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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 9 — Jul. 6, 2010
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Planar long-period grating filter based on long-range surface plasmon mode of buried metal stripe waveguide

Qing Liu and Kin Seng Chiang  »View Author Affiliations


Optics Express, Vol. 18, Issue 9, pp. 8963-8968 (2010)
http://dx.doi.org/10.1364/OE.18.008963


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Abstract

We propose a planar long-period grating filter based on coupling between the long-range surface plasmon mode and a cladding mode of a fully buried metal stripe waveguide. Using a 2.5-mm-long corrugation grating produced along the surface of an epoxy-clad aluminum stripe waveguide, we achieve a rejection band with a contrast of ~18 dB at the wavelength ~1500 nm, which can be tuned by ~25 nm with a temperature change of ~30°C. The experimental results agree closely with the simulation results. The filter could find applications in surface-plasmon-based integrated-optic circuits and biosensors.

© 2010 OSA

1. Introduction

Surface plasmons or surface plasmon polaritons, which are light waves propagating along an interface between a metal and a dielectric material [1

1. J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33(8), 5186–5201 (1986). [CrossRef]

], have attracted much interest in recent years for their many potential applications in integrated optics and nanophotonics [2

2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

]. A thin metal stripe, in particular, supports a long-range surface plasmon (LRSP) mode that can propagate over a distance of several millimeters with a low loss [3

3. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]

]. LRSP modes have been explored for the development of inexpensive and compact integrated optical devices, such as Y-splitters [4

4. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005). [CrossRef]

,5

5. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-3-977. [CrossRef] [PubMed]

], multimode interference devices [4

4. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005). [CrossRef]

,5

5. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-3-977. [CrossRef] [PubMed]

], couplers [4

4. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005). [CrossRef]

7

7. S. Park, J. T. Kim, J.-S. Shin, and S.-Y. Shin, “Hybrid vertical directional coupling between a long range surface plasmon polariton waveguide and a dielectric waveguide,” Opt. Commun. 282(23), 4513–4517 (2009). [CrossRef]

], modulators [8

8. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833–5835 (2004). [CrossRef]

], switches [8

8. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833–5835 (2004). [CrossRef]

], and attenuators [9

9. G. Gagnon, N. Lahoud, G. A. Mattiussi, and P. Berini, “Thermally activated variable attenuation of long-range surface plasmon-polariton waves,” J. Lightwave Technol. 24(11), 4391–4402 (2006). [CrossRef]

]. Bragg grating filters based on periodic corrugation along the width [10

10. S. Jetté-Charbonneau, R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of Bragg gratings based on long-ranging surface plasmon polariton waveguides,” Opt. Express 13(12), 4674–4682 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-12-4674. [CrossRef] [PubMed]

] or the thickness [11

11. A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightwave Technol. 24(2), 912–918 (2006). [CrossRef]

] of a metal stripe have also been demonstrated. A comprehensive review of LRSP-based optical devices can be found in Ref. 12

12. P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photon. 1(3), 484–588 (2009). [CrossRef]

. In this paper, we propose a new LRSP-based grating, which is formed on the surface of the dielectric cladding of a fully buried metal stripe and designed to couple between the LRSP mode of the metal stripe and a co-propagating cladding mode. The grating requires a long period (10 – 100 μm), compared with a Bragg grating, so it is a kind of long-period waveguide grating (LPWG) [13

13. Q. Liu, K. S. Chiang, K. P. Lor, and C. K. Chow, “Temperature sensitivity of a long-period waveguide grating in a channel waveguide,” Appl. Phys. Lett. 86(24), 241115 (2005). [CrossRef]

]. The grating functions as a broadband rejection filter and offers a number of advantages, including easy fabrication, low back reflection, and good wavelength tunability. A special feature of the LRSP mode is that its field extends deeply into the cladding, which makes possible strong coupling to a cladding mode with a shallow grating formed on the cladding surface. Because of that, we can form the grating on the cladding at the last step of the fabrication process, which means that the grating parameters and hence its performance can be determined accurately from a fully characterized waveguide. On the other hand, LPWG filters based on all-dielectric waveguides where the grating is formed in the core [13

13. Q. Liu, K. S. Chiang, K. P. Lor, and C. K. Chow, “Temperature sensitivity of a long-period waveguide grating in a channel waveguide,” Appl. Phys. Lett. 86(24), 241115 (2005). [CrossRef]

