Abstract

Optically controlled phase shifters are desirable for optical communication, sensors, and signal processing due to their simple implementation and low cost. We propose an all-fiber phase shifter assisted by graphene’s photothermal effect. In a graphene-coated microfiber, graphene’s ohmic heating promises efficient fiber index change and phase shift via the thermo-optic effect. On a fabricated device with a length of 5 mm, we obtain a phase shift exceeding 21π with a nearly linear slope of 0.091π/mW (0.192π/mW) when pumped by 980 nm (1540 nm) light, which enables all-optical switching with an extinction ratio of 20 dB and a rise (fall) time of 9.1 ms (3.2 ms) following the 10%–90% rule. This graphene-assisted index change and phase shifter featured with all-in-fiber, low power requirement, and ease of fabrication may open the door for graphene’s realistic applications in all-optical signal processing.

© 2015 Optical Society of America

An optical phase shifter is crucial in a variety of fiber optic applications, including optical communication, interfere sensors, and signal processing. Specifically, an all-in-fiber phase shifter is more desirable for fiber systems due to the polarization insensitivity, low temperature coefficient, simple packaging, and minimization of insertion loss and back reflection. Various all-fiber phase shifters have been developed based on mechanical deformation and acousto- and electro-optic effects [1,2]. Compared with these techniques, an all-optical method is advantageous because of simple implementation, low cost, and remote use. Nonlinear processes in fiber, for instance, cross-phase modulation and stimulated Brillouin scattering, have been employed to realize all-optical phase shifters successfully [3]. However, due to the weak intrinsic nonlinearity in silica, significant pump power and/or fiber length was required to achieve considerable phase changes. One possible route to reduce the pump power is doping fiber with transition metal ions, color centers, or rare earths, which changes the fiber index by the pump-induced thermal effect or depletion of the ground state. A broadband 360° rf phase shifter and efficient time delay (900 ps) have been demonstrated in erbium–ytterbium co-doped fiber gratings with hundreds of milliwatts of pump power [46].

In this Letter, we describe an alternative method for all-optical phase control by integrating a microfiber with a graphene film. The two-dimensional electronic system of graphene promises many remarkable optical properties, such as 2.3% uniform absorbance [7] and nonlinear susceptibility as high as |χ(3)|107 esu [8]. Relying on graphene’s flexibility and two-dimensional structure, various graphene-integrated geometries have been demonstrated in fiber optics to realize enhanced light–matter interaction [9] and novel devices, including fiber lasers [10], sensors [11], and all-optical modulators [12]. Here, we employ graphene’s strong optical absorption and excellent thermal properties to accomplish an all-fiber phase shifter. In a graphene-coated microfiber (GMF), interacting with the microfiber’s evanescent field, graphene generates Joule heating effectively and subsequently heats the microfiber. The temperature rise in the microfiber will induce a considerable index change and phase shift via the thermo-optic effect. We observe that on a GMF with a diameter of 10 μm and a length of 5 mm, a phase shift exceeding 21π is possible with slopes of 0.091 and 0.192π/mW when pumped by light at wavelengths of 980 and 1540 nm, respectively. Compared with the technique based on doped fiber [4,6], the graphene-assisted method could be realized with a standard fiber and the power requirement is lower, which could reduce the cost and complexity of fiber devices.

To make a GMF, we pulled a standard telecom single-mode fiber into a microfiber by flame heating. As displayed in Fig. 1(a), a microfiber with a uniform diameter of 10μm over a length of 5mm was obtained, which was characterized under an optical microscope. While a thinner microfiber promises stronger interaction between the optical evanescent field and graphene [12], we employed the 10 μm microfiber to ensure a moderate propagation attenuation. The graphene film used was synthesized on a copper foil by chemical vapor deposition and consisted of five graphene layers to provide stronger interaction with the evanescent field than the single-layer graphene [7]. The number of layers was distinguished by a transmission electron microscope and Raman spectroscopy [13]. To integrate graphene onto the microfiber, we etched away the copper foil with a 10% ferric chloride solution and washed the released graphene film in distilled water several times, which then floated to the water surface. The microfiber, fixed on a glass slide, was submerged in the water and covered by the graphene film after the removal of the water. After drying the device overnight, the microfiber coated with graphene was separated from the glass slide using a tungsten probe with a micromanipulator. A finished device is displayed in Fig. 1(b). To evaluate light absorption by the graphene film, we measured the fiber transmission spectra before and after graphene transfer, as shown in the blue and red curves of Fig. 1(c), respectively. A propagation attenuation curve is depicted in the black line, which is calculated by comparing the two measured spectra. Since graphene’s absorbance is constant over a broad wavelength range, the measured propagation attenuation is almost flat with a value of 5.4dB around the 1540 nm wavelength. The attenuation is slightly higher at the longer wavelength, which has a stronger evanescent field in the graphene film [12]. The attenuation of a 980 nm light was measured as well, showing a value of 2.1dB.

 figure: Fig. 1.

Fig. 1. Optical microscope images of the tapered microfiber (a) before and (b) after graphene transfer, (c) measured transmission spectra of the microfiber before (blue) and after (red) graphene transfer, where the black line shows the propagation attenuation calculated from the two measured spectra, (d) radial distribution of the simulated guiding mode in GMF at wavelengths of 980 nm (red) and 1540 nm (blue) with a zoomed distribution around the fiber edge, and the upper inset shows a two-dimensional mode distribution at 1540 nm (graphene is indicated by the white line).

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We also numerically simulated the light-guiding in GMF using a finite element analysis technique (COMSOL Multiphysics). In the simulation model, a 4 nm thick graphene layer was located at the surface of a 10 μm thick microfiber. For graphene’s refractive index, we calculated it according to the intraband and interband conductivities described in Ref. [14], which had a value of 2.52+i*2.24 at the wavelength of 1550 nm. Here, the doping level of graphene was chosen as 0.2 eV, which was slightly high after the wetting transfer [15]. In Fig. 1(d), we plot the radial distributions of modes at wavelengths of 980 and 1540 nm, and the upper inset shows the two-dimensional mode distribution at 1540 nm. The light fields around the graphene layer are plotted in the zoomed image, showing an abrupt variation due to the index discontinuity. The light intensity in the graphene layer is higher for mode at 1540 nm, which therefore induces more absorption in the graphene. We then calculated the propagation attenuations of the two modes from their complex propagation constants, which are 0.41 and 1.04dB/mm for the modes at 980 and 1540 nm, respectively. The calculated values are close to the measured attenuations in our fabricated device.

As a result of the zero bandgap in graphene, no radiative process is involved in the electronic relaxation when pumped by a low-power light. Hence, in the GMF, graphene could generate ohmic heating effectively by absorbing the evanescent field and heat the microfiber. Note that the heating of the fiber could induce a phase change by changing the refractive index via the thermo-optic effect and by longitudinal expansion of the fiber. Since the second contribution amounts to less than 2% of the first one [16], in the remainder of this Letter we only include the thermal index change. To examine the thermally induced phase change, we established a Mach–Zehnder interferometer (MZI) by inserting the GMF in one arm [17], as schematically shown in Fig. 2(a). Considering the propagation loss in the GMF, we employed 90/10 and 50/50 couplers as the input splitter and output combiner to maximize the visibility of the interference fringe. The pump and signal were combined into the system through a wavelength-division multiplexer (WDM) before the input splitter. At the output of the MZI, the signal was extracted by the combination of a fiber Bragg grating (FBG) and a fiber optic circulator (C), and then measured by a telecom photodiode (PD). In the measurements, the pump light was supplied by a 980 nm laser diode (LD) or a 1540 nm distributed feedback laser, and the signal light source was a telecom tunable laser (TL) with a linewidth of 400 kHz.

 figure: Fig. 2.

Fig. 2. (a) Schematic of the experimental setup for measuring the phase shift in GMF, (b) measured interference fringes without (blue) and with (red) pump.

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By tuning the signal light from 1550 to 1551 nm with a step of 0.002 nm, we measured the MZI output with the 980 nm pump turned off and on, as shown in Fig. 2(b). The results present interference fringes with a uniform pitch of 0.094nm and a high extinction ratio exceeding 21 dB. With a 2.9 mW signal incident into the MZI, the maximum output power was 0.32 mW. The insertion loss mainly resulted from the attenuation of the GMF, the losses of the fiber couplers, the FBG, and the circulator. After switching on the 980 nm pump light with an incident power of 5.3 mW, we observed a 0.024 nm blueshift of the interference fringe without any distortion of the pitch or intensity. This result indicates the pump light induces a 0.51π phase shift over the 5 mm long GMF. To further study the pump-induced phase change, we tuned the pump power gradually and monitored the shift of the interference fringe. The measurement result is plotted as a relation between the calculated phase shift and the incident pump power, as shown in the blue dotted line of Fig. 3(a). With the incident pump power increased to 230 mW, which was limited by the maximum output of our laser diode, we achieved a phase change exceeding 21π with a nearly linear slop of 0.091π/mW. Before the integration of graphene, we did a comparison experiment using the bare microfiber, which showed a 0.18π phase shift with the 230 mW pump. Compared with the graphene-assisted phase shift, this effect is so weak that we would omit it in the next discussion. We also implemented an optically controlled phase shift using a pump light at 1540 nm, as shown in Fig. 3(b). Because more light was absorbed by graphene at a longer pump wavelength, a larger phase change slope of 0.192π/mW was obtained, which is consistent with the mode analysis in Fig. 1(d). Even higher efficiency can be achieved by changing the five-layer graphene into a thicker one, though at the expense of insertion loss. According to the thermo-optic effect in silica fiber, the phase change Δϕ at wavelength λ is determined by the temperature change ΔT in Δϕ=2πλdndTLΔT, where dndT=1.1×105K1 is the index temperature coefficient and L is the microfiber length. From the measured phase change in Fig. 3(a), we calculated the corresponding temperature change versus pump power, as depicted by the blue dotted line in Fig. 3(c). At the maximum pump power of 230 mW, the microfiber temperature rises by 95 K.

 figure: Fig. 3.

Fig. 3. Measured phase shifts in GMF at different incident powers of the (a) 980 nm and (b) 1540 nm pump, where the red dashed lines indicate linear fittings, (c) temperature changes of the GMF calculated from phase shifts in (a) (blue dotted line) and from the numerical analysis of the heat transfer process (red dashed line), where the inset is the steady-state heat distribution of the GMF cross section.

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To explain the experimental results, we numerically analyzed the laser-pumped thermal process in the GMF. Compared with the 10 μm diameter of the microfiber, the 5 mm graphene-coated region is long enough, and the longitudinal temperature gradient along the fiber resulting from the variation in graphene absorption is small. We therefore omitted, for the sake of simplicity, the longitudinal dependence of the temperature distribution and analyzed the heat transfer in the transversal plane of the GMF. With continuous pumping, the temperature distribution in the microfiber T(r) is described by the steady-state heat conduction equation

k2T(r)=Qs,
where k1.38W/m/K is the thermal conductivity of silica and Qs is the heat source per unit volume generated by graphene absorption. Because the thermal conductivity of graphene is three orders higher than that of silica, and the graphene film is thin enough compared with the microfiber diameter, we considered the graphene film as a uniform surface heat source and neglected its inside heat transfer. To solve Eq. (1), we employed a boundary condition for heat flow out of the fiber edge through the natural air convection, which can be expressed as kT(r)|r=r0=h(T)(T(r0)T0). Here, T0 is the room temperature, T(r0) is the temperature at the fiber edge (r=r0), and h(T) is the heat transfer coefficient of air, which is mainly determined by the physical constants of air, microfiber dimensions, and temperature difference at the fiber edge [18].

The heat source Qs can be calculated from the model electric field E in the graphene film using Qs=12ε0ωIm(εr)|E|2, where ε0 is the permittivity of vacuum, ω is the angular frequency of light, and εr is the relative permittivity of graphene. Combining this with the guiding mode in Fig. 1(d), we calculated the steady-state temperature distribution in the GMF, as shown in the inset of Fig. 3(c). The microfiber presents a flat temperature distribution inside, which is same as that reported in Ref. [19], so that the thermo-optic index change in the fiber will not distort the optical mode. We further solved the fiber temperature change as a function of the pump power to quantitatively examine our experimental results. Note that, as indicated by the blue dotted line in Fig. 3(c), the temperature change calculated from the measured phase shift is not a linear function of the pump power. This can be attributed to the fact that when the temperature at the fiber edge is large enough, the parameter h(T) can no longer be assumed as a constant. Therefore, to determine this parameter, we modeled the microfiber as a long horizontal cylinder cooled via the natural air convection, which has been well studied [16,18]. In the model, the heat transfer coefficient can be simplified into h(T)=A+B(ΔT/D)0.25 [18], where D is the microfiber diameter, A is the coefficient when the surface temperature of the cylinder is the same as room temperature, and B is a parameter governing the temperature-dependent term. We then calculated the steady-state temperature change versus pump power with h(T) corrected by the COMSOL solver iteratively. The obtained result is plotted in the red dashed line of Fig. 3(c), which nicely fits the experimental results. The related A and B fitting parameters are 431 and 0.7, respectively, which are close to the values obtained in Ref. [16].

Based on the developed graphene-assisted phase shifter, we implemented all-optical switching on the MZI. Fixing the signal at 1550 nm and increasing the 980 nm pump power gradually, we monitored the output power of the signal. The measured result depicted in Fig. 4(a) indicates the signal is switched on and off periodically by varying the pump power, and the extinction ratio is in excess of 20 dB over a pump power variation of 11mW. The temporal response was then examined by modulating the pump into a square wave with a mechanical chopper. Figure 4(b) shows the result with a modulation period of 50 ms. Here, the rise (fall) process corresponds to the removal (presence) of the pump light. Fitting the rise and fall edges of the measured modulation signal to exponential decay functions of 1exp(t/τr) and exp(t/τf), respectively, we obtained the rise/fall time constants of 4/1.4 ms. We also calculated the time taken for the signal to change from 10% to 90% of the step height, which is normally defined in analog signal processing. Theoretically, the 10%–90% rise/fall time is 2.2 times the exponential time constant. As indicated by the green lines in Fig. 4(b), the rise/fall time is 9.1/3.2 ms following the 10%–90% rule. Compared with the fall time, the longer rise time is due to the fact that it takes time for heat to be dissipated from the microfiber to air [16]. The measured response speed is much faster than that of thermo-optic switching in doped fiber [16]. We attribute this to the small volume of the GMF and fast heat dissipation resulting from the high heat transfer coefficient, as demonstrated in a nonlinear microfiber resonator [20]. By immersing the GMF in water to assist the heat dissipation, we expect the operation speed can be improved to hundreds of kilohertz [21].

 figure: Fig. 4.

Fig. 4. (a) All-optical switching by the GMF, (b) temporal response of the optical switching.

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In conclusion, we have described a graphene-assisted all-fiber phase shifter, which can be optically controlled with a low pump power. By depositing a graphene film onto a microfiber, the strong light–matter interaction and nonradiative electronic relaxation in graphene enable an efficient generation of ohmic heating, which heats the microfiber and induces index change. In a 5 mm long GMF, we obtained a phase change exceeding 21π with a nearly linear slope of 0.09π/mW, which therefore promised an efficient all-optical switch. Due to the small diameter of the microfiber, the phase shifter and switcher have a considerably fast response, showing a rise (fall) time of 9.1 (3.2) ms following the 10%–90% rule. Even lower operation power and faster response speed can be achieved with thinner microfiber, though at the expense of device insertion loss. In addition, due to the cylindrical symmetry of the microfiber and uniform absorbance of graphene, the GMF phase shifter should have very low polarization dependence loss. Considering the ease of fabrication, low cost, low power requirement, and amount of phase change achieved, the proposed all-fiber phase shifter is comparable with commercial ones [22,23]. Similar to the wide employment of doped fiber [46,16,21], the graphene-assisted fiber index change can also be incorporated into other passive fiber devices to extend their applications, such as FBGs and fiber loop resonators. The work is therefore expected to open the door for graphene’s realistic applications in optical signal processing.

FUNDING INFORMATION

973 program (2012CB921900); National Natural Science Foundation of China (NSFC) (11404264, 61377035, 61405161); Fundamental Research Funds for the Central Universities (3102014JCQ01085).

The authors are grateful to Mei Qi and Zhaoyu Ren for providing graphene samples.

References

1. A. Bhatti, H. S. Al-Raweshidy, and G. Murtaza, Opt. Commun. 176, 355 (2000). [CrossRef]  

2. O. Tarasenko and W. Margulis, Opt. Lett. 32, 1356 (2007). [CrossRef]  

3. A. Loayssa and F. J. Lahoz, IEEE Photon. Technol. Lett. 18, 208 (2006). [CrossRef]  

4. W. Liu and J. Yao, Opt. Lett. 39, 922 (2014). [CrossRef]  

5. H. Shahoei and J. Yao, IEEE Photon. Technol. Lett. 24, 818 (2012). [CrossRef]  

6. K. Qian, L. Zhan, H. Li, X. Hu, J. Peng, L. Zhang, and Y. Xia, Opt. Express 17, 22217 (2009).

7. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, Science 320, 1308 (2008). [CrossRef]  

8. E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, Phys. Rev. Lett. 105, 97401 (2010). [CrossRef]  

9. J. Kou, J. Chen, Y. Chen, F. Xu, and Y. Lu, Optica 1, 307 (2014). [CrossRef]  

10. Y. Song, S. Jang, W. Han, and M. Bae, Appl. Phys. Lett. 96, 051122 (2010). [CrossRef]  

11. Y. Wu, B. Yao, A. Zhang, Y. Rao, Z. Wang, Y. Cheng, Y. Gong, W. Zhang, Y. Chen, and K. S. Chiang, Opt. Lett. 39, 1235 (2014).

12. W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014). [CrossRef]  

13. M. Qi, Y. Zhou, F. Hu, X. Xu, W. Li, A. Li, J. Bai, and Z. Ren, J. Phys. Chem. C 118, 15054 (2014). [CrossRef]  

14. S. Mikhailov and K. Ziegler, Phys. Rev. Lett. 99, 016803 (2007). [CrossRef]  

15. X. Gan, R. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, D. Walker, J. Hone, T. Heinz, and D. Englund, Nano Lett. 13, 691 (2013). [CrossRef]  

16. M. K. Davis, S. Member, M. J. F. Digonnet, and R. H. Pantell, J. Lightwave Technol. 16, 1013 (1998). [CrossRef]  

17. B. Yao, Y. Wu, Z. Wang, Y. Cheng, Y. Rao, Y. Gong, Y. Chen, and Y. Li, Opt. Express 21, 29818 (2013). [CrossRef]  

18. J. Welty, C. E. Wicks, G. L. Rorrer, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer, 5th ed. (Wiley, 2000).

19. X. Chen, Y. Chen, M. Yan, and M. Qiu, ACS Nano 6, 2550 (2012). [CrossRef]  

20. G. Vienne, Y. Li, L. Tong, and P. Grelu, Opt. Lett. 33, 1500 (2008). [CrossRef]  

21. R. J. Williams, N. Jovanovic, G. D. Marshall, and M. J. Withford, Opt. Express 18, 7714 (2010).

22. http://www.phoenixphotonics.com/website/products/fiber-phase-shifter.html.

23. http://www.directindustry.com/prod/general-photonics/phase-shifters-fiber-optic-36256-530013.html.

References

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  1. A. Bhatti, H. S. Al-Raweshidy, and G. Murtaza, Opt. Commun. 176, 355 (2000).
    [Crossref]
  2. O. Tarasenko and W. Margulis, Opt. Lett. 32, 1356 (2007).
    [Crossref]
  3. A. Loayssa and F. J. Lahoz, IEEE Photon. Technol. Lett. 18, 208 (2006).
    [Crossref]
  4. W. Liu and J. Yao, Opt. Lett. 39, 922 (2014).
    [Crossref]
  5. H. Shahoei and J. Yao, IEEE Photon. Technol. Lett. 24, 818 (2012).
    [Crossref]
  6. K. Qian, L. Zhan, H. Li, X. Hu, J. Peng, L. Zhang, and Y. Xia, Opt. Express 17, 22217 (2009).
  7. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, Science 320, 1308 (2008).
    [Crossref]
  8. E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, Phys. Rev. Lett. 105, 97401 (2010).
    [Crossref]
  9. J. Kou, J. Chen, Y. Chen, F. Xu, and Y. Lu, Optica 1, 307 (2014).
    [Crossref]
  10. Y. Song, S. Jang, W. Han, and M. Bae, Appl. Phys. Lett. 96, 051122 (2010).
    [Crossref]
  11. Y. Wu, B. Yao, A. Zhang, Y. Rao, Z. Wang, Y. Cheng, Y. Gong, W. Zhang, Y. Chen, and K. S. Chiang, Opt. Lett. 39, 1235 (2014).
  12. W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014).
    [Crossref]
  13. M. Qi, Y. Zhou, F. Hu, X. Xu, W. Li, A. Li, J. Bai, and Z. Ren, J. Phys. Chem. C 118, 15054 (2014).
    [Crossref]
  14. S. Mikhailov and K. Ziegler, Phys. Rev. Lett. 99, 016803 (2007).
    [Crossref]
  15. X. Gan, R. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, D. Walker, J. Hone, T. Heinz, and D. Englund, Nano Lett. 13, 691 (2013).
    [Crossref]
  16. M. K. Davis, S. Member, M. J. F. Digonnet, and R. H. Pantell, J. Lightwave Technol. 16, 1013 (1998).
    [Crossref]
  17. B. Yao, Y. Wu, Z. Wang, Y. Cheng, Y. Rao, Y. Gong, Y. Chen, and Y. Li, Opt. Express 21, 29818 (2013).
    [Crossref]
  18. J. Welty, C. E. Wicks, G. L. Rorrer, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer, 5th ed. (Wiley, 2000).
  19. X. Chen, Y. Chen, M. Yan, and M. Qiu, ACS Nano 6, 2550 (2012).
    [Crossref]
  20. G. Vienne, Y. Li, L. Tong, and P. Grelu, Opt. Lett. 33, 1500 (2008).
    [Crossref]
  21. R. J. Williams, N. Jovanovic, G. D. Marshall, and M. J. Withford, Opt. Express 18, 7714 (2010).
  22. http://www.phoenixphotonics.com/website/products/fiber-phase-shifter.html .
  23. http://www.directindustry.com/prod/general-photonics/phase-shifters-fiber-optic-36256-530013.html .

2014 (5)

W. Liu and J. Yao, Opt. Lett. 39, 922 (2014).
[Crossref]

Y. Wu, B. Yao, A. Zhang, Y. Rao, Z. Wang, Y. Cheng, Y. Gong, W. Zhang, Y. Chen, and K. S. Chiang, Opt. Lett. 39, 1235 (2014).

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014).
[Crossref]

M. Qi, Y. Zhou, F. Hu, X. Xu, W. Li, A. Li, J. Bai, and Z. Ren, J. Phys. Chem. C 118, 15054 (2014).
[Crossref]

J. Kou, J. Chen, Y. Chen, F. Xu, and Y. Lu, Optica 1, 307 (2014).
[Crossref]

2013 (2)

X. Gan, R. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, D. Walker, J. Hone, T. Heinz, and D. Englund, Nano Lett. 13, 691 (2013).
[Crossref]

B. Yao, Y. Wu, Z. Wang, Y. Cheng, Y. Rao, Y. Gong, Y. Chen, and Y. Li, Opt. Express 21, 29818 (2013).
[Crossref]

2012 (2)

X. Chen, Y. Chen, M. Yan, and M. Qiu, ACS Nano 6, 2550 (2012).
[Crossref]

H. Shahoei and J. Yao, IEEE Photon. Technol. Lett. 24, 818 (2012).
[Crossref]

2010 (3)

E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, Phys. Rev. Lett. 105, 97401 (2010).
[Crossref]

Y. Song, S. Jang, W. Han, and M. Bae, Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

R. J. Williams, N. Jovanovic, G. D. Marshall, and M. J. Withford, Opt. Express 18, 7714 (2010).

2009 (1)

2008 (2)

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, Science 320, 1308 (2008).
[Crossref]

G. Vienne, Y. Li, L. Tong, and P. Grelu, Opt. Lett. 33, 1500 (2008).
[Crossref]

2007 (2)

O. Tarasenko and W. Margulis, Opt. Lett. 32, 1356 (2007).
[Crossref]

S. Mikhailov and K. Ziegler, Phys. Rev. Lett. 99, 016803 (2007).
[Crossref]

2006 (1)

A. Loayssa and F. J. Lahoz, IEEE Photon. Technol. Lett. 18, 208 (2006).
[Crossref]

2000 (1)

A. Bhatti, H. S. Al-Raweshidy, and G. Murtaza, Opt. Commun. 176, 355 (2000).
[Crossref]

1998 (1)

Al-Raweshidy, H. S.

A. Bhatti, H. S. Al-Raweshidy, and G. Murtaza, Opt. Commun. 176, 355 (2000).
[Crossref]

Bae, M.

Y. Song, S. Jang, W. Han, and M. Bae, Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

Bai, J.

M. Qi, Y. Zhou, F. Hu, X. Xu, W. Li, A. Li, J. Bai, and Z. Ren, J. Phys. Chem. C 118, 15054 (2014).
[Crossref]

Bao, J.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014).
[Crossref]

Bhatti, A.

A. Bhatti, H. S. Al-Raweshidy, and G. Murtaza, Opt. Commun. 176, 355 (2000).
[Crossref]

Blake, P.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, Science 320, 1308 (2008).
[Crossref]

Booth, T. J.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, Science 320, 1308 (2008).
[Crossref]

Chen, B.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014).
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W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014).
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X. Gan, R. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, D. Walker, J. Hone, T. Heinz, and D. Englund, Nano Lett. 13, 691 (2013).
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X. Gan, R. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, D. Walker, J. Hone, T. Heinz, and D. Englund, Nano Lett. 13, 691 (2013).
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Geim, A. K.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, Science 320, 1308 (2008).
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Gong, Y.

Grelu, P.

Grigorenko, A. N.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, Science 320, 1308 (2008).
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E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, Phys. Rev. Lett. 105, 97401 (2010).
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Y. Song, S. Jang, W. Han, and M. Bae, Appl. Phys. Lett. 96, 051122 (2010).
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X. Gan, R. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, D. Walker, J. Hone, T. Heinz, and D. Englund, Nano Lett. 13, 691 (2013).
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E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, Phys. Rev. Lett. 105, 97401 (2010).
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Hone, J.

X. Gan, R. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, D. Walker, J. Hone, T. Heinz, and D. Englund, Nano Lett. 13, 691 (2013).
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M. Qi, Y. Zhou, F. Hu, X. Xu, W. Li, A. Li, J. Bai, and Z. Ren, J. Phys. Chem. C 118, 15054 (2014).
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Hu, X.

Hu, Z.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014).
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Y. Song, S. Jang, W. Han, and M. Bae, Appl. Phys. Lett. 96, 051122 (2010).
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Kou, J.

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A. Loayssa and F. J. Lahoz, IEEE Photon. Technol. Lett. 18, 208 (2006).
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M. Qi, Y. Zhou, F. Hu, X. Xu, W. Li, A. Li, J. Bai, and Z. Ren, J. Phys. Chem. C 118, 15054 (2014).
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Li, H.

Li, L.

X. Gan, R. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, D. Walker, J. Hone, T. Heinz, and D. Englund, Nano Lett. 13, 691 (2013).
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M. Qi, Y. Zhou, F. Hu, X. Xu, W. Li, A. Li, J. Bai, and Z. Ren, J. Phys. Chem. C 118, 15054 (2014).
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W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014).
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Li, X.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014).
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Li, Y.

Liu, W.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014).
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A. Loayssa and F. J. Lahoz, IEEE Photon. Technol. Lett. 18, 208 (2006).
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Lu, Y.

Mak, K. F.

X. Gan, R. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, D. Walker, J. Hone, T. Heinz, and D. Englund, Nano Lett. 13, 691 (2013).
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Margulis, W.

Marshall, G. D.

Member, S.

Meng, C.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014).
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E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, Phys. Rev. Lett. 105, 97401 (2010).
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S. Mikhailov and K. Ziegler, Phys. Rev. Lett. 99, 016803 (2007).
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E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, Phys. Rev. Lett. 105, 97401 (2010).
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A. Bhatti, H. S. Al-Raweshidy, and G. Murtaza, Opt. Commun. 176, 355 (2000).
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R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, Science 320, 1308 (2008).
[Crossref]

Novoselov, K. S.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, Science 320, 1308 (2008).
[Crossref]

Pantell, R. H.

Peng, J.

Peres, N. M. R.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, Science 320, 1308 (2008).
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M. Qi, Y. Zhou, F. Hu, X. Xu, W. Li, A. Li, J. Bai, and Z. Ren, J. Phys. Chem. C 118, 15054 (2014).
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X. Chen, Y. Chen, M. Yan, and M. Qiu, ACS Nano 6, 2550 (2012).
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M. Qi, Y. Zhou, F. Hu, X. Xu, W. Li, A. Li, J. Bai, and Z. Ren, J. Phys. Chem. C 118, 15054 (2014).
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E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, Phys. Rev. Lett. 105, 97401 (2010).
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H. Shahoei and J. Yao, IEEE Photon. Technol. Lett. 24, 818 (2012).
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W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014).
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Shiue, R.

X. Gan, R. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, D. Walker, J. Hone, T. Heinz, and D. Englund, Nano Lett. 13, 691 (2013).
[Crossref]

Song, Y.

Y. Song, S. Jang, W. Han, and M. Bae, Appl. Phys. Lett. 96, 051122 (2010).
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R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, Science 320, 1308 (2008).
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J. Welty, C. E. Wicks, G. L. Rorrer, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer, 5th ed. (Wiley, 2000).

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J. Welty, C. E. Wicks, G. L. Rorrer, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer, 5th ed. (Wiley, 2000).

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Wu, Y.

Xia, Y.

Xiao, Y.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014).
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M. Qi, Y. Zhou, F. Hu, X. Xu, W. Li, A. Li, J. Bai, and Z. Ren, J. Phys. Chem. C 118, 15054 (2014).
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Xu, Y.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014).
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Yan, M.

X. Chen, Y. Chen, M. Yan, and M. Qiu, ACS Nano 6, 2550 (2012).
[Crossref]

Yao, B.

Yao, J.

W. Liu and J. Yao, Opt. Lett. 39, 922 (2014).
[Crossref]

H. Shahoei and J. Yao, IEEE Photon. Technol. Lett. 24, 818 (2012).
[Crossref]

Yao, X.

X. Gan, R. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, D. Walker, J. Hone, T. Heinz, and D. Englund, Nano Lett. 13, 691 (2013).
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Zhang, A.

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S. Mikhailov and K. Ziegler, Phys. Rev. Lett. 99, 016803 (2007).
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ACS Nano (1)

X. Chen, Y. Chen, M. Yan, and M. Qiu, ACS Nano 6, 2550 (2012).
[Crossref]

Appl. Phys. Lett. (1)

Y. Song, S. Jang, W. Han, and M. Bae, Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

IEEE Photon. Technol. Lett. (2)

A. Loayssa and F. J. Lahoz, IEEE Photon. Technol. Lett. 18, 208 (2006).
[Crossref]

H. Shahoei and J. Yao, IEEE Photon. Technol. Lett. 24, 818 (2012).
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J. Lightwave Technol. (1)

J. Phys. Chem. C (1)

M. Qi, Y. Zhou, F. Hu, X. Xu, W. Li, A. Li, J. Bai, and Z. Ren, J. Phys. Chem. C 118, 15054 (2014).
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Nano Lett. (2)

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, Nano Lett. 14, 955 (2014).
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X. Gan, R. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, D. Walker, J. Hone, T. Heinz, and D. Englund, Nano Lett. 13, 691 (2013).
[Crossref]

Opt. Commun. (1)

A. Bhatti, H. S. Al-Raweshidy, and G. Murtaza, Opt. Commun. 176, 355 (2000).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Optica (1)

Phys. Rev. Lett. (2)

E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, Phys. Rev. Lett. 105, 97401 (2010).
[Crossref]

S. Mikhailov and K. Ziegler, Phys. Rev. Lett. 99, 016803 (2007).
[Crossref]

Science (1)

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, Science 320, 1308 (2008).
[Crossref]

Other (3)

J. Welty, C. E. Wicks, G. L. Rorrer, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer, 5th ed. (Wiley, 2000).

http://www.phoenixphotonics.com/website/products/fiber-phase-shifter.html .

http://www.directindustry.com/prod/general-photonics/phase-shifters-fiber-optic-36256-530013.html .

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Figures (4)

Fig. 1.
Fig. 1. Optical microscope images of the tapered microfiber (a) before and (b) after graphene transfer, (c) measured transmission spectra of the microfiber before (blue) and after (red) graphene transfer, where the black line shows the propagation attenuation calculated from the two measured spectra, (d) radial distribution of the simulated guiding mode in GMF at wavelengths of 980 nm (red) and 1540 nm (blue) with a zoomed distribution around the fiber edge, and the upper inset shows a two-dimensional mode distribution at 1540 nm (graphene is indicated by the white line).
Fig. 2.
Fig. 2. (a) Schematic of the experimental setup for measuring the phase shift in GMF, (b) measured interference fringes without (blue) and with (red) pump.
Fig. 3.
Fig. 3. Measured phase shifts in GMF at different incident powers of the (a) 980 nm and (b) 1540 nm pump, where the red dashed lines indicate linear fittings, (c) temperature changes of the GMF calculated from phase shifts in (a) (blue dotted line) and from the numerical analysis of the heat transfer process (red dashed line), where the inset is the steady-state heat distribution of the GMF cross section.
Fig. 4.
Fig. 4. (a) All-optical switching by the GMF, (b) temporal response of the optical switching.

Equations (1)

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k 2 T ( r ) = Q s ,

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