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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 13 — Jul. 1, 2013
  • pp: 15280–15286
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Thermo-optic mode extinction modulator based on graphene plasmonic waveguide

Jin Tae Kim, Kwang Hyo Chung, and Choon-Gi Choi  »View Author Affiliations


Optics Express, Vol. 21, Issue 13, pp. 15280-15286 (2013)
http://dx.doi.org/10.1364/OE.21.015280


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Abstract

We developed a thermo-optic (TO) mode extinction modulator based on graphene plasmonic waveguide. For compact device design and fabrication, the graphene plasmonic waveguide and heating element are configured all-in-one. Thermally induced inhomogeneous refractive-index distribution of the polymer near the microribbon cut off the long-range surface plasmon polariton (LRSPP) stripe mode propagating along a graphene microribbon. Numerical modeling are conducted on the time-dependent temperature (and hence the refractive-index) distribution by resistive heating element inside the graphene TO modulator. Experimental results demonstrate 30 dB attenuation with 12 mW electrical power injection at a telecom wavelength and exhibit a good agreement with the thermal modeling.

© 2013 OSA

1. Introduction

Graphene, one-atom-thick planar sheet of carbon atoms densely packed in a honeycomb crystal lattice, has attracted great attention due to its extraordinary mechanical, electric, magnetic, thermal, and photonic properties [1

1. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007). [CrossRef] [PubMed]

]. In photonics, graphene has been considered as a versatile optical material for novel optoelectronic devices such as solar cell, organic light emitting devices, ultrafast lasers, and touch screens [2

2. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010). [CrossRef]

]. The linear dispersion of the Dirac fermions in graphene allowed us to develop a wide bandwidth optical modulator, a photo-detector, and a polarizer [3

3. T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4(5), 297–301 (2010). [CrossRef]

5

5. Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011). [CrossRef]

].

Recent theoretical investigations on graphene-based photonic devices exhibited that graphene embedded in a homogenous dielectric can serve as a lightwave guiding medium [6

6. S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99(1), 016803 (2007). [CrossRef] [PubMed]

8

8. M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009). [CrossRef]

]. Pristine graphene with very low chemical potential behaves like a semiconductor and capable of guiding of a transverse-electric (TE)-polarization electromagnetic surface wave [6

6. S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99(1), 016803 (2007). [CrossRef] [PubMed]

]. If graphene is highly doped, it behaves like a thin metal film and allows to guiding a transverse-magnetic (TM)-polarization electromagnetic surface wave [7

7. G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008). [CrossRef]

, 8

8. M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009). [CrossRef]

]. Similar to a thin metal stripe that supports low loss long-range surface-plasmon-polariton (LRSPP) stripe mode [9

9. P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photon. 1(3), 484–588 (2009). [CrossRef]

], graphene microribbons allow to guiding the LRSPP stripe mode with the averaged extinction ratio of 19 dB at a wavelength of 1.31 µm and exhibited successful 2.5 Gbps optical data transmission [10

10. J. T. Kim and S.-Y. Choi, “Graphene-based plasmonic waveguides for photonic integrated circuits,” Opt. Express 19(24), 24557–24562 (2011). [CrossRef] [PubMed]

]. Different from the conventional metal, the Fermi level of graphene is tunable by applying gate bias voltage (or doping) so that graphene’s charge carrier density (conductivity) and interband transition (via excitation of electron-hole pairs) are changeable [8

8. M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009). [CrossRef]

, 12

12. Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012). [CrossRef] [PubMed]

]. By alternating the graphene’s properties, the characteristics of the LRSPP stripe mode propagating along graphene microribbon are modulated. For further advancement of graphene plasmonics-based photonic integrated circuit, different kinds of novel photonic devices are intensively under developing [4

4. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011). [CrossRef] [PubMed]

, 11

11. J. T. Kim and C.-G. Choi, “Graphene-based polymer waveguide polarizer,” Opt. Express 20(4), 3556–3562 (2012). [CrossRef] [PubMed]

14

14. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]

].

