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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 7 — Apr. 8, 2013
  • pp: 8240–8250
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Long-range plasmonic directional coupler switches controlled by nematic liquid crystals

D. C. Zografopoulos and R. Beccherelli  »View Author Affiliations


Optics Express, Vol. 21, Issue 7, pp. 8240-8250 (2013)
http://dx.doi.org/10.1364/OE.21.008240


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Abstract

A liquid-crystal tunable plasmonic optical switch based on a long-range metal stripe directional coupler is proposed and theoretically investigated. Extensive electro-optic tuning of the coupler’s characteristics is demonstrated by introducing a nematic liquid crystal layer above two coplanar plasmonic waveguides. The switching properties of the proposed plasmonic structure are investigated through rigorous liquid-crystal studies coupled with a finite-element based analysis of light propagation. A directional coupler optical switch is demonstrated, which combines very low power consumption, low operation voltages, adjustable crosstalk and coupling lengths, along with sufficiently reduced insertion losses.

© 2013 OSA

1. Introduction

Plasmonics, the scientific field dealing with the properties of plasmons, i.e., oscillating optical fields of free electron gases present in metallic structures, has become one of the most active research topics in the last years. The exploitation of unique properties of plasmons, such as light localization beyond the diffraction limit, offers a broad spectrum of unprecedented capabilities, which has already led to the demonstration of numerous applications. These span over a broad range of disciplines, with nano-scaled integrated photonics platforms [1

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

], nano-antennas, superlenses and ultrafast nanoplasmonics [2

2. M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express 19, 22029–22106 (2011) [CrossRef] [PubMed] .

], as well as advanced chemical detection techniques like surface-enhanced Raman spectroscopy (SERS) [3

3. E. Le Ru and P. Etchegoin, Principles of Surface Enhanced Raman Spectroscopy and Related Plasmonic Effects (Elsevier, Amsterdam, 2009).

], biomedical sensoristic and treatment techniques [4

4. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010) [CrossRef] .

] and solar energy conversion being key, yet not exclusive, examples.

Focusing on the context of integrated photonics circuitry, plasmons manifest as localized light waves that propagate along metal/dielectric interfaces, termed as surface plasmon polaritons (SPPs). The manipulation and routing of such optical waves has allowed for the demonstration of numerous plasmonic waveguides of different light confinement scales, which constitute promising solutions in view of future integrated photonics platforms for broadband optical signal processing as both intra- [5

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

8

8. S. Papaioannou, D. Kalavrouziotis, K. Vyrsokinos, J.-C. Weeber, K. Hassan, L. Markey, A. Dereux, A. Kumar, S. I. Bozhevolnyi, M. Baus, T. Tekin, D. Apostolopoulos, H. Avramopoulos, and N. Pleros, “Active plasmonics in WDM traffic switching applications,” Sci. Rep. 2, 652 (2012) [CrossRef] [PubMed] .

] and inter-chip optical interconnects [9

9. J. J. Ju, S. Park, M.-S. Kim, J. T. Kim, S. K. Park, Y. J. Park, and M.-H. Lee, “40 Gbits/s light signal transmission in long-range surface plasmon waveguides,” Appl. Phys. Lett. 91, 171117 (2007) [CrossRef] .

12

12. J. T. Kim, J. J. Ju, S. Park, M.-S. Kim, S. K. Park, and M.-H. Lee, “Chip-to-chip optical interconnect using gold long-range surface plasmon polariton waveguides,” Opt. Express 16, 13133–13138 (2008) [CrossRef] [PubMed] .

].

The latter, in particular, are based on plasmonic long-range waveguides consisting in thin metal stripes [13

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

] that are characterized by single-mode low propagation losses, measured down to sub-dB/cm levels for thin silver stripes in telecom wavelength [10

10. S. Park, J. J. Ju, J. T. Kim, M.-S. Kim, S. K. Park, J.-M. Lee, W.-J. Lee, and M.-H. Lee, “Sub-dB/cm propagation loss in silver stripe waveguides,” Opt. Express 17, 697–702 (2009) [CrossRef] [PubMed] .

