太赫兹区石墨烯光吸收特性对其复光电导的依赖
|
摘要
采用转移矩阵方法,在含石墨烯的多层介质结构中,研究了太赫兹频域的光传输过程。在多层结构中,光吸收表现为多个吸收峰,且吸收峰的位置依赖于入射光频率、入射角和石墨烯化学势。随着石墨烯化学势和石墨烯层数的增加,吸收率增大,石墨烯光导虚部增大,吸收峰的位置蓝移。周期性吸收峰发生在反射光干涉相消的条件下,且可通过两条主要反射光间的相位差来理解。因此,可基于光传输中石墨烯吸收峰的位置和强度来给出石墨烯的化学势、能级展宽因子参数。给出了与石墨烯材料相关的可提高石墨烯吸收率、降低透射率的参数条件。
The transfer matrix method is used to study the optical transport process in a terahertz frequency region in grapheme-containing multilayer dielectric structures.In the multilayer structures,the optical absorption exhibits as multiple absorption peaks,and the position of these peaks depends on the incident frequency,incident angle and graphene chemical potential.With the increase of the graphene chemical potential and the layer number of the graphene,the absorptivity increases and the imaginary part of the graphene conductivity increases,and the position of the absorption peak shifts blue.The periodic absorption peak occurs under the condition that the reflected light interference is cancelled,and can be understood by the phase difference between the two main reflected lights.Therefore,the chemical potential and energy level broadening factor parameters of the graphene can be given based on the position and intensity of the graphene absorption peak in the light transmission.The parameter conditions related to the graphene materials which can improve the absorptivity of graphene and reduce the transmittance are given.
The transfer matrix method is used to study the optical transport process in a terahertz frequency region in grapheme-containing multilayer dielectric structures.In the multilayer structures,the optical absorption exhibits as multiple absorption peaks,and the position of these peaks depends on the incident frequency,incident angle and graphene chemical potential.With the increase of the graphene chemical potential and the layer number of the graphene,the absorptivity increases and the imaginary part of the graphene conductivity increases,and the position of the absorption peak shifts blue.The periodic absorption peak occurs under the condition that the reflected light interference is cancelled,and can be understood by the phase difference between the two main reflected lights.Therefore,the chemical potential and energy level broadening factor parameters of the graphene can be given based on the position and intensity of the graphene absorption peak in the light transmission.The parameter conditions related to the graphene materials which can improve the absorptivity of graphene and reduce the transmittance are given.
引文
[1]Novoselov K S,Geim A K,Morozov S V,et al.Two-dimensional gas of massless Dirac fermions in graphene[J].Nature,2005,438(7065):197-200.
[2]Zhang Y B,Tan Y W,Stormer H L,et al.Experimental observation of the quantum Hall effect and Berry's phase in graphene[J].Nature,2005,438(7065):201-204.
[3]Morozov S V,Novoselov K S,Katsnelson M I,et al.Giant intrinsic carrier mobilities in graphene and its bilayer[J].Physical Review Letters,2008,100(1):016602.
[4]Katsnelson M I,Novoselov K S,Geim A K.Chiral tunnelling and the Klein paradox in graphene[J].Nature Physics,2006,2(9):620-625.
[5]Falkovsky L A,Pershoguba S S.Optical far-infrared properties of a graphene monolayer and multilayer[J].Physical Review B,2007,76(15):153410.
[6]Hanson G W.Dyadic Green′s functions and guided surface waves for a surface conductivity model of graphene[J].Journal of Applied Physics,2008,103(6):064302.
[7]Falkovsky L A,Varlamov A A.Space-time dispersion of graphene conductivity[J].The European Physical Journal B,2007,56(4):281-284.
[8]Stauber T,Peres N M R,Geim A K.Optical conductivity of graphene in the visible region of the spectrum[J].Physical Review B,2008,78(8):085432.
[9]Ashton M,Paul J,Sinnott S B,et al.Topologyscaling identification of layered solids and stable exfoliated 2D materials[J].Physical Review Letters,2017,118(10):106101.
[10]Castellanos-Gomez A.Black phosphorus:narrow gap,wide applications[J].The Journal of Physical Chemistry Letters,2015,6(21):4280-4291.
[11]Li Z Q,Henriksen E A,Jiang Z,et al.Dirac charge dynamics in graphene by infrared spectroscopy[J].Nature Physics,2008,4(7):532-535.
