Abstract

A plane-polarized laser wave with a wavelength of 441.6nm illuminates a cladding optical fiber with a diameter of about 18to38μm at normal incidence. A measured angular distribution of the intensity of the scattered wave corresponds well with the differential cross section of a rigorous theoretical calculation of a coaxial double cylinder over a wide range of scattering angle. The diameter and refractive index of the cladding and core of the illuminated part of a fiber have been determined accurately for each uncertainty.

© 2009 Optical Society of America

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References

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  1. T. Sonobe, N. Hiroi, M. Takenaka, Y. Nakano, and H. Fujita, “OPLEAF fiber array for high density optical IC,” Trans .Inst. Electr. Eng. E 126, 255-260 (2006).
    [CrossRef]
  2. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), Sec. 6.2.
  3. A. W. Adey, “Scattering of electromagnetic waves by coaxial cylinders,” Can. J. Phys. 34, 510-520 (1956).
    [CrossRef]
  4. C. C. H. Tang, “Backscattering from dielectric-coated infinite cylindrical obstacles,” J. Appl. Phys. 28, 628-633 (1957).
    [CrossRef]
  5. L. S. Watkins, “Scattering from side-illuminated cladding glass fibers for determination of fiber parameters,” J. Opt. Soc. Am. 64, 767-772 (1974).
    [CrossRef]
  6. G. R. Cunnington Jr., T. W. Tong, and P. S. Swathi, “Angular scattering of radiation from coated cylindrical fibers,” J. Quant. Spectrosc. Radiat. Transf. 48, 353-362 (1992).
    [CrossRef]
  7. F. Tajima and Y. Nishiyama,“Light scattering from a birefringent cylinder, spider silk, slimmer than the wavelength approaches dipole radiation,” J. Opt. Soc. Am. A 22, 1127-1131 (2005).
    [CrossRef]
  8. F. Tajima and Y. Nishiyama, “Multiple scattering effect in the Young-like interference pattern of an optical wave scattered by a double cylinder,” Opt. Rev. 15, 75-83 (2008).
    [CrossRef]

2008

F. Tajima and Y. Nishiyama, “Multiple scattering effect in the Young-like interference pattern of an optical wave scattered by a double cylinder,” Opt. Rev. 15, 75-83 (2008).
[CrossRef]

2006

T. Sonobe, N. Hiroi, M. Takenaka, Y. Nakano, and H. Fujita, “OPLEAF fiber array for high density optical IC,” Trans .Inst. Electr. Eng. E 126, 255-260 (2006).
[CrossRef]

2005

1992

G. R. Cunnington Jr., T. W. Tong, and P. S. Swathi, “Angular scattering of radiation from coated cylindrical fibers,” J. Quant. Spectrosc. Radiat. Transf. 48, 353-362 (1992).
[CrossRef]

1974

1957

C. C. H. Tang, “Backscattering from dielectric-coated infinite cylindrical obstacles,” J. Appl. Phys. 28, 628-633 (1957).
[CrossRef]

1956

A. W. Adey, “Scattering of electromagnetic waves by coaxial cylinders,” Can. J. Phys. 34, 510-520 (1956).
[CrossRef]

Adey, A. W.

A. W. Adey, “Scattering of electromagnetic waves by coaxial cylinders,” Can. J. Phys. 34, 510-520 (1956).
[CrossRef]

Cunnington, G. R.

G. R. Cunnington Jr., T. W. Tong, and P. S. Swathi, “Angular scattering of radiation from coated cylindrical fibers,” J. Quant. Spectrosc. Radiat. Transf. 48, 353-362 (1992).
[CrossRef]

Fujita, H.

T. Sonobe, N. Hiroi, M. Takenaka, Y. Nakano, and H. Fujita, “OPLEAF fiber array for high density optical IC,” Trans .Inst. Electr. Eng. E 126, 255-260 (2006).
[CrossRef]

Hiroi, N.

T. Sonobe, N. Hiroi, M. Takenaka, Y. Nakano, and H. Fujita, “OPLEAF fiber array for high density optical IC,” Trans .Inst. Electr. Eng. E 126, 255-260 (2006).
[CrossRef]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), Sec. 6.2.

Nakano, Y.

T. Sonobe, N. Hiroi, M. Takenaka, Y. Nakano, and H. Fujita, “OPLEAF fiber array for high density optical IC,” Trans .Inst. Electr. Eng. E 126, 255-260 (2006).
[CrossRef]

Nishiyama, Y.

F. Tajima and Y. Nishiyama, “Multiple scattering effect in the Young-like interference pattern of an optical wave scattered by a double cylinder,” Opt. Rev. 15, 75-83 (2008).
[CrossRef]

F. Tajima and Y. Nishiyama,“Light scattering from a birefringent cylinder, spider silk, slimmer than the wavelength approaches dipole radiation,” J. Opt. Soc. Am. A 22, 1127-1131 (2005).
[CrossRef]

Sonobe, T.

T. Sonobe, N. Hiroi, M. Takenaka, Y. Nakano, and H. Fujita, “OPLEAF fiber array for high density optical IC,” Trans .Inst. Electr. Eng. E 126, 255-260 (2006).
[CrossRef]

Swathi, P. S.

G. R. Cunnington Jr., T. W. Tong, and P. S. Swathi, “Angular scattering of radiation from coated cylindrical fibers,” J. Quant. Spectrosc. Radiat. Transf. 48, 353-362 (1992).
[CrossRef]

Tajima, F.

F. Tajima and Y. Nishiyama, “Multiple scattering effect in the Young-like interference pattern of an optical wave scattered by a double cylinder,” Opt. Rev. 15, 75-83 (2008).
[CrossRef]

F. Tajima and Y. Nishiyama,“Light scattering from a birefringent cylinder, spider silk, slimmer than the wavelength approaches dipole radiation,” J. Opt. Soc. Am. A 22, 1127-1131 (2005).
[CrossRef]

Takenaka, M.

T. Sonobe, N. Hiroi, M. Takenaka, Y. Nakano, and H. Fujita, “OPLEAF fiber array for high density optical IC,” Trans .Inst. Electr. Eng. E 126, 255-260 (2006).
[CrossRef]

Tang, C. C. H.

C. C. H. Tang, “Backscattering from dielectric-coated infinite cylindrical obstacles,” J. Appl. Phys. 28, 628-633 (1957).
[CrossRef]

Tong, T. W.

G. R. Cunnington Jr., T. W. Tong, and P. S. Swathi, “Angular scattering of radiation from coated cylindrical fibers,” J. Quant. Spectrosc. Radiat. Transf. 48, 353-362 (1992).
[CrossRef]

Watkins, L. S.

Can. J. Phys.

A. W. Adey, “Scattering of electromagnetic waves by coaxial cylinders,” Can. J. Phys. 34, 510-520 (1956).
[CrossRef]

J. Appl. Phys.

C. C. H. Tang, “Backscattering from dielectric-coated infinite cylindrical obstacles,” J. Appl. Phys. 28, 628-633 (1957).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transf.

G. R. Cunnington Jr., T. W. Tong, and P. S. Swathi, “Angular scattering of radiation from coated cylindrical fibers,” J. Quant. Spectrosc. Radiat. Transf. 48, 353-362 (1992).
[CrossRef]

Opt. Rev.

F. Tajima and Y. Nishiyama, “Multiple scattering effect in the Young-like interference pattern of an optical wave scattered by a double cylinder,” Opt. Rev. 15, 75-83 (2008).
[CrossRef]

Trans .Inst. Electr. Eng. E

T. Sonobe, N. Hiroi, M. Takenaka, Y. Nakano, and H. Fujita, “OPLEAF fiber array for high density optical IC,” Trans .Inst. Electr. Eng. E 126, 255-260 (2006).
[CrossRef]

Other

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), Sec. 6.2.

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the system.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

Photograph of sample (A).

Fig. 4
Fig. 4

Angular distribution of scattering intensity for E from (a) 4 to 40, (b) 40 to 80, (c) 80 to 120, and (d) 120 to 154  deg . Circles are measured data. Solid lines show the optimum theoretical curves.

Fig. 5
Fig. 5

Same as Fig. 4 for E .

Tables (1)

Tables Icon

Table 1 Optimum Values of n 1 , 2 or n 1 , 2 and D 1 , 2 , Their Uncertainties, and Uncertainty Indices

Equations (14)

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E inn ( r , ϕ ) = m = 0 i m J m ( n 2 k r ) A ( m ) cos ( m ϕ ) ,
E ann ( r , ϕ ) = m = 0 i m [ E 1 ( m ) H m ( 1 ) ( n 1 k r ) + E 2 ( m ) H m ( 2 ) ( n 2 k r ) ] cos ( m ϕ ) ,
E out ( r , ϕ ) = m = 0 i m [ ( 2 δ m 0 ) J m ( k r ) + B ( m ) H m ( 1 ) ( k r ) ] cos ( m ϕ ) ,
A ( m ) J m ( n 2 k r 20 ) = E 1 ( m ) H m ( 1 ) ( n 1 k r 20 ) + E 2 ( m ) H m ( 2 ) ( n 1 k r 20 ) ,
n 2 A ( m ) J m ( n 2 k r 20 ) = n 1 [ E 1 ( m ) H m ( 1 ) ( n 1 k r 20 ) + E 2 ( m ) H m ( 2 ) ( n 1 k r 20 ) ] ,
E 1 ( m ) H m ( 1 ) ( n 1 k r 10 ) + E 2 ( m ) H m ( 2 ) ( n 1 k r 10 ) = ( 2 δ m 0 ) J m ( k r 10 ) + B ( m ) H m ( 1 ) ( k r 10 ) ,
n 1 [ E 1 ( m ) H m ( 1 ) ( n 1 k r 10 ) + E 2 ( m ) H m ( 2 ) ( n 1 k r 10 ) ] = ( 2 δ m 0 ) J m ( k r 10 ) + B ( m ) H m ( 1 ) ( k r 10 ) .
E sct ( r , ϕ ) = m = 0 i m B ( m ) H m ( 1 ) ( k r ) cos ( m ϕ ) 2 π k r e i { k r ( π 4 ) } m = 0 ( 1 ) m B ( m ) cos ( m ϕ ) = 2 π k r e i { k r ( π 4 ) } m = 0 B ( m ) cos ( m θ sc )
σ ( θ sc ) = 2 π k | m = 0 B ( m ) cos ( m θ sc ) | 2 ,
B ( m ) = J m ( k r 10 ) c 1 ( m ) + J m ( k r 10 ) c 2 ( m ) H m ( 1 ) ( k r 10 ) c 1 ( m ) H m ( 1 ) ( k r 10 ) c 2 ( m ) ( 2 δ m 0 ) .
( c 1 ( m ) c 2 ( m ) ) = ( H m ( 1 ) ( n 1 k r 10 ) H m ( 2 ) ( n 1 k r 10 ) n 1 H m ( 1 ) ( n 1 k r 10 ) n 1 H m ( 2 ) ( n 1 k r 10 ) ) × ( n 1 H m ( 2 ) ( n 1 k r 20 ) H m ( 2 ) ( n 1 k r 20 ) n 1 H m ( 1 ) ( n 1 k r 20 ) H m ( 1 ) ( n 1 k r 20 ) ) ( J m ( n 2 k r 20 ) n 2 J m ( n 2 k r 20 ) ) .
U I ( n 1 , D 1 , n 2 , D 2 ) = { i [ I i I 0 σ α ( θ i ) ] 2 N } 1 2 ( i I i N ) .
I i opt = I 0 opt σ α ( θ i ; n 1 opt , , D 2 opt ) ,
U I opt ( n 1 u , D 1 u , n 2 u , D 2 u ) = U I min .

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