OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 27291–27305
« Show journal navigation

Nanosecond thermo-optical dynamics of polymer loaded plasmonic waveguides

J.-C. Weeber, T. Bernardin, M. G. Nielsen, K. Hassan, S. Kaya, J. Fatome, C. Finot, Alain Dereux, and N. Pleros  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 27291-27305 (2013)
http://dx.doi.org/10.1364/OE.21.027291


View Full Text Article

Acrobat PDF (2340 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The thermo-optical dynamics of polymer loaded surface plasmon waveguide (PLSPPW) based devices photo-thermally excited in the nanosecond regime is investigated. We demonstrate thermo-absorption of PLSPPW modes mediated by the temperature-dependent ohmic losses of the metal and the thermally controlled field distribution of the plasmon mode within the metal. For a PLSPPW excited by sub-nanosecond long pulses, we find that the thermo-absorption process leads to modulation depths up to 50% and features an activation time around 2ns whereas the relaxation time is around 800ns, four-fold smaller than the cooling time of the metal film itself. Next, we observe the photo-thermal activation of PLSPPW racetrack shaped resonators at a time scale of 300ns followed however by a long cooling time (18μs) attributed to the poor heat diffusivity of the polymer. We conclude that nanosecond excitation combined to high thermal diffusivity materials opens the way to high speed thermo-optical plasmonic devices.

© 2013 OSA

1. Introduction

Thermo-optical (TO) effects are to date the most common way to control dynamically integrated plasmonic components such as variable attenuators [1

1. G. Gagnon, N. Lahoud, G. Mattiussi, and P. Berini, “Thermally activated variable attenuation of long-range surface plasmon polariton waves,” J. Lightwave Technol. 24, 4391–4409 (2006). [CrossRef]

, 2

2. K. Leosson, T. Rosenzveig, P. G. Hermannsson, and A. Boltasseva, “Compact plasmonic variable optical attenuator,” Opt. Express 20, 15546–15552 (2008). [CrossRef]

] and low bandwidth modulators [3

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

, 4

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

]. Initially implemented by using waveguided long-range surface plasmon modes [5

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

], more compact thermo-optical plasmon based devices relying on dielectric loaded surface plasmon waveguides [6

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

8

8. S. Massenot, J. Grandidier, A. Bouhelier, G. Colas des Francs, L. Markey, J.-C. Weeber, A. Dereux, J. Renger, M. U. Gonzalez, and R. Quidant, “Polymer-metal waveguides characterization by Fourier plane leakage radiation microscopy,” Appl. Phys. Lett. 91, 243102 (2007). [CrossRef]

] have been proposed [9

9. O. Tsilipakos, T. V. Yioultsis, and E. E. Kriezis, “Theoretical analysis of thermally tunable microring resonator filters made of dielectric-loaded plasmonic waveguides,” J. Appl. Phys. 106, 093109 (2009). [CrossRef]

11

11. A. Pitilakis and E. E. Kriezis, “Longitudinal 2×2 switching configurations based on thermo-optically addressed dielectric-loaded plasmonic waveguides,” J. Lightwave Technol. 29, 2636–2646 (2011). [CrossRef]

] and demonstrated [12

12. 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, 1207–1216 (2010). [CrossRef] [PubMed]

15

15. K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, O. Pitilakis, and E. E. Kriezis, “Thermo-optic plasmo-photonic mode interference switches based on dielectric loaded waveguides,” Appl. Phys. Lett. 99, 241110 (2011). [CrossRef]

]. So far, and most often, the dielectric loading material is a polymer deposited onto a metal film or strip and in this respect the waveguides will be denoted hereafter as polymer loaded surface plasmon waveguides (PLSPPWs).

Single-mode PLSPPWs feature cross-sections with typical sub-micron dimensions enabling low-loss coupling with passive silicon-on-insulator circuitry [16

16. R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, and H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10, 4851–4857 (2010). [CrossRef]

18

18. O. Tsilipakos, A. Pitilakis, T. Yioultsis, S. Papaioannou, K. Vyrsokinos, G. D. Kalavrouziotis, D. Giannoulis, H. Apostolopoulos, T. Avramopoulos, M. Tekin, M. Baus, K. Karl, J.-C. Hassan, L. Weeber, A. Markey, S. Dereux, A. Kumar, Bozhevolnyi, N. Pleros, and E. Kriezis, “Interfacing dielectric-loaded plasmonic and silicon photonic waveguides: Theoretical analysis and experimental demonstration,” IEEE J. Quantum Electron. 48, 678–687 (2012). [CrossRef]

]. The ability of integrating PLSPPW devices into a photonic passive circuitry has triggered the development and the demonstration of hybrid Si-PLSPPW thermally-activated routers for controlling high-bit rate traffic at the system level [19

19. D. Kalavrouziotis, S. Papaioannou, K. Vyrsokinos, L. Markey, A. Dereux, G. Giannoulis, D. Apostolopoulos, H. Avramopoulos, and N. Pleros, “Demonstration of a plasmonic MMI switch in 10-Gb/s true data traffic conditions,” IEEE Photon. Technol. Lett. 24, 1819–1822 (2012). [CrossRef]

21

21. G. Giannoulis, D. Kalavrouziotis, D. Apostolopoulos, S. Papaioannou, A. Kumar, S. I. Bozhevolnyi, L. Markey, K. Hassan, J.-C. Weeber, M. Dereux, A. Baus, M. Karl, T. Tekin, O. Tsilipakos, A. K. Pitilakis, E. E. Kriezis, K. Vyrsokinos, H. Avramopoulos, and N. Pleros, “Data transmission and thermo-optic tuning performance of dielectric-loaded plasmonic structures hetero-integrated on a silicon chip,” IEEE Photon. Technol. Lett. 24, 374–376 (2012). [CrossRef]

]. The key interest of the plasmon based devices in the context of thermo-optical control resides in the fact that the metal sustaining the plasmon mode can also be used as an heating electrode. However, photo-thermal activation of thermo-plasmonic devices is also an appealing approach. Indeed, this ”all-optical” control offers the possibility to tune parameters such as the incident pump wavelength and/or polarization to optimize the TO devices activation [22

22. J.-C. Weeber, K. Hassan, L. Saviot, A. Dereux, C. Boissière, O. Durupthy, C. Chaneac, E. Burov, and A. Pastouret, “Efficient photo-thermal activation of gold nanoparticle-doped polymer plasmonic switches,” Opt. Express 20, 27636–27649 (2012). [CrossRef] [PubMed]

].

