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Optics Express

  • Editor: Martijn de Sterke
  • Vol. 16, Iss. 20 — Sep. 29, 2008
  • pp: 15546–15552
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Compact plasmonic variable optical attenuator

Kristjan Leosson, Tiberiu Rosenzveig, Petur Gordon Hermannsson, and Alexandra Boltasseva  »View Author Affiliations


Optics Express, Vol. 16, Issue 20, pp. 15546-15552 (2008)
http://dx.doi.org/10.1364/OE.16.015546


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Abstract

We demonstrate plasmonic nanowire-based thermo-optic variable optical attenuators operating in the 1525-1625 nm wavelength range. The devices have a footprint as low as 1 mm, extinction ratio exceeding 40 dB, driving voltage below 3 V, and full modulation bandwidth of 1 kHz. The polarization dependent loss is shown to be critically dependent on the nanowire geometry but devices with polarization-dependent loss as low as ±2.5 dB PDL over most of the attenuation range have been fabricated. We propose an even more compact device design to reduce insertion loss to approximately 1 dB.

© 2008 Optical Society of America

1. Introduction

Surface plasmon photonics has received considerable attention in recent years [1

1. S.A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007).

]. A good deal of research has focused on plasmonic waveguiding and basic components operating at telecommunications wavelengths [2

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

,3

3. A. Degiron, P. Berini, and D. R. Smith, “Guiding light with long-range plasmons,” Opt. Photon. News 19, 29–34 (2008). [CrossRef]

], where the optical properties of metals tend to be favourable. This emphasis has been motivated by the prospect of realizing highly integrated optical components by utilizing the strong light confinement possible at metal surfaces. However, two main factors still prevent plasmonic components from competing with current and emerging platforms for integrated optics: high loss and strong polarization dependence. In order to address these issues, we have previously investigated metallic nanowires that guide light of arbitrary polarization with comparatively low loss [4

4. K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, “Long-range surface plasmon polariton nanowire waveguides for device applications,” Opt. Express 14, 314–319 (2006). [CrossRef] [PubMed]

]. In the present work, we demonstrate a compact variable optical attenuator with a high extinction ratio based on such a waveguide. We believe that this device represents a first step towards a viable plasmonic integrated optical component design compatible with current technologies.

Optical components used in modern telecommunications systems are fabricated using a variety of technologies, each exhibiting particular strengths and weaknesses in terms of size, speed, cost, reliability, optical loss, power consumption, scalability, etc. [5

5. L. Eldada , “Optical communication components,” Rev. Sci. Instrum. 75, 575–593 (2004). [CrossRef]

] In particular, the variable optical attenuator (VOA) which is widely used in optical networks, can be realized using many different platforms, including opto-mechanics, MEMS, thermo-optics, electro-optics, microfluidics, liquid crystals or direct fibre manipulation. Advances in the development of reliable optical polymers for planar lightwave circuits [6

6. H. Ma, A.K.-Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: Materials processing and devices,” Adv. Mater. 14, 1339–1365 (2002). [CrossRef]

,7

7. L. Eldada, “Advances in Polymer Integrated Optics,” IEEE J. Sel. Top. Quantum Electron. 6, 54–68 (2000). [CrossRef]

] have made the planar polymer technology a prime candidate for meeting the demand for compact, highly scalable, low-cost optical components. Polymer materials are particularly suited for realizing integrated thermo-optic components since the absolute value of the thermo-optic coefficient dn/dT in polymers is an order of magnitude larger than that of glass. Various types of thermo-optic polymer VOAs, based on Mach-Zehnder [8

8. D. Li, Y. Zhang, L. Liu, and L. Xu, “Low consumption power variable optical attenuator with sol-gel derived organic/inorganic hybrid materials,” Opt. Express 14, 6029–6034 (2006). [CrossRef] [PubMed]

] or multimode-interferometers [9

9. X. Jiang, et al., “Compact Variable Optical Attenuator Based on Multimode Interference Coupler,” IEEE Photon. Technol. Lett 17, 2361–2363 (2005). [CrossRef]

] or on digital optical switches [10

10. Y.-O. Noh, H.-J. Lee, Y.-H. Won, and M.-C. Oh, “Polymer waveguide thermo-optic switches with -70 dB optical crosstalk,” Opt. Commun. 258, 18–22 (2006). [CrossRef]

], have been reported and some are commercially available.

