Active unidirectional propagation of surface plasmons at subwavelength slits

Highly efficient, active and compact, unidirectional surface plasmon (SP) propagator composed of double subwavelength slits; filled with organic electro-optic (EO) material is proposed and investigated. By selecting appropriate structure parameters, obtained by solving phase relations between slits, the relative phase of SP generated at the slit exit aperture can be tailored. Simulation results show under normal illumination and external voltage of 8.7 V, SP launching efficiency of 55% and unidirectional SP extinction ratio about 47dB at wavelength of 632.8 nm is achieved. The power consumption of the structure is on the order of 9 fJ/bit which meet the power consumption limitation for optical devices. Moreover, the structure is very compact with effective total length of 1.2 μm and thickness of 0.6 μm. ©2013 Optical Society of America OCIS codes: (250.5403) Plasmonics; (230.0250) Optoelectronics; (230.2090) Electro-optical devices; (130.3120) Integrated optics devices. 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Introduction
The light diffraction at subwavelength scales hinders the minimization of photonic components.Plasmonics that is based on exploiting coupling between light and collective electronic excitations within conducting materials known as surface plasmons (SP) paves a confident way beyond the diffraction limit for future optical integrated circuits.So far, a large diversity of plasmonic nanodevices has been theoretically proposed and experimentally demonstrated [1][2][3][4][5].A key device is a SP generator that may efficiently convert the exciting field into surface plasmon polaritons (SPPs).Unfortunately, conventional generators, such as prism and grating suffer from poor light-SPP coupling or massive size.To increase the light coupling efficiency and minimize the structure, subwavelength structures such as slits or ridges on metal surfaces offering small footprints were currently investigated [6][7][8][9].However, the direction of the SPPs generated from slits cannot be selected due to structure symmetry.The symmetric SPPs propagation may play as a limiting factor for building the efficient functionalized plasmonic circuits; therefore, the need for directional SP propagation is unavoidable.Over the past few years, numerous passive unidirectional SP generators have been developed [10][11][12][13][14][15].Two important figure-of-merits of SP propagators are the launching efficiency η in the desired direction and the extinction ratio r defined as the ratio between the SPPs intensity propagated into the desired direction and the intensity launched into the opposite direction.Meanwhile, tradeoff between launching efficiency, extinction ratio and size is still a big challenge.Most recently, Baron et al. designed a unidirectional SP propagator that composed of eleven subwavelength grooves; an extinction ratio of 38 dB and launching efficiency η larger than 52% was reported but unfortunately, the structure is massive nearly 8 µm [16].
Moreover, active plasmonic devices with externally controlled characteristic enable us to obtain compact devices with high functionality and low power consumption such as photodetection [17], florescence enhancements [18], subwavelength imaging and photolithography [19] and highly integrated nanophotonic devices [20,21].Alternatively investigating the active unidirectional SP propagator remains a main challenge to design plasmonics architecture than can actively couple light from photonics taper or free space to plasmonics components.A few schemes have been proposed and developed [22][23][24], Liu et al. by bridging the optical antenna theory and the concept of metamaterials developed an all optically controlled compact 1.2µm unidirectional antenna with extinction ratio of more than 23dB [22].Chen et al. reported another structure with coupling efficiency of 64% but the extinction ration in only 16.7 dB [23].To our knowledge, there is no reported structure for active directional SP propagator using external voltage.Here phase modulation of the SPPs is achieved by replacing the "dielectric" layers with the electrooptically active materials such as electro-optic organic crystals (4-dimethyl-amino-Nmethyl-4-stilbazolium tosylate (DAST) for our case) [25][26][27] and Indium tin oxide [28,29].The large electro-optic coefficient of organic crystals, high speed bandwidth operation, low dispersion, low dielectric constants, and compatible with integrated circuit (IC) technology make them ideal candidates for high frequency operation in optoelectronic applications [26,[30][31][32].Recently slot waveguide filled with EO polymers to electro-optically control the SPPs propagation for nanophotonics application was reported [26,[32][33][34][35][36][37][38].ITO, an In 2 O 3 based material that has been doped with Sn, has been widely used as transparent conducting oxides because of its two chief properties, its electrical conductivity and optical transparency, as well as the ease fabrication procedure to make an electrode.We proposed a novel device composed of two slits perforated on metallic silver and filled with electro-optic organic crystal which is sandwiched between silica and ITO layers as contacts.Through mutual interference of the two SP fields with different relative phases excited at the slit exit apertures, the field intensity along one direction on the metal surface can be enhanced or suppressed.Calculations, performed using 2D finite element method (FEM) demonstrate the proposed device offers better performance than those reported so far [15][16][17][18][21][22][23][24] with launching efficiency η of 55% and a large extinction ratio r ≈47 dB at λ = 632.8nm.In addition, the device is compact (1.2 μm length) and operates under normal illumination.The geometrical parameters were determined by theoretical calculations.