In this paper, we developed thermo-optic mode extinction modulator based on graphene plasmonic waveguide and investigated its optical characteristics at a wavelength of 1.55 μm. To perturb the guided LRSPP stripe mode along the graphene microribbon-based plasmonic waveguide, inhomogeneous refractive-index distribution is induced around the graphene microribbon by using an all-in-one graphene heater. Numerical simulations are conducted on the time-dependent temperature (and hence the refractive-index) distribution by resistive heating element inside the graphene thermo-optic (TO) modulator and compared with the experimental results.

2. Architectural concept and thermal modeling

Surface plasmon polaritons (SPPs) represent surface waves that can propagate along a metal–dielectric interface. For a thin metal film embedded in a dielectric, the SPP modes are excited at the upper and lower interfaces and then, form a low loss symmetric mode, i.e. long-range SPP (LRSPP) mode. If the metal film becomes a stripe by reducing its width, the two dimensional confinement of the LRSPP is possible and the LRSPP stripe mode is formed [9

9. P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photon. 1(3), 484–588 (2009). [CrossRef]

]. The field intensity of the LRSPP stripe mode is confined mostly in the adjacent dielectric medium rather than the thin metal stripe. Thus, the characteristics of the LRSPP stripe mode are highly dependent on the optical properties of the surrounding dielectric such as refractive-index and material loss. A small difference in the refractive-index of the superstrate and substrate of the metal stripe may cause an LRSPP stripe mode to be cut off [15

15. I. Breukelaar, R. Charbonneau, and P. Berini, “Long-range surface plasmon-polariton mode cutoff and radiation in embedded strip waveguides,” J. Appl. Phys. 100(4), 043104 (2006). [CrossRef]

]. With the aid of the thermo-optic effect of a polymer cladding, in-line heating element switches on and off the refractive index asymmetry by controlling electrical power injection, and consequently, turns on and off the guided mode cutoff [16

16. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833–5835 (2004). [CrossRef]

, 17

17. G. Gagnon, N. Lahoud, G. Mattiussi, and P. Berini, “Thermally activated variable attenuation of long-range surface plasmon-polariton waves,” J. Lightwave Technol. 24(11), 4391–4402 (2006). [CrossRef]

].

The CVD grown graphene may be considered as a quasi-two-dimensional electron gas system so that graphene microribbons used a guiding medium of the LRSPP stripe mode. In addition, graphene is used as a conductive metal-like thin film for transparent heater [18

18. J. Kang, H. Kim, K. S. Kim, S.-K. Lee, S. Bae, J.-H. Ahn, Y.-J. Kim, J.-B. Choi, and B. H. Hong, “High-performance graphene-based transparent flexible heaters,” Nano Lett. 11(12), 5154–5158 (2011). [CrossRef] [PubMed]

]. Therefore, the combination of the two abilities generates a synergetic effect on photonic devices. Figure 1
Fig. 1 (a) Schematic view of the proposed graphene-microribbon-based thermo-optic mode extinction modulator. The LRSPP stripe mode that propagates along the graphene stripe is extinguished (or perturbed) by thermally inducing inhomogeneous refractive-index distribution.
shows the schematic view of the proposed graphene-microribbon-based thermo-optic mode extinction modulator. It consists of a two graphene microribbon that is crossed and a polymer dielectric with a high thermo-optic coefficient. The in-line heating element is placed in the orthogonal direction. The under-cladding is placed on the Si substrate and the upper-cladding interfaces with air. The dielectric consists of the under- and upper-cladding layers having the same refractive-index and thermo-optic coefficient. The long graphene stripe supports the guidance of the LRSPP stripe mode [10

10. J. T. Kim and S.-Y. Choi, “Graphene-based plasmonic waveguides for photonic integrated circuits,” Opt. Express 19(24), 24557–24562 (2011). [CrossRef] [PubMed]

