OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 4 — Feb. 21, 2005
  • pp: 1150–1160
« Show journal navigation

Long-period gratings in polymer ridge waveguides

Q. Liu, K. S. Chiang, and K. P. Lor  »View Author Affiliations


Optics Express, Vol. 13, Issue 4, pp. 1150-1160 (2005)
http://dx.doi.org/10.1364/OPEX.13.001150


View Full Text Article

Acrobat PDF (268 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

1. Introduction

A large number of materials are available for the fabrication of optical waveguides, such as glass, lithium niobate, semiconductor, and polymer. Among these materials, polymer is relatively easy to process and also offers many favorable optical and electrical properties. Polymer can be spin-coated on glass, silica, silicon, etc., and therefore is compatible with most optical materials. In addition, it can provide a high degree of ruggedness and allow mass production of components at a low cost. A distinct feature of polymer, compared with other optical materials, is the strong temperature dependence of its refractive index. The large thermo-optic coefficient of polymer (about 25 times larger than that of glass) can be leveraged to produce efficient thermo-optically tunable components. For example, an LPWG filter, which can be tuned linearly over the entire C+L band (~90 nm) with a temperature control of ~10 °C, has been demonstrated with a polymer-clad ion-exchanged BK7 glass waveguide recently [9

9. 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]

]. Both the wavelength-tuning range and the temperature sensitivity of this filter exceed those achieved with LPFGs [10

10. 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]

,11

11. 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]

].

Among different polymers, benzocyclobutene (BCB), which is available from Dow Chemical, offers a number of advantages, such as good thermal stability (T g>350°C), low moisture uptake, good adhesion properties, and relatively low cost. It has been used widely as an optical waveguide material [12

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

,13

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

]. Recently, LPWGs in a BCB channel waveguide [14

14. 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]

] and a BCB rib waveguide [15

15. M. Kim, K. Kim, Y. Oh, and S. Shin, “Fabrication of an integrated optical filter using a large-core multimode waveguide vertically coupled to a single-mode waveguide,” Opt. Express , 11, 2211–2216 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-18-2211. [CrossRef] [PubMed]

] were demonstrated. The conventional technique of making an LPWG [14

14. 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]

] is by first corrugating the surface of the core of a waveguide with a prescribed pitch by photolithography and reactive ion etching (RIE), and then coating the core with a cladding with prescribed characteristics. By changing the stress in the waveguide through etching of the cladding width, a polarization-insensitive resonance wavelength thermally tunable from 1520 nm to 1610 nm with a temperature range of only 8 °C was achieved [14

14. 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]

].

In this paper, we report a comprehensive study of LPWGs in BCB ridge waveguides. Thanks to the ridge geometry, we are able to apply an accurate perturbation theory to the calculation of the phase-matching condition and the coupling coefficient of an LPWG. The theory simplifies tremendously the analysis and design of an LPWG and provides much insight into the transmission characteristics of the LPWG, including the temperature dependence of the resonance wavelength, the bandwidth, and the polarization independence of the resonance wavelength. We also describe the fabrication of a ridge waveguide and the writing of an LPWG on the cladding of the waveguide using the UV technique we recently proposed [16

16. 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).

]. The transmission characteristics of several fabricated LPWGs are discussed and compared with theoretical results. In particular, we demonstrate an LPWG that exhibits a polarization-independent resonance wavelength by controlling the waveguide dimensions.

2. Method of analysis

Figure 1 shows the cross section of a ridge waveguide, which consists of a substrate of refractive index ns , a guiding layer of refractive index n f and thickness d f, a cladding layer of refractive index n cl and thickness d cl, and an external medium of refractive index n ex that extends to infinity, where n f>n cl>n s, n ex. The guiding layer and the cladding have the same width w. We assume that only the fundamental quasi-TE and quasi-TM modes are guided, which are referred to as the E11x and E11y modes with effective indices N 11,i(i=x, y) where n cl<N 11,i<n f. A long-period grating with pitch Λ is introduced on the surface of the guiding layer or the cladding layer. The grating allows light coupling from the fundamental mode (E11x or E11y) to the cladding modes of the same polarization (Emnx or Emny ), whose effective indices Nmn ,i (m, n are integers except m=n=1) are smaller than n cl, i.e., n s<N mn ,i<n cl. The resonance wavelength λ 0, at which the coupling between the two modes is strongest, is determined by the phase-matching condition:

λ0=(N11,iNmn,i)Λ.
(1)
Fig. 1. Cross section of a ridge waveguide.

