Xu Cheng(程旭) Xu Zhou(周旭) Chen Huang(黃琛) Can Liu(劉燦) Chaojie Ma(馬超杰)Hao Hong(洪浩) Wentao Yu(于文韜) Kaihui Liu(劉開輝) and Zhongfan Liu(劉忠范)

1State Key Laboratory for Mesoscopic Physics,Frontiers Science Center for Nano-optoelectronics,School of Physics,Peking University,Beijing 100871,China

2Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials,

School of Physics and Telecommunication Engineering,South China Normal University,Guangzhou 510006,China

3Beijing Graphene Institute(BGI),Beijing 100095,China

4International Centre for Quantum Materials,Collaborative Innovation Center of Quantum Matter,Beijing 100871,China

5Center for Nanochemistry,College of Chemistry and Molecular Engineering,Peking University,Beijing 100871,China

Keywords: graphene,photonic crystal fiber,temperature sensor,high sensitivity,Fermi level

Optical fiber,as one of the most remarkable waveguides,possesses many intrinsic excellent features such as ultralow transmission loss, perfect single-mode transmission ability,anti-electromagnetic interference capacity and the compatibility for complex environments.[1-4]These characteristics have made it an attractive platform for all-fiber temperature sensors,which are widely used in applications such as fire monitoring, temperature distribution of engines, and magnetic resonance imaging.[5-7]Traditional optical fiber temperature sensors are mainly based on fiber gratings or interferometers, in which the environment temperature change leads to the variation of the grating pitch or the optical path difference in interferometers, and results in the change of the detecting signal.However,these fiber temperature sensors suffer from complicated structural design and wavelength resolved measurement system.[8-10]To break through this dilemma, some strategies have been developed, including combining optical fiber with functional thermo-sensitive materials.[11-13]

Originating from the atom-scale hexagonal lattice structure and unique Dirac band, graphene has exhibited exceptional electrical,optical and thermal properties.[14-23]Herein,the tunable light absorption ability under different environment temperatures endows graphene with the potential to sense temperature via simple sensor construction and direct power detecting system.[24-27]Considering atomic thickness of graphene and light-matter interaction enhancement capacity of optical fiber, it is mutually beneficial to integrate both for all-fiber temperature sensors. In the current manufacture technologies,side-polished and tapered optical fibers are most commonly used platforms to combine with graphene due to the evanescent wave coupling. However, these temperature sensors based on transfer techniques conventionally suffer from the distortion of the propagation mode or short interaction length with relatively low sensitivity,[28-33]which limit their practical applications. Besides, the influences of the Fermi level(EF)variation on light absorbance of graphene and the consequent sensor performance are still unclear,which may be a key point to further improve the sensitivity of the temperature sensors.[34]

Here, we propose a highly sensitive temperature sensor based on graphene photonic crystal fiber(Gr-PCF)(Fig.1(a)),in which the transmission mode is kept intact and the intensity of the transmitted light changes with temperature. Technically, the Gr-PCF can be massively fabricated by direct chemical vapor deposition method,[35]which endows it with the great potential in the practical application as a temperature sensor. This all-fiber temperature sensor theoretically exhibits a tunable sensitivity by modulating grapheneEF,and the highest sensitivity can reach～3.34×10?3dB/(cm·°C) withEF=0.435 eV under 1550 nm incident photon (～0.8 eV),dramatically enhanced compared with that at charge neutral point. Through optimizing the PCF structure, the sensitivity can be further enhanced by 10 times to 0.036 dB/(cm·°C).Our results provide a promising new way for high-performance allfiber temperature sensors based on Gr-PCF.

Fig. 1. Schematic illustration of Gr-PCF temperature sensor. (a) The configuration of Gr-PCF temperature sensor,in which the change of environment temperature can be monitored by the change of output light power. (b)Schematic of Gr-PCF cross-section,where graphene film is fully covered on the inner surface of air holes in PCF cladding(the hole diameter Φ and pitch Λ are both at micron scale).

In the as-designed Gr-PCF temperature sensor, a graphene film is attached tightly on the hole surface in PCF,where the PCF structure is selected according to the commercial one based on the total internal reflection theory for the practical application potential. In the cross-section of Gr-PCF,six circles of air holes are arranged periodically in the PCF cladding with the hole diameter(Φ)of 2.22μm and pitch(Λ)of 5.4μm(Fig.1(b),3 circles of air holes just for schematic diagram). Besides,the diameters of the solid core and the whole optical fiber are～8.6 and～125 μm, respectively. The selected PCF structure guarantees the endless single-mode property and low insertion loss with commercial single-mode fiber at the operating wavelength near 1550 nm.[36]The characterizations of the light distribution and transmission attenuation in the Gr-PCF at different temperatures are obtained by full-vector finite element simulation method.[37-40]As shown in the electric field distribution of the fundamental mode in Gr-PCF and the bare fiber, the addition of atomic thickness graphene film does not distort the propagation mode, which indicates the perfect integration ability of graphene and photonic crystal fiber (Figs. S1(a) and S1(b)). The propagating light in this fiber can continuously interact with the graphene film along the axis of the fiber via the evanescent wave coupling(Fig.S1(c)),which leads to the strong light-matter interaction.

The mechanism of this Gr-PCF temperature sensor is directly related to the Fermi-Dirac distribution change of the electrons in graphene with temperature at a givenEFsuch as the charge neutral point(Fig.2(a)). At the temperature of 0 K,the electrons are entirely distributed underEF(Fig. 2(a), left panel). Then with the temperature arising (T>0 K), some electrons possess larger kinetic energy and occupy higher energy levels aboveEF[41](Fig. 2(a), right panel). Hence, the temperature change contributes to the electron redistribution in the Dirac-cone energy band of graphene and further results in the variation of its conductivity(σGr)according to the Kubo formula,which is directly related to the complex refractive index(nGr):[25-27]

wherenF(ε)=1/{1+exp[(ε ?EF)/(kBT)]}is Fermi-Dirac distribution,εis the electron energy,kBis the Boltzmann constant,Tis the temperature,ωis the radian frequency,Γ is the scattering rate, ˉhis the reduced Planck’s constant,ε0is the vacuum permittivity, anddGris the graphene thickness. At the condition ofEF=0 eV and 1550 nm incident light, the imaginary part(k)ofnGrshows a decreasing trend with temperature rising from?100°C to 100°C, leading to the decrease of graphene absorption(Fig.2(b)). Meanwhile,the real part(n)ofnGrincreases with temperature(Fig.2(c)),bringing about the increase of the refractive index in fiber cladding and consequent enhancement of the normalized light intensityI(ratio of intensity at the innermost graphene position to that at the fiber core center) in Gr-PCF (Fig. 2(d)). Taking the combined influences ofkandninto account, the change of transmission attenuation in Gr-PCF with the temperature from?100°C to 100°C is demonstrated as～6.4×10?5dB for one-centimeter-long fiber (Fig. 2(e)), which shows the enormous potential to monitor temperature through light intensity change.

Considering the unique and adjustableEFcharacteristic of graphene,it is significant to modulate theEFfor optimizing the transmission attenuation and the sensitivity of the sensor.Therefore,we systematically investigate the influence ofEFon the performance of Gr-PCF temperature sensor, and find that the sensitivity can be highly improved whenEFis adjusted at a suitable level around 0.4 eV (half energy of the incident photon of 1550 nm, Fig. 3(a)). In this case, the transmission attenuation is much lower than that at the charge neutral point(EF=0 eV)and the difference of attenuations between?100°C and 100°C(|?A|)drastically changes withEFtuned around 0.4 eV, which indicates the possibility to enhance the sensitivity via tuningEF(Fig. S2). This attenuation change with temperature results from the combined effects ofkandn,which are related to the absorption of graphene and the light distribution at the innermost graphene film respectively and show an obvious change withEFadjusted around 0.4 eV at different temperatures(Figs.3(b)and 3(c)). In detail,the light transmission attenuation in Gr-PCF shows a decreasing trend with temperature from?100°C to 100°C withEFin the range of 0.35 eV to 0.40 eV, but an increasing trend withEFin the range of 0.40 eV to 0.45 eV(Fig.3(d)). Besides, whenEFis adjusted from 0.3 eV to 0.45 eV,kandnvary from～2.6 to～0.4 and～3.2 to～2.2 at a constant temperature of 0°C,respectively(Fig.S3),contributing the decreasing trend of the total transmission attenuation of Gr-PCF.For the practical sensor applications, it is important to obtain the high sensitivity with low total transmission attenuation by setting a suitableEF. As a result, the|?A| shows a maximum～0.668 dB/cm atEF=0.435 eV(four orders of magnitude improvement than that at 0 eV) with a relatively low attenuation compared to that at another peak position ofEF=0.365 eV(Figs.3(d)and 3(e)). This result also indicates～3.34×10?3dB/(cm·°C)sensitivity for temperature sensing,where the unit dB/(cm·°C)is used to describe temperature sensing ability of Gr-PCF for the unit fiber length. In principle, the absorption of graphene is directly dependent on the electron distribution at the energy level of half the incident photon energy(±0.4 eV for 1550 nm incident light). Hence, for the case ofEF=0.4 eV, the distribution probability at 0.4 eV (the same asEF) is always a constant 0.5, and that at?0.4 eV changes very slightly with temperature due to the large energy difference fromEF,which results in a very small attenuation fluctuation with temperature atEF=0.4 eV compared to that atEF=0.435 eV(Fig.3(e)).

Fig.2.Temperature sensing property of Gr-PCF with EF=0 eV.(a)Fermi-Dirac distributions of electrons in graphene at different temperatures,resulting in the changes of the conductivity and complex refractive index of graphene. (b)-(e)The relative changes of the imaginary part ?k(b) and real part ?n (c) of graphene complex refractive index, the relative normalized intensity (ratio of intensity at the innermost graphene position to that at the fiber core center)?I(d),and the relative attenuation ?A(e)with temperatures from ?100°C to 100°C.Here ?represents difference between values at a given temperature and that at 0 °C,where k,n,I and A are 2.8326,2.9340,11.37467%and 4.04843 dB/cm at 0 °C,respectively.

Fig.3. Sensitivity enhancement of the Gr-PCF temperature sensor by modulating EF. (a)The simplified electrical band diagram of graphene with EF adjusted around 0.4 eV and 1550 nm input light. The imaginary part(b)and the real part(c)of graphene complex refractive index with different EF and temperatures. (d)Transmission attenuation in Gr-PCF with temperature under different EF around 0.4 eV region. (e)The|?A|(difference of light attenuations between temperatures of ?100 °C and 100 °C)change with different EF around 0.4 eV,showing a dip value at EF=0.4 eV and two peak values at EF=0.365 eV and EF=0.435 eV.The transmission attenuation at EF=0.435 eV is much lower than that at EF=0.365 eV(d).

Fig.4. Sensitivity enhancement by optimizing Gr-PCF structure. (a),(b)The dependence of normalized intensity I at graphene film regime(a)and transmission attenuation A(b)on air-hole diameter at EF=0.435 eV and 0°C.Both I and A show an obvious decreasing with hole diameter increasing. (c)The change of|?A|with different hole diameters,exhibiting an evident change from ～7.2 dB/cm to ～0.07 dB/cm with hole diameter increasing and the sensitivity of ～0.036 dB/(cm·°C)for 1μm hole diameter. The endless single mode transmission property is kept at different hole diameters and pitches.

In addition, the sensor sensitivity is also related to the strength of light-matter interaction in Gr-PCF, which can be improved by optimizing the PCF structure.[42]The performance of sensitivity with different PCF structures is studied on the condition ofEF=0.435 eV,meanwhile,the endless single mode transmission property is kept by elaborately designing the sizes of the hole diameter and pitch.[36]With theΦreduced from 5μm to 1μm and the temperature of 0°C,the normalized intensityIat graphene film regime of Gr-PCF shows a strong enhancement from～4.9% to～24.2% (Fig. 4(a)).Considering influences of both the light intensity change at the innermost graphene position and the given graphene absorption, the transmission attenuation also shows an increasing trend withΦchanging from 5 μm to 1 μm (Fig. 4(b)).Furthermore,the difference of attenuations(|?A|,between the temperatures of?100°C and 100°C) demonstrates an obvious enhancement with reducingΦ(Fig. 4(c)), which indicates temperature sensitivity of～3.6×10?2dB/(cm·°C)withΦ=1μm,～10 times improvement than that of conventional PCF withΦ=2.22 μm (Fig. 3(e)). Overall, the decrease of hole diameter in PCF leads to the enhanced light-graphene interaction,and results in dramatically increased sensitivity.

In summary, a highly sensitive temperature fiber sensor based on Gr-PCF with the intact transmission mode is proposed theoretically by modulatingEFand optimizing the PCF structure. WithEF～0.435 eV (35 meV higher than the half energy of the incident photon),the sensitivity can be enhanced by four orders of magnitudes to～3.34×10?3dB/(cm·°C)with a relatively low transmission attenuation. Furthermore,with the hole diameter optimized to 1μm,the sensitivity can be improved to～0.036 dB/(cm·°C), which demonstrates a huge potential in highly sensitive temperature sensors. Our strategy provides a new way for the design of high performance all-fiber temperature sensors targeting next-generation optical fiber applications. Furthermore,considering the excellent properties of various nanomaterials such as sufficient volume, high catalytic activity, specific adsorption capacity and remarkable electrocatalytic property,[43-45]these nanomaterials have demonstrated enormous potential to make up for the shortages of intrinsic graphene in the mentioned aspects and be integrated with PCF to target for broadening types or functions of sensors with high performance.