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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 21 — Oct. 8, 2012
  • pp: 23201–23214
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Microwave and optical saturable absorption in graphene

Zhiwei Zheng, Chujun Zhao, Shunbin Lu, Yu Chen, Ying Li, Han Zhang, and Shuangchun Wen  »View Author Affiliations


Optics Express, Vol. 20, Issue 21, pp. 23201-23214 (2012)
http://dx.doi.org/10.1364/OE.20.023201


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Abstract

We report on the first experiments on saturable absorption in graphene at microwave frequency band. Almost independent of the incident frequency, microwave absorbance of graphene always decreases with increasing the power and reaches at a constant level for power larger than 80 µW, evidencing the microwave saturable absorption property of graphene. Optical saturable absorption of the same graphene sample was also experimentally confirmed by an open-aperture Z-scan technique by one laser at telecommunication band and another pico-second laser at 1053 nm, respectively. Herein, we are able to conclude that graphene is indeed a broadband saturable absorber that can operate at both microwave and optical band.

© 2012 OSA

1. Introduction

Graphene, an atomic layer of conjugated sp2 carbon atoms arranged in a two dimensional hexagonal lattice, possesses many exceptional electrical and optical properties, due to its unique linear electronic band [1

1. E. McCann, “Asymmetry gap in the electronic band structure of bilayer graphene,” Phys. Rev. B 74(16), 161403 (2006). [CrossRef]

,2

2. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005). [CrossRef] [PubMed]

]. Its Dirac point type of energy band-gap structure endows that graphene can readily absorb photons ranging from the visible to the infrared with the record strong inter-band transition efficiency. The wideband optical absorption property provokes the realization of an ultrafast graphene photo-detector with bandwidth exceeding 500 GHz [3

3. F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009). [CrossRef] [PubMed]

], a broadband graphene optical modulator [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]

] and a broadband graphene polarizer [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]

]. Under intensive illumination, optical absorbance of graphene decreases with increasing the light intensity and becomes saturated once the incident light exceeds a threshold power, as a consequence of Pauli blocking principle, that is, valence band depletion and conductance band filling blocks further absorption [6

6. R. N. Zitter, “Saturated optical absorption through band filling in semiconductors,” Appl. Phys. Lett. 14(2), 73–74 (1969). [CrossRef]

,7

7. Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009). [CrossRef]

]. This property already makes graphene widely applicable in the mode-locking of different types of lasers [8

8. W. D. Tan, C. Y. Su, R. J. Knize, G. Q. Xie, L. J. Li, and D. Y. Tang, “Mode locking of ceramic Nd:yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96(3), 031106 (2010). [CrossRef]

18

18. D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010). [CrossRef]

]. Worthy of mentioning are graphene mode-locked Nd:yttrium aluminum garnet laser at 1064 nm [8

8. W. D. Tan, C. Y. Su, R. J. Knize, G. Q. Xie, L. J. Li, and D. Y. Tang, “Mode locking of ceramic Nd:yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96(3), 031106 (2010). [CrossRef]

], Ytterbium-doped fiber lasers at 1069.8 nm [9

9. L. M. Zhao, D. Y. Tang, H. Zhang, X. Wu, Q. Bao, and K. P. Loh, “Dissipative soliton operation of an ytterbium-doped fiber laser mode locked with atomic multilayer graphene,” Opt. Lett. 35(21), 3622–3624 (2010). [CrossRef] [PubMed]

], Cr:forsterite laser at 1250 nm [10

10. W. B. Cho, J. W. Kim, H. W. Lee, S. Bae, B. H. Hong, S. Y. Choi, I. H. Baek, K. Kim, D.-I. Yeom, and F. Rotermund, “High-quality, large-area monolayer graphene for efficient bulk laser mode-locking near 1.25 μm,” Opt. Lett. 36(20), 4089–4091 (2011). [CrossRef] [PubMed]

], erbium doped fiber laser with wavelength tunable from 1570 to 1600 nm [11

11. H. Zhang, D. Tang, R. J. Knize, L. Zhao, Q. Bao, and K. P. Loh, “Graphene mode locked, wavelength-tunable, dissipative soliton fiber laser,” Appl. Phys. Lett. 96(11), 111112 (2010). [CrossRef]

], Tm:YAlO3 laser near 2 µm [12

12. J. Liu, Y. G. Wang, Z. S. Qu, L. H. Zheng, L. B. Su, and J. Xu, “Graphene oxide absorber for 2 μm passive mode-locking Tm: YAlO3 laser,” Laser Phys. Lett. 9(1), 15–19 (2012). [CrossRef]

], CO laser at 5 µm and CO2 laser at 10.6 µm [13

13. E. D. Obraztsova, M. G. Rybin, A. V. Tausenev, V. A. Shotniev, V. R. Sorochenko, P. S. Rusakov, and I. I. Kondrashov, “Graphene for laser applications,” presented at the Graphene 2012 International Conference, Brussels, Belgium, 10–13 Apr. 2012.

]. Those results demonstrate that graphene has important applications at optical band.

Equally fascinating, graphene also shows unusual electromagnetic response of Dirac quasi-particles with several anomalous properties even in the absence of magnetic field [19

19. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Unusual microwave response of Dirac quasiparticles in graphene,” Phys. Rev. Lett. 96(25), 256802 (2006). [CrossRef] [PubMed]

]. Recently, microwave response of graphene at weak power regime had already been investigated, for example, propagation of microwave in graphene [20

20. G. Deligeorgis, M. Dragoman, D. Neculoiu, D. Dragoman, G. Konstantinidis, A. Cismaru, and R. Plana, “Microwave propagation in graphene,” Appl. Phys. Lett. 95(7), 073107 (2009). [CrossRef]

], microwave switching of top-gate field effect graphene transistor [21

21. G. Deligeorgis, M. Dragoman, D. Neculoiu, D. Dragoman, G. Konstantinidis, A. Cismaru, and R. Plana, “Microwave switching of graphene field effect transistor at and far from the Dirac point,” Appl. Phys. Lett. 96(10), 103105 (2010). [CrossRef]

] and microwave frequency multiplier [22

22. H. Wang, D. Nezich, J. Kong, and T. Palacios, “Graphene frequency multipliers,” IEEE Electron Device Lett. 30(5), 547–549 (2009). [CrossRef]

], demonstrating that graphene may also have attractive application at microwave band. Naturally, one fundamental question arises: in view that graphene shows nontrivial optical absorption feature, how about its microwave response at high power regime?

Moreover, strong nonlinear electromagnetic response of graphene in microwave and THz region was also theoretically predicted in Refs [23

23. S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys. Condens. Matter 20(38), 384204 (2008). [CrossRef] [PubMed]

26

26. E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010). [CrossRef] [PubMed]

]. However, direct experimental evidence on the nonlinear microwave response of graphene was not yet provided. In this contribution, we aimed at the experimental investigation of nonlinear absorption in graphene and uncovered that graphene also exhibits broadband saturable absorption at microwave band for the first time. Regardless of the microwave frequency from 96 GHz to 100 GHz, saturable absorption feature can be always observed, with saturable power varied from 28.8 µW to 79.6 µW and modulation depth of 4.58%~12.77%. Based on an open-aperture Z-scan technique by one laser wavelength with central wavelength tunable from 1525 nm to 1570 nm and another laser at 1053 nm, broadband optical saturable absorption of the same graphene sample was also characterized, with saturable intensity of about 7.89 MW/cm2 at the wavelength of telecommunication band and 10.32 MW/cm2 at wavelength at 1053 nm, respectively.

2. Results and discussion

2.1. Characterization of graphene

The graphene dispersion has been prepared by liquid-phase exfoliation of graphite [27

27. Y. Hernandez, V. Nicolosi, M. Lotya, F. M. Blighe, Z. Sun, S. De, I. T. McGovern, B. Holland, M. Byrne, Y. K. Gun’Ko, J. J. Boland, P. Niraj, G. Duesberg, S. Krishnamurthy, R. Goodhue, J. Hutchison, V. Scardaci, A. C. Ferrari, and J. N. Coleman, “High-yield production of graphene by liquid-phase exfoliation of graphite,” Nat. Nanotechnol. 3(9), 563–568 (2008). [CrossRef] [PubMed]

,28

28. M. Lotya, Y. Hernandez, P. J. King, R. J. Smith, V. Nicolosi, L. S. Karlsson, F. M. Blighe, S. De, Z. Wang, I. T. McGovern, G. S. Duesberg, and J. N. Coleman, “Liquid phase production of graphene by exfoliation of graphite in surfactant/water solutions,” J. Am. Chem. Soc. 131(10), 3611–3620 (2009). [CrossRef] [PubMed]

]. Graphene dispersions were prepared by adding graphite at an initial concentration of 5 mg/mL to 100 mL PVP solution (0.1 mg/mL). Ultrasonication was carried out in a table-top ultrasonic cleaner for 10 hours. Gravity sedimentation was standing for more than 10 days after sonication, and then stable graphene dispersion up to 6 months. Then the graphene dispersion was diluted and drop cast on the quartz substrate using a dropper. Raman spectroscope was used to evaluate the crystallininity and scanning electron microscopy (SEM) was used to characterize the morphology of graphene, as shown in Fig. 1
Fig. 1 (a) The graphene sample on quartz plate for microwave and optical saturable absorption measurement. (a) Raman spectra of the graphene sample. (b) The SEM image of the graphene sample.
.

2.2. Characterization of microwave source

An external cavity laser (ECL) was used to achieve a continuous-wave light at 1565.3 nm. The optical carrier was modulated by a single arm Mach–Zehnder LiNbO3 intensity modulator (Fujitsu, 3dB bandwidth >25 GHz) which is driven by a 25 GHz microwave signal. Here, an electrical frequency doubler (Doubler) is used to generate 25 GHz microwave signal by doubling a 12.5 GHz radio-frequency (RF). Since the driving voltage is 0.34 V, the odd-order optical sidebands are sufficiently suppressed in order that the extinction ratio of the second-order sidebands can be larger than 40 dB, as shown in Fig. 2(a). In order to obtain two well-distinguished second-order sidebands, a 50/100 GHz two-output interleaver is used to eliminate the optical carrier. We can observe that the first-order sidebands have an intensity of 30 dB lower than the second-order sideband, as shown in Fig. 2(b). After being amplified through a commercial EDFA, optical signal still exhibits high quality with a wavelength separation between the two second-order sidebands of 0.8 nm (corresponding to 100 GHz) as shown in Fig. 2(c). An optical attenuator is used to alter the PD input power, which therefore makes the output microwave power widely adjustable. The 100 GHz electrical signal is generated by beating two second-order sidebands with a high-speed photodiode (U2t, 100-GHz PD). Then, the electrical signal is amplified by the narrow-band electrical amplifier (work frequency, 96 GHz ~100 GHz) and finally the microwave is radiated from a W-band antenna with a gain of 25 dB (for details, refer to Appendix A).

We can tune the as-generated microwave with a frequency interval of 0.8 GHz through changing the RF frequency with a frequency interval 0.1 GHz (for details, refer to Appendix A). Due to bandwidth limitation of the narrow-band electrical amplifier (EA), the frequency tuning range is confined to be only 4 GHz. The 100 GHz microwave radiation from antenna is amplitude modulated by using a 30 Hz chopper (TTI, c-995), and its output power is then detected by an absolute THz power meter (Thoumas Keating Instruments THz Power Meter). The aperture diameter of chopper is 15 mm with a slot width of 4.5 mm and the distance between the antenna and power meter is 5 cm. The graphene sample deposited on the glass substrate has a diameter of is 25 mm and a thickness of 1 mm. The glass substrate is placed on the horizontal translation stage perpendicular to the aperture of chopper.