Except when implemented with ultra-high quality factor resonators with corresponding narrow spectral range of operation [23

23. M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Opt. Express 15, 17458–17481 (2007). [CrossRef] [PubMed]

], the main limitation of TO devices, whatever the material platform, is their moderate response times in the range of a few microseconds. For TO-PLSPPW routers integrated into a silicon on insulator circuitry, response times around 3–4μs have been obtained [19

19. D. Kalavrouziotis, S. Papaioannou, K. Vyrsokinos, L. Markey, A. Dereux, G. Giannoulis, D. Apostolopoulos, H. Avramopoulos, and N. Pleros, “Demonstration of a plasmonic MMI switch in 10-Gb/s true data traffic conditions,” IEEE Photon. Technol. Lett. 24, 1819–1822 (2012). [CrossRef]

, 20

20. S. Papaioannou, D. Kalavrouziotis, K. Vyrsokinos, J.-C. Weeber, K. Hassan, L. Markey, A. Dereux, A. Kumar, S. I. Bozhevolnyi, T. Baus, M. Tekin, D. Apostolopoulos, H. Avramopoulos, and N. Pleros, “Active plasmonics in WDM traffic switching applications,” Sci. Rep. 2, 1358–1361 (2012). [CrossRef]

]. Although many dc or low-frequency characterizations of TO-PLSPPW devices have been reported, the dynamics of the thermo-optical response of these components has not been investigated in details. It is therefore the main objective of this work to analyze experimentally and numerically the PLSPPW dynamics down to the nanosecond time scale. For this purpose, we operate a photo-thermal excitation of the PLSPPW devices by using a Q-switched nanosecond pulsed visible (532nm) pump laser. The nanosecond pulse can be viewed, in the first approximation, as a delta-function excitation from which the overall TO dynamics of the PLSPPWs can be extracted. However, beyond PLSPPW TO dynamics, we also consider the use of nanosecond pulses for fast photo-thermal activation of our devices. In this context, the pulse is used as a pre-conditioning of the TO component by abruptly setting it into its hot state. Our approach can be viewed as the optical equivalent of the so-called ”pre-emphasis driving” recently operated for fast reconfiguration of electrically driven silicon-based TO devices [24

24. A. H. Atabaki, A. A. Eftekhar, S. Yegnanarayanan, and A. Adibi, “Sub-100-nanosecond thermal reconfiguration of silicon photonic devices,” Opt. Express 21, 15706–15718 (2013). [CrossRef] [PubMed]

].

The study is organized as follows. The experimental setup based on a combined leakage radiation microscope and a fiber-to-fiber characterization scheme is briefly described in section two along with the fabrication process of our samples. We detail in the third section our model of the PLSPPW TO response relying on a numerical computation of temperature distributions for a nanosecond photo-thermal excitation coupled to an effective index method. In section four, we investigate the thermo-absorption of a PLSPPW mode traveling along straight waveguides irradiated by nanosecond pulses. We demonstrate depth of modulations as large as 50% and we find that the presence of the polymer impacts the thermo-absorption dynamics at the sub-nanosecond scale. In this way, we show that the heat diffusion into the polymer over characteristic lengths around 20nm is detectable from the PLSPPW properties. Next, we consider in section five, the TO dynamics of photo-thermally excited PLSPPW racetracks resonators. We demonstrate an activation of the resonators at a time scale of 300ns followed however by a cool down characteristic time of about 18μs. By analyzing the origin of these performances from the thermal properties of our polymer-based configuration, we conclude that nanosecond photo-thermal excitation is a convenient approach for the development of high-speed TO plasmonic devices.

2. Experimental

Fig. 1 (a) Schematic view of the experimental setup combining a leakage radiation microscope and a fiber-to-fiber detection scheme. (b) and (c) Typical leakage radiation images recorded during the alignment procedure of the two lensed-fibers. (b) The infrared signal coupled by means of the left grating creates the output scattering spot shown by the arrow. For alignment purposes the output fiber is also coupled to an infrared source to generate the spot surrounded by the dashed perimeter. (c) At the end of the coarse alignment procedure, the spots generated by the input and output fibers are respectively located on the input and output grating couplers.

3. Thermo-optical modeling

Fig. 2 (a) Schematic view of the two-dimensional configuration for temperature distribution computation. The PLSPPW has a 0.5 μm×0.5μm cross-section. The computation windows shown by the dashed line perimeter has a width of 35μm and a total height 2hs=20μm and is discretized over up to 125×103 rectangular non-regular meshes. A Neumann condition (∂T/∂x = 0) is applied onto the x = 0 boundary in order to account for the symmetry of the configuration. Dirichlet conditions at the room temperature are applied on the three other boundaries. (b) Electric field distribution generated by the illumination of the PLSPPW by a gaussian beam with a waist of 10μm. (c)-(d)-(e) Temperature distribution in the PLSPPW for a 0.6ns-FWHM gaussian pulse reaching its maximum in the metal plane at t = 5ns.

