Abstract

A new type of gratings superposed spatially in laterally separated areas of the guide is introduced and analyzed using coupled-mode theory. The guided mode overlaps the constituent gratings and sees the superposition of them. Also, special characteristics that the structure might synthesize are considered, including one example where a phase-only sampled split grating provides zero response for out-of-band channels. A conventional grating requires both phase- and amplitude- sampling for zero out-of-band channels. The split grating, however, requires alignment of the constituent gratings in addition to requirements on the accuracy of the amplitude and pitch structures.

© 2005 Optical Society of America

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References

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Electron. Lett.

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972-1974 (1994).
[CrossRef]

M. G. Xu, J. L. Archambault, L. Reekie, and J. P. Dakin, “Discrimination between strain and temperature effects using dual-wavelength fibre grating sensors,” Electron. Lett. 30, 1085-1087 (1994).
[CrossRef]

S. A. Hetzel, A. Bateman, and J. P. McGeehan, “LINC Transmitter,” Electron. Lett. 27, 844-846 (1991).
[CrossRef]

IEEE J. Quantum Electron.

A. V. Buryak, K. Y. Kolossovski, and D. Yu. Stepanov, “Optimization of Refractive Index Sampling for Multichannel Fiber Bragg Gratings,” IEEE J. Quantum Electron. 39, 91-98 (2003).
[CrossRef]

IEEE Photon. Technol. Lett.

K. Zhou, A. G. Simpson, X. Chen, L. Zhang, and I. Bennion, “Fiber Bragg Grating Sensor Interrogation System Using a CCD Side Detection Method With Superimposed Blazed Gratings,” IEEE Photon. Technol. Lett. 16, 1549-1551 (2004).
[CrossRef]

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled Fiber Grating Based-Dispersion Slope Compensator ,” IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

J.E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R.B. Wilcox, and J. Zweiback, “Dammann Fiber Bragg Gratings and Phase-Only Sampling for High Channel Counts,” IEEE Photon. Technol. Lett. 14, 1309-1311 (2002).
[CrossRef]

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-Sampled Fiber Bragg Gratings for Identical Multiple Wavelength Operation,” IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Proc. Optical Fiber Communication Conf.

Y. Painchaud,A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensation,” in Proc. Optical Fiber Communication Conference (Optical Society of America, Washington, DC, 2002) paper ThAA5.

Other

A. Martinez, M. Dubov, I. Y. Khrushchev, I. Bennion, “Femtosecond Inscription of Superimposed, Non-Overlapping Fibre Bragg Gratings,” presented at the 30th European Conference on Optical Communication, Stockholm, Sweden, 5-9 Sept. 2004, <a href="http://www.aston.ac.uk/~khrushci/Research/ECOC_04_FBG.pdf.">http://www.aston.ac.uk/~khrushci/Research/ECOC_04_FBG.pdf.</a>

A. Safaai-Jazi and T. L. Gradishar, “Gratings with Independently Apodized Layers,” presented at the Southeast Regional Meeting on Optoelectronics, Photonics, and Imaging, Charlotte, North Carolina, 18-19 Sept. 2000.

M. Guy, “Recent Advances in Fiber Bragg Grating Technology Enable Cost-Effective Fabrication of High-Performance Optical Components,” Physics in Canada 60, 2004.

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Figures (3)

Fig. 1.
Fig. 1.

Slab waveguide written with spatially superposed gratings.

Fig. 2.
Fig. 2.

Sampling functions of unsplit and equivalent split gratings. Sampling function s(z)=a(z)exp[(z)] of the unsplit grating. (a) Amplitude a(z) and (b) normalized phase ϕ(z)/2π. Sampling functions of the split grating. (c) Normalized phase in the volume y<b/2 and (d) in y>b/2. (e) Nine channel reflectivity response.

Fig. 3.
Fig. 3.

Sampling functions of an unsplit grating and equivalent split grating. For the unsplit grating (a) the pure-real sampling function. For the split grating (b) profile of the index change (red curve) and index change itself (blue curve) in the volume y<b/2 versus position along the grating (four sampling periods are shown.) (c) Profile and index change in the volume y>b/2. (d) Four channel reflectivity response.

