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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 25 — Dec. 5, 2011
  • pp: 25298–25311
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Loss compensation in long-range dielectric-loaded surface plasmon-polariton waveguides

Sonia M. García-Blanco, Markus Pollnau, and Sergey I. Bozhevolnyi  »View Author Affiliations


Optics Express, Vol. 19, Issue 25, pp. 25298-25311 (2011)
http://dx.doi.org/10.1364/OE.19.025298


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Abstract

Loss compensation in long-range dielectric-loaded surface plasmon-polariton waveguides is theoretically analyzed when rare-earth-doped double tungstate crystalline material is used as the gain medium in three different waveguide configurations. We study the effect of waveguide geometry on loss compensation at the telecom wavelength of 1.55 μm, and demonstrate that a material gain as small as 12.5 dB/cm is sufficient for lossless propagation of plasmonic modes with sub-micron lateral confinement when using waveguide ridges with gain.

© 2011 OSA

1. Introduction

Surface plasmon polaritons (SPPs), evanescent electromagnetic waves propagating along metal-dielectric interfaces, have been the subject of numerous studies due to their unique properties promising applications in a variety of fields, such as optical biosensing [1

1. Q. Min, C. Chen, P. Berini, and R. Gordon, “Long range surface plasmons on asymmetric suspended thin film structures for biosensing applications,” Opt. Express 18(18), 19009–19019 (2010). [CrossRef] [PubMed]

], data storage [2

2. M. Mansuripur, A. R. Zakharian, A. Lesuffleur, S.-H. Oh, R. J. Jones, N. C. Lindquist, H. Im, A. Kobyakov, and J. V. Moloney, “Plasmonic nano-structures for optical data storage,” Opt. Express 17(16), 14001–14014 (2009). [CrossRef] [PubMed]

], photovoltaic cells [3

3. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]

], and highly integrated photonic circuits [4

4. S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits (Pan Stanford Publishing Pte. Ltd, 2009).

]. The great interest in plasmonic waveguides is largely due to their capability to confine the electromagnetic field below the diffraction limit, which can potentially lead to photonic circuits suitable for very large scale integration [4

4. S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits (Pan Stanford Publishing Pte. Ltd, 2009).

]. Another interesting feature of SPP waveguides is the high sensitivity to their immediate environment that makes them very attractive for realizing ultra-sensitive optical sensors [1

1. Q. Min, C. Chen, P. Berini, and R. Gordon, “Long range surface plasmons on asymmetric suspended thin film structures for biosensing applications,” Opt. Express 18(18), 19009–19019 (2010). [CrossRef] [PubMed]

]. Furthermore, the presence of metal in the midst of propagating mode fields enables a direct and very efficient electrical control of their propagation characteristics by making use of, for example, thermo-optic effects [5

5. 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]

, 6

6. O. Tsilipakos, E. E. Kriezis, and S. I. Bozhevolnyi, “Thermo-optic microring resonator switching elements made of dielectric-loaded plasmonic waveguides,” J. Appl. Phys. 109(7), 073111 (2011). [CrossRef]

].

Many different plasmonic waveguiding configurations have been proposed and demonstrated over the past few years [7

7. A. V. Krasavin and A. V. Zayats, “Silicon-based plasmonic waveguides,” Opt. Express 18(11), 11791–11799 (2010). [CrossRef] [PubMed]

16

16. J. Gosciniak, T. Holmgaard, and S. I. Bozhevolnyi, “Theoretical analysis of long-range dielectric-loaded surface plasmon polariton waveguides,” J. Lightwave Technol. 29(10), 1473–1481 (2011). [CrossRef]

]. In general, SPP waveguides are subject to a trade-off between mode-field confinement and propagation loss due to absorption in the metal, exhibiting either good optical confinement but short propagation distances, typically in the few tens of micrometers (e.g., dielectric-loaded SPP waveguides [13

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

]), or long propagation distances (in the millimeter range) that necessitate large mode profiles (e.g., long-range SPP waveguides [14

14. 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]

]). Recently, a novel type of plasmonic waveguide configuration was proposed, long-range dielectric-loaded surface plasmon-polariton (LR-DLSPP) waveguides that combine the millimeter-range propagation with a relatively strong mode confinement [15

15. T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010). [CrossRef] [PubMed]

, 16

16. J. Gosciniak, T. Holmgaard, and S. I. Bozhevolnyi, “Theoretical analysis of long-range dielectric-loaded surface plasmon polariton waveguides,” J. Lightwave Technol. 29(10), 1473–1481 (2011). [CrossRef]

]. Reduced propagation losses provided by this novel structure (albeit at the expense of higher tolerances and increased complexity of configuration) permit enlarging the range of gain materials that can be selected for loss compensation.

