θ δ θ .
F 0 = E 0 δ f / cos ϕ δ A .
F = T E 0 δ f / [ 1 ( sin ϕ / m ) 2 ] 1 / 2 δ A .
S ( m , ϕ ) = { T sin ϕ cos ϕ / [ 1 ( sin ϕ / m ) 2 ] 1 / 2 } × | δ ϕ / δ ( cos θ ) | .
S ( m , ϕ ) = T m 3 μ / { ( m 2 + μ 2 1 ) 1 / 2 | 6 μ 2 + m 2 2 + [ ( 4 μ m 2 + 6 μ 6 μ 3 ) / ( m 2 + μ 2 1 ) 1 / 2 ] | } ,
A i = π a 2 | sin 2 ϕ i + 1 sin 2 ϕ i |
F 0 = E 0 f i / A i ,
F i = T i E 0 f i / A i ,
S ( m , ϕ i ) = T i ( A i / A i ) .

Metrics