Attenuators based on plasmonic stripe waveguides embedded in polymers [11

11. T. Nikolajsen, K. Leosson, and S.I. Bozhevolnyi, “In-line extinction modulator based on long-range surface plasmon polaritons,” Opt. Commun. 244, 455–459 (2005). [CrossRef]

,12

12. S. Park and S. H. Song, “Polymeric variable optical attenuator based on long range surface plasmon polaritons,” Electron. Lett. 42, 402–404 (2006). [CrossRef]

] or sandwiched between glass and polymer [13

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

], have also been demonstrated. Here, attenuation occurs by increased absorption in the metal and/or radiation out of the waveguides, caused by refractive index gradients induced by heating up the waveguide core or by using an adjacent heater. The devices are based on long-range surface plasmon polariton (LRSPP) stripe waveguides, dimensioned to minimize propagation loss (PL) and coupling loss (CL) to standard single-mode fibres [11

11. T. Nikolajsen, K. Leosson, and S.I. Bozhevolnyi, “In-line extinction modulator based on long-range surface plasmon polaritons,” Opt. Commun. 244, 455–459 (2005). [CrossRef]

,13

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

]. A common problem of these devices is their high insertion loss (6-10 dB) and single-polarization operation.

2. Simulation

In order to compete with existing technologies, a plasmonic VOA must meet the target specifications of low insertion loss (<=1 dB), high attenuation (>=20 dB), low polarization-dependent and wavelength-dependent loss over the whole attenuation range, and low power consumption. Furthermore, response times (limited by heat transfer) should be similar to other thermo-optic components. We used computer simulations to determine the optimum structure for a plasmonic attenuator meeting as many of these specifications as possible.

The fact that a metal-dielectric interface only supports a TM-polarized surface wave means that orthogonal polarizations can only be transmitted if the metallic waveguide is symmetric with respect to 90° rotation. A simple geometry which fulfils this condition is the square-cross-section nanowire waveguide first suggested by Berini [14

14. P. Berini, “Optical Waveguide Structures,” US patent number 6,741,782 (2004).

]. In contrast to the plasmonic stripe waveguides that support a long-ranging supermode composed of coupled modes associated with the top and bottom surfaces of the metal film, the nanowire waveguide has two degenerate long-ranging modes formed by superpositions of four coupled corner plasmon polariton modes. These supermodes, denoted E(1,0) and E(0,1) by Jung et al. [15

15. J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding,” Phys. Rev. B 76, 035434 (2007).

], have their electric field pointing primarily in the x and y directions, respectively.

Following the approach of Jung et al. [15

15. J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding,” Phys. Rev. B 76, 035434 (2007).

], we performed finite-element analysis of gold nanowires embedded in a dielectric cladding. Calculations were performed using COMSOL Multiphysics® (RF module) to determine the plasmonic modes in our devices. We modelled the cross-section of gold nanowire waveguides (n=0.52+10.7i, interpolated from the data of Johnson & Christy [16

16. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).

]) embedded in a 24-µm thick dielectric cladding (n=1.535, corresponding to our experimental conditions outlined below) bounded by air and silicon (n=3.48) on the top and bottom, respectively. We used rounded-square cross-sections (5 nm corner radius) for the wires with a maximum mesh density (<1 nm grid size) at the corners. Details of the corner rounding have been shown to have minimal effect on the calculation [15

15. J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding,” Phys. Rev. B 76, 035434 (2007).

]. It should be emphasized, however, that the finite cladding thickness significantly influences the mode as the wire gets narrower. Due to the extra confinement, the finite cladding thickness results in higher propagation loss for a given wire cross-section, compared to the case of an “infinite” cladding assumed in previously published work [14

14. P. Berini, “Optical Waveguide Structures,” US patent number 6,741,782 (2004).

,15

15. J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding,” Phys. Rev. B 76, 035434 (2007).

]. The magnitude and direction of the electric field of the E(0,1) mode in a symmetric nanowire is shown in Fig. 1. At distances larger than a few 100 nm from the surface of the wire, the electric field is purely y-polarized. The x-polarized E(1,0) mode is obtained simply by 90° rotation about the z-axis.