Table 1. Thermal and optical parameters of the materials used in our thermo-optical model.

table-icon
View This Table

4. Thermo-absorption dynamics of PLSPP waveguides

The thermo-modulation of the signal intensity transmitted through a straight PLSPPW is mediated by the temperature dependence of the PLSPPW mode damping constant. Many works have been devoted to the thermally induced change of the real effective index of PLSPPWs (thermo-optical effect) but so far and to the best of our knowledge, none of them have addressed the temperature dependence of the PLSPPW mode imaginary effective index (thermo-absorption effect). This dependence deserves a careful examination as it impacts the performances of PLSPPW devices in practical applications. Waveguiding in a PLSPPW results from the combined actions of metal and polymer from which the vertical and lateral field confinement of the guided mode originates respectively. These two materials are then expected to contribute to the thermo-optical properties of a PLSPPW. At this stage, it is instructive to refer to the situation of a SPP mode traveling at an interface between a metal and a dielectric. At telecom wavelengths, metal of interest for plasmonic applications are such that |εm|εm where εm and εm are the real and imaginary part of the relative dielectric function of the metal. The relative dielectric function εd of typical dielectric media such as standard polymers is also small compare to |εm| in such a way that the temperature derivative of the SPP mode damping constant kspp is given by [29

29. H. Raether, Surface Plasmons on Smooth and Rough Surface and on Gratings (Springer-Verlag, 1988).

]:
Tkspp=kspp(32Tεdεd+Tεmεm2Tεmεm)
(3)
where the notation T is used in place of ∂/∂T. The metal contribution to the SPP thermo-absorption is not only mediated by the ohmic losses (through Tεm) but also by the temperature-dependent εm. At telecom wavelengths, where the dielectric function of noble metals are dominated by the free-electron contribution, the ohmic losses depend on temperature mostly through the electron-phonon scattering rate whereas a change of the free-electron density resulting from a thermally induced lattice volume expansion is at the origin of the Tεm coefficient. The dielectric medium contributes also to the SPP thermo-absorption through the change of the SPP field confinement within the metal which depends on Tεd. For a PLSPPW with a complex geometry, the respective contribution of the metal and the dielectric to the thermo-absorption effect is difficult to estimate. It is then useful to investigate first a situation where the dielectric medium contribution is expected to be negligible such as in the case of a SPP mode traveling at a gold/air interface.

Fig. 3 (a) Scanning electron microscope image of the in and out grating couplers (scale bar=50μm). (b) (resp. (c)) Typical leakage radiation microscope images of the plasmon jet (1540nm) propagating at the Au/air interface with the pump beam off (resp. on, cut-on filter off). The pump spot features a gaussian intensity distribution in I(r)=I(0)exp(r2/wr2) with a waist of wr = 50μm. (d)-(e)-(f) Observation of the thermo-absorption of the SPP signal under the nanosecond excitation at different time scales. In (d) and (e), the dashed lines are the experimental signal whereas the solid lines are the computed thermo-absorption profiles for an interface SPP. The dashed-dotted line in (d) shows the temporal profile of the incident pulse used in the calculations.

We consider now the situation of a straight PLSPPW photo-thermally excited by the nanosecond pulsed beam. The excitation conditions are the same as for the interface SPP mode. Figures 4(a)–4(c) show respectively a scanning electron microscope image of the straight PLSPPW as well as a typical radiation leakage image of this waveguide with the pump spot off and on. Although we focus in this work onto the dynamics of the TO response of PLSPPWs, it is worth to consider first the curve displayed in Fig. 4(d) showing the depth of modulation of the signal collected at the output of the PLSPPW as a function of the average pump power. For an average pump power of 5.6mW, the depth of modulation is about 38% of the cold state signal amplitude, up to ten times larger than in the case of the interface SPP. This difference can be understood from the larger field confinement within the metal (and accordingly the shorter propagation length) for the PSLPPW mode compared to the SPP mode [31

31. S. Kaya, J.-C. Weeber, F. Zacharatos, K. Hassan, T. Bernardin, B. Cluzel, J. Fatome, and C. Finot, “Photo-thermally induced modulation of surface plasmon polariton propagation at telecommunication wavelengths,” Opt. Express 21, 22269–22284 (2013). [CrossRef] [PubMed]

]. Figures 4(e)–4(g) show the normalized signal SN recorded at different time scales. On the basis of the profiles displayed in Figs. 4(e) and 4(g), we find that the fall-time for the thermo-absorption of the PLSPPW mode is τF =1.7ns and the sub-μs rise-time drops at τR=800ns respectively two times longer and four-fold shorter than in the case of the interface SPP mode. For a PLSPPW, the normalized signal SN does not follow anymore the dynamics of the metal film temperature but results from the combined contributions of the metal and polymer as illustrated by Eq. (3). The activation time for the thermo-absorption of PLSPPWs can be explained from a slower thermalization of the gold film in the presence of the polymer but also from its negative TOC. The typical heat diffusion length for the pulse duration τp is L=2ατp [34

34. E. Marin, “Characteristic dimensions for heat transfer,” Lat. Am. J. Phys. Educ. 4, 56–60 (2010).

] where α is the thermal diffusivity (α = k/(ρCp)) of the material of interest. In our situation (αpoly =8.3×10−8m2s−1, τp ≃ 1ns), the heat diffusion length into the polymer is around 20nm. At the nanosecond scale, the temperature rise of the polymer generates a thin low index layer in contact with the metal film leading to a decrease of the PLSPPW mode field confinement into the metal and a corresponding increase of its propagation length. Hence, during the heating cycle, the increase of the metal losses is partly compensated by the PLSPPW mode field delocalization resulting in a longer activation time of the PLSPPW thermo-absorption process than for the Au/air SPP mode. At longer times, after the pulse, the temperature of the metal film drops and the propagation length of the PLSPPW mode increases accordingly. However the rise-time τR for PLSPPWs being about four times shorter than for the Au/air SPP, we conclude that the polymer still contributes to the increase of the PLSPPW damping distance during the cooling cycle. Once again, we note that our model fails to capture the dynamics of the thermo-absorption during the first nanoseconds whereas computed and experimental profiles are in good agreement for times larger than 5ns after the pulse. From these results, we conclude that our model is reliable for time scales larger than 10ns which is still of key interest to predict the performances of high bandwidth thermo-plasmonic devices. The assessment of the characteristic time for the polymer contribution to the TO PLSPPW dynamics is difficult to complete from thermo-absorption experiments owing to the metal contribution and requires the use of frequency resonant devices.