[12]Kuzmenko A B,van Heumen E,Carbone F,et al.Universal optical conductance of graphite[J].Physical Review Letters,2008,100(11):117401.
[13]Mak K F,Sfeir M Y,Wu Y,et al.Measurement of the optical conductivity of graphene[J].Physical Review Letters,2008,101(19):196405.
[14]Luo X G,Qiu T,Lu W B,et al.Plasmons in graphene:recent progress and applications[J].Materials Science and Engineering:R:Reports,2013,74(11):351-376.
[15]Xiao B G,Qin K,Xiao S S,et al.Metal-loaded graphene surface plasmon waveguides working in the terahertz regime[J].Optics Communications,2015,355:602-606.
[16]Thongrattanasiri S,Koppens F H L,García de Abajo F J.Complete optical absorption in periodically patterned graphene[J].Physical Review Letters,2012,108(4):047401.
[17]Fang Z Y,Wang Y M,Schlather A E,et al.Active tunable absorption enhancement with graphene nanodisk arrays[J].Nano Letters,2014,14(1):299-304.
[18]Yan H G,Low T,Zhu W J,et al.Damping pathways of mid-infrared plasmons in graphene nanostructures[J].Nature Photonics,2013,7(5):394-399.
[19]Bludov Y V,Vasilevskiy M I,Peres N M R.Mechanism for graphene-based optoelectronic switches by tuning surface plasmon-polaritons in monolayer graphene[J].Europhysics Letters,2010,92(6):68001.
[20]Otsuji T,Watanabe T,Tombet S A B,et al.Emission and detection of terahertz radiation using two-dimensional electrons in III-V semiconductors and graphene[J].IEEE Transactions on Terahertz Science and Technology,2013,3(1):63-71.
[21]Sensale-Rodriguez B,Yan R S,Rafique S,et al.Extraordinary control of terahertz beam reflectance in graphene electro-absorption modulators[J].Nano Letters,2012,12(9):4518-4522.
[22]Liu J T,Liu N H,Li J,et al.Enhanced absorption of graphene with one-dimensional photonic crystal[J].Applied Physics Letters,2012,101(5):052104.
[23]Hu J H,Huang Y Q,Duan X F,et al.Enhanced absorption of graphene strips with a multilayer subwavelength grating structure[J].Applied Physics Letters,2014,105(22):221113.
[24]Andryieuski A,Lavrinenko A V.Graphene metamaterials based tunable terahertz absorber:effective surface conductivity approach[J].Optics Express,2013,21(7):9144-9155.
[25]Merano M.Fresnel coefficients of a two-dimensional atomic crystal[J].Physical Review A,2016,93(1):013832.
[26]Blake P,Hill E W,Castro Neto A H,et al.Making graphene visible[J].Applied Physics Letters,2007,91(6):063124.
[27]Ying X X,Pu Y,Li Z,et al.Absorption enhancement of graphene Salisbury screen in the midinfrared regime[J].Journal of Optics,2015,44(1):59-67.
[28]Pu M B,Chen P,Wang Y Q,et al.Strong enhancement of light absorption and highly directive thermal emission in graphene[J].Optics Express,2013,21(10):11618-11627.
[29]Ryzhii V,Ryzhii M,Satou A,et al.Feasibility of terahertz lasing in optically pumped epitaxial multiple graphene layer structures[J].Journal of Applied Physics,2009,106(8):084507.
[2]Zhang Y B,Tan Y W,Stormer H L,et al.Experimental observation of the quantum Hall effect and Berry's phase in graphene[J].Nature,2005,438(7065):201-204.
[3]Morozov S V,Novoselov K S,Katsnelson M I,et al.Giant intrinsic carrier mobilities in graphene and its bilayer[J].Physical Review Letters,2008,100(1):016602.
[4]Katsnelson M I,Novoselov K S,Geim A K.Chiral tunnelling and the Klein paradox in graphene[J].Nature Physics,2006,2(9):620-625.
[5]Falkovsky L A,Pershoguba S S.Optical far-infrared properties of a graphene monolayer and multilayer[J].Physical Review B,2007,76(15):153410.
[6]Hanson G W.Dyadic Green′s functions and guided surface waves for a surface conductivity model of graphene[J].Journal of Applied Physics,2008,103(6):064302.