Very large optical gain, ~950 dB/cm, has recently been achieved in a rare-earth (RE)-doped double tungstate crystalline waveguide [29

29. D. Geskus, S. Aravazhi, S. M. García-Blanco, and M. Pollnau, “Giant optical gain in a rare-earth-ion-doped microstructure,” Adv. Mater. (Deerfield Beach Fla.) (accepted).

]. RE-doped gain materials do not exhibit the limitations of laser dyes or semiconductor gain materials discussed above. Furthermore, the optical gain provided by RE ions possesses very interesting features. RE gain materials can amplify very-high-rate signals in the small-signal-gain regime without distortion [30

30. J. D. Bradley, M. Costa e Silva, M. Gay, L. Bramerie, A. Driessen, K. Wörhoff, J. C. Simon, and M. Pollnau, “170 Gbit/s transmission in an erbium-doped waveguide amplifier on silicon,” Opt. Express 17, 22201–22208 (2009). [CrossRef] [PubMed]

]. They provide a large gain bandwidth up to a few tens of nanometers, which is interesting for broadband optical amplification and the generation of ultra-short laser pulses. Finally, they enable the production of very-narrow-linewidth lasers due to the lack of detrimental linewidth broadening effects characteristic of semiconductor lasers [31

31. E. H. Bernhardi, H. A. G. M. van Wolferen, L. Agazzi, M. R. H. Khan, C. G. H. Roeloffzen, K. Wörhoff, M. Pollnau, and R. M. de Ridder, “Ultra-narrow-linewidth, single-frequency distributed feedback waveguide laser in Al2O3:Er3+ on silicon,” Opt. Lett. 35(14), 2394–2396 (2010). [CrossRef] [PubMed]

]. When RE ions are doped into a double tungstate crystal, very large gain can be obtained due to the large absorption and emission cross-sections of RE ions in these materials [32

32. N. V. Kuleshov, A. A. Lagatsky, A. V. Podlipensky, V. P. Mikhailov, and G. Huber, “Pulsed laser operation of Y b-dope d KY(WO4))2 and KGd(WO4))2.,” Opt. Lett. 22(17), 1317–1319 (1997). [CrossRef] [PubMed]

] and the large dopant concentrations possible without significant luminescence quenching because of the large inter-ionic separation provided by the crystalline structure of double tungstates [29

29. D. Geskus, S. Aravazhi, S. M. García-Blanco, and M. Pollnau, “Giant optical gain in a rare-earth-ion-doped microstructure,” Adv. Mater. (Deerfield Beach Fla.) (accepted).

].

In this paper, loss compensation in LR-DLSPP waveguides due to optical gain provided by a RE-doped double tungstate material incorporated into the LR-DLSPP configuration is theoretically studied. Several structures are discussed in detail. The effect of different waveguide parameters on the efficiency of the material gain to compensate propagation losses is evaluated. Lossless propagation is predicted for material gain as low as 12.5 dB/cm, while maintaining a mode size comparable to conventional dielectric-loaded surface plasmon-polariton waveguides [13

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

].

2. Proposed structures

The generic LR-DLSPP structure includes a low-refractive-index substrate material, a buffer layer of a high-refractive-index material, a metal stripe and a dielectric ridge, the dimensions and refractive index of which should be chosen to balance the electric fields at both sizes of the gold stripe in order to ensure long-range propagation [15

15. T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010). [CrossRef] [PubMed]

, 16

16. J. Gosciniak, T. Holmgaard, and S. I. Bozhevolnyi, “Theoretical analysis of long-range dielectric-loaded surface plasmon polariton waveguides,” J. Lightwave Technol. 29(10), 1473–1481 (2011). [CrossRef]

]. The three waveguide geometries studied in this paper are shown in Fig. 1
Fig. 1 Layout of the LR-DLSPP structures with gain analyzed in this work: (a) Gain material, RE-doped double tungstate, as buffer layer and ridge in BCB; (b) gain material in the buffer and polyimide ridge; (c) gain material in the ridge, buffer layer in silicon nitride and 100-nm-thin BCB adhesive layer between buffer and ridge. The wavelength utilized in all the simulations is 1.55 μm.
and their corresponding material properties are summarized in Table 1

Table 1. Parameters of the Structures Used for the Simulations. λ = 1.55 μm

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. The radiation wavelength utilized throughout this study is chosen in the telecom wavelength range and equal to 1.55 μm.