Fig. 4 (a) Scanning electron microscope image of a typical PLSPPW equipped with grating couplers (scale bar=40μm). (b) (resp. (c)) Leakage radiation microscope images of the PLSPPW mode (1530nm) propagating at the Au/air interface with the pump beam off (resp. on, cut-on filter off). The excitation conditions are the same as in Fig. 3. (d) Depth of thermo-absorption of the PLSPPW mode as a function of the incident average pump power. The depth of modulation is defined with respect to the signal level in the cold sate. (e)-(f)-(g) Experimental and computed thermo-absorption of the PLSPPW signal under nanosecond excitation at different time scales. The solid lines are computed profiles whereas the dashed lines are experimental profiles. The dash-dotted line in Fig. 4(e) is the profile of the excitation pulse used in the calculations.

5. Thermo-optical dynamics of a PLSPPW ring resonator

Fig. 5 (a) Scanning electron microscope image of the racetrack shaped resonator coupled to a straight bus waveguide (scale bar=40μm). The radius of the resonator is R=5.5μm, straight interaction length with the bus waveguide is 6μm long and the nominal gap between the resonator and the bus waveguide is 250nm. (b) (resp. (c)) Leakage radiation microscope image of the resonator at 1560nm (resp. 1565nm). (d) Cold state spectrum of the resonator. (e) (resp. (f)) Thermo-optical response of the resonator under ns excitation for blue-detuned (resp. red-detuned) wavelengths compared to the cold state resonance of 1538nm. The photo-excitation is achieved with a large pump spot exciting simultaneously the resonator and the bus waveguide.

Figures 6(a) and 6(b) show the TO response of the photo-activated resonator at different time scales. The thermo-absorption of the PLSPPW mode occurring at a scale of 2ns, the abrupt drop of the signal in Fig. 6(a) is a reliable indication of the pump pulse arrival time from which the dynamics of the resonator can be accurately measured. The profile displayed in Fig. 6(a) indicates that the characteristic activation time for the PLSPPW resonator is τR = 280ns followed by a much longer relaxation time. We measure a 90%-10% fall time of τF =18μs on the profile shown in Fig. 6(b). The average temperature in the polymer and the metal film are plotted in Fig. 6(c) for the PLSPPW excited in the same conditions as in Fig. 2. The polymer slice in contact with the metal film, which is expected to contribute dominantly to the TO properties of the PLSPPW, reaches a maximum temperature (averaged over a thickness of 125nm) of only one fourth of the maximum metal film temperature. For slices at larger distances from the metal film, the temperature is maximum after a time characterizing the diffusion speed of the thermal pulse. The time dependent PLSPPW effective index neff = k′/k0 (k0 = 2π/λ0, λ0=1541nm) plotted in Fig. 6(d) has been obtained by means of the effective index method with the refractive index of each polymer slice evaluated from the temperature profiles of Fig. 6(c). The minimum effective index is reached 200ns after the excitation pulse, in reasonable agreement with the experiment given that no adjustable parameter is used for this calculation. The thermo-optical activation of the PLSPPW occurs at sub-μs time scale whereas the cooling time is clearly the main limitation to high-speed operation. Indeed, the cooling time for the thermo-optical response of the ring resonator is about 20 times larger than the thermo-absorption relaxation time along a straight PLSPPW. This difference results from the fact that the thermo-optical response depends upon the polymer temperature only whereas for thermo-absorption, the temperature of the metal film plays the dominant role. Beyond numerical modeling, the physical quantities of interest for improved TO performances are more conveniently identified from an approximate analytical model. When a short pulse with a fluence F is fully absorbed at t = 0 within a very thin layer at the surface of a semi-infinite medium occupying the z > 0 half-space, the temperature rise in the material at a distance z from the surface is approximated by [35

35. D. P. Brunco, J. A. Kittl, C. E. Otis, P. M. Goodwin, M. O. Thompson, and M. J. Aziz, “Time-resolved temperature measurements during pulsed laser irradiation using thin film metal thermometers,” Rev. Sci. Instrum. 64, 2615–2623 (1993). [CrossRef]

]:
ΔT(z,t)=Fεπtexp(z24αt)
(6)
where ε=kρCp is the thermal effusivity of the semi-infinite medium. We assume that the TO properties of the PLSPPWs can be analyzed from the temperature of a characteristic polymer slice located at a distance zeff from the surface of the metal film. For typical PLSPPW heights of 500nm, a reasonable choice for this effective distance is around zeff =250nm. According to Eq. (6), the temperature at zeff reaches its maximum value ΔTmax(zeff) ∝ F/(ρCpzeff) at t=τH=zeff2/(2α)=280ns in perfect but fortuitous agreement with the experiment. From this approach, we conclude however that a high thermal diffusivity of the TO active medium is the key parameter for the fast activation time of PLSPPW devices. The average temperature of the polymer slice in contact with the gold layer computed numerically is compared to fit models inspired by Eq. (6) in Fig. 6(d). We note that during the cooling cycle, the contribution of the exponential term in Eq 6 can be neglected in the first approximation. From this further approximation, one can show that the typical cooling time τC needed for the temperature at zeff to decrease from 90% to 10% of ΔTmax(zeff) is given by τC100πe2zeff2α. Although this equation leads to a cooling time about five-fold overestimated compared to the experiment, the diffusivity α appears to be once again the main parameter for controlling the cooling dynamics of the system. However, the response time is not the only parameter that should be considered in a practical device. As pointed out recently in ref. [36

36. J. Gosciniak and S. Bozhevolnyi, “Performances of thermo-optic components based on dielectric-loaded surface plasmon polariton waveguides,” Sci. Rep. 3, 1803 (2013). [CrossRef]