Equations (33)

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n ( x , y ) = { n 1 a < x < 0 , 0 < y < b n 2 otherwise
n ( x , y , z ) = n ( x , y ) + Δ n ( x , y , z )
Δ n ( x , y , z ) = f ri ( z ) [ 1 + cos ( 2 π z Λ + ϕ ri ( z ) ) ]
for a < x < 0 and ( i 1 ) b 4 < y < i b 4 ; i = 1 , 2 , 3 , 4 .
d ψ 1 dz = j ( ψ 1 C 11 + ψ 2 e j 2 β z C 12 )
d ψ 2 dz = j ( ψ 2 C 22 + ψ 1 e j 2 β z C 21 )
C km ( z ) = ω ε 0 4 sgn ( β k ) S ( n 2 n 2 ) e k * · e m ds
n 2 n 2 2 n ( x , y ) Δ n ( x , y , z ) , Δ n ( x , y , z ) n ( x , y )
C 11 ( z ) = σ ( z ) + exp ( j 2 π z Λ ) K SA ( z ) + exp ( j 2 π z Λ ) K SA * ( z )
K SA ( z ) = i = 1 4 K ri ( z ) exp [ j ϕ ri ( z ) ]
σ ( z ) = 2 i = 1 4 K ri ( z )
K ri ( z ) = ω ε o n 1 4 f ri ( z ) b i b i + 1 a 0 e 1 * · e 1 dxdy
C 21 ( z ) C 22 ( z ) C 11 ( z ) C 12 ( z )
Δ n ( x , y , z ) = f ri ( z ) cos ( 2 π z Λ + ϕ ri ( z ) ) + Δ n dci
for a < x < 0 and ( i 1 ) b 4 < y < i b 4 ; i = 1 , 2 , 3 , 4 .
σ ( z ) = ω ε o n 1 2 i = 1 4 Δ n dci b i b i + 1 a 0 e 1 * · e 1 dxdy
d ψ 1 ( z ) dz = j ψ 1 ( z ) σ ( z ) + j ψ 2 ( z ) exp [ j ( 2 β z 2 π z Λ ) ] K SA ( z )
d ψ 2 ( z ) dz = j ψ 2 ( z ) σ ( z ) j ψ 1 ( z ) exp [ j ( 2 β z 2 π z Λ ) ] K S A * ( z )
Δ n u a c ( z ) = f u ( z ) cos ( 2 π z Λ u + ϕ u ( z ) ) = 0.5 Σ i = 1 2 f ri ( z ) cos ( 2 π z Λ + ϕ ri ( z ) )
K SA ( z ) = ω ε o n 1 4 f u ( z ) exp [ j ϕ u ( z ) ] 0 b a 0 e 1 * · e 1 dxdy
s ( z ) = m = 4 4 exp ( j ϕ m ) exp ( j 2 m π z P )
ϕ m = [ 5 π 3 , π , π 3 , 0 , 0 , 0 , π 3 , π , 5 π 3 ] .
Δ n ( z ) = Re { f ( z ) exp [ j ( 2 π z Λ u + ϕ g ( z ) ) ] s ( z ) }
s 1 ( z ) = A 2 exp [ j ( ϕ ( z ) cos 1 ( a ( z ) A ) ) ] for the volume y < b / 2
s 2 ( z ) = A 2 exp [ j ( ϕ ( z ) + cos 1 ( a ( z ) A ) ) ] for the volume y > b / 2
Δ n 1 ( z ) = 2 Re { f ( z ) exp [ j ( 2 π z Λ + ϕ g ( z ) ) ] s 1 ( z ) } for the volume y < b / 2
Δ n 2 ( z ) = 2 Re { f ( z ) exp [ j ( 2 π z Λ + ϕ g ( z ) ) ] s 2 ( z ) } for the volume y > b / 2
s ( z ) = m = 1 4 exp ( j ϕ m ) exp ( j 2 ( 2 m 5 ) π z P )
ϕ 1 = ϕ 4 , ϕ 2 = ϕ 3
s 1 ( z ) = 3.08 + s ( z ) for the volume y < b / 2
s 2 ( z ) = 3.08 for the volume y > b / 2
Δ n 1 ( z ) = 2 f ( z ) s 1 ( z ) cos ( 2 π z Λ + ϕ g ( z ) ) for the volume y < b / 2
Δ n 2 ( z ) = 2 f ( z ) s 2 ( z ) cos ( 2 π z Λ + ϕ g ( z ) + π ) for the volume y > b / 2

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