3. Finite difference calculations

The different modes supported by the structures were calculated for a vacuum wavelength of 1.55 μm. The structures were verified to support a long-range SPP mode (TM polarized) and, in some cases, radiative TE modes with much shorter propagation distance than the main long-range SPP mode (i.e., typically less than a few tens of micrometers). From the imaginary part of the effective refractive index of the long-range SPP mode, the propagation losses (or gain when the sign is negative) of the different structures were calculated as:

α[dB/cm]=2×k0×Im(neff)×4.34
(1)

Here k0 is the vacuum wavevector, 2π/λ, where λ is the vacuum wavelength in cm, neff is the effective refractive index of the propagating SPP mode, and the factor 4.34 converts the loss value from 1/cm to dB/cm. The imaginary part of neff is positive for lossy materials, and becomes eventually negative for materials exhibiting sufficiently large optical gain. The absorption losses of RE-doped double tungstates responsible for the optical gain have been ignored in the simulations. In the case of passive structures, it has been assumed that the necessary optical pump power has been applied to the gain material in order to compensate for the absorption losses and obtain gain = loss = 0 (i.e., zero imaginary part of the refractive index). It has also been assumed that the gain achieved in the material is uniform. The anisotropy of the double tungstate materials has not been considered, as it was assumed that the waveguides are aligned along one of the major axes of the optical indicatrix.

The optical power confinement in the gain region is an important parameter, as it determines how effective the material gain is in compensating the propagation losses. Another important parameter is the mode size, especially in the x-direction, as it indicates the mode confinement in the different configurations. Depending on the application, a mode size as small as possible in one or both directions can be an important design parameter. The mode size has been calculated as the width of a Gaussian fit to the major component of the H-field at the level of 1/e of its maximum value.

4. Effect of waveguide structure on loss compensation

A number of waveguide parameters must be taken into account for optimization of the waveguide structure. These parameters comprise the ridge material, ridge size (width and height), buffer layer material and thickness, metal stripe material, thickness, and width, and substrate material. In this work, the metal was fixed to gold with a width of 200 nm and a thickness of 15 nm. The effect of the remaining parameters on the net gain finally achieved in the LR-DLSPP waveguides will be discussed in this section.

4.1 LR-DLSPP waveguide with BCB ridge

Structure 1 was simulated as described in Section 3. Figure 3
Fig. 3 (a) Mode profile for Structure 1 with hbuffer = 60 nm and hridge = wridge = 1.4 μm; (b) vertical line scan of the mode profile across the center of the metal stripe (x ~0). It can be seen that the electric field hardly penetrates inside the gain buffer material.
shows the transverse mode profile of the long-range SPP mode supported by the structure. A propagation loss of 3.6 dB/cm and mode width of 1.7 μm in the horizontal x-direction and 2.5 μm in the vertical y-direction were calculated for hbuffer = 60 nm and hridge = wridge = 1.4 μm. This structure exhibits two main drawbacks. Firstly, the thickness of the buffer layer is too thin to be easily realized in a double tungstate gain material. Secondly, as can be clearly seen in Fig. 3, the optical power confinement in the gain region (buffer layer) is very small (~2%). The much lower refractive index of the ridge structure is more favorable for the plasmonic mode than the high refractive index of the buffer, pulling a large fraction of the optical power above the metal stripe. As a consequence, this structure is not very efficient to obtain lossless propagation or propagation with net gain. In order to permit penetration of the mode into the gain region, a structure with a better balanced refractive index profile is desirable. This goal can be achieved by selecting a high-refractive-index material for the ridge, such as polyimide.