], the dynamics of electrically driven TO PLSPPW devices is improved at the expense of larger activation powers. For photo-thermal excitation, such an increase can be minimized by a stronger focusing of the pump beam at least in the case of small footprint devices. In addition, Eq. (6) indicates that the heating efficiency scales as the inverse of the thermal effusivity of the material. Combining this requirement to the large thermal diffusivity needed for high-speed operation, we conclude that the optimum material in this context should have a large thermal conductivity k and a small ρCp product. The above analysis has been conducted considering heat diffusion in the TO active medium whereas in the experimental situation the role of the substrate is also critical. The conclusions given for the TO material also applies for the substrate which should feature a high thermal diffusivity as well. In addition, the thermal diffusivities and effusivities of the TO medium and the substrate should also be close in order to prevent a poor heating of the TO medium as in our configuration [Fig. 6(c)] where heat diffusion is four times faster in the glass substrate than in the polymer load. On the basis of this analysis, we conclude that PLSPPW based TO devices operating in the sub-μs regime will be difficult to implement with standard polymers mostly due to their poor thermal diffusivity. In spite of their thermal properties, it is worth to note that sub-μs switching operations with PLSPPW based TO devices are achievable at the cost however of the implementation of sophisticated configurations such as a push-pull Mach-Zehnder interferometer. Indeed, for the latter, the switching speed is given by the typical activation time of each arm in the interferometer (in the range of 300ns in our case) whereas the relaxation time (several μs with PLSPPWs) imposes the switch latency [37

37. A. Nakamura, Y. Ueno, K. Tajima, J. Sasaki, T. Sugimoto, T. Kato, T. Shimoda, M. Itoh, H. Hatakeyama, T. Tamanuki, and T. Sasaki, “Demultiplexing of 168Gb/s data pulses with an hybrid-integrated symetric Mach-Zehnder all-optical switch,” IEEE Photon. Technol. Lett. 12, 425–427 (2000). [CrossRef]

]. Nevertheless, provided that high-speed TO devices are targeted, the polymer and the glass substrate used in this study must be replaced by highly thermally diffusive materials such as semi-conductors. For example, heat diffusivity of silicon (α ≃ 8 × 10−5m2s−1) is about three orders of magnitude larger than the polymer used in this study suggesting that the bandwidth of the TO semi-conductor loaded plasmonic devices could be extended up to several MHz.

Fig. 6 (a) Photo-thermal excitation of the resonator for a red-detuned signal wavelength (1541nm). The photo-excitation is achieved by using a large spot (wr =50μm) exciting the resonator and the bus waveguide (average power 7mW). The abrupt drop of the signal at t = 0 results from the thermo-absorption of the bus-waveguide mode and indicates the arrival time of the incident pulse. The activation (or heating) time of the resonator is 280ns. Long-time scale TO response of the resonator pump by a focused beam (wr ≃ 5μm) (see the inset) with an average power of 150μW. With the local excitation of the resonator, the thermo-absorption is not observed anymore. The characteristic cooling time is 18μs.(c) Comparison of the average temperature into the gold film and polymer slices of the PLSPPW with a thickness of 125nm for the photo-excitation by a nanosecond pulse (0.6ns FWHM) arriving onto the PLSPPW at t = 5ns. (d) Computation of the effective index of the PLSPPW mode from the temperature profiles displayed in (c). (e) Comparison of the average temperature profile of the first polymer slice (125nm) in contact with the metal film and different fit models inspired by Eq. (6).

6. Conclusion

In summary, we have experimentally and numerically investigated the dynamics of the thermo-modulation of PLSPPW devices photo-excited by nanosecond pulses. By operating a fiber-to-fiber detection scheme, we have demonstrated a response time for the thermo-absorption of the PLSPPW mode in the nanosecond regime at the scale of the pulse duration. Whatever the time scale, we have shown that the thermo-absorption of the PLSPPW mode is mediated by the temperature-dependent metal ohmic losses but also by the field distribution of the PLSPPW mode into the metal controlled by the polymer TOC. For a negative TOC, we observe a sub-μs thermo-modulation characteristic time (fall-time+rise-time) about four-fold shorter than the cooling time of the metal film itself. In addition, we find that the thermo-absorption amplitude for a PLSPPW mode is about 10 times larger than for a Au/air interface SPP photo-excited in the same conditions. On the basis of these results, we conclude that the thermo-absorption effect significantly impacts the performances of the PLSPPW based TO devices. Next, we have considered the thermo-optical response of PLSPPW racetrack resonators featuring well pronounced resonances. By choosing a signal wavelength either blue or red detuned compared to the cold state resonance, we have shown that the nanosecond pulse can activate the resonator at a time scale of 300ns however followed by a characteristic cooling time of about 18μs in our configuration. The slow TO dynamics of these resonators is attributed to the poor thermal diffusivity of both the polymer and the glass substrate used in this study. In spite of these poor thermal performances, we note that the nanosecond photo-thermal excitation is convenient for sub-μs activation which is the key feature for the fast pre-conditioning of the TO devices. Finally, it should be also pointed out that, as long as the metal of the plasmonic devices is used as the heat transducer for electrical or optical driving, the TO plasmonic devices will suffer from the detrimental effect of thermo-absorption of the plasmon mode and from the time delay imposed by heat diffusion from the metal to the thermo-optically active material. Interestingly, we note that photo-thermal excitation offers the unique possibility to circumvent all these limitations by localizing the absorption of the incident light within the TO active medium rather than in the metal. By combining the nanosecond pulsed photo-thermal approach to the use of inorganic materials featuring all high thermal diffusivity, TO plasmonic devices with several MHz bandwidth turn to be achievable. Actions for the fabrication of such devices are currently in progress and will be reported elsewhere.

Acknowledgments

This work has benefited from the financial support of the Agence Nationale de la Recherche through the P2N program project MASSTOR (Grant number ANR-11-NANO-022) and from the FP7 European Project PLATON (Grant Number: 249135). The authors also acknowledge the council of the Burgundy region for the technical support provided through the PARI-SMT3 funding of ARCEN and PICASSO platforms.

References and links

1.

G. Gagnon, N. Lahoud, G. Mattiussi, and P. Berini, “Thermally activated variable attenuation of long-range surface plasmon polariton waves,” J. Lightwave Technol. 24, 4391–4409 (2006). [CrossRef]

2.

K. Leosson, T. Rosenzveig, P. G. Hermannsson, and A. Boltasseva, “Compact plasmonic variable optical attenuator,” Opt. Express 20, 15546–15552 (2008). [CrossRef]

3.