]. Furthermore, they offer excellent mode matching to single-mode fibers (SMFs) with coupling values down to 0.1 dB measured for gold stripes butt-coupled to polarization-maintaining SMFs [11

11. J. J. Ju, S. Park, M.-S. Kim, J. T. Kim, S. K. Park, Y. J. Park, and M.-H. Lee, “Polymer-based long-range surface plasmon polariton waveguides for 10-Gbps optical signal transmission applications,” J. Lightwave Technol. 26, 1510–1518 (2008) [CrossRef] .

]. Their fabrication involves standard planar processing techniques, such as lithographic definition, metal vapor deposition, and lift-off, thus eliminating the need for deep etching techniques frequently required in the case of dielectric stripe/rib waveguides. Moreover, they are compatible with flexible polymer claddings, providing very good mechanical stability, a prerequisite, for instance, in the design of flexible printed circuit boards. Finally, LRSPP plasmonic waveguides provide the capability of dynamically controlling the optical signal by directly addressing the metal waveguides. Based on such properties, a variety of devices has been thus far demonstrated, such as modulators and switches, relying on the thermo-optic control of the background polymer refractive index, which is controlled via current injection through the metal waveguide [14

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

17

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

].

2. Liquid-crystal switching in side-coupled metal stripe plasmonic waveguides

The cross-section layout of the proposed plasmonic coupler switch is shown in Fig. 1(a). Two grounded Au stripes of dimensions w × t are embedded in a polymer background of total thickness hsub + hbuf, where hsub and hbuf are the thicknesses of the substrate and buffer layers, respectively. Above the buffer layer, a planar cell is infiltrated with a nematic liquid-crystalline material. A thin PMMA layer isolates the LC-layer from two ITO electrodes of width w placed directly above the Au stripes. The structure is backed by a low-index material, silica in this case. This configuration allows for the individual addressing of each plasmonic waveguide, by properly applying a voltage VLC on either ITO electrode, and minimizes the required applied voltage, since this is directly applied between the waveguiding Au stripes and the control electrodes. The application of the control voltage reorientates the LC molecules mainly in the region above a single Au stripe and thus tunes its optical properties, as it will be shown in this study. The local LC molecular orientation is described by the unit vector of the nematic director n, which is defined via the tilt and twist angles, as in Fig. 1(b). The total length of the LC-cell, which also defines the interaction length, is LC, as shown in the three-dimensional perspective of Fig. 1(c). Finally, the separation between the two Au stripes is equal to dC.

Fig. 1 (a) Cross-sectional view of the proposed LC-based plasmonic directional coupler and definition of material and structural parameters. Alignments layers (not shown) promote strong anchoring of the LC molecules along the z–axis at the LC/PMMA and LC/polymer interfaces. (b) Definition of tilt and twist angles that describe the nematic director local orientation. (c) Three-dimensional view of the proposed coupler. The coupling length is equal to LC and the separation between the two metal stripes is dC.

The rigorous study of LC reorientation when the control voltage is applied is a multiphysics problem, as it involves the elastic problem associated with LC deformations in the LC-layer bulk, inherently coupled to the electrostatic problem of the electric potential distribution in both LC and the surrounding dielectrics. This is achieved by solving for the set of three partial differential equations (PDEs) composed of two Euler-Lagrange equations that minimize the total energy stored in the LC region, along with Gauss’ law, with independent variables the electric potential V and the tilt and twist angles. The PDEs are solved on the nodes of a finite-element mesh, that descritizes the cross-section of the structure, as described in detail in [29

29. D. C. Zografopoulos, R. Beccherelli, A. C. Tasolamprou, and E. E. Kriezis, “Liquid-crystal tunable waveguides for integrated plasmonic components,” Photon. Nanostruct.: Fundam. Appl. 11, 73–84 (2013) [CrossRef] .

, 33

33. A. K. Pitilakis, D. C. Zografopoulos, and E. E. Kriezis, “In-line polarization controller based on liquid-crystal photonic crystal fibers,” J. Lightwave Technol. 29, 2560–2569 (2011) [CrossRef] .

]. An alternative approach involves the minimization of the total energy employing a weak formulation [34

34. B. Bellini and R. Beccherelli, “Modelling, design and analysis of liquid crystal waveguides in preferentially etched silicon grooves,” J. Phys. D: Appl. Phys. 42, 045111 (2009) [CrossRef] .