4.2 LR-DLSPP waveguide with polyimide ridge

For a passive structure (i.e., a material gain of 0 dB/cm), as the ridge width increases for a given ridge height [Fig. 4 (a)], the losses decrease and the location of the minimum loss shifts towards larger buffer thicknesses that balance increasing ridge widths. As the ridge width increases, the field intensity close to the metal layer decreases, because the mode is pulled both into the ridge and buffer layers, increasing the ratio between the mode power concentrated in dielectric regions and that in the (absorptive) metal region. The propagation losses are, therefore, reduced. For each ridge dimension, the waveguide structure providing minimum losses corresponds to the configuration for which the mode is balanced on the top and bottom of the metal stripe [15

15. T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010). [CrossRef] [PubMed]

]. For a given ridge height, as the ridge width increases, this condition is met for thicker buffer layers, as can be appreciated in Fig. 4 (a). As the ridge width increases, both the mode confinement to the active layer [Fig. 4 (e)] and the mode width in the x-direction [Fig. 4 (f)] increases. Comparison of Fig. 4 (a) to (d) indicates that with increasing material gain of the buffer layer the parameter space for which net gain is obtained increases. For a buffer layer material gain of 246 dB/cm [Fig. 4(d)] practically all investigated geometrical configurations exhibit net gain. A similar physical behavior governs the influence of ridge height on net loss (Fig. 5).

Two distinct zones can be observed. In the first zone (i.e., small buffer thickness), losses increase as the ridge height increases. In the second zone (i.e., large buffer thickness), the opposite behavior is observed. The behavior in both zones can again be qualitatively explained by the fact that the losses decrease, as the effective refractive indices above and below the metal stripe approach the point of balance. For small buffer layer thickness and fixed ridge width, as the height of the ridge increases, the structure moves farther away from this low-loss condition. For large buffer thickness, the opposite occurs: as the ridge height increases, the structure moves closer to the balanced condition. In all cases, the minimum propagation loss as a function of buffer thickness shifts to larger buffer thicknesses, as the height of the ridge increases. An increase of ridge height forces both the mode confinement to the active layer [Fig. 5 (e)] and the lateral mode width in the x-direction [Fig. 5 (f)] to decrease. Again, with increasing material gain of the buffer layer the parameter space for which net gain is obtained increases, and, for the highest investigated buffer layer material gain of 246 dB/cm [Fig. 5 (d)] practically all investigated geometrical configurations provide net gain.

4.3 LR-DPSPP with Si3N4 buffer layer and gain ridge

The net loss of such a structure was simulated as a function of thickness of the buffer layer for several ridge dimensions. The power confinement to the active region (in this case the ridge) and lateral mode dimension in the horizontal x-direction were also calculated. In Fig. 7 (a), (c), and (e)
Fig. 7 Structure 3: Net optical loss as a function of hbuffer for (a) hridge = 0.8 μm and various wridge and (b) wridge = 0.8 μm and various hridge; confinement of the optical power to the active material region (ridge) as a function of hbuffer for (c) hridge = 0.8 μm and several wridge and (d) wridge = 0.8 μm and several hridge; mode width in the x-direction as a function of hbuffer for (e) hridge = 0.8 μm and various wridge and (f) wridge = 0.8 μm and various hridge. The material gain was considered to be zero in all cases (passive structure).
, the effect of ridge width is shown for a given ridge height. As the ridge width increases, the propagation loss minimum shifts towards thicker buffer layers, consistent with the balancing of the effective refractive indices above and below the metal stripe. Furthermore, increasing the ridge width leads to a decrease of the minimum of the propagation losses, slight increase in mode waist in the horizontal x-direction, and increase of mode confinement to the active area (ridge). The latter effect improves the exploitation of available material gain, which is shown in Fig. 8
Fig. 8 Net optical loss in Structure 3 for hridge = 0.8 μm and various wridge when assuming a material gain of (a) 35 dB/cm and (b) 106 dB/cm.
for two values of material gain. The influence of the ridge height is shown in Fig. 7 (b), (d), and (f). As the ridge height increases, the propagation loss minimum shifts towards thicker buffer layers, again as a result of balancing the refractive indices at both sides of the metal. The mode size in the x-direction increases, as the ridge height decreases. This phenomenon can be intuitively explained by the squeezing out of the optical mode, as the ridge height decreases, forcing the mode to widen in the x-direction. The mode confinement to the ridge also decreases, because the mode is pushed towards the metal by a reduction of the ridge height.