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

4.

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

5.

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

6.

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

7.

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

8.

S. Massenot, J. Grandidier, A. Bouhelier, G. Colas des Francs, L. Markey, J.-C. Weeber, A. Dereux, J. Renger, M. U. Gonzalez, and R. Quidant, “Polymer-metal waveguides characterization by Fourier plane leakage radiation microscopy,” Appl. Phys. Lett. 91, 243102 (2007). [CrossRef]

9.

O. Tsilipakos, T. V. Yioultsis, and E. E. Kriezis, “Theoretical analysis of thermally tunable microring resonator filters made of dielectric-loaded plasmonic waveguides,” J. Appl. Phys. 106, 093109 (2009). [CrossRef]

10.

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, 073111 (2011). [CrossRef]

11.

A. Pitilakis and E. E. Kriezis, “Longitudinal 2×2 switching configurations based on thermo-optically addressed dielectric-loaded plasmonic waveguides,” J. Lightwave Technol. 29, 2636–2646 (2011). [CrossRef]

12.

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, 1207–1216 (2010). [CrossRef] [PubMed]

13.

J. Gosciniak, L. Markey, A. Dereux, and S. I. Bozhevolnyi, “Efficient thermo-optically controlled Mach–Zehnder interferometers using dielectric-loaded plasmonic waveguides,” Opt. Express 20, 16300–16309 (2012). [CrossRef]

14.

K. Hassan, J.-C. Weeber, L. Markey, and A. Dereux, “Thermo-optical control of dielectric loaded plasmonic racetrack resonators,” J. Appl. Phys. 110, 023106 (2011). [CrossRef]

15.

K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, O. Pitilakis, and E. E. Kriezis, “Thermo-optic plasmo-photonic mode interference switches based on dielectric loaded waveguides,” Appl. Phys. Lett. 99, 241110 (2011). [CrossRef]

16.

R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, and H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10, 4851–4857 (2010). [CrossRef]

17.

N. Pleros, E. E. Kriezis, and K. Vyrsokinos, “Optical interconnects using plasmonics and Si-photonics,” IEEE Photon. J. 3, 296–301 (2011). [CrossRef]

18.

O. Tsilipakos, A. Pitilakis, T. Yioultsis, S. Papaioannou, K. Vyrsokinos, G. D. Kalavrouziotis, D. Giannoulis, H. Apostolopoulos, T. Avramopoulos, M. Tekin, M. Baus, K. Karl, J.-C. Hassan, L. Weeber, A. Markey, S. Dereux, A. Kumar, Bozhevolnyi, N. Pleros, and E. Kriezis, “Interfacing dielectric-loaded plasmonic and silicon photonic waveguides: Theoretical analysis and experimental demonstration,” IEEE J. Quantum Electron. 48, 678–687 (2012). [CrossRef]

19.

D. Kalavrouziotis, S. Papaioannou, K. Vyrsokinos, L. Markey, A. Dereux, G. Giannoulis, D. Apostolopoulos, H. Avramopoulos, and N. Pleros, “Demonstration of a plasmonic MMI switch in 10-Gb/s true data traffic conditions,” IEEE Photon. Technol. Lett. 24, 1819–1822 (2012). [CrossRef]

20.

S. Papaioannou, D. Kalavrouziotis, K. Vyrsokinos, J.-C. Weeber, K. Hassan, L. Markey, A. Dereux, A. Kumar, S. I. Bozhevolnyi, T. Baus, M. Tekin, D. Apostolopoulos, H. Avramopoulos, and N. Pleros, “Active plasmonics in WDM traffic switching applications,” Sci. Rep. 2, 1358–1361 (2012). [CrossRef]

21.

G. Giannoulis, D. Kalavrouziotis, D. Apostolopoulos, S. Papaioannou, A. Kumar, S. I. Bozhevolnyi, L. Markey, K. Hassan, J.-C. Weeber, M. Dereux, A. Baus, M. Karl, T. Tekin, O. Tsilipakos, A. K. Pitilakis, E. E. Kriezis, K. Vyrsokinos, H. Avramopoulos, and N. Pleros, “Data transmission and thermo-optic tuning performance of dielectric-loaded plasmonic structures hetero-integrated on a silicon chip,” IEEE Photon. Technol. Lett. 24, 374–376 (2012). [CrossRef]

22.

J.-C. Weeber, K. Hassan, L. Saviot, A. Dereux, C. Boissière, O. Durupthy, C. Chaneac, E. Burov, and A. Pastouret, “Efficient photo-thermal activation of gold nanoparticle-doped polymer plasmonic switches,” Opt. Express 20, 27636–27649 (2012). [CrossRef] [PubMed]

23.

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Opt. Express 15, 17458–17481 (2007). [CrossRef] [PubMed]

24.

A. H. Atabaki, A. A. Eftekhar, S. Yegnanarayanan, and A. Adibi, “Sub-100-nanosecond thermal reconfiguration of silicon photonic devices,” Opt. Express 21, 15706–15718 (2013). [CrossRef] [PubMed]

25.

A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steiberger, F. Aussenegg, A. Leitner, and J. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B 149, 220–229 (2008). [CrossRef]

26.

J. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley and Sons, 1999).

27.

M. Nevière and E. Popov, Light Propagation in Periodic Media (Marcel Dekker, Inc., 2003).

28.

E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides: reflection pole method and wavevector density method,” J. Lightwave Technol. 17, 929–941 (1999). [CrossRef]

29.

H. Raether, Surface Plasmons on Smooth and Rough Surface and on Gratings (Springer-Verlag, 1988).

30.

M. G. Nielsen, J.-C. Weeber, K. Hassan, J. Fatome, C. Finot, S. Kaya, L. Markey, O. Albrektsen, S. I. Bozhevolnyi, G. Millot, and A. Dereux, “Grating couplers for fiber-to-fiber characterizations of stand-alone dielectric loaded surface plasmon waveguide components,” J. Lightwave Technol. 30, 3118–3125 (2012). [CrossRef]

31.