].

In this work the widely studied, commercially available, nematic mixture E7 is selected as the target LC material, characterized by low-frequency (measured at 1 KHz) dielectric constants perpendicular and parallel to the molecular director εo = 5.3 and εe = 18.6, respectively, and elastic constants K11, K22, K33 equal to 10.3, 7.4, and 16.48 pN, respectively [35

35. J. F. Strömer, E. P. Raynes, and C. V. Brown, “Study of elastic constant ratios in nematic liquid crystals,” Appl. Phys. Lett. 88, 051915 (2006) [CrossRef] .

]. The relative dielectric constants of the polymer, PMMA and SiO2 are set to 4, 3.6 [36

36. R. D. Schaller, L. F. Lee, J. C. Johnson, L. H. Haber, R. J. Saykally, J. Vieceli, I. Benjamin, T.-Q. Nguyen, and B. J. Schwartz, “The nature of interchain excitations in conjugated polymers: spatially-varying interfacial solvatochromism of annealed MEH-PPV films studied by near-field scanning optical microscopy (NSOM),” J. Phys. Chem. B 106, 9496–9506 (2002) [CrossRef] .

] and 3.9 [37

37. J. Robertson, “High dielectric constant oxides,” Eur. Phys. J. 28, 265–291 (2004).

], respectively. The LC and PMMA layers are correspondigly 5 μm and 1 μm thick, and the buffer and substrate thickness is, respectively, 2 μm and 10 μm. The ITO electrode’s thickness is 100 nm and the Au stripe’s dimensions are 5 μm × 15 nm.

Figure 2 shows the tilt and twist profiles in the LC layer plotted for dC = 3 and 7 μm, as well as the potential distribution for the first case, when a 2 V voltage is applied at the cross ITO electrode. As both Au stripes and the bar ITO electrode are grounded, the electric field profile is highly asymmetric, with significant voltage drop only in the region of the cross waveguide, considering the gold stripe on the right as the reference input waveguide. On the contrary, both angles are practically zero above the bar port, which is placed between grounded Au and ITO stripes. When the two waveguides approach each other, the electrostatic field shows a stronger horizontal component, which leads to significantly higher values for the twist angles. This is observed in the results of Fig. 3, which shows the maximum tilt and twist values calculated for an applied voltage between 1.5 and 2.5 V, as a function of the stripe separation dC. Calculations have been performed for a pretilt angle of 1°. It is demonstrated that twist is more sensitive than tilt to the variation of the distance dC. Nevertheless, in terms of the electro-optic tuning of the structure’s optical properties, it is the tilt angle that plays the most significant role, since it directly determines the effective refractive index along the y–axis, which is the one primarily sensed by TM-polarized light.

Fig. 2 (a) Tilt and (b) twist angle profile in the LC-layer for an applied voltage VLC = 2 V and a stripe separation equal to 3 and 7 μm. (c) Electric potential distribution plotted in the section between the silica substrates for dC = 3 μm.
Fig. 3 Maximum tilt and twist angles in the voltage range between VLC = 1.5 and 2.5 V for a stripe separation from dC = 1 to 10 μm. Shorter values of dC lead to higher twist angles owing to stronger interaction of the electrostatic field with the grounded Au stripe and opposite ITO that define the bar port.

3. Optical properties of side-coupled metal stripe liquid-crystal plasmonic switches: CROSS state

Fig. 4 Modal effective indices for the two TM-polarized supermodes supported of the coupler structure in the rest state (VLC = 0) as a function of the separation dC, and corresponding coupling length LC, defined as LC = 0.5λ0n, where Δn = nsymnasym, for λ0 = 1.55 μm.
Fig. 5 Electric field modal profiles for the (a) symmetric and (b) anti-symmetric coupler supermodes for dC = 7 μm and the (c) polymer and (d) LC-excitation modes.

Fig. 6 Crosstalk evolution along a total propagation distance equal to 2LC for three excitation scenarios: launching the polymer-input LRSPP mode (Fig. 5(a)), the LC-input LRSPP mode (Fig. 5(b)), or a superposition of the two coupler supermodes (Fig. 5(c–d)). The separation dC is equal to 7 μm.