Fig. 1. Calculated magnitude and direction (in the x-y plane) of the electric field of the y-polarized E(0,1) mode in the vicinity of the wire, illustrating the high field intensity close to the corners

Our calculations yielded a maximum achievable mode overlap of 93% (CL=0.3 dB) between a Gaussian fibre mode and the long-range modes of a square nanowire. For the particular case of a standard single mode fibre, with a mode-field diameter (MFD) of 10.5 µm, coupled to a gold wire embedded in a 24-µm thick BCB polymer, the maximum overlap occurs for wires with a 240 nm×240 nm cross-section (1550 nm wavelength). This nanowire size, however, gives a substantial propagation loss of approximately 8 dB/mm. For a 1-mm long device, a minimum calculated insertion loss of 4.0 dB is obtained for a 180 nm×180 nm cross-section (CL=1.1 dB/coupling, PL=1.7 dB/mm) which we used as a nominal design parameter in our devices.

In order to achieve optical attenuation, we use the concept of ref. [11

11. T. Nikolajsen, K. Leosson, and S.I. Bozhevolnyi, “In-line extinction modulator based on long-range surface plasmon polaritons,” Opt. Commun. 244, 455–459 (2005). [CrossRef]

], where light is expelled from the plasmonic waveguide by reducing the refractive index around the waveguide core. For a metallic waveguide embedded in a polymer (dn/dT <0), this is simply done by passing an electrical current through the metal, directly heating the volume around the waveguide. The device geometry used in the present work is illustrated in Fig. 2.

Fig. 2. (a) Schematic picture of the device geometry. The plasmonic nanowire waveguide is divided into short sections connected to common electrodes in order to increase device yield. (b) A 1-mm long chip containing 12 individual VOAs. Light is coupled to the device under test through polarization-maintaining optical fibres for extinction measurements. (c) Optical microscope image of a fully processed device, showing the layout of electrodes and contact pads.

3. Experiment

Our devices were fabricated as follows: A 100-mm silicon wafer was spin-coated with adhesion promoter (AP3000, DOW Chemical Co.) followed by a 12-µm thick layer of benzocyclobutene (BCB) polymer (CYCLOTENE 3022-57, DOW Chemical Co.). The BCB layer was cured in nitrogen atmosphere at 210°C for 40 minutes. The wafers were spin-coated with a 220-nm thick layer of ZEP520 electron beam resist (Zeon Corporation). The resist was covered with a 15 nm layer of thermally evaporated Al to avoid charge build-up during exposure and exposed in a JEOL-JBX9300FS electron-beam writer. The aluminium was removed by wet-etching before developing the resist using ZED-N50 developer (Zeon Corporation). Gold was deposited by e-beam evaporation to the desired wire thickness, followed by lift-off in resist remover. The wafer was then coated with a layer of photoresist (maN-1420, Micro Resist Technology GmbH) for patterning of contacts by UV-lithography. 300-nm thick gold contacts were fabricated using thermal deposition and lift-off in acetone. Finally, the wafer was covered with a second layer of BCB and hard-cured in nitrogen atmosphere at 250°C for 60 minutes. The wafer was diced into individual 1-mm and 2-mm long components. Contact pads were exposed by locally breaking off the polymer layer covering the pads. Fabricating electrically conducting millimetre-long, square-symmetric nanowires is a challenging task, and breaks commonly occur in our fabricated devices. In order to increase the device yield, we divided the waveguides into 200-µm long sections, individually connected to common electrodes (see Fig. 2). This resulted in an acceptable device yield, at the cost of increased propagation loss (due to isolation gaps and contact leads) and variation between individual devices (that might have one or more unheated sections).

