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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 5 — Mar. 1, 2010
  • pp: 5314–5319
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Fiber-coupled dielectric-loaded plasmonic waveguides

Jacek Gosciniak, Valentyn S. Volkov, Sergey I. Bozhevolnyi, Laurent Markey, Sébastien Massenot, and Alain Dereux  »View Author Affiliations


Optics Express, Vol. 18, Issue 5, pp. 5314-5319 (2010)
http://dx.doi.org/10.1364/OE.18.005314


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Abstract

Fiber in- and out-coupling of radiation guided by dielectric-loaded surface plasmon-polariton waveguides (DLSPPWs) is realized using intermediate tapered dielectric waveguides. The waveguide structures fabricated by large-scale UV-lithography consist of 1-µm-thick polymer ridges tapered from 10-µm-wide ridges deposited directly on a magnesium fluoride substrate to 1-µm-wide ridges placed on a 50-nm-thick and 100-µm-wide gold stripe. Using fiber-to-fiber transmission measurements at telecom wavelengths, the performance of straight and bent DLSPPWs is characterized demonstrating the overall insertion loss below 24 dB, half of which is attributed to the DLSPPW loss of propagation over the 100-µm-long distance.

© 2010 OSA

1. Introduction

Here we report on fiber in- and out-coupling of radiation guided by DLSPPWs using intermediate linearly tapered dielectric waveguides [Fig. 1(a)
Fig. 1 (a) Schematic representation of the proposed end-fire in/out coupling arrangement showing cleaved PM single-mode optical fibers and a fabricated sample with waveguide stripes. (b) Schematic layout of a device structure containing a DLSPPW waveguide integrated with ridge optical waveguides. The drawings (a) and (b) are not to scale. Optical microscope images showing top views: (c) the fragment of the cleaved edge of the sample and (d) the central part of the sample that features gold film area with PMMA strips forming straight DLSPPWs connected with funnels to input/output RPWs.
] and present experimentally measured fiber-to-fiber transmission spectra conducted at telecom wavelengths (1450-1600 nm) along with the theoretical analysis of coupling loss.

2. Experimental arrangement

All investigated waveguide structures were fabricated using deep UV lithography (wavelength of ~250 nm) with a Süss Microtech MJB4 mask aligner in the vacuum contact mode and a ~1-µm-thick layer of poly-methyl-methacrylate (PMMA) resist spin-coated on a (~750-µm-thick) magnesium fluoride (MgF2) substrate containing a central 50-nm-thick gold strip of ~100 µm in width [Fig. 1(b)]. The fabricated sample contained PMMA strips forming (~1-µm-wide) straight and bent DLSPPWs connected (via funnel structures of different lengths) with access (10-µm-wide) polymer waveguides outside the gold strip [Fig. 1(d)]. Funnel structures have been used in order to efficiently couple radiation from input ridge polymer waveguides (RPWs) (excited through the sample facet with the end-fire arrangement) to DLSPPWs and back [Fig. 1(a)]. Three tapering lengths (varying from 25 to 35 µm by steps of 5 µm) have been realized in order to identify the optimum funnel length [15

15. T. Holmgaard, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, P. Bolger, and A. V. Zayats, “Efficient excitation of dielectric-loaded surface plasmon-polariton waveguide modes at telecommunication wavelengths,” Phys. Rev. B 78(16), 165431 (2008). [CrossRef]

], while the access waveguide width was kept constant (10 µm) matching the dimension of a single-mode fiber (core diameter ~10 µm). The final fabrication step was a cleavage of the sample perpendicular to the RPWs resulting in ~2-mm-long and ~10-µm-wide ridge waveguides leading toward each side of the DLSPPW area. It should be noted, the edge quality of the cleaved sample was found to be varying from strip to strip [Fig. 1(c)] and strongly influencing the level of coupling losses in the fiber-to-fiber transmission measurements.

3. Characterization

Optical characterization of the fabricated straight DLSPPW structures has been carried out using standard transmission measurements with a tunable laser (wavelength range of 1450 – 1600 nm) as a radiation source and an optical spectrum analyzer (OSA) as a detector. TM∕TE-polarized laser radiation (the electric field is perpendicular/parallel to the sample surface plane) was launched into the input RPWs via end-fire coupling from a polarization-maintaining (PM) single-mode fiber. The adjustment of the in-coupling fiber with respect to the input RPW was accomplished by monitoring the output facet of the sample with the help of a far-field microscopic arrangement (with an IR-Vidicon camera and a properly adjusted 50 × microscope objective). It was observed that for a 1-µm-thick and 10-µm-wide RPW, the mode field diameter is symmetric and well matched to that of a standard PM single-mode fiber used in our experiments [cf. Figs. 2(a)
Fig. 2 Far-field microscope images of the mode profile observed at the output facet of (a) cleaved PM single-mode optical fiber and (b, c) output ridge polymer waveguide for both (b) TM and (c) TE polarizations of incident light at λ ≈1550 nm. (d) Total (fiber-to-fiber) transmission of 100-μm-long DLSPPWs connected by funnel structures (of different lengths) to 2-mm-long input/output RPWs as a function of the light wavelength.
and 2(b)]. The far-field observations have also confirmed the expected polarization properties of the DLSPPW mode [9

9. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007). [CrossRef]

], i.e. the efficient coupling of the RPW modes into DLSPPs has been found only with TM-polarized radiation [cf. Figs. 2(b) and 2(c)], and revealed a relatively low level of the total insertion loss. Following these experiments (that include also adjusting the in-coupling fiber position to maximize the coupling efficiency) we replaced the far-field microscopic arrangement with another PM single-mode fiber that was used to collect the out-coupled power and to send it to an OSA. During the experiments we checked that the tunable laser source was spectrally pure and mode hop free over the whole spectral range.

The transmission spectra were recorded in the wavelength range from 1450 to 1600 nm with the OSA sensitivity of −80 dBm for three straight DLSPPWs characterized by different funnel lengths [Fig. 2(d)]. It was found that, in general, the transmission for different DLSPPWs exhibited similar wavelength dependencies with the maximum transmission being detected (for all investigated waveguides) at the wavelength of ~1480 nm (gradually deteriorating for both longer and shorter wavelengths). Since the DLSPPW propagation loss decreases monotonously for longer wavelengths [9

9. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007). [CrossRef]

,15

15. T. Holmgaard, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, P. Bolger, and A. V. Zayats, “Efficient excitation of dielectric-loaded surface plasmon-polariton waveguide modes at telecommunication wavelengths,” Phys. Rev. B 78(16), 165431 (2008). [CrossRef]

], we believe that this maximum should be attributed to the realization of optimum conditions for the RPW-DLSPPW coupling. Furthermore, it is seen that, in the wavelength range of 1525 - 1600 nm, the transmission depends monotonously on the taper length, increasing with the decrease in the funnel angle. This trend is in a good agreement with experimental and theoretical findings reported recently for similar funnel structures excited with the prism coupling arrangement [11

11. T. Holmgaard, S. I. Bozhevolnyi, L. Markey, and A. Dereux, “Dielectric-loaded surface plasmon-polariton waveguides at telecommunication wavelengths: Excitation and characterization,” Appl. Phys. Lett. 92(1), 011124 (2008). [CrossRef]

,15

15. T. Holmgaard, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, P. Bolger, and A. V. Zayats, “Efficient excitation of dielectric-loaded surface plasmon-polariton waveguide modes at telecommunication wavelengths,” Phys. Rev. B 78(16), 165431 (2008). [CrossRef]

].

To get further insight into loss mechanisms of the developed fiber-DLSPPW-fiber coupling arrangement, we have evaluated the RPW-DLSPPW coupling loss using the effective-index method (EIM) approximation [9

9. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007). [CrossRef]

]. Within the EIM approximation, the most imperative loss factor is determined by the in-depth field matching (i.e., in the direction perpendicular to the surface plane). We have calculated the electric-field magnitude (depth) distributions for the fundamental modes of the RPW [Fig. 3(a)
Fig. 3 Distributions of electric field magnitude calculated (by use of effective-index method) along the longitudinal axis for ridge optical (a) and plasmonic (b) waveguides integrated within the device schematically shown in Fig. 1(b).
] and DLSPPW [Fig. 3(b)] and the corresponding overlap integral [16

16. G. T. Reed, and A. P. Knights, Silicon photonics: an introduction (Wiley & Sons, West Sussex, 2004).

] arriving at the RPW-DLSPPW coupling loss of ~3 dB. Similarly, by considering the (both lateral) field profiles for the PM single-mode fiber (with the core diameter being ~10 µm) and RPW we have calculated the overlap integral and the corresponding fiber-RPW coupling loss of ~3.6 dB. Taking into account the propagation loss (~12 dB at λ ≈1550 nm) calculated for 100-µm-long DLSPPWs, the total fiber-to-fiber power loss in the investigated arrangement was estimated to be at the level of ~25 dB. This loss level is in a good agreement with our experimental results [Fig. 2(d)], implying thereby that 25-µm-long (and longer) tapers do not introduce additional losses. One should also keep in mind that the length of the funnel waveguide sections can be significantly reduced (simultaneously preserving a high coupling efficiency) by the use of non-adiabatic planar tapers (e.g., taper forms based on splines), even though these structures are inherently more abrupt and should therefore be more difficult to manufacture [17

17. B. Luyssaert, P. Bienstman, P. Vandersteegen, P. Dumon, and R. Baets, “Efficient nonadiabatic planar waveguide tapers,” J. Lightwave Technol. 23(8), 2462–2468 (2005). [CrossRef]

]. Finally it should also be noted, that the fiber-RPW coupling loss can be significantly decreased (down to ~1.2 dB per facet) by use of the in-coupling fiber with a smaller (~4 µm) core diameter. Similar improvement is expected for the RPW-DLSPPW coupling when properly adjusting the polymer thickness.