The effective indices of the guided mode and the cladding modes of the waveguide can be calculated accurately from the following perturbation formula [17

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

]:

Nmn,i2=Nn1,i2m2π2w2k02[12dfwV(Δ1Δ2)12(12Δ2Si)],
(2)

where Sx =1 and Sy =0. In Eq. (2), V=(1/2)d f k 0(nf2-ns2)1/2 is the normalized frequency (with k 0=2π/λ the free-space wavenumber and λ the free-space wavelength), Δ1=(nf2-ns2)/2nf2 and Δ2=(nf2-nex2)/2nf2 are the relative index steps, and n-1,i is the effective index of the TEn-1 (for i=x) or TMn-1 (for i=y) mode of the four-layer slab waveguide formed by extending the width of the ridge waveguide to infinity. The perturbation formula is accurate, as long as the external index is sufficiently low, i.e., n f-n sn f-n ex and the mode of concern is not close to cutoff [17

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

].

For all the numerical results given in subsequent sections, unless stated otherwise, the following waveguide parameters are used: n s=1.444, n f=1.54, n cl=1.50, n ex=1.0 (air), and d f=2.0 µm. These values are typical of a polymer waveguide fabricated on a silica substrate. The cladding thickness d cl and the waveguide width w, which are important design parameters, are allowed to vary. Material dispersion and thermally induced stress birefringence are ignored in the calculation. We only consider the coupling to the first cladding mode. The coupling to a higher-order mode can be analyzed by the same approach.

2.1 Phase-matching curves

The phase-matching condition given by Eq. (1) governs the dependence of the resonance wavelength λ 0 on the grating pitch Λ and, therefore, plays a central role in the study of long-period gratings. The variation of λ 0 with Λ (the phase-matching curve) is shown in Fig. 2 for different values of cladding thickness and waveguide width. As shown in Fig. 2(a), when the cladding is relatively thick (d cl≥4 µm), λ 0 increases linearly with Λ. When the cladding is thin, however, the relationship between λ 0 and Λ is no longer linear. It is also noted in Fig. 2(a) that the phase-matching curves for the quasi-TE and quasi-TM modes can become close as the cladding thickness changes and, in fact, cross each other at a particular value of cladding thickness (d cl=3 µm). This implies the presence of a specific LPWG design where the couplings for both polarizations occur at the same wavelength, as in the case of an LPWG in a slab waveguide [8

8. Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21, 3399–3405 (2003). [CrossRef]

]. The phase-matching curves for the LPWGs with different waveguide widths are shown in Fig. 2(b). Only the phase-matching curves for the quasi-TE polarization are given as the results for the quasi-TM polarization are similar (and therefore not shown). It is clear from Fig. 2(b) that the phase-matching condition depends only weakly on the waveguide width provided that the cladding mode of concern remains above cut-off.

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).

The difference in the effective index squared between the guided mode (m=n=1) and the first cladding mode (m=1, n=2) is obtained from Eq. (2) as

N11,i2N12,i2=N0,i2N1,i2
(3)

which is independent of the waveguide width. Note that 0,i and 1,i are the effective indices of the first two modes of the four-layer slab waveguide. From Eq. (1) and Eq. (3), the grating pitch required for a given resonance wavelength λ0 is given by

Λ=λ0N11,iN12,iλ0N0,iN1,i.
(4)

The grating pitch for a ridge waveguide is insensitive to the waveguide width and, therefore, can be approximated by that for the four-layer slab waveguide obtained by extending the width of the ridge waveguide to infinity. This result is very much of practical significance as the slab waveguide is an intermediate step in the fabrication of the ridge waveguide and the effective indices of the slab waveguide can be measured accurately by the well-known prism-coupler technique. This special property of the ridge waveguide helps the realization of LPWGs with more predictable characteristics.