4. Optical properties of side-coupled metal stripe liquid-crystal plasmonic switches: BAR state

Fig. 7 Crosstalk values and insertion losses for the cross-state of the coupler as a function of stripe separation dC for the two realistic excitation scenarios under study.
Fig. 8 Crosstalk evolution for the two excitation scenarios at VLC = 0 and VLC = VC = 1.954 V, which correspond to operation in the CROSS and BAR state, respectively, for a propagation distance equal to the coupling length LC = 2.275 mm. Inset shows the insertion losses of the component for both operation states and excitation profiles.

Fig. 9 Optical power propagation at 100 nm above the metal stripes for the (a) cross and (b) bar operation states calculated for the LC-excitation scenario, with parameters as in Fig. 8. The associated multimedia files monitor power coupling at the coupler’s cross-section for the (a) cross ( Media 1) and (b) bar ( Media 2) state.

The inset in Fig. 8 shows the insertion losses of the component, which are by 0.07 dB higher in the bar-state, owing to a slightly better coupling efficiency of the excitation modes to the guided supermodes of the coupler in the cross-state. In this analysis, the LC material was considered to be lossless. Absorption losses are likely below 1 dB/cm, as measured for the pure compound 5CB, one of the components of E7 [52

52. S.-T. Wu, “Absorption measurements of liquid crystals in the ultraviolet, visible, and infrared,” J. Appl. Phys. 84, 4462–4465 (1998) [CrossRef] .

]. In practice, however, LC photonic waveguiding structures exhibit scattering losses, which may range typically in the range from few [31

31. A. d’Alessandro, B. Bellini, D. Donisi, R. Beccherelli, and R. Asquini, “Nematic liquid crystal optical channel waveguides on silicon,” IEEE J. Quantum Electron. 42, 1084–1090 (2006) [CrossRef] .

, 32

32. D. Donisi, B. Bellini, R. Beccherelli, R. Asquini, G. Gilardi, M. Trotta, and A. d’Alessandro, “A switchable liquid-crystal optical channel waveguide on silicon,” IEEE J. Quantum Electron. 46, 762–768 (2010) [CrossRef] .

] to tens of dB/cm [30

30. J. Pfeifle, L. Alloatti, W. Freude, J. Leuthold, and C. Koos, “Silicon-organic hybrid phase shifter based on a slot waveguide with a liquid-crystal cladding,” Opt. Express 20, 15359–15376 (2012) [CrossRef] [PubMed] .

]. We have repeated the study of the coupler as in Fig. 8 by introducing different levels of losses via the imaginary part of the LC indices, such that the individual LC-waveguide formed in the switched LC-layer, i.e., in the absence of the plasmonic waveguides at V = VLC, exhibits propagation losses of 5 and 20 dB/cm. The insertion losses of the device were practically unaffected in all cases examined with reference to the cross-state, since the amount of optical power that enters the LC layer was found less than 3%. In the bar-state, a part of the propagating optical field enters in the high-index LC-zone formed under the control ITO electrode, as shown in the multimedia file associated with Fig. 9(b). In that case, the insertion losses for both excitation scenarios were found to increase by 0.1 and 0.7 dB, respectively, for the two levels of losses considered.

The switching speed of the device is expected in the millisecond range, as in typical nematic LC photonic components [53

53. I. W. Steward, The Static and Dynamic Continuum Theory of Liquid Crystals (Taylor & Francis, London, 2004).

], which is sufficient for light reconfiguration and routing applications. The power consumption of the device can be estimated as PCfVLC2, where C is the device capacitance and f = 1 ÷ 10 KHz the LC-switching frequency. By denoting as C* the capacitance per unit length, an upper limit Cmax* could be given by considering the in-series capacitance combination of the three layers between the control electrodes, i.e., PMMA, LC, and polymer buffer. For relative permittivity and layer thickness values as in Section 2, this upper limit is approximately 40 pF/m. Assuming a device length of 2.5 mm, a driving voltage of 2 V, and a driving frequency of 1 KHz, the estimated power consumption is 0.4 nW, orders of magnitude lower than in thermo-optic plasmonic switching devices [8

8. S. Papaioannou, D. Kalavrouziotis, K. Vyrsokinos, J.-C. Weeber, K. Hassan, L. Markey, A. Dereux, A. Kumar, S. I. Bozhevolnyi, M. Baus, T. Tekin, D. Apostolopoulos, H. Avramopoulos, and N. Pleros, “Active plasmonics in WDM traffic switching applications,” Sci. Rep. 2, 652 (2012) [CrossRef] [PubMed] .