Tight mode confinement in the lateral cross section is one of the most attractive DLSPPW features [9

9. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007). [CrossRef]

,10

10. A. V. Krasavin and A. V. Zayats, “Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 90(21), 211101 (2007). [CrossRef]

] amenable to the realization of compact S-bends and Y-splitters [11

11. T. Holmgaard, S. I. Bozhevolnyi, L. Markey, and A. Dereux, “Dielectric-loaded surface plasmon-polariton waveguides at telecommunication wavelengths: Excitation and characterization,” Appl. Phys. Lett. 92(1), 011124 (2008). [CrossRef]

,12

12. T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Bend- and splitting loss of dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 16(18), 13585–13592 (2008). [CrossRef] [PubMed]

]. Current transmission investigations of the fiber-coupled DLSPPWs containing different S-bends are in progress, and their detailed account will be published elsewhere. We present here only preliminary results concerning the influence of the off-set parameter d (ranging from 4 to 16 µm) on the total power loss (Fig. 4
Fig. 4 Optical microscope images of the fabricated and characterized S-bend structures with (a, d) 4, (b, e) 8 and (c, f) 16 µm displacements over a distance of 10 µm along with corresponding mode profiles observed at the output facets of S-bends at λ ≈1550 nm. The level of total (fiber-to-fiber) loss shown in (d-f) is normalized to the transmission through the straight DLSPPW.
). Using the same fiber-to-fiber arrangement [Fig. 1(a)], we characterized S-bends (with different offsets d) and observed a rather efficient transmission with the additional (bend) loss being close to ~1.2 dB (for the smallest offset d ≈4 µm) that gradually deteriorated for larger offsets due to the SPP radiation out of the bend [12

12. T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Bend- and splitting loss of dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 16(18), 13585–13592 (2008). [CrossRef] [PubMed]

]. Note that the obtained results are in good agreement with the already reported investigations (conducted using near-field optical microscopy) of similar S-bends structures [11

11. T. Holmgaard, S. I. Bozhevolnyi, L. Markey, and A. Dereux, “Dielectric-loaded surface plasmon-polariton waveguides at telecommunication wavelengths: Excitation and characterization,” Appl. Phys. Lett. 92(1), 011124 (2008). [CrossRef]

,12

12. T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Bend- and splitting loss of dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 16(18), 13585–13592 (2008). [CrossRef] [PubMed]

]. The performance of the considered structures could be further improved by optimizing the structural parameters so as to achieve the better DLSPPW mode confinement (e.g., by tuning the width of the fabricated DLSPPWs) that would allow to achieve higher transmission through the S-bends.

4. Conclusion

In conclusion, we have developed and investigated the fiber-coupled DLSPPW-based waveguide structures, in which intermediate tapered dielectric waveguides were used to funnel the radiation to and from the plasmonic waveguides. The waveguide structures, consisting of 1-µm-thick polymer ridges tapered from 10-µm-wide ridges deposited directly on a magnesium fluoride substrate to 1-µm-wide ridges placed on a 50-nm-thick and 100-µm-wide gold stripe, were fabricated by large-scale UV-lithography. Using fiber-to-fiber transmission measurements at telecom wavelengths, the performance of straight and bent DLSPPWs has been characterized demonstrating the overall insertion loss below 24 dB, half of which was attributed to the DLSPPW loss of propagation over the 100-µm-long distance. We have discussed the possibilities for further improvement of the developed configuration that we find very promising for practical applications.

After completion of this work, we have used the presented coupling configuration for the realization of thermo-optic control of DLSPPW-based components [18

18. J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18(2), 1207–1216 (2010). [CrossRef] [PubMed]

].

Acknowledgement

This work was supported by EC FP6 STREP “Polymer-based nanoplasmonic components and devices (PLASMOCOM).”

References and links

1.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, 1st ed. (Springer, Berlin, 1988).

2.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008). [CrossRef]

3.

S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits, (World Scientific Publishing, Singapore, 2008).

4.

E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102(20), 203904 (2009). [CrossRef] [PubMed]

5.

A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotechnol. 3(11), 660–665 (2008). [CrossRef] [PubMed]

6.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [CrossRef] [PubMed]

7.

C. Reinhardt, S. Passinger, B. N. Chichkov, C. Marquart, I. P. Radko, and S. I. Bozhevolnyi, “Laser-fabricated dielectric optical components for surface plasmon polaritons,” Opt. Lett. 31(9), 1307–1309 (2006). [CrossRef] [PubMed]

8.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006). [CrossRef]

9.

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007). [CrossRef]

10.

A. V. Krasavin and A. V. Zayats, “Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 90(21), 211101 (2007). [CrossRef]

11.

T. Holmgaard, S. I. Bozhevolnyi, L. Markey, and A. Dereux, “Dielectric-loaded surface plasmon-polariton waveguides at telecommunication wavelengths: Excitation and characterization,” Appl. Phys. Lett. 92(1), 011124 (2008). [CrossRef]

12.

T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Bend- and splitting loss of dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 16(18), 13585–13592 (2008). [CrossRef] [PubMed]

13.

T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Wavelength selection by dielectric-loaded plasmonic components,” Appl. Phys. Lett. 94(5), 051111 (2009). [CrossRef]

14.

J. Grandidier, G. C. des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, C. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9(8), 2935–2939 (2009). [CrossRef] [PubMed]

15.

T. Holmgaard, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, P. Bolger, and A. V. Zayats, “Efficient excitation of dielectric-loaded surface plasmon-polariton waveguide modes at telecommunication wavelengths,” Phys. Rev. B 78(16), 165431 (2008). [CrossRef]

16.

G. T. Reed, and A. P. Knights, Silicon photonics: an introduction (Wiley & Sons, West Sussex, 2004).

17.

B. Luyssaert, P. Bienstman, P. Vandersteegen, P. Dumon, and R. Baets, “Efficient nonadiabatic planar waveguide tapers,” J. Lightwave Technol. 23(8), 2462–2468 (2005). [CrossRef]

18.

J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18(2), 1207–1216 (2010). [CrossRef] [PubMed]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Optics at Surfaces

History
Original Manuscript: January 15, 2010
Revised Manuscript: February 19, 2010
Manuscript Accepted: February 19, 2010
Published: February 26, 2010

Citation
Jacek Gosciniak, Valentyn S. Volkov, Sergey I. Bozhevolnyi, Laurent Markey, Sébastien Massenot, and Alain Dereux, "Fiber-coupled dielectric-loaded plasmonic waveguides," Opt. Express 18, 5314-5319 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-5314


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References

  1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, 1st ed. (Springer, Berlin, 1988).
  2. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008). [CrossRef]
  3. S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits, (World Scientific Publishing, Singapore, 2008).
  4. E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett. 102(20), 203904 (2009). [CrossRef] [PubMed]
  5. A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotechnol. 3(11), 660–665 (2008). [CrossRef] [PubMed]
  6. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [CrossRef] [PubMed]
  7. C. Reinhardt, S. Passinger, B. N. Chichkov, C. Marquart, I. P. Radko, and S. I. Bozhevolnyi, “Laser-fabricated dielectric optical components for surface plasmon polaritons,” Opt. Lett. 31(9), 1307–1309 (2006). [CrossRef] [PubMed]
  8. B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006). [CrossRef]
  9. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007). [CrossRef]
  10. A. V. Krasavin and A. V. Zayats, “Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 90(21), 211101 (2007). [CrossRef]
  11. T. Holmgaard, S. I. Bozhevolnyi, L. Markey, and A. Dereux, “Dielectric-loaded surface plasmon-polariton waveguides at telecommunication wavelengths: Excitation and characterization,” Appl. Phys. Lett. 92(1), 011124 (2008). [CrossRef]
  12. T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Bend- and splitting loss of dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 16(18), 13585–13592 (2008). [CrossRef] [PubMed]
  13. T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, and A. V. Zayats, “Wavelength selection by dielectric-loaded plasmonic components,” Appl. Phys. Lett. 94(5), 051111 (2009). [CrossRef]
  14. J. Grandidier, G. C. des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, C. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9(8), 2935–2939 (2009). [CrossRef] [PubMed]
  15. T. Holmgaard, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin, P. Bolger, and A. V. Zayats, “Efficient excitation of dielectric-loaded surface plasmon-polariton waveguide modes at telecommunication wavelengths,” Phys. Rev. B 78(16), 165431 (2008). [CrossRef]
  16. G. T. Reed, and A. P. Knights, Silicon photonics: an introduction (Wiley & Sons, West Sussex, 2004).
  17. B. Luyssaert, P. Bienstman, P. Vandersteegen, P. Dumon, and R. Baets, “Efficient nonadiabatic planar waveguide tapers,” J. Lightwave Technol. 23(8), 2462–2468 (2005). [CrossRef]
  18. J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18(2), 1207–1216 (2010). [CrossRef] [PubMed]

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