Abstract

We report the design and fabrication of long-period waveguide gratings (LPWGs) in benzocyclobutene (BCB) ridge waveguides. We apply an accurate perturbation theory to analyze the LPWGs. In particular, the phase-matching condition, the coupling coefficients, the temperature dependence of the resonance wavelength, the bandwidth, and the polarization dependence of the resonance wavelength are discussed. Several LPWGs in BCB ridge waveguides are fabricated by a UV-writing technique using a KrF excimer laser. The transmission spectra of the gratings are measured and discussed. An LPWG with a polarization-insensitive resonance wavelength at a specific temperature is demonstrated. Experimental results agree well with the theory. Our results are useful for the design of LPWG-based devices for various applications.

© 2005 Optical Society of America

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References

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Appl. Opt.

Appl. Phys. A.

A. K. Baker and P. E. Dyer, “Refractive-index modulation of PolyMethylMethAcrylate (PMMA) thin films by KrF-laser irradiation,” Appl. Phys. A. 57, 543-544 (1993).
[CrossRef]

Electron. Lett.

K. S. Chiang, Y. Liu, M. N. Ng, and S. Li, “Coupling between two parallel long-period fibre gratings,” Electron. Lett. 36, 1408-1409 (2000).
[CrossRef]

A. A. Abramov, A. Hale, R. S. Windeler, and T. A. Strasser, “Widely tunable long-period fibre gratings,” Electron. Lett. 35, 81-82 (1999).
[CrossRef]

K. S. Chiang, C. K. Chow, H. P. Chan, Q. Liu and K. P. Lor, “Widely tunable polymer long-period waveguide grating with polarization-insensitive resonance wavelength,” Electron. Lett. 40, 422-423 (2004).
[CrossRef]

IEEE J. Quantum Electron.

W. P. Wong and K. S. Chiang, “Design of polarization-insensitive bragg gratings in zero-birefringence ridge waveguides, ” IEEE J. Quantum Electron. 37, 1138-1145 (2001).
[CrossRef]

IEEE J. Select. Topics Quantum Electron.

L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” IEEE J. Select. Topics Quantum Electron. 6, 54–68 (2000).
[CrossRef]

IEEE Photon. Technol. Lett.

S. Y. Cheng, K. S. Chiang, and H. P. Chan, “Birefringence in benzocyclobutene strip optical waveguides,” IEEE Photon. Technol. Lett. 15, 700-702 (2003).
[CrossRef]

K. P. Lor, Q. Liu, and K. S. Chiang, “UV-written long-period gratings on polymer waveguides,” IEEE Photon. Technol. Lett. 17(3), (2005) (to be published).

X. Shu, T. Allsop, B. Gwandu, L. Zhang, and I. Bennion, “High-temperature sensitivity of long-period gratings in B-Ge codoped fiber,” IEEE Photon. Technol. Lett. 13, 818-820 (2001).
[CrossRef]

C. F. Kane and R. R. Krchnavek, “Benzocyclobutene optical waveguides,” IEEE Photon. Technol. Lett. 7, 535–537 (1995).
[CrossRef]

P. F. Wysocki, J. B. Judkins, R. P. Espindola, M. Andrejco, and A. M. Vengsarkar, “Broad-band erbium-doped fiber amplifier flattened beyond 40 nm using long-period grating filter,” IEEE Photon. Technol. Lett. 9, 1343-1345 (1997).
[CrossRef]

M. N. Ng, Z. Chen, and K. S. Chiang, “Temperature compensation of long- period fiber grating for refractive-index sensing with bending effect,” IEEE Photon. Technol. Lett. 14, 361-362 (2002).
[CrossRef]

K. S. Chiang, K. P. Lor, C. K. Chow, H. P. Chan, V. Rastogi, and Y. M. Chu, “Widely tunable long-period gratings fabricated in polymer-clad ion-exchanged glass waveguides,” IEEE Photon. Technol. Lett. 15, 1094-1096 (2003).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

K. S. Chiang, “Dispersion characteristics of strip dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 39, 349-352 (1991).
[CrossRef]

J. Lightwave Technol.

OECC 2004

Y. M. Chu, Q. Liu, and K. S. Chiang, “Control of temperature sensitivity of long-period waveguide grating by etching of cladding,” in Proceedings of 9th Optoelectronics and Communications Conference, (OECC 2004, Yokohama, Japan, 2004), 920-921.