] do not have this advantage and are more difficult to fabricate reliably. Moreover, the large spot size of the LRSP mode facilitates the launching and the detection of the mode with standard single-mode fibers. To demonstrate the operation principle of the device, we fabricated an epoxy-clad aluminum (Al) stripe waveguide that contained a carefully designed 2.5-mm-long grating engraved on the cladding surface. The transmission spectrum of the filter shows a rejection band of ~18 dB at the wavelength ~1500 nm, which can be tuned by ~25 nm with a temperature change of ~30 °C. Our experimental and simulation results agree well. This filter could be used in integrated-optic circuits and biosensors.

2. Filter configuration and operation principle

The proposed grating filter is shown in Fig. 1
Fig. 1 A planar long-period grating with pitch Λ and corrugation depth Δh formed on the surface of a dielectric-clad metal stripe waveguide.
, which consists of a thin metal stripe buried completely in a finite dielectric cladding. Light waves are confined in the x-y plane and propagate along the z direction. A grating with corrugation depth Δh and pitch Λ is formed on the cladding surface to induce coupling between the LRSP mode and a selected cladding mode. For the realization of a practical device, low-loss metal (such as gold or silver) and dielectric material should be used [3

3. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]

12

12. P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photon. 1(3), 484–588 (2009). [CrossRef]

,14

14. J. Jiang, C. L. Callender, S. Jacob, J. P. Noad, S. Chen, J. Ballato, and D. W. Smith Jr., “Long-range surface plasmon polariton waveguides embedded in fluorinated polymer,” Appl. Opt. 47(21), 3892–3900 (2008). [CrossRef] [PubMed]

]. Limited by our experimental conditions, however, we employed Al and epoxy OPTOCAST 3505 (Electronic Materials Inc) as the metal stripe and cladding materials and a SiO2/Si wafer as the substrate. Although Al and epoxy are not the optimal materials, they are easy to process and good enough to demonstrate the principle of the filter.

We calculate the modes of the waveguide with a finite difference method [15

15. S. J. Al-Bader, “Optical transmission on metallic wires—fundamental modes,” IEEE J. Quantum Electron. 40(3), 325–329 (2004). [CrossRef]

] using the following experimental parameters: Al thickness = 15 nm, Al width = 2 μm, Al permittivity = − 253.93 − 46.08j [16

16. E. Palik, Handbook of Optical Constants of Solids, (Academic, 1985).

], epoxy thickness = 11.5 μm, epoxy refractive index = 1.51161 (measured at 1536 nm), and SiO2 substrate index = 1.444. We assume an infinitely wide cladding and an Al stripe placed at the center of the cladding in the y direction. The LRSP mode is a transverse-magnetic (TM) mode, which has a magnetic-field component in the x direction and a major electric-field component in the y direction. Our calculation shows that the waveguide supports six TM cladding modes confined in the y direction. In principle, the grating can be designed to couple light from the LRSP mode to any of the cladding modes [17

17. 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(12), 3399–3405 (2003). [CrossRef]

]. Here we choose the fourth TM cladding mode. The electric-field distributions of the LRSP mode and the chosen cladding mode at the wavelength 1536 nm are shown in Fig. 2(a) and (b)
Fig. 2 Electric-field distributions of (a) the LRSP mode and (b) the fourth vertically confined cladding mode of a 15-nm thick and 2-μm wide Al stripe waveguide buried in an 11.5-μm thick epoxy cladding.
, respectively. As shown in Fig. 2(a), the LRSP mode has a large and simple field pattern and, therefore, can be excited efficiently with a single-mode fiber. For the present waveguide design, an excitation efficiency of ~75% can be achieved with a standard single-mode fiber SMF-28, which has a core radius of 4.1 μm and a numerical aperture of 0.12. The excitation efficiency can be further improved by optimizing the dimensions of the metal stripe and the cladding [14

14. J. Jiang, C. L. Callender, S. Jacob, J. P. Noad, S. Chen, J. Ballato, and D. W. Smith Jr., “Long-range surface plasmon polariton waveguides embedded in fluorinated polymer,” Appl. Opt. 47(21), 3892–3900 (2008). [CrossRef] [PubMed]