Transmission measurements were carried out using a tuneable laser (Tunics Plus, GN Nettest) coupled to a polarization-maintaining fibre (Nufern PM1550-HP). The fibre was manually aligned to the plasmonic waveguide for maximum transmission. The signal was picked up at the output end using standard single mode fibre (Corning SMF-28) or a polarization maintaining fibre (as above) and measured with a calibrated Ge photodiode or a fast InGaAs detector (Thorlabs, Inc.) for response time measurements. For extinction measurements, index matching liquid was used between the fibre and the sample to improve the coupling. Polarization dependent loss was measured with the Jones matrix method (using an Agilent/Hewlett-Packard 8509b Lightwave Polarization Analyzer) as well as by measuring the insertion loss while scanning the input state of polarization over the full Poincaré sphere. Mode images for different polarizations were obtained by imaging the output facet of the devices onto an infrared Vidicon camera (Hamamatsu) using a 0.85 NA 60× objective, while varying the polarization of the input fibre.

3. Results

Images of the mode output of a fabricated device are shown in Figs. 3(a) and (b), for input light polarized along the y or the x-direction, respectively. Both modes are close to circular with very similar mode shapes. In our devices, the x-polarized E(1,0) mode is always associated with higher insertion loss and more stray light in the cladding, possibly due to a slight deviation from square symmetry and/or increased scattering by the 500-nm wide contact leads.

The field intensity profiles directly above the nanowire (along the dashed line in Fig. 1), for the E(0,1) and E(1,0) modes, are shown in Fig. 3(c). The strong field intensity at the corners of the nanowire waveguide is a property of the surface plasmon polariton wave and cannot be imaged using free-space optics. In order to compare the measured mode profiles with the results of the simulation, we must therefore take into account the spatial resolution of our imaging system. We therefore performed a 2D-convolution of the calculated intensity distribution (time-averaged power) with a response function corresponding to the spatial resolution of our imaging system, given by 1.21×λ/NA. Horizontal mode profiles were obtained by integrating the resulting intensity distribution along the y-axis. Experimentally obtained mode images were similarly integrated for the comparison.

We find that the experimental data is in excellent agreement with the resolution-corrected simulated profiles. The best fit to the measured data was obtained for a 190 nm×190 nm wire which is close to the nominal dimensions of our fabricated structures (180 nm×180 nm). The minimum measured insertion loss (5 dB and 8 dB for the E(0,1) mode in 1-mm and 2-mm long devices, respectively) was higher than expected from simulations (4.1 dB and 6.3 dB, respectively), presumably due to the combined effects of scattering due to metal roughness, scattering and absorption by contact leads and loss in the cladding. The insertion loss of a 1-mm device varied by ±1 dB over the tuning range of the laser, covering the C- and L-bands (1525-1625 nm). The lowest polarization dependent loss (PDL) measured in our 1-mm devices was 1.2 dB, although typical values were in the 3-6 dB range.

In order to determine the extinction characteristics, we measured the fibre-to-fibre loss of the attenuators while applying voltage to the electrodes and monitoring the electrical power dissipated as heat in the device. The input polarization was fixed at 45° with respect to the x and y axes while the intensity of x and y-polarized light transmitted through the device was measured separately using a polarizer in front of the detector. Fig. 4 shows results for three different devices. As the applied power increases, the transmitted intensity drops for both polarizations. In some cases, attenuation of over 40 dB was measured (e.g. for the E(0,1) mode in Fig. 4(c)). The response time of the device was measured to be 500 µs for heating and 1 ms for cooling, with a 3-dB decrease in modulation depth occuring at around 5 kHz for a fixed driving voltage amplitude.

Measurements of the electrical resistance of the nanowire waveguide indicated a temperature increase in the metal of about 80 K at 30 mW/mm applied power. Finite-element simulations of heat transfer in our devices yielded the same value and confirmed that at this level of heating, the real part of the effective refractive index of the long-range plasmonic modes in a symmetric wire is closely approaching that of unbound modes propagating in the cladding, increasing substantially the radiative loss from the waveguides.

The PDL over the attenuation range varied substantially between devices. Symmetric wires may exhibit different PDL at zero applied power (compare Figs. 4(a) and (b)) while the relative extinction ratio for each mode can be similar (PDL varying within ±2.5 dB over most of the attenuation range). Slightly asymmetric wires (width > height), however, exhibit large PDL at higher attenuation, indicating that the x-polarized mode is more easily coupled out of the wire while the y-polarized mode is more strongly bound. It is clear that achieving consistently low PDL in this type of attenuator requires fabrication tolerances below 10 nm for patterning of the metal stripes.