[7]Falkovsky L A,Varlamov A A.Space-time dispersion of graphene conductivity[J].The European Physical Journal B,2007,56(4):281-284.
[8]Stauber T,Peres N M R,Geim A K.Optical conductivity of graphene in the visible region of the spectrum[J].Physical Review B,2008,78(8):085432.
[9]Ashton M,Paul J,Sinnott S B,et al.Topologyscaling identification of layered solids and stable exfoliated 2D materials[J].Physical Review Letters,2017,118(10):106101.
[10]Castellanos-Gomez A.Black phosphorus:narrow gap,wide applications[J].The Journal of Physical Chemistry Letters,2015,6(21):4280-4291.
[11]Li Z Q,Henriksen E A,Jiang Z,et al.Dirac charge dynamics in graphene by infrared spectroscopy[J].Nature Physics,2008,4(7):532-535.
[12]Kuzmenko A B,van Heumen E,Carbone F,et al.Universal optical conductance of graphite[J].Physical Review Letters,2008,100(11):117401.
[13]Mak K F,Sfeir M Y,Wu Y,et al.Measurement of the optical conductivity of graphene[J].Physical Review Letters,2008,101(19):196405.
[14]Luo X G,Qiu T,Lu W B,et al.Plasmons in graphene:recent progress and applications[J].Materials Science and Engineering:R:Reports,2013,74(11):351-376.
[15]Xiao B G,Qin K,Xiao S S,et al.Metal-loaded graphene surface plasmon waveguides working in the terahertz regime[J].Optics Communications,2015,355:602-606.
[16]Thongrattanasiri S,Koppens F H L,García de Abajo F J.Complete optical absorption in periodically patterned graphene[J].Physical Review Letters,2012,108(4):047401.
[17]Fang Z Y,Wang Y M,Schlather A E,et al.Active tunable absorption enhancement with graphene nanodisk arrays[J].Nano Letters,2014,14(1):299-304.
[18]Yan H G,Low T,Zhu W J,et al.Damping pathways of mid-infrared plasmons in graphene nanostructures[J].Nature Photonics,2013,7(5):394-399.
[19]Bludov Y V,Vasilevskiy M I,Peres N M R.Mechanism for graphene-based optoelectronic switches by tuning surface plasmon-polaritons in monolayer graphene[J].Europhysics Letters,2010,92(6):68001.
[20]Otsuji T,Watanabe T,Tombet S A B,et al.Emission and detection of terahertz radiation using two-dimensional electrons in III-V semiconductors and graphene[J].IEEE Transactions on Terahertz Science and Technology,2013,3(1):63-71.
[21]Sensale-Rodriguez B,Yan R S,Rafique S,et al.Extraordinary control of terahertz beam reflectance in graphene electro-absorption modulators[J].Nano Letters,2012,12(9):4518-4522.
[22]Liu J T,Liu N H,Li J,et al.Enhanced absorption of graphene with one-dimensional photonic crystal[J].Applied Physics Letters,2012,101(5):052104.
[23]Hu J H,Huang Y Q,Duan X F,et al.Enhanced absorption of graphene strips with a multilayer subwavelength grating structure[J].Applied Physics Letters,2014,105(22):221113.
[24]Andryieuski A,Lavrinenko A V.Graphene metamaterials based tunable terahertz absorber:effective surface conductivity approach[J].Optics Express,2013,21(7):9144-9155.
[25]Merano M.Fresnel coefficients of a two-dimensional atomic crystal[J].Physical Review A,2016,93(1):013832.
[26]Blake P,Hill E W,Castro Neto A H,et al.Making graphene visible[J].Applied Physics Letters,2007,91(6):063124.
[27]Ying X X,Pu Y,Li Z,et al.Absorption enhancement of graphene Salisbury screen in the midinfrared regime[J].Journal of Optics,2015,44(1):59-67.
[28]Pu M B,Chen P,Wang Y Q,et al.Strong enhancement of light absorption and highly directive thermal emission in graphene[J].Optics Express,2013,21(10):11618-11627.
[29]Ryzhii V,Ryzhii M,Satou A,et al.Feasibility of terahertz lasing in optically pumped epitaxial multiple graphene layer structures[J].Journal of Applied Physics,2009,106(8):084507.