2.2 Coupling coefficients

The strength of the rejection band of an LPWG is governed by the coupling coefficients κi , where i=x and y for the quasi-TE and quasi-TM polarizations, respectively [7

7. V. Rastogi and K. S. Chiang, “Long-period gratings in planar optical waveguides,” Appl. Opt. 41, 6351–6355 (2002). [CrossRef] [PubMed]

,8

8. Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21, 3399–3405 (2003). [CrossRef]

]. For a ridge waveguide, the mode field can be expressed accurately as a product of the fields in the x and y directions [18

18. 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]

]. The coupling coefficients of the LPWG in the ridge waveguide can thus be expressed in terms of those of the LPWG in the appropriate slab waveguide:

κx=ΓTMxκTEy
κy=ΓTExκTMy,
(5)

where ΓTEx and ΓTMx are the confinement factors for the TE0 and TM0 modes of the slab waveguide formed by extending the thickness of the rectangular core to infinity, and κTEy and κTMy are the coupling coefficients for the LPWG in the slab waveguide formed by extending the width of the rectangular core to infinity. The dependence of the confinement factors on the waveguide width is shown in Fig. 3. Because the index difference between the waveguide material and air is large, the mode field is well confined in the x direction. Therefore, both ΓTEx and ΓTMx are close to 1 and Eq. (5) can be simplified to

κxκTEy
κyκTMy
(6)

which are insensitive to the waveguide width. The expressions for κTEy and κTMy can be found in [7

7. V. Rastogi and K. S. Chiang, “Long-period gratings in planar optical waveguides,” Appl. Opt. 41, 6351–6355 (2002). [CrossRef] [PubMed]

] for a phase grating and in [8

8. Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21, 3399–3405 (2003). [CrossRef]

] for a corrugation grating.

Fig. 3. Confinement factor Γ as a function of waveguide width w.

2.3 Temperature sensitivity

The temperature sensitivity of the resonance wavelength of an LPWG, 0/dT, can also be derived from a perturbation theory, as in the case of an LPFG [19

19. 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]

]. The result is

dλ0dTγ[Cf(η11fηmnf)+Ccl(η11clηmncl)]Λ
(7)

with

γ=11Λ(dN11,idλdNmn,idλ),
(8)

dλ0dTγ(CfCcl)(η11fηmnf)Λ.
(9)

The temperature sensitivity of an LPWG depends on the thermal-optic coefficients of the materials and the waveguide structure, especially the cladding thickness. The variation of 0/dT with the cladding thickness is shown in Fig. 4(b) for different values of C cl (assuming C f=-1.0×10-4/°C and λ 0=1550 nm). In practice, the value of C cl can be changed by changing the polymer material for the cladding. It can be seen from Fig. 4(b) that the temperature sensitivity of an LPWG can be controlled over a wide range by simply controlling the cladding thickness or by carefully tuning the difference between C f and C cl. These curves also exhibit the flip-flop behavior due to the factor γ. In the case of a thick cladding, the cladding mode is confined mainly in the cladding and the guided mode is confined mainly in the guiding layer. The fractional power difference, η 11f-η mnfη 11f, is not much affected by the cladding thickness. Therefore, according to Eq. (9), the magnitude of 0/dT is insensitive to the cladding thickness and the sign of 0/dT is determined by the sign of C f-C cl. The condition of zero temperature sensitivity is thus given by C cl=C f, which is the same as that for an LPFG. As the cladding becomes thinner, the cladding mode is pushed deeper into the guiding layer/substrate and, at the same time, the guided mode penetrates more into the cladding. As the cladding becomes thin enough, the fractional powers of the modes in the guiding layer and the cladding become comparable and highly sensitive to the cladding thickness. The condition of zero temperature sensitivity is given by C f (η 11f-η mnf)+C cl (η 11cl-η mncl )=0.