Finally, for obtaining a manufacturable design it is important that the waveguide behavior does not change drastically if the ridge height or width or thicknesses of the buffer and adhesive layer vary within typical fabrication tolerances. In Fig. 8, the minima for the ridge dimensions 0.8 μm × 0.8 μm are flatter than those for the ridge dimensions 0.8 μm × 0.5 μm. Therefore, the larger ridge will be more tolerant to small variations of the buffer thickness (in this case determined by control of the Si3N4 deposition process). Furthermore, at the target buffer thickness, hbuffer = 0.35 μm, the curves corresponding to ridge widths of 0.8 μm and 0.7 μm are very close to each other. Thus, a small variation of the ridge width, controlled by the lithography and etching processes, should have very little influence on the characteristics of the final devices. The same applies for the ridge height [Fig. 7 (b)]. The influence of thickness of the adhesive layer has been analyzed for a passive structure with 0.8 μm × 0.8 μm ridge size. As the thickness of the adhesive increases, the mode becomes more confined in the ridge, losing its plasmonic character. A tolerance of ~50 nm around the 100-nm target can, however, be tolerated. (See Table 2

Table 2. Waveguide Dimensions and Mode Profiles for Large Ridge Structure (Waveguide 1) and Smaller Ridge Structure (Waveguide 2), Showing Influence of Ridge on Mode Size and Minimum Gain Required for Lossless Propagation—Mode Profiles, Re[Ey], Also Shown

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.)

6. Conclusions

Loss compensation in plasmonic waveguides will pave the road toward utilization of these structures in a wide range of novel devices by permitting full exploitation of their potential. In this paper, a detailed investigation of the compensation of propagation loss in LR-DLSPP waveguides using RE-doped double tungstates as the gain material has been presented for three different configurations that were selected keeping in mind manufacturability using fabrication and assembly equipment commonly available in standard microfabrication cleanrooms. In the first two structures, the gain material is integrated as a buffer layer. We found that only a small fraction of the mode power is confined within the material gain region, making this approach not very favorable for loss compensation. Nevertheless, using a high-refractive-index ridge made of polyimide (n ~1.9) resulted in an increased mode confinement to the gain material. It was also found that, in the design of optimized structures, one should consider simultaneously the LR-SPP waveguide dimensions and the available material gain. For example, it was demonstrated that a material gain of 37 dB/cm is sufficient to achieve lossless propagation in a LR-DLSPP waveguide structure with a 1.6 × 1.6 µm2 ridge and a 375-nm-thick buffer layer. In general, configurations with larger mode fractions within the gain (buffer) layer resulted in larger lateral mode widths, which are detrimental with respect to the bend loss (that increases with the mode width) and maximum achievable density of waveguide components [15

15. T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010). [CrossRef] [PubMed]

, 16

16. J. Gosciniak, T. Holmgaard, and S. I. Bozhevolnyi, “Theoretical analysis of long-range dielectric-loaded surface plasmon polariton waveguides,” J. Lightwave Technol. 29(10), 1473–1481 (2011). [CrossRef]

].

In the third structure, the gain material was integrated as the ridge material. A 100-nm-thin BCB layer was introduced between the gold stripe and the waveguide ridge in order to ease manufacturability. This structure ensures a considerably higher confinement of the mode optical power in the active material region, making the LR-DLSPP waveguide configuration much more amenable with respect to loss compensation. A material gain as low as 12.5 dB/cm is sufficient to allow for lossless propagation in a waveguide structure with a 0.8 × 0.8 µm2 ridge and 350-nm-thick buffer layer. Simultaneously, the hybrid LR-DLSPP mode supported by this structure has a lateral width of only 0.92 μm.

Ackowledgments

The authors acknowledge support from the COST Action MP0702: Towards functional sub-wavelength photonic structures. Dr. García-Blanco acknowledges support from the FP7 Marie Curie Career Integration Grant PCIG09-GA-2011-29389, technical support and useful discussions with from PhoeniX B.V., and useful discussions with Manfred Hammer and Hugo Hoekstra. The financial support of the Danish Council for Independent Research (FTP-project No. 09-072949 ANAP) is also appreciated (SIB).

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R. M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (2011). [CrossRef] [PubMed]

27.

R. A. Flynn, C. S. Kim, I. Vurgaftman, M. Kim, J. R. Meyer, A. J. Mäkinen, K. Bussmann, L. Cheng, F. S. Choa, and J. P. Long, “A room-temperature semiconductor spaser operating near 1.5 μm,” Opt. Express 19(9), 8954–8961 (2011). [CrossRef] [PubMed]

28.

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007). [CrossRef]

29.

D. Geskus, S. Aravazhi, S. M. García-Blanco, and M. Pollnau, “Giant optical gain in a rare-earth-ion-doped microstructure,” Adv. Mater. (Deerfield Beach Fla.) (accepted).

30.

J. D. Bradley, M. Costa e Silva, M. Gay, L. Bramerie, A. Driessen, K. Wörhoff, J. C. Simon, and M. Pollnau, “170 Gbit/s transmission in an erbium-doped waveguide amplifier on silicon,” Opt. Express 17, 22201–22208 (2009). [CrossRef] [PubMed]

31.