2.3. Microwave saturable absorption

The above-mentioned microwave source was used to investigate the microwave response of graphene. In the system, the microwave power can be adjusted from 30 μW to 450 μW by varying the PD input power. The microwave power (starting from the minimum power of 30 μW to the maximum power of 450 μW) could be automatically measured by an absolute terahertz power meter. Over 5000 spots were detected and averaged, and no significant intensity variation was found. The microwave source showed excellent long term stability, and its output power kept at a reasonably constant value, as shown in Fig. 3
Fig. 3 The minimum and maximum power curves of 96~100 GHz microwave sources, with respect to different time.
. By moving the horizontal translation stage, the microwave power without passing through the graphene sample was measured by the power meter. In order to sufficiently reduce experimental errors, 200 data points are averaged as the input power at one PD input power. Moreover, by continuously varying PD input power, a series of microwave powers under different PD input power are recorded as input power P1. By further moving horizontal translation stage and thereby placing the graphene sample close at the center of the chopper aperture, microwave power transmitted through graphene sample could be measured. Similarly, microwave powers under different PD input power could be also recorded as input power P2. Finally, upon dividing the power data of P2 by P1, change of microwave transmittance T against different input powers could be characterized.

Similar to the optical absorbance model in Ref [7

7. Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009). [CrossRef]

], the microwave absorbance of graphene as a function of increasing microwave intensity could be described by:

α(I)=αs1+I/Is+αns
(1)

The corresponding transmittance T can be fitted by
T(I)=1(αs1+I/Is+αns)
(2)
where, we define Is as the saturable power intensity which is the microwave power required in a steady state to reduce the absorption to half of its unbleached value, αs as the saturable loss, and αns as the non-saturable loss. The saturable absorption properties of graphene have been summarized (for details, refer to Appendix B).

By continuously varying the microwave frequency from 96 GHz to 100 GHz, with a frequency interval of 0.8 GHz, saturable absorption under different microwave frequencies have been summarized in Fig. 4
Fig. 4 Power dependent microwave saturable absorption in graphene at different frequencies. Circles: experimental results; solid curve: fitting results.
. The inferred saturable intensity is found to be slightly wavelength dependent, which slightly decreases towards longer wavelengths as shown in Fig. 5(a)
Fig. 5 Relations between the inferred microwave frequency and (a) saturation intensity, (b) modulation depth.
. The modulation depth is 4.58%~12.77% as shown in Fig. 5(b).

2.4. Optical saturable absorption

Optical saturable absorption of graphene could be measured by using an open-aperture Z-scan technique. The experimental setup is schematized in Fig. 6(a)
Fig. 6 (a) Schematic of the Z-scan setup. EDFA: Erbium doped fiber amplifier; BS: beam splitter; D1 and D2: power meters. (b) A Z-scan curve at 1550 nm. (c) The corresponding saturable absorption curve at 1550 nm. (d) Wavelength dependent saturable absorption curve. (e) Wavelength dependent saturable intensity curve.
similar to Ref [34

34. H. Zhang, S. Virally, Q. Bao, L. Kian Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012). [CrossRef] [PubMed]

], which has been adapted to thin-film measurement. A pico-second fiber laser with center wavelength tunable from 1525 nm to 1570 nm is used as the laser source. These pulses emitted from the laser are amplified through an EDFA, and then focused by a 20 times microscope objective. The beam waist was measured and fitted to be 3 μm (for details, refer to Appendix C, D). A portion of the input laser beam is picked off by the beam splitter and measured by detector D1 as the reference of the optical power.

The same graphene sample is placed perpendicularly to the beam axis. By translating the sample through the focal plane with a Newport ESP301 linear motorized stage along its propagation (Z) axis, output power was measured by detector D2 continuously. Dividing the data from D2 by the data from D1, a Z-scan curve with a strong peak near the focus point was obtained in Fig. 6(b). Taking account of the change of the beam waist and the relative position with respect to the focusing objective, the transmittance as a function of the incident laser fluence was shown in Fig. 6(c). Fitting this curve by the Eq. (2) yields a saturable intensity of about 7.89 MW cm–2 at wavelength of 1550 nm.

Then, by continuously shifting the center wavelength of the pico-second fiber laser from 1525 nm to 1570 nm, with a wavelength separation of about 5 nm, saturable absorption curves against laser fluencies under different laser wavelengths are shown in Fig. 6(d). By fitting those curves, saturation depth of the graphene sample is found to about 6%, which slightly decreases towards longer wavelengths. The inferred saturable intensity is slightly wavelength dependent, as shown in Fig. 6(e).

The optical saturable absorption of graphene at 1053 nm has also been measured using the similar method in Ref [7

7. Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009). [CrossRef]

]. The nonlinear absorption measurement apparatus is shown in Fig. 7(a)
Fig. 7 (a) Schematic experimental setup for measuring nonlinear power dependent absorption of graphene samples. (b) Power-dependent nonlinear absorption properties at 1053 nm.
. The laser source is the seed pico-second oscillator mode-locked by the broadband semiconductor saturable absorber of High-Q pico-second regenerative amplifiers (RA) system (Pico-REGEN, High Q Laser, Watertown, MA). The pulse duration is 75 ps and repetition rate is 80 MHz. By placing the graphene sample near the focus point of the 500 mm lens and adjusting the input laser power, the transmittance can be measured, as shown in Fig. 7(b). Fitting this curve yields a saturable intensity of about 10.32 MW cm–2 at the wavelength of 1053 nm.

To take the advantage of the broadband optical saturable absorption, the same graphene sample is employed to passively mode lock an erbium-doped fiber laser at 1564 nm (for details, refer to Appendix E). It is a weakly birefringent cavity fiber laser, where an artificial birefringence filter is induced by the cavity birefringence, with tunable filter bandwidth. As transmittance of the artificial birefringence filter varies with the cavity birefringence, therefore, in our laser simply adjusting the orientation of the intra cavity polarization controller the peak wavelength of the mode-locked pulses can be tuned.

2.5. Discussions

Graphs of the valence band and the conduction band in graphene are smooth-sided cones that almost meet at one point, called the Dirac point. Graphene has a small band gap in the range of several meV [35

35. A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009). [CrossRef]

], indicating that graphene can absorb microwave photons at an arbitrary frequency around 100 GHz. Figure 8
Fig. 8 Schematic of microwave saturable absorption in graphene under different incident frequencies.
shows schematic of microwave saturable absorption in graphene at different microwave frequencies. Through the absorption of microwave photons with energy of ħω, electrons at the valence band with energy of EFħω/2 can be excited to the corresponding conduction band with energy of EF + ħω/2. Despite of broadband microwave response, the absorbance is intensity dependent. Under weak irradiation, microwave photons can be continuously depleted through the excitation of the electrons from the valence band to the conduction band. However, under sufficiently strong microwave irradiation, owing to the Pauli blocking principle, the newly generated carriers fill the valence bands, preventing further excitation of electrons at valance band and therefore allowing microwave transmitted without absorption, which interprets the mechanism of graphene saturable absorption. The threshold fluence to saturate the absorption of graphene is termed as saturable fluence, which is proportional to the total amount of electrons at the valance band covering from EFħω/2 to EF. Correspondingly, graphene shows weaker saturable fluence at the microwave frequency ω1 than that at ω2 because larger amount of electrons are filled at the valance band at the microwave frequency at ω1. The higher the microwave frequency, the higher the saturable fluence, which can explain why saturable intensity decreases towards longer wavelength in Fig. 5. Concerning the Z-scan measurement, if a continuous wave at the same wavelength and mean power as the pulse laser is used as the input laser source, the typical peak Z-scan curve is never found while only featureless flat curve is observed. This indicates that a CW is unable to saturate the absorption of graphene because the peak power of CW is significantly weak and below the saturation threshold. In view that microwave frequency (100 GHz) is three orders of magnitude smaller than optical frequency (1550 nm corresponds to 193 THz), saturable intensity at microwave band should be much lower than that at optical band and therefore a CW microwave with power higher than 80 µW is able to saturate the absorption of graphene.

Based on the microwave saturable absorption behavior of graphene, we anticipate that several novel graphene microwave devices could be eventually realized through borrowing concepts from the well-developed graphene optics research. 1) The broadband microwave saturable absorption renders graphene suitable for the mode-locking of Microwave Amplification by Stimulation Emission of Radiation (MASER), which was theoretically proposed by L. Mertz in 1974 [36

36. L. Mertz, “Mode-locked maser theory of pulsars,” Astrophys. Space Sci. 30(1), 43–55 (1974). [CrossRef]

] but not yet experimentally verified. By placing a graphene microwave saturable absorber inside a MASER cavity, frequency-tunable and ultra-short pulses at microwave band could be produced from a graphene mode-locked MASER. 2) Owing to one advantage that work function of graphene can be controlled by either chemical doping, applying an external electrical or magnetic field, one can expect the controlling, tuning and tailoring of microwave saturable absorption of graphene. Correspondingly, it may enable the generation of graphene microwave modulator, in which modulation is achieved by actively tuning the Fermi level of graphene, similar to the structure of graphene-based broadband optical modulator [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]

], which may be comparable to, if not better than, the traditional microwave modulator in terms of speed, cost and broad bandwidth. 3) Broadband graphene polarizer at microwave band, which replies on the coupling and interaction between micrometer electromagnetic-wave and graphene, could be realized as well by following the geometry of broadband graphene optical polarizer [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]

].

3. Conclusion

In summary, we uncover that graphene also shows saturable absorption at microwave band for the first time. This unique microwave property renders graphene as a promising broadband saturable absorber with potential applications at both optical and microwave band. Further exploration on nonlinear microwave property of graphene may lead to new graphene microwave devices (microwave saturable absorber, modulator, polarizer, etc) and also pave the way for applications of graphene based microwave communications: such as microwave signal processing, broad-band wireless access networks, sensor networks, radar, satellite communications, and so on.

Appendix

A. Others on microwave source

An optical carrier via an intensity modulator (IM), which is driven by a microwave signal with 2fRFfrequency, the IM output field can be expressed as:
Eout1(t)=E0(t)cos(2πf0t)10α/20γexp[jπVRFVπcos(2π2fRFt+θ)]+                E0(t)cos(2πf0t)10α/20(1γ)exp[jπVRFVπcos(2π2fRFt)+jπVbiasVπ]
(3)
where E0 is the amplitude of the optical field, Vπis the half-wave voltage of the modulator, VRF, fRF and θ are the voltage amplitude, frequency, and phase of the microwave signal, respectively, Vbias is the dc bias voltage applied to IM, γ is the power splitting ratio of the two IM arms, and α is the IM insertion loss.

For an ideal IM, γ is about 0.5 and α is approximately zero. The field of the optical signal can be written as:
Eout1=E02{cos[2πf0t+βcos(4πfRFt+θ)]+cos[2πf0t+βcos(4πfRFt)+φ)]}
(4)
whereβ=πVRF/Vπ is modulation depth of the modulator and φ=πVbias/Vπ is constant phase shift.

When expanding Eq. (4) by using Bessel Functions and set φ=2kπ,(k=0,1,2) and θ=π, the odd-order optical sidebands are suppressed, the optical signal can be written as:
Eout1=E0[cos(2πf0t)J0(β)+2cos(2πf0t)n=1(1)nJ2n(β)cos(8nπfRFt)]
(5)
where Jn is the Bessel function of the first kind of order n.

Eliminating the carrier by an optical interleaver and ignoring higher than second-order Bessel functions, the signal only has two second-order optical sidebands, which can be approximately expressed as:

Eout2(t)E0J2(β)[cos(2πf0t+8πfRFt)+cos(2πf0t8πfRFt)]
(6)

Beating using a square-law PD, the generated microwave signal is:
Imicrowave=μ|Eout2(t)|2μE02J22(β)cos[(2π(8fRFt)]
(7)
where μ is the responsivity of the PD. Setting fRF = 12~12.5 GHz, the 96~100 GHz microwave signal is obtained.

In order to measure the generated the microwave signal, the sub-harmonically pumped conversion mixer system is used to down conversion the microwave signal as shown in Fig. 9(a)
Fig. 9 (a) The setup for detecting the generated microwave signal. (b) The spectrum of IF signal. ESA: electrical spectrum analyzer.
. The system is comprised of three parts: microwave signal, the local oscillator signal and intermediate frequency (IF) signal. The generated 100 GHz microwave signal under test is received by an antenna, and then the signal is inputted to the subharmonically pumped mixer, which is driven by a local oscillator (LO) signal. The output signal of mixer is the intermediate frequency (IF) signal and the frequency relationship between them can use the following formula,
fmicrowave=fIF+2fLO
(8)
where the local oscillator (LO) frequency is 49.48 GHz, it is obtained by using a frequency multiplier (FM). The spectrum of IF is shown in Fig. 9(b) and the frequency is 0.98 GHz. According to the Eq. (8), the frequency of microwave is about 100 GHz.

B. Microwave saturable absorption

Graphene as a function of increasing microwave power can be described by:
α(P)=αs1+P/Ps=αsexp(P/Ps)
(9)
where Ps is the saturable power, defined as the optical power required in a steady state to reduce the absorption to half of its unbleached value, αs and αns are the saturable and non-saturable loss. The corresponding transmittance fitting equation of graphene can be written by:
T(P)=1ααns=1αsexp(P/Ps)αns
(10)
where αS, Ps,αns is the fitting parameters.

The fitted saturable absorption parameters, αS, PSand αns are summarized in Table 1

Table 1. Saturable absorption properties of graphene

table-icon
View This Table
.

C. Z-scan modeling

Saturable absorption can be modeled by the following equation:
dIdζ=α01+I/ISIβ0I02σΔNI
(11)
where α0 is the one photon absorption (including intrinsic free carrier absorption) coefficient, β0 is the fundamental three-photon absorption (TPA) coefficient, and σ0 is free carrier absorption (FCA) cross section. Is characterizes the saturable absorption intensity; the intensity I at the radial position r, time t, the position ς in the sample, and the location of the sample z is denoted as I(z, ς, r, t).

For graphene, we only consider the one photon absorption.

dIdζ=α01+I/ISI
(12)

The boundary condition required to solve the above equation is the input intensity which is assumed to be a Gaussian:
I(z,0,r,t)=I0[w0w(z)]2exp[2r2w(z)2]exp[t2τ02]
(13)
where w0 is the beam waist at the focus, w(z)=w01+(z/z0)2 is the beam radius at z, z0=πw02/λ is the diffraction length of the beam, τ0 is the half width at of the maximum of the pulse, and λ is the wavelength.

From Eq. (12), we can get the following conclusion
I(ς=0)I(ς=L)dII=ς=0ς=Lα01+I/Isdς
(14)
where L is the thickness of graphene sample.

From Eq. (14), we can get
ln[I(ς=L)I(ς=0)]=α0L1+I/Is
(15)
Treal=exp(α0L1+I/Is)1α0L1+I/Is
(16)
where Treal is the transmittance of laser passing through the graphene sample. However, to analyze the Z-scan data of graphene saturable absorption, normally, we use the normalized transmittance:

T=TrealTreal(I=0)=(1α0L1+I/Is)11α0L
(17)

We can use Eq. (15) to determine the intensity I:

I(z)=I01+z2/z02
(18)

In conclusion,

T(z)=[1α0L(1+z2/z02)1+z2/z02+I0/Is]11α0L
(19)

However, in the measurement, the focus point is not always at z=0, we have used the following modified equation to fit the saturable absorption curve.
T(z)={1α0LIs[z02+(zzc)2]Is[z02+(zzc)2]+I0z02}11α0L
(20)
here, zc is the position for the maximum transmittance.

D. Laser beam characterization

A beam profiler was used to measure the beam waist from a Pritel picosecond laser. Firstly, we ensure that after the focusing objective, the laser beam axis is perpendicular to the pin hole of the beam profiler, which is mounted upon the translation stage. Then, finely adjusting the position of the beam profiler through the Newport ESP301 linear motorized stage, the laser beam intensity distribution before and after the focus point can be captured by the beam profiler. Figure 10
Fig. 10 (a) Typical laser optical spectrum. (b) Relation between the laser beam waist and the relative position with respect to the focusing objective. (c) Beam intensity profile near the focus point. (d) Relation between laser beam intensity and the relative position of the focusing objective for an optical input power of about 3 mW.
shows a typical laser spectrum, the relation between the laser beam waist and the relative position of the focusing objective and the beam intensity profile near the focus point. Based on the relation between the measured laser beam waist and limited by the detection resolution of the beam profiler, the beam waist near the focus point is measured to be as broad as 10 μm. The exact beam waist can be further inferred through fitting a typical Z-scan curve, which gives an estimated beam waist of 3 μm.

For the 1053 nm laser source, the optical spectrum and the focal spot have been measured, as shown in Fig. 11
Fig. 11 (a) The optical spectrum of 1053 nm laser. (b) The image of the focal spot by CCD.
. The full width at half maximum (FWHM) of the laser is about 0.1 nm and the beam waist is about 75 μm, respectively.

E. Laser mode locking for the same graphene sample

Using the same the grapheme sample, we have implemented a laser mode locking experiment. Figure 12(a)
Fig. 12 (a) Schematic of the experimental setup. (b) soliton spectra. (c) Oscilloscope trace of the soliton. (d) An autocorrelation trace of the laser emission.
shows the sketch of the experimental setup of the fiber laser. It is an erbium-doped fiber ring laser made of pure abnormal dispersion fibers. The total cavity length is about 169 m, which contains a 1.1 m EDF. The GVDs of EDF and SMF are –20 ps2/km and –23 ps2/km at 1550 nm, respectively. A polarization independent isolator (PII) is used to force the unidirectional operation of the ring cavity. An intra-cavity polarization controller (PC) is used to adjust the cavity birefringence. A 980/1550 nm WDM coupler is used to couple the pump light and a 10% fiber coupler is used to output the laser emission. The laser is pumped by a 980 nm pump laser. Finally, a pigtailed fiber bench spacing about 9 cm is added to this cavity. To integrate the graphene sample into the fiber laser cavity, we insert the sample into the fiber bench in the ring cavity.

If the graphene sample is absent in the ring cavity, there are stable continuous wave output. When the graphene sample is inserted into the cavity, the mode-locking pulse can be generated by adjusting PC. Self-started mode locking of the laser occurred at the incident pump power of about 70 mW. The optical spectrum of the mode locked pulses is centered at 1564.4 nm and has a 3dB bandwidth of 1.1 nm as shown in Fig. 12(b). We have observed the Kelly sidebands on the spectrum, indicating the soliton operation. Figure 12(c) shows the measured oscilloscopes trace within nanosecond time scale. The pulse circulated in the cavity with the fundamental cavity repetition rate 1.21 MHz. Figure 12(d) is the measured autocorrelation trace of the mode locked pulses. It has a FWHW width of 3.81 ps. If a Sech2 pulse is assumed, the pulse duration is 2.47 ps.

Acknowledgment

The authors thank Dr. Encai Ou (College of Chemistry and Chemical Engineering, Hunan University) for the help with the graphene preparation. This work is partially supported by the National 973 Program of China (Grant No. 2012CB315701), the National Natural Science Foundation of China (Grant No. 61025024), the National 863 Program of China (Grant No. 2011AA010203), Program for New Century Excellent Talents in University of China (Grant No. NCET 11-0135), and Hunan Provincial Natural Science Foundation of China (Grant No. 12JJ7005).

References and links

1.

E. McCann, “Asymmetry gap in the electronic band structure of bilayer graphene,” Phys. Rev. B 74(16), 161403 (2006). [CrossRef]

2.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005). [CrossRef] [PubMed]

3.

F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009). [CrossRef] [PubMed]

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.

R. N. Zitter, “Saturated optical absorption through band filling in semiconductors,” Appl. Phys. Lett. 14(2), 73–74 (1969). [CrossRef]

7.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009). [CrossRef]

8.

W. D. Tan, C. Y. Su, R. J. Knize, G. Q. Xie, L. J. Li, and D. Y. Tang, “Mode locking of ceramic Nd:yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96(3), 031106 (2010). [CrossRef]

9.

L. M. Zhao, D. Y. Tang, H. Zhang, X. Wu, Q. Bao, and K. P. Loh, “Dissipative soliton operation of an ytterbium-doped fiber laser mode locked with atomic multilayer graphene,” Opt. Lett. 35(21), 3622–3624 (2010). [CrossRef] [PubMed]

10.

W. B. Cho, J. W. Kim, H. W. Lee, S. Bae, B. H. Hong, S. Y. Choi, I. H. Baek, K. Kim, D.-I. Yeom, and F. Rotermund, “High-quality, large-area monolayer graphene for efficient bulk laser mode-locking near 1.25 μm,” Opt. Lett. 36(20), 4089–4091 (2011). [CrossRef] [PubMed]

11.

H. Zhang, D. Tang, R. J. Knize, L. Zhao, Q. Bao, and K. P. Loh, “Graphene mode locked, wavelength-tunable, dissipative soliton fiber laser,” Appl. Phys. Lett. 96(11), 111112 (2010). [CrossRef]

12.

J. Liu, Y. G. Wang, Z. S. Qu, L. H. Zheng, L. B. Su, and J. Xu, “Graphene oxide absorber for 2 μm passive mode-locking Tm: YAlO3 laser,” Laser Phys. Lett. 9(1), 15–19 (2012). [CrossRef]

13.

E. D. Obraztsova, M. G. Rybin, A. V. Tausenev, V. A. Shotniev, V. R. Sorochenko, P. S. Rusakov, and I. I. Kondrashov, “Graphene for laser applications,” presented at the Graphene 2012 International Conference, Brussels, Belgium, 10–13 Apr. 2012.

14.

Y. M. Chang, H. Kim, J. H. Lee, and Y. W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97(21), 211102 (2010). [CrossRef]

15.

A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011). [CrossRef]

16.

Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96(5), 051122 (2010). [CrossRef]

17.

H. Kim, J. Cho, S. Y. Jang, and Y. M. Song, “Deformation-immunized optical deposition of graphene for ultrafast pulsed lasers,” Appl. Phys. Lett. 98(2), 021104 (2011). [CrossRef]

18.

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010). [CrossRef]

19.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Unusual microwave response of Dirac quasiparticles in graphene,” Phys. Rev. Lett. 96(25), 256802 (2006). [CrossRef] [PubMed]

20.

G. Deligeorgis, M. Dragoman, D. Neculoiu, D. Dragoman, G. Konstantinidis, A. Cismaru, and R. Plana, “Microwave propagation in graphene,” Appl. Phys. Lett. 95(7), 073107 (2009). [CrossRef]

21.

G. Deligeorgis, M. Dragoman, D. Neculoiu, D. Dragoman, G. Konstantinidis, A. Cismaru, and R. Plana, “Microwave switching of graphene field effect transistor at and far from the Dirac point,” Appl. Phys. Lett. 96(10), 103105 (2010). [CrossRef]

22.

H. Wang, D. Nezich, J. Kong, and T. Palacios, “Graphene frequency multipliers,” IEEE Electron Device Lett. 30(5), 547–549 (2009). [CrossRef]

23.

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys. Condens. Matter 20(38), 384204 (2008). [CrossRef] [PubMed]

24.

A. R. Wright, X. G. Xu, J. C. Cao, and C. Zhang, “Strong nonlinear optical response of graphene in the terahertz regime,” Appl. Phys. Lett. 95(7), 072101 (2009). [CrossRef]

25.

A. R. Wright, J. C. Cao, and C. Zhang, “Enhanced optical conductivity of bilayer graphene nanoribbons in the terahertz regime,” Phys. Rev. Lett. 103(20), 207401 (2009). [CrossRef] [PubMed]

26.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010). [CrossRef] [PubMed]

27.

Y. Hernandez, V. Nicolosi, M. Lotya, F. M. Blighe, Z. Sun, S. De, I. T. McGovern, B. Holland, M. Byrne, Y. K. Gun’Ko, J. J. Boland, P. Niraj, G. Duesberg, S. Krishnamurthy, R. Goodhue, J. Hutchison, V. Scardaci, A. C. Ferrari, and J. N. Coleman, “High-yield production of graphene by liquid-phase exfoliation of graphite,” Nat. Nanotechnol. 3(9), 563–568 (2008). [CrossRef] [PubMed]

28.

M. Lotya, Y. Hernandez, P. J. King, R. J. Smith, V. Nicolosi, L. S. Karlsson, F. M. Blighe, S. De, Z. Wang, I. T. McGovern, G. S. Duesberg, and J. N. Coleman, “Liquid phase production of graphene by exfoliation of graphite in surfactant/water solutions,” J. Am. Chem. Soc. 131(10), 3611–3620 (2009). [CrossRef] [PubMed]

29.

J. J. O’Reilly, P. M. Lane, R. Heidemann, and R. Hofstetter, “Optical generation of very narrowlinewidth millimetrewave signals,” Electron. Lett. 28, 2309–2311 (1992).

30.

J. Yu, G.-K. Chang, Z. Jia, A. Chowdhury, M.-F. Huang, H.-C. Chien, Y.-T. Hsueh, W. Jian, C. Liu, and Z. Dong, “Cost-effective optical millimeter technologies and field demonstrations for very high throughput wireless-over-fiber access systems,” J. Lightwave Technol. 28(16), 2376–2397 (2010). [CrossRef]

31.

W. Li and J. Yao, “Investigation of photonically assisted microwave frequency multiplication based on external modulation,” IEEE Trans. Microw. Theory Tech. 58(11), 3259–3268 (2010). [CrossRef]

32.

L. Chen, H. Wen, and S. Wen, “A radio-over-fiber system with a novel scheme for millimeter-wave generation and wavelength reuse for up-link connection,” IEEE Photon. Technol. Lett. 18(19), 2056–2058 (2006). [CrossRef]

33.

Y. Li, Z. Zheng, L. Chen, S. Wen, and D. Fan, “Polarization-insensitive wavelength-division-multiplexing optical millimeter wave generation based on copolarized pump four wave mixing in a semiconductor optical amplifier,” Appl. Opt. 48(16), 3008–3013 (2009). [CrossRef] [PubMed]

34.

H. Zhang, S. Virally, Q. Bao, L. Kian Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012). [CrossRef] [PubMed]

35.

A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009). [CrossRef]

36.

L. Mertz, “Mode-locked maser theory of pulsars,” Astrophys. Space Sci. 30(1), 43–55 (1974). [CrossRef]

OCIS Codes
(140.7090) Lasers and laser optics : Ultrafast lasers
(320.7110) Ultrafast optics : Ultrafast nonlinear optics
(350.4010) Other areas of optics : Microwaves
(160.4236) Materials : Nanomaterials

ToC Category:
Materials

History
Original Manuscript: July 20, 2012
Revised Manuscript: September 19, 2012
Manuscript Accepted: September 21, 2012
Published: September 25, 2012

Citation
Zhiwei Zheng, Chujun Zhao, Shunbin Lu, Yu Chen, Ying Li, Han Zhang, and Shuangchun Wen, "Microwave and optical saturable absorption in graphene," Opt. Express 20, 23201-23214 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-21-23201


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References

  1. E. McCann, “Asymmetry gap in the electronic band structure of bilayer graphene,” Phys. Rev. B74(16), 161403 (2006). [CrossRef]
  2. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005). [CrossRef] [PubMed]
  3. F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol.4(12), 839–843 (2009). [CrossRef] [PubMed]
  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. R. N. Zitter, “Saturated optical absorption through band filling in semiconductors,” Appl. Phys. Lett.14(2), 73–74 (1969). [CrossRef]
  7. Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater.19(19), 3077–3083 (2009). [CrossRef]
  8. W. D. Tan, C. Y. Su, R. J. Knize, G. Q. Xie, L. J. Li, and D. Y. Tang, “Mode locking of ceramic Nd:yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett.96(3), 031106 (2010). [CrossRef]
  9. L. M. Zhao, D. Y. Tang, H. Zhang, X. Wu, Q. Bao, and K. P. Loh, “Dissipative soliton operation of an ytterbium-doped fiber laser mode locked with atomic multilayer graphene,” Opt. Lett.35(21), 3622–3624 (2010). [CrossRef] [PubMed]
  10. W. B. Cho, J. W. Kim, H. W. Lee, S. Bae, B. H. Hong, S. Y. Choi, I. H. Baek, K. Kim, D.-I. Yeom, and F. Rotermund, “High-quality, large-area monolayer graphene for efficient bulk laser mode-locking near 1.25 μm,” Opt. Lett.36(20), 4089–4091 (2011). [CrossRef] [PubMed]
  11. H. Zhang, D. Tang, R. J. Knize, L. Zhao, Q. Bao, and K. P. Loh, “Graphene mode locked, wavelength-tunable, dissipative soliton fiber laser,” Appl. Phys. Lett.96(11), 111112 (2010). [CrossRef]
  12. J. Liu, Y. G. Wang, Z. S. Qu, L. H. Zheng, L. B. Su, and J. Xu, “Graphene oxide absorber for 2 μm passive mode-locking Tm: YAlO3 laser,” Laser Phys. Lett.9(1), 15–19 (2012). [CrossRef]
  13. E. D. Obraztsova, M. G. Rybin, A. V. Tausenev, V. A. Shotniev, V. R. Sorochenko, P. S. Rusakov, and I. I. Kondrashov, “Graphene for laser applications,” presented at the Graphene 2012 International Conference, Brussels, Belgium, 10–13 Apr. 2012.
  14. Y. M. Chang, H. Kim, J. H. Lee, and Y. W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett.97(21), 211102 (2010). [CrossRef]
  15. A. Martinez, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett.99(12), 121107 (2011). [CrossRef]
  16. Y. W. Song, S. Y. Jang, W. S. Han, and M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett.96(5), 051122 (2010). [CrossRef]
  17. H. Kim, J. Cho, S. Y. Jang, and Y. M. Song, “Deformation-immunized optical deposition of graphene for ultrafast pulsed lasers,” Appl. Phys. Lett.98(2), 021104 (2011). [CrossRef]
  18. D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett.97(20), 203106 (2010). [CrossRef]
  19. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Unusual microwave response of Dirac quasiparticles in graphene,” Phys. Rev. Lett.96(25), 256802 (2006). [CrossRef] [PubMed]
  20. G. Deligeorgis, M. Dragoman, D. Neculoiu, D. Dragoman, G. Konstantinidis, A. Cismaru, and R. Plana, “Microwave propagation in graphene,” Appl. Phys. Lett.95(7), 073107 (2009). [CrossRef]
  21. G. Deligeorgis, M. Dragoman, D. Neculoiu, D. Dragoman, G. Konstantinidis, A. Cismaru, and R. Plana, “Microwave switching of graphene field effect transistor at and far from the Dirac point,” Appl. Phys. Lett.96(10), 103105 (2010). [CrossRef]
  22. H. Wang, D. Nezich, J. Kong, and T. Palacios, “Graphene frequency multipliers,” IEEE Electron Device Lett.30(5), 547–549 (2009). [CrossRef]
  23. S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys. Condens. Matter20(38), 384204 (2008). [CrossRef] [PubMed]
  24. A. R. Wright, X. G. Xu, J. C. Cao, and C. Zhang, “Strong nonlinear optical response of graphene in the terahertz regime,” Appl. Phys. Lett.95(7), 072101 (2009). [CrossRef]
  25. A. R. Wright, J. C. Cao, and C. Zhang, “Enhanced optical conductivity of bilayer graphene nanoribbons in the terahertz regime,” Phys. Rev. Lett.103(20), 207401 (2009). [CrossRef] [PubMed]
  26. E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett.105(9), 097401 (2010). [CrossRef] [PubMed]
  27. Y. Hernandez, V. Nicolosi, M. Lotya, F. M. Blighe, Z. Sun, S. De, I. T. McGovern, B. Holland, M. Byrne, Y. K. Gun’Ko, J. J. Boland, P. Niraj, G. Duesberg, S. Krishnamurthy, R. Goodhue, J. Hutchison, V. Scardaci, A. C. Ferrari, and J. N. Coleman, “High-yield production of graphene by liquid-phase exfoliation of graphite,” Nat. Nanotechnol.3(9), 563–568 (2008). [CrossRef] [PubMed]
  28. M. Lotya, Y. Hernandez, P. J. King, R. J. Smith, V. Nicolosi, L. S. Karlsson, F. M. Blighe, S. De, Z. Wang, I. T. McGovern, G. S. Duesberg, and J. N. Coleman, “Liquid phase production of graphene by exfoliation of graphite in surfactant/water solutions,” J. Am. Chem. Soc.131(10), 3611–3620 (2009). [CrossRef] [PubMed]
  29. J. J. O’Reilly, P. M. Lane, R. Heidemann, and R. Hofstetter, “Optical generation of very narrowlinewidth millimetrewave signals,” Electron. Lett.28, 2309–2311 (1992).
  30. J. Yu, G.-K. Chang, Z. Jia, A. Chowdhury, M.-F. Huang, H.-C. Chien, Y.-T. Hsueh, W. Jian, C. Liu, and Z. Dong, “Cost-effective optical millimeter technologies and field demonstrations for very high throughput wireless-over-fiber access systems,” J. Lightwave Technol.28(16), 2376–2397 (2010). [CrossRef]
  31. W. Li and J. Yao, “Investigation of photonically assisted microwave frequency multiplication based on external modulation,” IEEE Trans. Microw. Theory Tech.58(11), 3259–3268 (2010). [CrossRef]
  32. L. Chen, H. Wen, and S. Wen, “A radio-over-fiber system with a novel scheme for millimeter-wave generation and wavelength reuse for up-link connection,” IEEE Photon. Technol. Lett.18(19), 2056–2058 (2006). [CrossRef]
  33. Y. Li, Z. Zheng, L. Chen, S. Wen, and D. Fan, “Polarization-insensitive wavelength-division-multiplexing optical millimeter wave generation based on copolarized pump four wave mixing in a semiconductor optical amplifier,” Appl. Opt.48(16), 3008–3013 (2009). [CrossRef] [PubMed]
  34. H. Zhang, S. Virally, Q. Bao, L. Kian Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett.37(11), 1856–1858 (2012). [CrossRef] [PubMed]
  35. A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81(1), 109–162 (2009). [CrossRef]
  36. L. Mertz, “Mode-locked maser theory of pulsars,” Astrophys. Space Sci.30(1), 43–55 (1974). [CrossRef]

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