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. (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.

2.4 3-dB bandwidth

Assuming complete power transfer, the full width at half maximum (FWHM) of the resonance peak, Δλ 3dB, is given by [20

20. X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long period fiber gratings,” J. Lightwave Technol. 20, 255–266 (2002). [CrossRef]

]

Δλ3dB=γ0.8λ02LΔneff=γΛ0.8λ0L,
(10)

2.5 Polarization dependence

The resonance wavelengths for the quasi-TE and quasi-TM polarizations are in general different. To facilitate the discussion of this property, we use a waveguide parameter Dmn , which is defined as [8

8. Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21, 3399–3405 (2003). [CrossRef]

]

Dmn(N11,xNmn,x)(N11,yNmn,y).
(11)

According to Eq. (1), Dmn is a measure of the difference between the resonance wavelengths of the quasi-TE and quasi-TM polarizations. According to Eq. (4), we obtain

D12(N11,xN12,x)(N11,yN12,y)(N0,xN1,x)(N0,yN1,y)D12.
(12)

Therefore, D 12 can be estimated from 12 for the slab waveguide, which is a measurable parameter. The condition required for achieving a polarization-insensitive resonance wavelength is Dmn =0. The factor Dmn depends on both the geometry and the material of the waveguide. The cladding thickness required for D 12=0 is shown in Fig. 6(a) as a function of the resonance wavelength. The results are in fact close to those for a slab waveguide [8

8. Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21, 3399–3405 (2003). [CrossRef]

], as implied by Eq. (12). The waveguide width can also affect the polarization dependence of the grating, though to a much less extent, as shown in Fig. 6(b).

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.

3. Waveguide and grating fabrication

We formed a long-period grating on the surface of the epoxy cladding by the UV technique we proposed recently [16

16. 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).

]. The UV source we used was a KrF excimer laser, which generated UV pulses at 248 nm with a full width at half maximum (FWHM) of 23 ns. The energy density of the UV pulses was set at 10 mJ/cm2. We found that the UV light changed both the refractive index and the thickness of the epoxy film [16

16. 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).

], in agreement with the findings for a different polymer material, PMMA [22

22. 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]

]. These results suggest the possibility of inducing a grating in the epoxy cladding of the ridge waveguide.

Fig. 7. SEM image of a typical fabricated epoxy-clad BCB ridge waveguide.

4. Experimental results and discussion

The effects of the cladding thickness on the resonance wavelength of an LPWG and its temperature sensitivity have been studied experimentally with slab waveguides [23

23. 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.

]. Similar results are expected for ridge waveguides. In the present experimental work, we focus on the effects arising from a change in the width of the ridge waveguide.

Figure 8 shows the measured resonance wavelengths at 20.8 °C for several LPWGs in ridge waveguides with different waveguide widths. As shown in Fig. 7, the sidewalls of the fabricated waveguide were not absolutely straight, so we used the average of the maximum and minimum widths measured from the SEM image. The error was around 0.1 µm. The calculated results are also shown in the figure for comparison. The measured results agree quite well with the theoretical values. As expected, the resonance wavelength varies slowly with the waveguide width. Furthermore, the difference between the resonance wavelengths for the quasi-TE and quasi-TM polarizations is insensitive to the waveguide width, in agreement with the prediction in Section 2.5.

Fig. 8. Measured (points) and theoretical (lines) resonance wavelengths at 20.8 °C for LPWGs in ridge waveguides with different waveguide widths.

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.

5. Conclusion

With the help of an accurate perturbation theory, we carry out a detailed analysis of an LPWG in a ridge waveguide. Analytical expressions are presented to highlight the characteristics of the LPWG, including the phase-matching condition, the coupling coefficients, the 3-dB bandwidth, the temperature sensitivity of the resonance wavelength, and the polarization dependence of the resonance wavelength. We also present the transmission characteristics of several experimental LPWGs that were formed in BCB/epoxy ridge waveguides by the UV-writing technique. The dependence of the resonance wavelength on the width of the waveguide is discussed and an LPWG showing a polarization-insensitive resonance wavelength at a specific temperature is demonstrated. The experimental results are found to agree well with the theoretical calculations. Our results provide a better understanding of the properties of LPWGs and should facilitate the design of LPWG-based devices.