, 14

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

, 17

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

].

5. Conclusions

In brief, we have presented the design and analysis of a liquid-crystal long-range plasmonic directional coupler switch and investigated into its performance characteristics, namely coupling length, crosstalk and insertion losses. It has been demonstrated that coupling lengths in the few millimeter range allow for crosstalk values better than −10 dB with insertion losses lower than 2 dB and a switching voltage below 2 V. The material and structural parameters involved are compatible with standard fabrication processes, namely polymer spin-coating and metal patterning, deposition and lift-off, as demonstrated in numerous Au/polymer LRSPP fabricated components [13

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

]. The LC-cell thickness and alignment techniques are also typical of planar cells infiltrated with nematic materials. These components are proposed as an ultra-low power solution, free from issues of their thermo-optic analogues, such as thermal crosstalk, diffusion and electromigration, in integrated photonic architectures for optical inter-chip interconnects.

Acknowledgments

This work was supported by the Marie-Curie Intra-European Fellowship ALLOPLASM (FP7-PEOPLE-2010-IEF-273528), within the 7th European Community Framework Programme.

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30.

J. Pfeifle, L. Alloatti, W. Freude, J. Leuthold, and C. Koos, “Silicon-organic hybrid phase shifter based on a slot waveguide with a liquid-crystal cladding,” Opt. Express 20, 15359–15376 (2012) [CrossRef] [PubMed] .

31.

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32.

D. Donisi, B. Bellini, R. Beccherelli, R. Asquini, G. Gilardi, M. Trotta, and A. d’Alessandro, “A switchable liquid-crystal optical channel waveguide on silicon,” IEEE J. Quantum Electron. 46, 762–768 (2010) [CrossRef] .

33.

A. K. Pitilakis, D. C. Zografopoulos, and E. E. Kriezis, “In-line polarization controller based on liquid-crystal photonic crystal fibers,” J. Lightwave Technol. 29, 2560–2569 (2011) [CrossRef] .

34.

B. Bellini and R. Beccherelli, “Modelling, design and analysis of liquid crystal waveguides in preferentially etched silicon grooves,” J. Phys. D: Appl. Phys. 42, 045111 (2009) [CrossRef] .

35.

J. F. Strömer, E. P. Raynes, and C. V. Brown, “Study of elastic constant ratios in nematic liquid crystals,” Appl. Phys. Lett. 88, 051915 (2006) [CrossRef] .

36.

R. D. Schaller, L. F. Lee, J. C. Johnson, L. H. Haber, R. J. Saykally, J. Vieceli, I. Benjamin, T.-Q. Nguyen, and B. J. Schwartz, “The nature of interchain excitations in conjugated polymers: spatially-varying interfacial solvatochromism of annealed MEH-PPV films studied by near-field scanning optical microscopy (NSOM),” J. Phys. Chem. B 106, 9496–9506 (2002) [CrossRef] .

37.

J. Robertson, “High dielectric constant oxides,” Eur. Phys. J. 28, 265–291 (2004).

38.

C. Vassallo, Optical Waveguide Concepts (Elsevier, Amsterdam, 1991).

39.

Norland Products, Optical Adhesives, (www.norlandprod.com).

40.

M. Wang, ed., Lithography (InTech, 2010) [CrossRef] .

41.

CYCLOTENE, Dow Chemical, (www.dow.com).

42.

J. Li, S.-T. Wu, S. Brugioni, R. Meucci, and S. Faetti, “Infrared refractive indices of liquid crystals,” J. Appl. Phys. 97, 073501 (2005) [CrossRef] .

43.

B. Tatian, “Fitting refractive-index data with the Sellmeier dispersion formula,” Appl. Opt. 23, 4477–4485 (1984) [CrossRef] [PubMed] .

44.

E. D. Palik, Handbook of optical constants of solids (Orlando, FL, Academic, 1985).

45.