]. The short graphene microribbon in the orthogonal direction generates heat when electric current is applied via the large metal pad. Because of negative thermo-optic coefficient, the refractive-index of the dielectric decreases. The under- and upper-claddings interface with silicon and air, respectively. The thermal conductivities of the two interfacing materials are different so that the refractive-index distribution becomes inhomogeneous. Thus, the guided LRSPP stripe mode is extinguished. If the heater is off, the refractive-index of the dielectric is recovered to the initial state. Then, the guiding of the mode is supported again. By switching the heater element, the proposed graphene-based plasmonic waveguide serves as a mode extinction modulator.

Numerical simulations were conducted on the temperature (and hence the refractive-index) distribution by resistive heating inside the graphene TO modulator. Transient heat-up and cool-down of the modulator was also numerically investigated for the comparison with experimental results. A commercial CFD (computational fluid dynamics) software, CFD-ACE + (CFDRC Corp.), was utilized and the heat transfer module in CFD-ACE + was used to simulate the conduction heat transfer. The grid arrangement and the time step were tested for the stability and the speed of the simulations. Three dimensional structured grids were utilized and the total number of grids was set to around 500,000. The properties of the materials constituting the device adopted for the simulations are listed in Table 1

Table 1. Material properties

table-icon
View This Table
. The reflective-index of the polymer layer was assumed to be linearly decreased with the temperature, Δn = 1.45 – 1.7 x 10−4 (T – 20). T is temperature in Celsius.

The schematic numerical model is shown with an isometric view in Fig. 2
Fig. 2 Isometric views of the graphene TO modulator and simulated temperature increase after 12 mW electrical input power is injected. The dimensions of the device are exhibited.
. The simulated three-dimensional temperature increase for 12 mW electrical input power injection is exhibited too. The condition of uniform heat flux was imposed on the heated graphene layer. The thermal resistivity values between the layers were neglected. The thin wall model in CFD-ACE + was used to model a relatively thin graphene layer (modeled as 3.5 nm). The convective heat transfer condition (convective heat transfer coefficient, h = 10 Wm−2 K−1 with ambient temperature, To = 20 °C) was set to the top of the device. The side wall of the device was assumed to be thermally insulated. The bottom surface of the device was assumed to be contacted with heat sink of 20 °C. As expected, thermal gradient is generated along the heater. Thermal flow occurred along the graphene microribbon for lightwave guiding since the graphene microribbon waveguide and heater is all-in-one. The width and length of the heater is 10 µm and 210 µm, respectively. The length and width of the graphene microribbon for lightwave guiding are 1,500 µm and 10 µm, respectively. In device fabrication, the length of the graphene microribbon is 7 mm. The thicknesses of the under- and upper-claddings are the same as 20 µm.

Figure 3(a)
Fig. 3 (a) Temperature and (b) refractive-index distribution after 12 mW electrical input power was injected. (c) Temporal behavior of the graphene heater.
depicts the simulated temperature distribution at the maximally-heated state over the cross section of the heater structure including 10 µm-wide graphene plasmonic waveguide. The injected electrical power is 12 mW, which is maximum electrical input power in this study. The maximum temperature in the graphene heater is about 125.6 °C. The temperature profile along the vertical center axis of the left (or right) heater decreases gradually as the distance from the heater increase. The temperature gradient of the under-cladding in the vertical direction is steeper than that of upper cladding because the Si substrate serves as a heat sinker. Thermal energy is transferred along the graphene microribbon because graphene is a good thermal conductor. Thus, the temperature at the graphene plasmonic waveguide is lower than other region. Figure 3(b) shows the calculated refractive-index distribution based on the two-dimensional temperature profile. The thermo-optic coefficient is negative so that the refractive-index under thermal gradient becomes low. The higher temperature is the lower the refractive-index is. Here, we considered that the refractive-index of the Si substrate is the same to that of the cladding. Due to high thermal diffusivity of the Si, the temperature difference is not occurred with the electrical power injection and, consequently, its refractive-index change is negligible. The guided LRSPP stripe mode may be extinguished (or perturbed) by the thermally induced inhomogeneous refractive-index distribution around the graphene plasmonic waveguide. Figure 3(c) shows the temporal behavior of the graphene heater. The temperature is monitored at the hottest point of the graphene heater. The heating and cooling times for reaching to 99% of maximum and minimum temperature are measured to be 14.8 ms and 16.0 ms, respectively. With this result, we may expect that the rise and falling times of the fabricated mode distinction modulator are coincident with the temporal behavior.