]. On the other hand, as shown in Fig. 2(b), the cladding mode has a complicated pattern that cannot be excited efficiently with a single-mode fiber. The wavelength at which the coupling between the two modes is strongest (the resonance wavelength) is determined by the phase-matching condition [13

13. Q. Liu, K. S. Chiang, K. P. Lor, and C. K. Chow, “Temperature sensitivity of a long-period waveguide grating in a channel waveguide,” Appl. Phys. Lett. 86(24), 241115 (2005). [CrossRef]

,17

17. 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(12), 3399–3405 (2003). [CrossRef]

], λ 0 = (N LRSPN cl)Λ, where N LRSP and N cl are the real parts of the mode indices of the LRSP mode and the cladding mode, respectively. The calculated values of N LRSP and N cl are 1.5105 and 1.4784, respectively, which gives a grating pitch of 47.85 μm at the resonance wavelength 1536 nm. The calculated propagation loss for the LRSP mode (which only accounts for the ohmic loss of the Al stripe) is ~2.5 dB/cm. We choose a grating length of 2.5 mm, which is long enough to contain a large number of grating periods and short enough to limit the loss. Given the grating length, we can determine the corrugation depth Δh needed to produce a strong rejection band [17

17. 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(12), 3399–3405 (2003). [CrossRef]

]. According to our calculation with the coupled-mode theory [17

17. 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(12), 3399–3405 (2003). [CrossRef]

], to achieve zero transmission at the resonance wavelength 1536 nm, the corrugation depth required is 406 nm with a 2.5-mm-long grating, which is only 3.5% of the cladding thickness and should not introduce significant losses to the modes.

3. Device fabrication

To fabricate the device, a layer of epoxy was first spin-coated on a SiO2/Si wafer, where the SiO2 layer was 3 μm thick. The epoxy was exposed to ultra-violet (UV) light at a power density of 350 mW/cm2 for 5 minutes and post-cured at 130 °C for 30 minutes. The thickness and the refractive index of the epoxy layer, measured with a step profiler (Ambios Technology, Model XP-2) and a prism-coupler system (Metricon, Model 2010), respectively, were 5.75 μm and 1.51161 at 1536 nm for the TM polarization. By means of a negative mask and standard photolithographic processes, a set of 2-μm-wide openings separated by 60 μm was patterned on the epoxy layer with photoresist AZ 5206E (Clariant Inc). A 15-nm-thick aluminum film was then deposited on the surface of the patterned sample with a thermal evaporation system (Edwards, Model Auto 306) and the excess metal was removed with a lift-off process. A second layer of epoxy was spin-coated on the sample to the same thickness as the first layer and cured. To ensure full curing of the epoxy and thus improve its stability, the sample went through additional thermal curing at 130°C for 60 minutes.

4. Measurement results and discussion

The LRSP mode was launched into and extracted from the waveguide with standard single-mode fibers placed at the two ends of the waveguide. The propagation losses for the LRSP mode, measured with and without the grating, respectively, at 1536 nm (off resonance) with a transmission method [18

18. W. J. Wang, S. Honkanen, S. I. Najafi, and A. Tervonen, “Loss characteristics of potassium and silver double-ion-exchanged glass waveguides,” J. Appl. Phys. 74(3), 1529–1533 (1993). [CrossRef]

], were both ~4.6 dB/cm, which confirms that the grating caused negligible loss to the LRSP mode. The loss was larger than the calculated value that ignores the material loss of the epoxy (~2 dB/cm). The transmission spectrum for the TM polarization was measured with a broadband light source (KOHERAS, Model SuperK Compact) and an optical spectrum analyzer. A heat pump was placed under the waveguide to control its operating temperature. The normalized transmission spectra at three temperatures are shown in Fig. 5
Fig. 5 Normalized transmission spectra of the filter measured at 24.2, 34.5, and 46.7°C with the insets showing the output near-field images (taken at 24.2°C) at the resonance wavelength 1500 nm and an off-resonance wavelength 1536 nm.
. We can see a clear rejection band at 1500 nm at 24.2 °C that has a contrast of ~18 dB and a 3-dB bandwidth of ~19 nm. By taking into account the effect of reducing the average cladding thickness by corrugation, the calculated resonance wavelength and contrast (with Λ = 48 μm and Δh = 366 nm) are 1493 nm and 18.8 dB, respectively, which compare well with the experimental results. To provide a more direct demonstration of the operation of the grating, we took the output near-field images of the filter (at 24.2°C) with an infrared vidicon camera (Hamamatsu, Model C2741-03) at the resonance wavelength 1500 nm and an off-resonance wavelength 1536 nm, respectively, and display the results as insets in Fig. 5. As shown by the images, light is coupled from the LRSP mode into the cladding mode at the resonance wavelength, while stays in the LRSP mode at the off-resonance wavelength.

Figure 6
Fig. 6 Temperature dependence of the resonance wavelength of the grating.
shows the change of the resonance wavelength with the temperature from 24.2 to 55.3°C. The resonance wavelength shifts towards a shorter wavelength by ~25 nm as the temperature changes by ~30°C. The variation of the rejection contrast with the temperature is due to the change of the refractive index of the epoxy, which affects the mode-field distributions (and hence the overlapping of the coupled modes in the grating area) and thus leads to a change in the grating contrast [17

17. 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(12), 3399–3405 (2003). [CrossRef]

]. The temperature sensitivity of the filter is comparable to that of some particularly sensitive all-dielectric LPWG filters [13

13. Q. Liu, K. S. Chiang, K. P. Lor, and C. K. Chow, “Temperature sensitivity of a long-period waveguide grating in a channel waveguide,” Appl. Phys. Lett. 86(24), 241115 (2005). [CrossRef]

].

5. Conclusion

In summary, we propose a planar long-period grating filter based on coupling between the LRSP mode and a cladding mode of a fully buried metal stripe waveguide. Our experimental filter using a 2.5-mm-long corrugation grating on an epoxy-clad Al stripe waveguide shows a rejection of 18 dB at 1500 nm (at ~24°C), which can be tuned by ~25 nm with a temperature control of ~30°C. It should be possible to improve the performance of the filter by using low-loss metal (gold or silver) and dielectric as the waveguide materials. Compared with conventional all-dielectric LPWG filters [13

13. Q. Liu, K. S. Chiang, K. P. Lor, and C. K. Chow, “Temperature sensitivity of a long-period waveguide grating in a channel waveguide,” Appl. Phys. Lett. 86(24), 241115 (2005). [CrossRef]

], this filter allows the grating to be formed on the cladding surface at the last step of the fabrication process, which offers significant advantages in terms of the convenience in the fabrication process and the accuracy in the control of the grating parameters. It is possible to fabricate the device using an even simpler technique, such as a laser-writing technique (for photosensitive cladding) or an imprinting technique (for polymer cladding). The filter could find applications in surface-plasmon-based integrated-optic circuits. Its large sensitivity to environmental parameters could be further explored for the realization of optical biosensors.

Acknowledgments

This research was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project CityU 111907].

References and links

1.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33(8), 5186–5201 (1986). [CrossRef]

2.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

3.

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]

4.

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005). [CrossRef]

5.

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-3-977. [CrossRef] [PubMed]

6.

H. S. Won, K. C. Kim, S. H. Song, C.-H. Oh, P. S. Kim, S. Park, and S. I. Kim, “Vertical coupling of long-range surface plasmon polaritons,” Appl. Phys. Lett. 88(1), 011110 (2006). [CrossRef]

7.

S. Park, J. T. Kim, J.-S. Shin, and S.-Y. Shin, “Hybrid vertical directional coupling between a long range surface plasmon polariton waveguide and a dielectric waveguide,” Opt. Commun. 282(23), 4513–4517 (2009). [CrossRef]

8.

T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833–5835 (2004). [CrossRef]

9.

G. Gagnon, N. Lahoud, G. A. Mattiussi, and P. Berini, “Thermally activated variable attenuation of long-range surface plasmon-polariton waves,” J. Lightwave Technol. 24(11), 4391–4402 (2006). [CrossRef]

10.

S. Jetté-Charbonneau, R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of Bragg gratings based on long-ranging surface plasmon polariton waveguides,” Opt. Express 13(12), 4674–4682 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-12-4674. [CrossRef] [PubMed]

11.

A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightwave Technol. 24(2), 912–918 (2006). [CrossRef]

12.

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photon. 1(3), 484–588 (2009). [CrossRef]

13.

Q. Liu, K. S. Chiang, K. P. Lor, and C. K. Chow, “Temperature sensitivity of a long-period waveguide grating in a channel waveguide,” Appl. Phys. Lett. 86(24), 241115 (2005). [CrossRef]

14.