S. Laux, N. Kaiser, A. Zöller, R. Götzelmann, H. Lauth, and H. Bernitzki, “Room-temperature deposition of indium tin oxide thin films with plasma ion-assisted evaporation,” Thin Solid Films 335, 1–5 (1998) [CrossRef] .

46.

T. Srivastava and A. Kumar, “Comparative study of directional couplers utilizing long-range surface plasmon polaritons,” Appl. Optics 49, 2397–2402 (2010) [CrossRef] .

47.

A. Degiron, C. Dellagiacoma, J. G. McIlhargey, G. Shvets, O. J. F. Martin, and D. R. Smith, “Simulations of hybrid long-range plasmon modes with application to 90° bends,” Opt. Lett. 32, 2354–2356 (2007) [CrossRef] [PubMed] .

48.

I. Abdulhalim, “Surface plasmon TE and TM waves at the anisotropic film-metal interface,” J. Opt. A: Pure Appl. Opt. 11, 015002 (2009) [CrossRef] .

49.

R. Li, C. Cheng, F.-F. Ren, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, “Hybridized surface plasmon polaritons at an interface between a metal and a uniaxial crystal,” Appl. Phys. Lett. 92, 141115 (2008) [CrossRef] .

50.

COMSOL Multiphysics v4.3a, (www.comsol.com).

51.

M. Stallein, C. Kolleck, and G. Mrozynski, “Improved analysis of the coupling of optical waves into multimode waveguides using overlap integrals,” in “PIERS 2005 Proceedings,” (Hangzhou, China, 2005), pp. 464–468.

52.

S.-T. Wu, “Absorption measurements of liquid crystals in the ultraviolet, visible, and infrared,” J. Appl. Phys. 84, 4462–4465 (1998) [CrossRef] .

53.

I. W. Steward, The Static and Dynamic Continuum Theory of Liquid Crystals (Taylor & Francis, London, 2004).

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(200.4650) Optics in computing : Optical interconnects
(230.3720) Optical devices : Liquid-crystal devices
(240.6680) Optics at surfaces : Surface plasmons
(130.4815) Integrated optics : Optical switching devices

ToC Category:
Integrated Optics

History
Original Manuscript: December 27, 2012
Revised Manuscript: February 26, 2013
Manuscript Accepted: March 3, 2013
Published: March 28, 2013

Citation
D. C. Zografopoulos and R. Beccherelli, "Long-range plasmonic directional coupler switches controlled by nematic liquid crystals," Opt. Express 21, 8240-8250 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-8240


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  44. E. D. Palik, Handbook of optical constants of solids (Orlando, FL, Academic, 1985).
  45. S. Laux, N. Kaiser, A. Zöller, R. Götzelmann, H. Lauth, and H. Bernitzki, “Room-temperature deposition of indium tin oxide thin films with plasma ion-assisted evaporation,” Thin Solid Films335, 1–5 (1998). [CrossRef]
  46. T. Srivastava and A. Kumar, “Comparative study of directional couplers utilizing long-range surface plasmon polaritons,” Appl. Optics49, 2397–2402 (2010). [CrossRef]
  47. A. Degiron, C. Dellagiacoma, J. G. McIlhargey, G. Shvets, O. J. F. Martin, and D. R. Smith, “Simulations of hybrid long-range plasmon modes with application to 90° bends,” Opt. Lett.32, 2354–2356 (2007). [CrossRef] [PubMed]
  48. I. Abdulhalim, “Surface plasmon TE and TM waves at the anisotropic film-metal interface,” J. Opt. A: Pure Appl. Opt.11, 015002 (2009). [CrossRef]
  49. R. Li, C. Cheng, F.-F. Ren, J. Chen, Y.-X. Fan, J. Ding, and H.-T. Wang, “Hybridized surface plasmon polaritons at an interface between a metal and a uniaxial crystal,” Appl. Phys. Lett.92, 141115 (2008). [CrossRef]
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  52. S.-T. Wu, “Absorption measurements of liquid crystals in the ultraviolet, visible, and infrared,” J. Appl. Phys.84, 4462–4465 (1998). [CrossRef]
  53. I. W. Steward, The Static and Dynamic Continuum Theory of Liquid Crystals (Taylor & Francis, London, 2004).

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