S. Kaya, J.-C. Weeber, F. Zacharatos, K. Hassan, T. Bernardin, B. Cluzel, J. Fatome, and C. Finot, “Photo-thermally induced modulation of surface plasmon polariton propagation at telecommunication wavelengths,” Opt. Express 21, 22269–22284 (2013). [CrossRef] [PubMed]

32.

R. J. Baseman, N. M. Froberg, J. C. Andreshak, and Z. Schlesinger, “Minimum fluence for laser blow-off of thin gold films at 248 and 532nm,” Appl. Phys. Lett. 56, 1412–1414 (1990). [CrossRef]

33.

X. Chen, Y. Chen, Y. Min, and M. Qiu, “Nanosecond photothermal effect in plasmonic nanostructures,” ACS Nano 6, 2550–2556 (2012). [CrossRef] [PubMed]

34.

E. Marin, “Characteristic dimensions for heat transfer,” Lat. Am. J. Phys. Educ. 4, 56–60 (2010).

35.

D. P. Brunco, J. A. Kittl, C. E. Otis, P. M. Goodwin, M. O. Thompson, and M. J. Aziz, “Time-resolved temperature measurements during pulsed laser irradiation using thin film metal thermometers,” Rev. Sci. Instrum. 64, 2615–2623 (1993). [CrossRef]

36.

J. Gosciniak and S. Bozhevolnyi, “Performances of thermo-optic components based on dielectric-loaded surface plasmon polariton waveguides,” Sci. Rep. 3, 1803 (2013). [CrossRef]

37.

A. Nakamura, Y. Ueno, K. Tajima, J. Sasaki, T. Sugimoto, T. Kato, T. Shimoda, M. Itoh, H. Hatakeyama, T. Tamanuki, and T. Sasaki, “Demultiplexing of 168Gb/s data pulses with an hybrid-integrated symetric Mach-Zehnder all-optical switch,” IEEE Photon. Technol. Lett. 12, 425–427 (2000). [CrossRef]

OCIS Codes
(160.3900) Materials : Metals
(160.6840) Materials : Thermo-optical materials
(240.6680) Optics at surfaces : Surface plasmons
(130.4815) Integrated optics : Optical switching devices
(130.5460) Integrated optics : Polymer waveguides

ToC Category:
Plasmonics

History
Original Manuscript: July 18, 2013
Revised Manuscript: October 3, 2013
Manuscript Accepted: October 7, 2013
Published: November 4, 2013

Virtual Issues
Surface Plasmon Photonics (2013) Optics Express

Citation
J.-C. Weeber, T. Bernardin, M. G. Nielsen, K. Hassan, S. Kaya, J. Fatome, C. Finot, Alain Dereux, and N. Pleros, "Nanosecond thermo-optical dynamics of polymer loaded plasmonic waveguides," Opt. Express 21, 27291-27305 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-27291