E. H. Bernhardi, H. A. G. M. van Wolferen, L. Agazzi, M. R. H. Khan, C. G. H. Roeloffzen, K. Wörhoff, M. Pollnau, and R. M. de Ridder, “Ultra-narrow-linewidth, single-frequency distributed feedback waveguide laser in Al2O3:Er3+ on silicon,” Opt. Lett. 35(14), 2394–2396 (2010). [CrossRef] [PubMed]

32.

N. V. Kuleshov, A. A. Lagatsky, A. V. Podlipensky, V. P. Mikhailov, and G. Huber, “Pulsed laser operation of Y b-dope d KY(WO4))2 and KGd(WO4))2.,” Opt. Lett. 22(17), 1317–1319 (1997). [CrossRef] [PubMed]

33.

M. L. Thèye, “Investigation of the optical properties of Au by means of thin semitransparent films,” Phys. Rev. B 2(8), 3060–3078 (1970). [CrossRef]

34.

R. H. French, J. M. Rodríguez-Parada, M. K. Yang, R. A. Derryberry, and N. T. Pfeiffenberger, “Optical properties of polymeric materials for concentrator photovoltaic systems,” Sol. Energy Mater. Sol. Cells 95(8), 2077–2086 (2011). [CrossRef]

35.

http://www.phoenixbv.com/index.php

OCIS Codes
(160.5690) Materials : Rare-earth-doped materials
(230.7370) Optical devices : Waveguides
(250.5403) Optoelectronics : Plasmonics
(230.4480) Optical devices : Optical amplifiers

ToC Category:
Optics at Surfaces

History
Original Manuscript: September 6, 2011
Revised Manuscript: September 29, 2011
Manuscript Accepted: September 29, 2011
Published: November 23, 2011

Citation
Sonia M. García-Blanco, Markus Pollnau, and Sergey I. Bozhevolnyi, "Loss compensation in long-range dielectric-loaded surface plasmon-polariton waveguides," Opt. Express 19, 25298-25311 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-25298


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  27. R. A. Flynn, C. S. Kim, I. Vurgaftman, M. Kim, J. R. Meyer, A. J. Mäkinen, K. Bussmann, L. Cheng, F. S. Choa, and J. P. Long, “A room-temperature semiconductor spaser operating near 1.5 μm,” Opt. Express19(9), 8954–8961 (2011). [CrossRef] [PubMed]
  28. M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics1(10), 589–594 (2007). [CrossRef]
  29. D. Geskus, S. Aravazhi, S. M. García-Blanco, and M. Pollnau, “Giant optical gain in a rare-earth-ion-doped microstructure,” Adv. Mater. (Deerfield Beach Fla.) (accepted).
  30. J. D. Bradley, M. Costa e Silva, M. Gay, L. Bramerie, A. Driessen, K. Wörhoff, J. C. Simon, and M. Pollnau, “170 Gbit/s transmission in an erbium-doped waveguide amplifier on silicon,” Opt. Express17, 22201–22208 (2009). [CrossRef] [PubMed]
  31. E. H. Bernhardi, H. A. G. M. van Wolferen, L. Agazzi, M. R. H. Khan, C. G. H. Roeloffzen, K. Wörhoff, M. Pollnau, and R. M. de Ridder, “Ultra-narrow-linewidth, single-frequency distributed feedback waveguide laser in Al2O3:Er3+ on silicon,” Opt. Lett.35(14), 2394–2396 (2010). [CrossRef] [PubMed]
  32. N. V. Kuleshov, A. A. Lagatsky, A. V. Podlipensky, V. P. Mikhailov, and G. Huber, “Pulsed laser operation of Y b-dope d KY(WO4))2 and KGd(WO4))2.,” Opt. Lett.22(17), 1317–1319 (1997). [CrossRef] [PubMed]
  33. M. L. Thèye, “Investigation of the optical properties of Au by means of thin semitransparent films,” Phys. Rev. B2(8), 3060–3078 (1970). [CrossRef]
  34. R. H. French, J. M. Rodríguez-Parada, M. K. Yang, R. A. Derryberry, and N. T. Pfeiffenberger, “Optical properties of polymeric materials for concentrator photovoltaic systems,” Sol. Energy Mater. Sol. Cells95(8), 2077–2086 (2011). [CrossRef]
  35. http://www.phoenixbv.com/index.php

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