Fig. 3. Images of the output facet of a 2-mm long, nominally 180 nm×180 nm square nanowire waveguide for (a) y-polarized and (b) x-polarized input light, corresponding to the E(0,1) and E(1,0) long-range corner plasmon polariton supermodes, respectively. The red arrows indicate the direction of the dominating electric field component of the output light. (c) The field intensity along the dashed line in Fig. 1 for the orthogonally polarized long-range modes (thin red lines) and the x-profile of the full calculated 2D intensity distribution of the same calculation, corrected for finite image resolution, integrated along the y-axis (thick red lines) and normalized in intensity. The experimental points represent the x-profile of panels a and b, integrated along the y-axis and scaled in absolute intensity. Results for the two modes are nearly identical, except for the increased background level in case of the x-polarized mode. The simulated data was obtained for a 190 nm×190 nm wire, which gave the best fit to the experimental profiles.

Evidently, our fabricated devices still suffer from too high insertion loss to meet the target specifications listed above, even with improvements in contact geometry, wire quality and coupling. Nevertheless, several strategies can be pursued in order to reach acceptable loss values. Coupling loss to narrow wires with low propagation loss can be significantly reduced using large mode area waveguides at the input and output. This, however, would limit the bending radius of other components and lead to lower integration density. On-chip mode conversion similarly requires propagation lengths that would counteract the advantages of a compact attenuator. Engineering the refractive index profile of the cladding, however, might provide a means of tailoring the mode size while maintaining acceptable propagation loss. Shorter devices would also reduce the overall insertion loss, reaching approximately 1 dB for 100-µm long wires. The extinction ratio achievable with such devices is yet to be determined.

Fig. 4. The upper panels show fibre-to-fibre insertion loss for three different device geometries. The input was linearly polarized at 45° with respect to the waveguide axes and the x and y-polarized output was measured. Insertion loss is plotted relative to the direct fibre-to-fibre transmission of each polarization direction. The difference between the x and y-polarized insertion loss is plotted in the lower panels, illustrating the variation between devices and the high sensitivity to small variations in the cross-sectional geometry. The maximum driving voltage in all cases is below 3V.

4. Conclusions

In conclusion, we have demonstrated a nanowire-based plasmonic variable optical attenuator with a 1-mm footprint, >20 dB extinction ratio, <3V driving voltage and >1 kHz modulation bandwidth, operating in the 1525-1625 nm wavelength range. The minimum dimensions of the structures are within the capabilities of current photolithographic techniques and the device structure is compatible with a planar polymer processing platform. The PDL at high attenuation was shown to be critically dependent on the square symmetry of the nanowire waveguide, with a <5% tolerance in the width-to-height ratio of the metal wire.

Acknowledgments

We thank P. Shi at Danchip, Technical University of Denmark (DTU), for assistance with e-beam lithography and C. Peucheret at the Department of Photonics Engineering, DTU, for providing the PDL test equipment. The project was supported by the Icelandic Research Fund. T.R. acknowledges support from the Eimskip Research Fund at the University of Iceland. A.B. acknowledges support from the Danish Research Council for Technology and Production Sciences (FTP).

References and links

1.

S.A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007).

2.

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

3.

A. Degiron, P. Berini, and D. R. Smith, “Guiding light with long-range plasmons,” Opt. Photon. News 19, 29–34 (2008). [CrossRef]

4.

K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, “Long-range surface plasmon polariton nanowire waveguides for device applications,” Opt. Express 14, 314–319 (2006). [CrossRef] [PubMed]

5.

L. Eldada , “Optical communication components,” Rev. Sci. Instrum. 75, 575–593 (2004). [CrossRef]

6.

H. Ma, A.K.-Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: Materials processing and devices,” Adv. Mater. 14, 1339–1365 (2002). [CrossRef]

7.

L. Eldada, “Advances in Polymer Integrated Optics,” IEEE J. Sel. Top. Quantum Electron. 6, 54–68 (2000). [CrossRef]

8.

D. Li, Y. Zhang, L. Liu, and L. Xu, “Low consumption power variable optical attenuator with sol-gel derived organic/inorganic hybrid materials,” Opt. Express 14, 6029–6034 (2006). [CrossRef] [PubMed]

9.