Acknowledgments

The authors wish to thank C. K. Chow and H. P. Chan for their technical assistance and useful discussions. This work was supported by the grants from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. CityU 1160/01E and CityU 1255/03E].

References and links

1.

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]

2.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996). [CrossRef]

3.

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]

4.

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

5.

V. Bhatia, D. Campbell, R. O. Claus, and A. M. Vengsarkar, “Simultaneous strain and temperature measurement with long-period gratings,” Opt. Lett. 22, 648–650 (1997). [CrossRef] [PubMed]

6.

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]

7.

V. Rastogi and K. S. Chiang, “Long-period gratings in planar optical waveguides,” Appl. Opt. 41, 6351–6355 (2002). [CrossRef] [PubMed]

8.

Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21, 3399–3405 (2003). [CrossRef]

9.

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]

10.

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]

11.

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]

12.

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

13.

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

14.

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]

15.

M. Kim, K. Kim, Y. Oh, and S. Shin, “Fabrication of an integrated optical filter using a large-core multimode waveguide vertically coupled to a single-mode waveguide,” Opt. Express , 11, 2211–2216 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-18-2211. [CrossRef] [PubMed]

16.

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).

17.

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

18.

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]

19.

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]

20.

X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long period fiber gratings,” J. Lightwave Technol. 20, 255–266 (2002). [CrossRef]

21.

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]

22.

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]

23.

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.

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(130.3120) Integrated optics : Integrated optics devices
(250.5460) Optoelectronics : Polymer waveguides

ToC Category:
Research Papers

History
Original Manuscript: January 5, 2005
Revised Manuscript: December 30, 2004
Published: February 21, 2005

Citation
Q. Liu, K. Chiang, and K. Lor, "Long-period gratings in polymer ridge waveguides," Opt. Express 13, 1150-1160 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-4-1150


Sort:  Journal  |  Reset  

References

  1. 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]
  2. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58-65 (1996). [CrossRef]
  3. 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]
  4. M. Das and K. Thyagarajan, “Dispersion control with use of long-period fiber gratings,” Opt. Commun. 190, 159-163 (2001). [CrossRef]
  5. V. Bhatia, D. Campbell, R. O. Claus, and A. M. Vengsarkar, “Simultaneous strain and temperature measurement with long-period gratings,” Opt. Lett. 22, 648-650 (1997). [CrossRef] [PubMed]
  6. 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]
  7. V. Rastogi and K. S. Chiang, “Long-period gratings in planar optical waveguides,” Appl. Opt. 41, 6351-6355 (2002). [CrossRef] [PubMed]
  8. Q. Liu, K. S. Chiang, and V. Rastogi, “Analysis of corrugated long-period gratings in slab waveguides and their polarization dependence,” J. Lightwave Technol. 21, 3399-3405 (2003). [CrossRef]
  9. 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]
  10. 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]
  11. 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]
  12. C. F. Kane and R. R. Krchnavek, “Benzocyclobutene optical waveguides,” IEEE Photon. Technol. Lett. 7, 535–537 (1995). [CrossRef]
  13. L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” IEEE J. Select. Topics Quantum Electron. 6, 54–68 (2000). [CrossRef]
  14. 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]
  15. M. Kim, K. Kim, Y. Oh, S. Shin, “Fabrication of an integrated optical filter using a large-core multimode waveguide vertically coupled to a single-mode waveguide,” Opt. Express, 11, 2211-2216 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-18-2211.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-18-2211.</a> [CrossRef] [PubMed]
  16. 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).
  17. K. S. Chiang, “Dispersion characteristics of strip dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 39, 349-352 (1991). [CrossRef]
  18. 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]
  19. 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]
  20. X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long period fiber gratings,” J. Lightwave Technol. 20, 255–266 (2002). [CrossRef]
  21. 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]
  22. 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]
  23. 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.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited