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Graphene plasmonic lens for manipulating energy flow.

Wang G, Liu X, Lu H, Zeng C - Sci Rep (2014)

Bottom Line: Because photons are uncharged, it is still difficult to effectively control them by electrical means.It is found that the proposed lens can be utilized to focus and collimate the GP waves propagating along the graphene sheet.As an application of such a lens, the image transfer of two point sources with a separation of λ₀/30 is demonstrated.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an 710119, China.

ABSTRACT
Manipulating the energy flow of light is at the heart of modern information and communication technologies. Because photons are uncharged, it is still difficult to effectively control them by electrical means. Here, we propose a graphene plasmonic (GP) lens to efficiently manipulate energy flow by elaborately designing the thickness of the dielectric spacer beneath the graphene sheet. Different from traditional metal-based lenses, the proposed graphene plasmonic lens possesses the advantages of tunability and excellent confinement of surface plasmons. It is found that the proposed lens can be utilized to focus and collimate the GP waves propagating along the graphene sheet. Particularly, the lens is dispersionless over a wide frequency range and the performance of lens can be flexibly tuned by adjusting the bias voltage. As an application of such a lens, the image transfer of two point sources with a separation of λ₀/30 is demonstrated.

No MeSH data available.


Related in: MedlinePlus

Evolution of effective mode indices of GP waves as a function of the dielectric spacer thickness with Vg = 20 V (a), and the bias voltage with h = 200 nm (b) for different frequencies.In calculations, the temperature T is 300 K and relaxation time of graphene sheet is 0.5 ps.
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f2: Evolution of effective mode indices of GP waves as a function of the dielectric spacer thickness with Vg = 20 V (a), and the bias voltage with h = 200 nm (b) for different frequencies.In calculations, the temperature T is 300 K and relaxation time of graphene sheet is 0.5 ps.

Mentions: Within the random-phase approximation, the dynamic optical response of graphene can be derived from the Kubo's formula consisting of the interband and intraband contributions: σg = σinter + σintra33. In the THz and infrared ranges, the intraband transition of electrons dominates. On condition that μc ≫ kBT, where kB is the Boltzmann's constant, the surface conductivity of graphene can be simplified to a Drude-like form2534here τ is the momentum relaxation time, e and are the electron charge and reduced Planck's constant, respectively. The carrier relaxation time τ determined by the carrier mobility μ in graphene as τ = μμc/(eVf2)35. Recently, it has been reported that the carrier mobility of μ = 8000 cm2/(V·s) of graphene can be obtained by mechanical cleavage of bulk graphite and then transferred to SiO2/Si substrate36, and μ = 230000 cm2/(V·s) can be experimentally achieved in high-quality suspended graphene37. When the chemical potential μc is 0.15 eV with a certain gate voltage38, the above carrier motilities correspond to the relaxation times of τ = 0.12 ps and τ = 3.45 ps, respectively. Here, we choose τ = 0.5 ps. This value follows the ballistic transport features of graphene, whose mean free path was measured to be up to 500 nm at room temperature16. It should be noted that the carrier relaxation time τ can affect the imaginary part of the effective mode index of the graphene, which may result in the distortion of images and the deteriorated focusing effect. In practice, therefore, the carrier mobility and relaxation time should be appropriately tuned to reduce the distortion of images and the deteriorated focusing effect. In our analysis, , where Vf = 106 m/s is the Fermi velocity and ns is the sheet doping of graphene32. In the proposed Selfoc lens, ns can be controlled using an external bias voltage following where Cox = εr2ε0/h is the gate capacitance, and Vg is the external bias voltage32. Based on the above equations, the effective mode indices nGP ( = kGP/k0) of GP waves for different thicknesses of dielectric spacer and bias voltages can be obtained. As shown in Fig. 2, it is found that nGP can be adjusted by tuning the h and Vg. In the following discussions, we mainly employ the changing of h to control the effective mode index nGP and manipulate the propagation of GP waves in graphene. The influences of bias voltage Vg on the performance of the proposed Selfoc lens are discussed in the Supplementary Materials.


Graphene plasmonic lens for manipulating energy flow.

Wang G, Liu X, Lu H, Zeng C - Sci Rep (2014)

Evolution of effective mode indices of GP waves as a function of the dielectric spacer thickness with Vg = 20 V (a), and the bias voltage with h = 200 nm (b) for different frequencies.In calculations, the temperature T is 300 K and relaxation time of graphene sheet is 0.5 ps.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3921639&req=5

f2: Evolution of effective mode indices of GP waves as a function of the dielectric spacer thickness with Vg = 20 V (a), and the bias voltage with h = 200 nm (b) for different frequencies.In calculations, the temperature T is 300 K and relaxation time of graphene sheet is 0.5 ps.
Mentions: Within the random-phase approximation, the dynamic optical response of graphene can be derived from the Kubo's formula consisting of the interband and intraband contributions: σg = σinter + σintra33. In the THz and infrared ranges, the intraband transition of electrons dominates. On condition that μc ≫ kBT, where kB is the Boltzmann's constant, the surface conductivity of graphene can be simplified to a Drude-like form2534here τ is the momentum relaxation time, e and are the electron charge and reduced Planck's constant, respectively. The carrier relaxation time τ determined by the carrier mobility μ in graphene as τ = μμc/(eVf2)35. Recently, it has been reported that the carrier mobility of μ = 8000 cm2/(V·s) of graphene can be obtained by mechanical cleavage of bulk graphite and then transferred to SiO2/Si substrate36, and μ = 230000 cm2/(V·s) can be experimentally achieved in high-quality suspended graphene37. When the chemical potential μc is 0.15 eV with a certain gate voltage38, the above carrier motilities correspond to the relaxation times of τ = 0.12 ps and τ = 3.45 ps, respectively. Here, we choose τ = 0.5 ps. This value follows the ballistic transport features of graphene, whose mean free path was measured to be up to 500 nm at room temperature16. It should be noted that the carrier relaxation time τ can affect the imaginary part of the effective mode index of the graphene, which may result in the distortion of images and the deteriorated focusing effect. In practice, therefore, the carrier mobility and relaxation time should be appropriately tuned to reduce the distortion of images and the deteriorated focusing effect. In our analysis, , where Vf = 106 m/s is the Fermi velocity and ns is the sheet doping of graphene32. In the proposed Selfoc lens, ns can be controlled using an external bias voltage following where Cox = εr2ε0/h is the gate capacitance, and Vg is the external bias voltage32. Based on the above equations, the effective mode indices nGP ( = kGP/k0) of GP waves for different thicknesses of dielectric spacer and bias voltages can be obtained. As shown in Fig. 2, it is found that nGP can be adjusted by tuning the h and Vg. In the following discussions, we mainly employ the changing of h to control the effective mode index nGP and manipulate the propagation of GP waves in graphene. The influences of bias voltage Vg on the performance of the proposed Selfoc lens are discussed in the Supplementary Materials.

Bottom Line: Because photons are uncharged, it is still difficult to effectively control them by electrical means.It is found that the proposed lens can be utilized to focus and collimate the GP waves propagating along the graphene sheet.As an application of such a lens, the image transfer of two point sources with a separation of λ₀/30 is demonstrated.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an 710119, China.

ABSTRACT
Manipulating the energy flow of light is at the heart of modern information and communication technologies. Because photons are uncharged, it is still difficult to effectively control them by electrical means. Here, we propose a graphene plasmonic (GP) lens to efficiently manipulate energy flow by elaborately designing the thickness of the dielectric spacer beneath the graphene sheet. Different from traditional metal-based lenses, the proposed graphene plasmonic lens possesses the advantages of tunability and excellent confinement of surface plasmons. It is found that the proposed lens can be utilized to focus and collimate the GP waves propagating along the graphene sheet. Particularly, the lens is dispersionless over a wide frequency range and the performance of lens can be flexibly tuned by adjusting the bias voltage. As an application of such a lens, the image transfer of two point sources with a separation of λ₀/30 is demonstrated.

No MeSH data available.


Related in: MedlinePlus