J. Jiang, C. L. Callender, S. Jacob, J. P. Noad, S. Chen, J. Ballato, and D. W. Smith Jr., “Long-range surface plasmon polariton waveguides embedded in fluorinated polymer,” Appl. Opt. 47(21), 3892–3900 (2008). [CrossRef] [PubMed]

15.

S. J. Al-Bader, “Optical transmission on metallic wires—fundamental modes,” IEEE J. Quantum Electron. 40(3), 325–329 (2004). [CrossRef]

16.

E. Palik, Handbook of Optical Constants of Solids, (Academic, 1985).

17.

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(12), 3399–3405 (2003). [CrossRef]

18.

W. J. Wang, S. Honkanen, S. I. Najafi, and A. Tervonen, “Loss characteristics of potassium and silver double-ion-exchanged glass waveguides,” J. Appl. Phys. 74(3), 1529–1533 (1993). [CrossRef]

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(130.3120) Integrated optics : Integrated optics devices
(230.7390) Optical devices : Waveguides, planar
(240.6680) Optics at surfaces : Surface plasmons
(130.7408) Integrated optics : Wavelength filtering devices

ToC Category:
Diffraction and Gratings

History
Original Manuscript: February 22, 2010
Revised Manuscript: April 6, 2010
Manuscript Accepted: April 7, 2010
Published: April 14, 2010

Virtual Issues
Vol. 5, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Qing Liu and Kin Seng Chiang, "Planar long-period grating filter based on long-range surface plasmon mode of buried metal stripe waveguide," Opt. Express 18, 8963-8968 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-9-8963


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References

  1. J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33(8), 5186–5201 (1986). [CrossRef]
  2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
  3. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]
  4. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005). [CrossRef]
  5. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-3-977 . [CrossRef] [PubMed]
  6. H. S. Won, K. C. Kim, S. H. Song, C.-H. Oh, P. S. Kim, S. Park, and S. I. Kim, “Vertical coupling of long-range surface plasmon polaritons,” Appl. Phys. Lett. 88(1), 011110 (2006). [CrossRef]
  7. S. Park, J. T. Kim, J.-S. Shin, and S.-Y. Shin, “Hybrid vertical directional coupling between a long range surface plasmon polariton waveguide and a dielectric waveguide,” Opt. Commun. 282(23), 4513–4517 (2009). [CrossRef]
  8. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833–5835 (2004). [CrossRef]
  9. G. Gagnon, N. Lahoud, G. A. Mattiussi, and P. Berini, “Thermally activated variable attenuation of long-range surface plasmon-polariton waves,” J. Lightwave Technol. 24(11), 4391–4402 (2006). [CrossRef]
  10. S. Jetté-Charbonneau, R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of Bragg gratings based on long-ranging surface plasmon polariton waveguides,” Opt. Express 13(12), 4674–4682 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-12-4674 . [CrossRef] [PubMed]
  11. A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightwave Technol. 24(2), 912–918 (2006). [CrossRef]
  12. P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photon. 1(3), 484–588 (2009). [CrossRef]
  13. Q. Liu, K. S. Chiang, K. P. Lor, and C. K. Chow, “Temperature sensitivity of a long-period waveguide grating in a channel waveguide,” Appl. Phys. Lett. 86(24), 241115 (2005). [CrossRef]
  14. J. Jiang, C. L. Callender, S. Jacob, J. P. Noad, S. Chen, J. Ballato, and D. W. Smith., “Long-range surface plasmon polariton waveguides embedded in fluorinated polymer,” Appl. Opt. 47(21), 3892–3900 (2008). [CrossRef] [PubMed]
  15. S. J. Al-Bader, “Optical transmission on metallic wires—fundamental modes,” IEEE J. Quantum Electron. 40(3), 325–329 (2004). [CrossRef]
  16. E. Palik, Handbook of Optical Constants of Solids, (Academic, 1985).
  17. 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(12), 3399–3405 (2003). [CrossRef]
  18. W. J. Wang, S. Honkanen, S. I. Najafi, and A. Tervonen, “Loss characteristics of potassium and silver double-ion-exchanged glass waveguides,” J. Appl. Phys. 74(3), 1529–1533 (1993). [CrossRef]

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