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. G. Gagnon, N. Lahoud, G. Mattiussi, and P. Berini, “Thermally activated variable attenuation of long-range surface plasmon polariton waves,” J. Lightwave Technol.24, 4391–4409 (2006). [CrossRef]
  2. K. Leosson, T. Rosenzveig, P. G. Hermannsson, and A. Boltasseva, “Compact plasmonic variable optical attenuator,” Opt. Express20, 15546–15552 (2008). [CrossRef]
  3. T. Nikolajsen, K. Leosson, and S. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett.85, 5833–5835 (2004). [CrossRef]
  4. T. Nikolajsen, K. Leosson, and S. Bozhevolnyi, “In-line extinction modulator based on long-range surface plasmon polarintons,” Opt. Commun.244, 455–459 (2005). [CrossRef]
  5. P. Berini, “Plasmon-polariton waves guided by thin lossy metals of finite width: Bound modes of symmetric structures,” Phys. Rev. B61, 10484–10503 (2000). [CrossRef]
  6. T. Holmgaard and S. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon waveguides,” Phys. Rev. B75, 245405 (2007). [CrossRef]
  7. A. V. Krasavin and A. V. Zayats, “Passive photonic elements based on dielectric-loaded surface plasmon waveguides,” Appl. Phys. Lett.90, 211101 (2007). [CrossRef]
  8. S. Massenot, J. Grandidier, A. Bouhelier, G. Colas des Francs, L. Markey, J.-C. Weeber, A. Dereux, J. Renger, M. U. Gonzalez, and R. Quidant, “Polymer-metal waveguides characterization by Fourier plane leakage radiation microscopy,” Appl. Phys. Lett.91, 243102 (2007). [CrossRef]
  9. O. Tsilipakos, T. V. Yioultsis, and E. E. Kriezis, “Theoretical analysis of thermally tunable microring resonator filters made of dielectric-loaded plasmonic waveguides,” J. Appl. Phys.106, 093109 (2009). [CrossRef]
  10. 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, 073111 (2011). [CrossRef]
  11. A. Pitilakis and E. E. Kriezis, “Longitudinal 2×2 switching configurations based on thermo-optically addressed dielectric-loaded plasmonic waveguides,” J. Lightwave Technol.29, 2636–2646 (2011). [CrossRef]
  12. 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. Express18, 1207–1216 (2010). [CrossRef] [PubMed]
  13. J. Gosciniak, L. Markey, A. Dereux, and S. I. Bozhevolnyi, “Efficient thermo-optically controlled Mach–Zehnder interferometers using dielectric-loaded plasmonic waveguides,” Opt. Express20, 16300–16309 (2012). [CrossRef]
  14. K. Hassan, J.-C. Weeber, L. Markey, and A. Dereux, “Thermo-optical control of dielectric loaded plasmonic racetrack resonators,” J. Appl. Phys.110, 023106 (2011). [CrossRef]
  15. K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, O. Pitilakis, and E. E. Kriezis, “Thermo-optic plasmo-photonic mode interference switches based on dielectric loaded waveguides,” Appl. Phys. Lett.99, 241110 (2011). [CrossRef]
  16. R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, and H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett.10, 4851–4857 (2010). [CrossRef]
  17. N. Pleros, E. E. Kriezis, and K. Vyrsokinos, “Optical interconnects using plasmonics and Si-photonics,” IEEE Photon. J.3, 296–301 (2011). [CrossRef]
  18. O. Tsilipakos, A. Pitilakis, T. Yioultsis, S. Papaioannou, K. Vyrsokinos, G. D. Kalavrouziotis, D. Giannoulis, H. Apostolopoulos, T. Avramopoulos, M. Tekin, M. Baus, K. Karl, J.-C. Hassan, L. Weeber, A. Markey, S. Dereux, A. Kumar, Bozhevolnyi, N. Pleros, and E. Kriezis, “Interfacing dielectric-loaded plasmonic and silicon photonic waveguides: Theoretical analysis and experimental demonstration,” IEEE J. Quantum Electron.48, 678–687 (2012). [CrossRef]
  19. D. Kalavrouziotis, S. Papaioannou, K. Vyrsokinos, L. Markey, A. Dereux, G. Giannoulis, D. Apostolopoulos, H. Avramopoulos, and N. Pleros, “Demonstration of a plasmonic MMI switch in 10-Gb/s true data traffic conditions,” IEEE Photon. Technol. Lett.24, 1819–1822 (2012). [CrossRef]
  20. S. Papaioannou, D. Kalavrouziotis, K. Vyrsokinos, J.-C. Weeber, K. Hassan, L. Markey, A. Dereux, A. Kumar, S. I. Bozhevolnyi, T. Baus, M. Tekin, D. Apostolopoulos, H. Avramopoulos, and N. Pleros, “Active plasmonics in WDM traffic switching applications,” Sci. Rep.2, 1358–1361 (2012). [CrossRef]
  21. G. Giannoulis, D. Kalavrouziotis, D. Apostolopoulos, S. Papaioannou, A. Kumar, S. I. Bozhevolnyi, L. Markey, K. Hassan, J.-C. Weeber, M. Dereux, A. Baus, M. Karl, T. Tekin, O. Tsilipakos, A. K. Pitilakis, E. E. Kriezis, K. Vyrsokinos, H. Avramopoulos, and N. Pleros, “Data transmission and thermo-optic tuning performance of dielectric-loaded plasmonic structures hetero-integrated on a silicon chip,” IEEE Photon. Technol. Lett.24, 374–376 (2012). [CrossRef]
  22. J.-C. Weeber, K. Hassan, L. Saviot, A. Dereux, C. Boissière, O. Durupthy, C. Chaneac, E. Burov, and A. Pastouret, “Efficient photo-thermal activation of gold nanoparticle-doped polymer plasmonic switches,” Opt. Express20, 27636–27649 (2012). [CrossRef] [PubMed]
  23. M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Opt. Express15, 17458–17481 (2007). [CrossRef] [PubMed]
  24. A. H. Atabaki, A. A. Eftekhar, S. Yegnanarayanan, and A. Adibi, “Sub-100-nanosecond thermal reconfiguration of silicon photonic devices,” Opt. Express21, 15706–15718 (2013). [CrossRef] [PubMed]
  25. A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steiberger, F. Aussenegg, A. Leitner, and J. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B149, 220–229 (2008). [CrossRef]
  26. J. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley and Sons, 1999).
  27. M. Nevière and E. Popov, Light Propagation in Periodic Media (Marcel Dekker, Inc., 2003).
  28. E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides: reflection pole method and wavevector density method,” J. Lightwave Technol.17, 929–941 (1999). [CrossRef]
  29. H. Raether, Surface Plasmons on Smooth and Rough Surface and on Gratings (Springer-Verlag, 1988).
  30. M. G. Nielsen, J.-C. Weeber, K. Hassan, J. Fatome, C. Finot, S. Kaya, L. Markey, O. Albrektsen, S. I. Bozhevolnyi, G. Millot, and A. Dereux, “Grating couplers for fiber-to-fiber characterizations of stand-alone dielectric loaded surface plasmon waveguide components,” J. Lightwave Technol.30, 3118–3125 (2012). [CrossRef]
  31. S. Kaya, J.-C. Weeber, F. Zacharatos, K. Hassan, T. Bernardin, B. Cluzel, J. Fatome, and C. Finot, “Photo-thermally induced modulation of surface plasmon polariton propagation at telecommunication wavelengths,” Opt. Express21, 22269–22284 (2013). [CrossRef] [PubMed]
  32. R. J. Baseman, N. M. Froberg, J. C. Andreshak, and Z. Schlesinger, “Minimum fluence for laser blow-off of thin gold films at 248 and 532nm,” Appl. Phys. Lett.56, 1412–1414 (1990). [CrossRef]
  33. X. Chen, Y. Chen, Y. Min, and M. Qiu, “Nanosecond photothermal effect in plasmonic nanostructures,” ACS Nano6, 2550–2556 (2012). [CrossRef] [PubMed]
  34. E. Marin, “Characteristic dimensions for heat transfer,” Lat. Am. J. Phys. Educ.4, 56–60 (2010).
  35. D. P. Brunco, J. A. Kittl, C. E. Otis, P. M. Goodwin, M. O. Thompson, and M. J. Aziz, “Time-resolved temperature measurements during pulsed laser irradiation using thin film metal thermometers,” Rev. Sci. Instrum.64, 2615–2623 (1993). [CrossRef]
  36. J. Gosciniak and S. Bozhevolnyi, “Performances of thermo-optic components based on dielectric-loaded surface plasmon polariton waveguides,” Sci. Rep.3, 1803 (2013). [CrossRef]
  37. A. Nakamura, Y. Ueno, K. Tajima, J. Sasaki, T. Sugimoto, T. Kato, T. Shimoda, M. Itoh, H. Hatakeyama, T. Tamanuki, and T. Sasaki, “Demultiplexing of 168Gb/s data pulses with an hybrid-integrated symetric Mach-Zehnder all-optical switch,” IEEE Photon. Technol. Lett.12, 425–427 (2000). [CrossRef]

Cited By

Alert me when this paper is cited

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


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited