Abstract

The fabrication of narrowband highly reflecting filters in single-mode step-index fibers was reported recently by Hill et al. [ Appl. Phys. Lett. 32, 647 ( 1978)]. The underlying effect on which these filters are based is a photoinduced refractive-index change in the GeO2 used as a core dopant SiO2 fibers. A study is reported aimed at the characterization of such optical fiber filters. A theoretical model is developed, and relevant fiber parameters are determined through intercomparison with experiment. In this way, both the magnitude of the photoinduced index change and its dependence on the writing power coupled into the fiber are determined.

© 1981 Optical Society of America

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References

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  1. K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
    [CrossRef]
  2. A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
    [CrossRef]
  3. D. Marcuse, Bell Syst. Tech. J. 52, 817 (1973).
  4. A. Yariv, M. Nawkamura, IEEE J. Quantum Electron. QE-13, 233 (1977).
    [CrossRef]
  5. B. S. Kawasaki, K. O. Hill, D. C. Johnson, Y. Fujii, Opt. Lett. 3, 66 (1978).
    [CrossRef] [PubMed]
  6. Yoshi Fujii, Canadian Communication Research Centre; private communication.
  7. A. M. Glass, Opt. Eng. 17, 470 (1978).
    [CrossRef]

1978 (3)

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[CrossRef]

A. M. Glass, Opt. Eng. 17, 470 (1978).
[CrossRef]

B. S. Kawasaki, K. O. Hill, D. C. Johnson, Y. Fujii, Opt. Lett. 3, 66 (1978).
[CrossRef] [PubMed]

1977 (1)

A. Yariv, M. Nawkamura, IEEE J. Quantum Electron. QE-13, 233 (1977).
[CrossRef]

1973 (2)

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

D. Marcuse, Bell Syst. Tech. J. 52, 817 (1973).

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[CrossRef]

B. S. Kawasaki, K. O. Hill, D. C. Johnson, Y. Fujii, Opt. Lett. 3, 66 (1978).
[CrossRef] [PubMed]

Fujii, Yoshi

Yoshi Fujii, Canadian Communication Research Centre; private communication.

Glass, A. M.

A. M. Glass, Opt. Eng. 17, 470 (1978).
[CrossRef]

Hill, K. O.

B. S. Kawasaki, K. O. Hill, D. C. Johnson, Y. Fujii, Opt. Lett. 3, 66 (1978).
[CrossRef] [PubMed]

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[CrossRef]

Johnson, D. C.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[CrossRef]

B. S. Kawasaki, K. O. Hill, D. C. Johnson, Y. Fujii, Opt. Lett. 3, 66 (1978).
[CrossRef] [PubMed]

Kawasaki, B. S.

B. S. Kawasaki, K. O. Hill, D. C. Johnson, Y. Fujii, Opt. Lett. 3, 66 (1978).
[CrossRef] [PubMed]

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[CrossRef]

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 52, 817 (1973).

Nawkamura, M.

A. Yariv, M. Nawkamura, IEEE J. Quantum Electron. QE-13, 233 (1977).
[CrossRef]

Yariv, A.

A. Yariv, M. Nawkamura, IEEE J. Quantum Electron. QE-13, 233 (1977).
[CrossRef]

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

Appl. Phys. Lett. (1)

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[CrossRef]

Bell Syst. Tech. J. (1)

D. Marcuse, Bell Syst. Tech. J. 52, 817 (1973).

IEEE J. Quantum Electron. (2)

A. Yariv, M. Nawkamura, IEEE J. Quantum Electron. QE-13, 233 (1977).
[CrossRef]

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

Opt. Eng. (1)

A. M. Glass, Opt. Eng. 17, 470 (1978).
[CrossRef]

Opt. Lett. (1)

Other (1)

Yoshi Fujii, Canadian Communication Research Centre; private communication.

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Figures (10)

Fig. 1
Fig. 1

Theoretical reflectance as a function of the filter length at Bragg wavelength (λc) for different values of induced index perturbation (Δ). Curves A, B, and C correspond to Δ of 3.0 × 10−4, 2.0 × 10−4, and 1.0 × 10−4, respectively, and have effective cutoff length (Lcutoff) of 0.376,0.565, and 1.129 cm, respectively.

Fig. 2
Fig. 2

Theoretical effective cutoff length of optical fiber filters as a function of the induced index perturbation.

Fig. 3
Fig. 3

Theoretical spectral bandwidth of the optical fiber filters as a function of the induced index perturbation.

Fig. 4
Fig. 4

Schematic of the apparatus for the fabrication of optical fiber filters. The argon laser is oscillating on a single longitudinal mode at 0.5145 μm with 1 W of output power. The 50× microscope objective and the quartz clamp are mounted on a micropositioner and a piezoelectric micropositioner, respectively. The fiber is allowed to hang loose between the input and output ends without any stretching.

Fig. 5
Fig. 5

Schematic of the apparatus for scanning the optical fiber filters. The source is a 50-W projection lamp. Both the microscope objective and input end V-groove magnetic mount (VGMM) are mounted on micropositioners. The output end VGMM is mounted on a piezoelectric micropositioner, which is itself mounted on a two-stage rotationer. Entrance and exit slits of the 0.5-m monochromator are set at 10 μm, and the photomultiplier (PM) tube is running at 1 kv with an effective impedance of 1 MΩ.

Fig. 6
Fig. 6

Comparison between experimental and theoretical curves of reflectance as a function of the filter length for a WP of 50 mW.

Fig. 7
Fig. 7

Effective cutoff length of the filters as a function of the WP measured in the experiments.

Fig. 8
Fig. 8

Induced index perturbation Δ vs the WP using both sets of experimental data.

Fig. 9
Fig. 9

Spectral bandwidth of the filter as a function of the WP (using both sets of experimental data).

Fig. 10
Fig. 10

Induced index perturbation Δ vs the square of the WP using both sets of experimental data.

Equations (12)

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R ( L , λ ) = Ω 2 sinh 2 ( S L ) Δ β 2 sinh 2 ( S L ) + S 2 cosh 2 ( S L ) for Ω 2 > Δ β 2 , = Ω 2 sin 2 ( Q L ) Δ β 2 - Ω 2 cos 2 ( Q L ) for Ω 2 < Δ β 2 ,
2 ψ r 2 + 1 r ψ r + 1 r 2 2 ψ ϕ 2 + 2 ψ z 2 + n i 2 k 2 = 0 ,
ψ ( r , ϕ , z , t ) = F ( r ) cos ( ν ϕ ) exp [ i ( w t - β z ) ] ,
( z ) = [ n 0 2 + Δ cos ( θ z ) ] in core region , = n 0 2 in cladding region ,
E = ν = 1 N a ν E v , H = ν = 1 N b ν H v ,
d C μ + d z = Ω i C μ - exp ( i 2 Δ β z ) ,
d C μ - d z = Ω i C μ + exp ( - i 2 Δ β z ) ,
a μ + = b μ + , a μ - = - b μ - , c μ + = a μ + exp ( i β μ z ) , c μ - = a μ - exp ( - i β μ z ) , β μ = eigen propagation constant , Δ β = β μ - ( π / Λ ) ,
Ω = ( Δ ω 0 8 P ) 0 a 0 2 π E ν 2 r d r d ϕ ,
C + ( z ) = - exp ( i Δ β z ) [ Δ β sinh ( S L ) - i S cosh ( S L ) ] { Δ β sinh [ S ( z - L ) ] + i S cosh [ S ( z - L ) ] } ,
C - ( z ) = Ω exp ( - i Δ β z ) [ sinh ( S L ) - i S cosh ( S L ) ] sinh [ S ( z - L ) ] ,
R ( λ , L ) = | C - ( 0 ) C + ( 0 ) | 2 T ( λ , L ) = | C + ( L ) C + ( 0 ) | 2 .

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