3. Experiment and discussion

We fabricated the proposed graphene-based thermo-optic modulator. First, an under-cladding material is spin-coated, and then cured with UV light. Graphene film grown by a thermal chemical vapor deposition (CVD) method is transferred on the under-cladding layer. 0.1 µm-thick Au contact pads were evaporated thermally on the transferred graphene by using shadow mask. Consequently, crossroad-like graphene microribbon structure was defined by O2 plasma ash process followed by a standard lithographic technique. The under-clad materials were spin-coated again forming the over-cladding layer. Finally, the contact pads are opened.

For dielectric layers, we used a commercial UV-curable polymer with the refractive-index of 1.45, Exguide ZPU series from ChemOptics (www.chemoptics.co.kr). The propagation loss and the birefringence (nTEnTM) of the optical polymer material at a wavelength of 1.55 µm are less than 0.35 dB/cm and 0.001, respectively. The thermo-optic coefficient of the polymer material is –1.7 × 10−4 °C–1. The graphene films are synthesized using 300 nm-thick Ni sputtered on SiO2/Si substrates. After etching the catalytic Ni films, the isolated graphene films were transferred to the under-cladding for device fabrication.

To investigate the characteristics of the fabricated thermo-optic modulator, the light from an optical source was scrambled to generate un-polarized light. Then, TM-polarization light is launched at the input facet of the fabricated graphene plasmonic waveguides by using a single-mode polarization maintaining fiber (PMF). The infrared images of the guided mode were detected by a charge-coupled device (CCD), while applying electric current. After measuring the infrared images, the output light were collected by a PMF, and the transmitted powers were measured with an optical power meter to evaluate insertion loss.

Figure 4(a)
Fig. 4 (a) Raman spectrum of the transferred graphene on a SiO2/Si substrate. The inset depicts the fabricated graphene microribbon-based modulator. (b) Guided modes of the fabricated graphene-microribbon-based mode extinction modulator. Circular guided mode is cut off when 12 mW electrical input power is injected.
shows the Raman shift of the graphene on the SiO2. The inset depicts the fabricated graphene microribbon-based modulator. Graphene microribbon for lightwave guidance, Au metal pad, and graphene heater that crosses the graphene microribbons are clearly shown. The Raman spectra measured with a 532 nm excitation laser shows the presence of the G peak (at 1,580 cm–1) and the 2D peak (at 2,700 cm–1). Based on the 2D/G intensity ratios obtained from several different locations, we concluded that the CVD-grown graphene film consists of ~10 layers of graphene.

The effect of heating on the mode extinction is clearly observed in the bottom figure of Fig. 4(b). As the electrical input power is applied, the circular spot disturbed and output optical intensity also deceases. With 10 mW electrical input power, the guided mode disappeared. The thermally induced mode extinction is mainly determined by magnitude of electrical input power because inhomogeneous temperature distribution around the heated stripe is dynamic as electrical input power increases. The refractive-index of the cladding polymer decreases as the heater temperature increases. The thermal distribution due to the graphene heater is inhomogeneous so that the refractive-index distribution is also inhomogeneous and may be similar to the index profile shown in Fig. 3(b). The refractive-index above the graphene microribbon waveguide (n = 1.440) is slightly higher than that above the graphene heater (n = 1.432). Thus, light is confined above the graphene microribbon while being confined in the region where the refractive-index is comparatively high. In the lateral direction at the center of the graphene plasmonic waveguide, symmetric refractive-index distribution is predicted. This symmetry may result in symmetric light perturbation when electrical current is injected. However, the bottom figure of Fig. 4(b) shows asymmetric light perturbation. This is attributed to the inhomogeneous heat generation by graphene heater. Graphene film synthesized based on Ni catalysis consists of various domains having ~10 layers of graphene. Lack of uniformity induces more inhomogeneous refractive-index distribution in surrounding dielectric in the lateral direction. The refractive-index gradient becomes higher as the electrical input power increases. Thus, mode extinction (or perturbation) is in line with the increase of electrical input power.

Figure 5(a)
Fig. 5 (a) Measured optical power attenuation as a function of applied electrical power and (b) temporal response of the modulator.
exhibits the attenuation characteristics according to the applied electrical power and 5(b) represent the temporal response of the fabricated optical modulator. Without current injection, the insertion loss is expected to be 22.7 dB, which includes the propagation loss of 2.3 dB/mm and the coupling loss of 3.3 dB/facet. However, the measured insertion loss of the graphene plasmonic waveguide is 2.5 dB. This is attributed to the presence of the cross-line heater in the graphene microribbon. As expected from the detected guided mode profile of Fig. 4(b), light amplitude coupled to the PMF decrease as the applied electrical input power increases. As a result, the normalized transmission power of the modulator decreases with increase of electric input power. 30 dB-attenuation is achievable with an electrical power of 12.5 mW, thus constituting very high attenuation at low electrical power consumption. Figure 5(b) shows the temporal responses of the fabricated modulator. The falling and rising times are measured to be 15 ms and 10 ms, respectively. These results are coincident with the temporal behavior of the temperature (and hence refractive-index) as shown in Fig. 3(c). The experimental heating time of the heater to the maximum temperature is similar than that of the theoretical prediction. Thus, the falling time of the modulator (15 ms) is nearly the same to that of the prediction (14.8 ms). On the other hand, the cooling of heater is fast so that the rising time of the modulator (10 ms) is faster than that of the prediction (16.0 ms).

4. Conclusion

We developed thermo-optic mode extinction modulator based on graphene plasmonic waveguides. The long-range surface plasmon polariton (LRSPP) stripe mode propagating along graphene microribbon is cut off by thermally induced inhomogeneous refractive-index distribution of the polymer near the microribbon. Numerical modeling are conducted on the time-dependent temperature (and hence the refractive-index) distribution is in a good agreement with experimental results. We concluded that graphene plasmonic device has huge potential for development of photonic integrated circuits.

Acknowledgments

This work was supported by the Creative Research Program of the ETRI (13ZE1110), Korea and a grant (Code No. 2011-0031660) from the Center for Advanced Soft Electronics under the Global Frontier Research Program of the Ministry of Education, Science and Technology, Korea.

References and links

1.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007). [CrossRef] [PubMed]

2.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010). [CrossRef]

3.

T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4(5), 297–301 (2010). [CrossRef]

4.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011). [CrossRef] [PubMed]

5.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011). [CrossRef]

6.

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99(1), 016803 (2007). [CrossRef] [PubMed]

7.

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008). [CrossRef]

8.

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009). [CrossRef]

9.

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photon. 1(3), 484–588 (2009). [CrossRef]

10.

J. T. Kim and S.-Y. Choi, “Graphene-based plasmonic waveguides for photonic integrated circuits,” Opt. Express 19(24), 24557–24562 (2011). [CrossRef] [PubMed]

11.

J. T. Kim and C.-G. Choi, “Graphene-based polymer waveguide polarizer,” Opt. Express 20(4), 3556–3562 (2012). [CrossRef] [PubMed]

12.

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012). [CrossRef] [PubMed]

13.

J. T. Kim, J. Kim, H. Choi, C.-G. Choi, and S.-Y. Choi, “Graphene-based photonic devices for soft hybrid optoelectronic systems,” Nanotechnology 23(34), 344005 (2012). [CrossRef] [PubMed]

14.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]

15.

I. Breukelaar, R. Charbonneau, and P. Berini, “Long-range surface plasmon-polariton mode cutoff and radiation in embedded strip waveguides,” J. Appl. Phys. 100(4), 043104 (2006). [CrossRef]

16.

T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833–5835 (2004). [CrossRef]

17.

G. Gagnon, N. Lahoud, G. Mattiussi, and P. Berini, “Thermally activated variable attenuation of long-range surface plasmon-polariton waves,” J. Lightwave Technol. 24(11), 4391–4402 (2006). [CrossRef]

18.

J. Kang, H. Kim, K. S. Kim, S.-K. Lee, S. Bae, J.-H. Ahn, Y.-J. Kim, J.-B. Choi, and B. H. Hong, “High-performance graphene-based transparent flexible heaters,” Nano Lett. 11(12), 5154–5158 (2011). [CrossRef] [PubMed]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(230.7370) Optical devices : Waveguides
(160.4236) Materials : Nanomaterials

ToC Category:
Integrated Optics

History
Original Manuscript: March 6, 2013
Revised Manuscript: May 24, 2013
Manuscript Accepted: June 11, 2013
Published: June 19, 2013

Citation
Jin Tae Kim, Kwang Hyo Chung, and Choon-Gi Choi, "Thermo-optic mode extinction modulator based on graphene plasmonic waveguide," Opt. Express 21, 15280-15286 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-15280


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References

  1. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater.6(3), 183–191 (2007). [CrossRef] [PubMed]
  2. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics4(9), 611–622 (2010). [CrossRef]
  3. T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics4(5), 297–301 (2010). [CrossRef]
  4. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature474(7349), 64–67 (2011). [CrossRef] [PubMed]
  5. Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics5(7), 411–415 (2011). [CrossRef]
  6. S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett.99(1), 016803 (2007). [CrossRef] [PubMed]
  7. G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys.103(6), 064302 (2008). [CrossRef]
  8. M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80(24), 245435 (2009). [CrossRef]
  9. P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photon.1(3), 484–588 (2009). [CrossRef]
  10. J. T. Kim and S.-Y. Choi, “Graphene-based plasmonic waveguides for photonic integrated circuits,” Opt. Express19(24), 24557–24562 (2011). [CrossRef] [PubMed]
  11. J. T. Kim and C.-G. Choi, “Graphene-based polymer waveguide polarizer,” Opt. Express20(4), 3556–3562 (2012). [CrossRef] [PubMed]
  12. Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano6(5), 3677–3694 (2012). [CrossRef] [PubMed]
  13. J. T. Kim, J. Kim, H. Choi, C.-G. Choi, and S.-Y. Choi, “Graphene-based photonic devices for soft hybrid optoelectronic systems,” Nanotechnology23(34), 344005 (2012). [CrossRef] [PubMed]
  14. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics6(11), 749–758 (2012). [CrossRef]
  15. I. Breukelaar, R. Charbonneau, and P. Berini, “Long-range surface plasmon-polariton mode cutoff and radiation in embedded strip waveguides,” J. Appl. Phys.100(4), 043104 (2006). [CrossRef]
  16. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett.85(24), 5833–5835 (2004). [CrossRef]
  17. G. Gagnon, N. Lahoud, G. Mattiussi, and P. Berini, “Thermally activated variable attenuation of long-range surface plasmon-polariton waves,” J. Lightwave Technol.24(11), 4391–4402 (2006). [CrossRef]
  18. J. Kang, H. Kim, K. S. Kim, S.-K. Lee, S. Bae, J.-H. Ahn, Y.-J. Kim, J.-B. Choi, and B. H. Hong, “High-performance graphene-based transparent flexible heaters,” Nano Lett.11(12), 5154–5158 (2011). [CrossRef] [PubMed]

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