Opt. Commun.

M. Das and K. Thyagarajan, “Dispersion control with use of long-period fiber gratings,” Opt. Commun. 190, 159-163 (2001).
[CrossRef]

M. N. Ng and K. S. Chiang, “Thermal effects on the transmission spectra of long-period fiber gratings,” Opt. Commun. 208, 321-327 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

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Figures (9)

Fig. 1.
Fig. 1.

Cross section of a ridge waveguide.

Fig. 2.
Fig. 2.

Phase-matching curves of an LPWG in a ridge waveguide with n s=1.444, n f=1.54 n cl=1.50, n ex=1.0, and d f=2.0 µm at different values of (a) cladding thickness d cl (w=4.0 µm) and (b) waveguide width w (d cl=4.0 µm).

Fig. 3.
Fig. 3.

Confinement factor Γ as a function of waveguide width w.

Fig. 4.
Fig. 4.

(a) Modal dispersion factor γ and grating pitch as a function of the cladding thickness for a ridge waveguide with n s=1.444, n f=1.54, n cl=1.50, n ex=1.0, d f=2.0 µm, and w=4.0 µm for λ 0=1550 nm. (b) Dependence of the temperature sensitivity on the cladding thickness for a range of values of C cl with C f=-1.0×10-4/°C for the ridge waveguide.

Fig. 5.
Fig. 5.

(a) Modal dispersion factor γ and grating pitch as a function of the waveguide width for a ridge waveguide with n s=1.444, n f=1.54, n cl=1.50, n ex=1.0, d f=2.0 µm, and d cl=4.0 µm for λ 0=1550 nm. (b) Dependence of the temperature sensitivity on the waveguide width for a range of values of C cl with C f=-1.0×10-4/°C for the ridge waveguide.

Fig. 6.
Fig. 6.

(a) The cladding thickness d cl and (b) the waveguide width w required for achieving the polarization-independence condition D 12=0 as a function of the resonance wavelength for a ridge waveguide with n s=1.444, n f=1.54, n cl=1.50, n ex=1.0, and d f=2.0 µm. w=4.0 µm and d cl=3.0 µm are assumed in (a) and (b), respectively.

Fig. 7.
Fig. 7.

SEM image of a typical fabricated epoxy-clad BCB ridge waveguide.

Fig. 8.
Fig. 8.

Measured (points) and theoretical (lines) resonance wavelengths at 20.8 °C for LPWGs in ridge waveguides with different waveguide widths.

Fig. 9.
Fig. 9.

(a) Normalized transmission spectra of a UV-written LPWG measured at 22.2 °C showing an almost polarization-independent resonance wavelength. (b) Dependence of the resonance wavelength of the UV-written LPWG on the temperature.

Equations (14)

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

λ 0 = ( N 11 , i N mn , i ) Λ .
N mn , i 2 = N n 1 , i 2 m 2 π 2 w 2 k 0 2 [ 1 2 d f w V ( Δ 1 Δ 2 ) 1 2 ( 1 2 Δ 2 S i ) ] ,
N 11 , i 2 N 12 , i 2 = N 0 , i 2 N 1 , i 2
Λ = λ 0 N 11 , i N 12 , i λ 0 N 0 , i N 1 , i .
κ x = Γ TM x κ TE y
κ y = Γ TE x κ TM y ,
κ x κ TE y
κ y κ TM y
d λ 0 dT γ [ C f ( η 11 f η mn f ) + C cl ( η 11 cl η mn cl ) ] Λ
γ = 1 1 Λ ( d N 11 , i d λ d N mn , i d λ ) ,
d λ 0 dT γ ( C f C cl ) ( η 11 f η mn f ) Λ .
Δ λ 3 dB = γ 0.8 λ 0 2 L Δ n eff = γ Λ 0.8 λ 0 L ,
D mn ( N 11 , x N mn , x ) ( N 11 , y N mn , y ) .
D 12 ( N 11 , x N 12 , x ) ( N 11 , y N 12 , y ) ( N 0 , x N 1 , x ) ( N 0 , y N 1 , y ) D 12 .

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