X. Jiang, et al., “Compact Variable Optical Attenuator Based on Multimode Interference Coupler,” IEEE Photon. Technol. Lett 17, 2361–2363 (2005). [CrossRef]

10.

Y.-O. Noh, H.-J. Lee, Y.-H. Won, and M.-C. Oh, “Polymer waveguide thermo-optic switches with -70 dB optical crosstalk,” Opt. Commun. 258, 18–22 (2006). [CrossRef]

11.

T. Nikolajsen, K. Leosson, and S.I. Bozhevolnyi, “In-line extinction modulator based on long-range surface plasmon polaritons,” Opt. Commun. 244, 455–459 (2005). [CrossRef]

12.

S. Park and S. H. Song, “Polymeric variable optical attenuator based on long range surface plasmon polaritons,” Electron. Lett. 42, 402–404 (2006). [CrossRef]

13.

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

14.

P. Berini, “Optical Waveguide Structures,” US patent number 6,741,782 (2004).

15.

J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding,” Phys. Rev. B 76, 035434 (2007).

16.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).

OCIS Codes
(130.2790) Integrated optics : Guided waves
(230.3120) Optical devices : Integrated optics devices
(230.7390) Optical devices : Waveguides, planar
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Integrated Optics

History
Original Manuscript: August 7, 2008
Revised Manuscript: September 12, 2008
Manuscript Accepted: September 13, 2008
Published: September 17, 2008

Citation
Kristjan Leosson, Tiberiu Rosenzveig, Petur G. Hermannsson, and Alexandra Boltasseva, "Compact plasmonic variable optical attenuator," Opt. Express 16, 15546-15552 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15546


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References

  1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007).
  2. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi,"Surface plasmon circuitry," Phys. Today 61, 44-50 (2008). [CrossRef]
  3. A. Degiron, P. Berini, and D. R. Smith, "Guiding light with long-range plasmons," Opt. Photon. News 19, 29-34 (2008). [CrossRef]
  4. K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, "Long-range surface plasmon polariton nanowire waveguides for device applications," Opt. Express 14, 314-319 (2006). [CrossRef] [PubMed]
  5. L. Eldada, "Optical communication components," Rev. Sci. Instrum. 75, 575-593 (2004). [CrossRef]
  6. H. Ma, A.K.-Y. Jen, and L. R. Dalton, "Polymer-based optical waveguides: Materials processing and devices," Adv. Mater. 14, 1339-1365 (2002). [CrossRef]
  7. L. Eldada, "Advances in Polymer Integrated Optics," IEEE J. Sel. Top. Quantum Electron. 6, 54-68 (2000). [CrossRef]
  8. D. Li, Y. Zhang, L. Liu, and L. Xu, "Low consumption power variable optical attenuator with sol-gel derived organic/inorganic hybrid materials," Opt. Express 14, 6029-6034 (2006). [CrossRef] [PubMed]
  9. X. Jiang,  et al., "Compact Variable Optical Attenuator Based on Multimode Interference Coupler," IEEE Photon. Technol. Lett 17, 2361-2363 (2005). [CrossRef]
  10. Y.-O. Noh, H.-J. Lee, Y.-H. Won, and M.-C. Oh, "Polymer waveguide thermo-optic switches with -70 dB optical crosstalk," Opt. Commun. 258, 18-22 (2006). [CrossRef]
  11. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, "In-line extinction modulator based on long-range surface plasmon polaritons," Opt. Commun. 244, 455-459 (2005). [CrossRef]
  12. S. Park and S. H. Song, "Polymeric variable optical attenuator based on long range surface plasmon polaritons," Electron. Lett. 42, 402-404 (2006). [CrossRef]
  13. G. Gagnon, N. Lahoud, G. Mattiussi, and P. Berini, "Thermally activated variable attenuation of long-range surface plasmon-polariton waves," J. Lightwave Technol. 24, 4391-4402 (2006). [CrossRef]
  14. P. Berini, "Optical Waveguide Structures," US patent number 6,741,782 (2004).
  15. J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, "Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding," Phys. Rev. B 76, 035434 (2007).
  16. P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).

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