Device structure and theoretical model
A schematic of the plasmonic directional generator based on double-slit with identical widths (w) of 100 nm and interspace distance-center to center-(d) of 1008 nm perforated on silver film with 254 nm thickness (t) is shown in Fig. 1.The metallic layer is sandwiched between 10 nm high optical transmittance and low sheet resistance ITO layers as top and bottom electrode to induce the bias.Silica with refractive index of 1.45 [9] and 27 nm thicknesses on top and 25 nm on bottom used to separate metallic layer from ITO electrodes preventing unwanted carried injection and distribution in metallic layer.In the next section, the reason of choosing these values will be explained.The slits also were filled with DAST but only the DAST in left slit touches the ITO layers, this leads the external voltage only changes the refractive index of DAST in left slit.MGF 2 , a transparent layer over an extremely wide range of wavelengths, considered as substrate with thickness of 200 nm and refractive index of 1.38 [22].The structure can be fabricated by using magnetron sputtering to deposit a thin layer of ITO on substrate and following by Silica and silver layer.The slits can be milled by using focused ion beam milling [15].Graphoepitaxy, which utilizes lithographically defined structures to modify crystal growth, can be used to obtain device-quality crystals of DAST which is faster than by a solution-growth technique and chemical vapor deposition (CVD).DAST an organic material with a refractive index of 2.2, exhibits a large EO coefficient (dn/dE = 3.41nm/V) compared with that of standard inorganic EO materials such as LiNbO 3 (dn/dE = r 33 n 3 /2 = 0.16 nm/V), because of a large delocalized π electron system [32].In fact the physics behind the macroscopic electro-optic coefficient is complicated.The quantum mechanics behavior of EO material molecules under applied electric field, related to the first and second molecular hyperpolarizability and angle between the poling field direction and the chromophore principal axis, well studied through the papers [26,33,39].Here we merely use the experimental reported value of electro-optic coefficient [32].In our calculations, we assumed that the EO material is transparent (Imε = 0) in the wavelength range of interest, and that the incident light is a TM-polarized wave (magnetic field parallel to the y direction) with 632.8 nm wavelength.We assumed that the EO material is poled along the x direction, so the change in refractive index only happens at z-direction.
The presence of silica layer under metallic layer creates a hybrid waveguide structure.The hybrid optical waveguide consisting of a dielectric layer sandwiched between metal and high index materials assists surface plasmon polaritons to travel over large distances (40-150 mm) with strong mode connement (ranging from λ 2 /400 toλ 2 /40) [40][41][42].In all the simulations, the permittivity of the silver and ITO is described by the Drude model: where for silver the high-frequency bulk permittivity ε ∞ = 4.2, the bulk plasmon frequency ω p = 1.346*10 16 rad/ s, and the electron collision frequency Γ = 9.617*10 13 rad/ s., the result fits the result fits the permittivity of silver in near-infrared range [43].For incident wavelength of 632.8 nm, silver permittivity is obtains as ε m = −16.24+ i0.66.For ITO ε ∞ equals 3.9 [29], and Γ is 1.8*10 14 1/s −1 [44], that result in ε ITO = 3.45 + i0.21, for our working wavelength [45].In presence of applied voltage (electric field) the carrier density in ITO layer changes, to obtain a proper estimation of this effect Thomas-Fermi screening theory for deriving the carrier distribution for a given voltage should be employed.Following the Thomas-Fermi approach the total free carrier density and the potential are related by [46]: E F and h are the Fermi energy and Planck's constant, respectively.The electron effective mass, m eff , for ITO is 0.35 * m e [47] in terms of the free electron mass m e = 9.1*10 −31 kg.N 0 , the carrier density when there is no external voltage, is in the order of 9.25*10 26 m −3 .The boundary value problem is needed to obtain the potential distribution Ф (z) and then to calculate the induced carrier density N(z) in the ITO layer [46].Once the carrier density is obtained, by using plasma frequency ω p : then the permittivity of ITO layer can be determined by the Drude formula (Eq.( 1)).It has been exhibited the relative change of the free carrier density in the thin ITO layer is estimated to be 1% for a 10 V voltage applied and reaches 9.34*10 26 m −3 which cannot affect the permittivity considerably [46], since our applied external voltage is lower therefore the change in carrier density and thereby permittivity will be much smaller.
The following advantages for our structure can be specified: • Relatively high carrier mobility and the low enough carrier density of ITO, which used as electrodes, result in a small change in real part of the dielectric permittivity under our applied voltage.
• The narrow low refractive index dielectric layer between metallic layer and ITO provides hybrid surface plasmon waveguides with higher confinement, longer propagation length, and lower lose compare to regular structures.
• Because of the instructive interference of propagating SPPs at exit of slits, the double slit structure has higher light transmission than single slit.
• DAST which is compatible with SOI technology has a high electro-optic coefficient, so the energy consumption is very low.
• The structure is very compact and for desired wavelength or slits, appropriate structure parameters can be determined by applying phase retardation equations.Nanoslits perforated in metal film with width smaller than the incident wavelength as shown in the inset of Fig. 2 provides the necessary momentum for the SP modes excitation and scatters part of incident radiation into a plasmonic channel.Once the SPPs reach the slit exit aperture, some of them are scattered into free-space radiation, while the remainder propagate on the metal-dielectric interface.Because of multi-reflection effect inside the nanoslit that is a direct prove of Fabry-Perot resonator nature of nanoslit, the SPPs wavelength squeezes and effective refractive index for nanoslit can be introduced.The effective refractive index dependence on the dielectric medium and slit width for narrower slits can be approximated as [48]: where w is the slit width, ε m and ε d are the dielectric constants of the metal and dielectric, respectively.Figure 2 depicts the relationship between slit width and its effective index N eff for three dielectric mediums as vacuum, DAST and a dielectric with refractive index of 2.3.Figure 2 also implies that changing the slit width or filling the slit region with different dielectrics can tune the phase retardation of the SP generated at the slit exit aperture.

Simulation result
As mentioned before two important figure-of-merits of SP propagators are the launching efficiency η in the desired direction and the asymmetrical SPP extinction ratio r defined as r = 10 logP d /P u , where P d and P u represent the SPP intensity propagated into the desired direction and the intensity launched into the opposite direction.To calculate these parameters, two line power monitors along the Silica thickness are set at 2µm away from the slits to detect the magnetic field distribution as seen in Fig. 1(b).In all simulation, the results are based on the recorded parameters of these monitors.To optimize the structure parameters, some consideration should be done over layers thickness.A compromise must be made between conductivity and transparency of ITO layer, since increasing the thickness and increasing the concentration of charge carriers will increase the material's conductivity, but decrease its transparency.Simulation results show that ITO and substrate thickness should be 10 nm and 200 nm respectively.In fact, the change in substrate thickness has small influence on output results.The thickness of Silica is should be approximately equals with SPPs penetration depth which is about 30 nm [49].In the absence of external voltage (OFF state) two slits have identical refractive index; The TM-polarized light source causing a fraction of the energy to be coupled into SPP modes at the Ag/SIO 2 interface; propagating equally along left and right interfaces as seen in Fig. 3(a) and the remaining to be transmitted or reflected.Magnetic field intensity along Xdirection for Ag/SIO 2 is shown in Fig. 3(b); the magnetic field along left side is larger than right side which attributes to prolonging the DAST to silica layer at left slit.It is worthy to note that most of SPPs concentrate within the hybrid layer.When an external voltage is applied the refractive index of the DAST with the EO coefficient of dn/dE = 3.41 nm/V will change via this equation: Where V is the external voltage applied to the structure via the ITO electrodes, h, the distance between two electrodes.As mentioned before the material within a nanoslit obtains an effective refractive index which is higher than its own refractive index.Figure 4 shows the relation between the effective refractive index of DAST for different voltage range from 5 V to 10 V when h fixed at 300 nm, obtained via Eqs.( 4) and ( 5) and noting ε d = n 2 .The inset plot shows the effective refractive index difference for different voltages.4) and ( 5).The inset plot shows the effective refractive index versus applied voltage.
When the voltage is ON, the refractive index of left slit increases.Our goal is to design the structure in a way that propagating SPs, generated at the exit aperture of the each slit, travel along one direction on the metal/Silica interface, which can be achieved by modulating the phase difference of SPPs launched separately from the two slits.This requires that SPs interfere constructively along one direction while destructively along the opposite direction, i.e., the relative phases of SPs at two exit apertures take the forms [8]: where φ 1 and φ 2 are the relative phases of generated SPs at the exit apertures for the left and right slits filled with DAST, respectively.d is the interspacing between two slits and M is an arbitrary integer.Since the relative phase and the effective index have the relation of φ 1 = N eff- left t2π/λ + φ', and φ 2 = N eff-right t2π/λ where t is the film thickness, λ is the wavelength of the incident light, N eff-left and N eff-right are the effective refractive index of the left and right slit when the voltage is ON.The propagating light through OE layer undergoes a phase delay, φ', which can be calculated as [50]: where h is the distance between two electrodes.Simple manipulation of Eqs. ( 6), ( 7) and ( 8) yields: According to Eqs. ( 5) and ( 9) higher voltage yields in larger effective refractive index differences and thereby thicker metallic film but shorter interspace distances, vice versa lower voltage yield in lower effective refractive index differences thereby thinner metallic film but longer interspace distances.For an increase in refractive index from 2.2 to 2.3 (lowest increase in the order of 10 −1 ), the required voltage is about 8.7 V which is low voltage compatible with silicon electronics.The width w and wavelength are chosen as 100 nm and 632.8 nm; respectively from Eq. ( 4) the effective refractive index change is 0.21, after substituting the parameters in Eq. ( 9) the film thickness obtains as 254 nm.For this thickness, maximum phase retardation will happen between slits.In addition, from Eqs. ( 6) and ( 7), the interspacing d can be calculated as d = (4N + 1)λ SP /4.The dispersion relation of structure with double ITO layers and metallic film is complicated to be solved analytically.Obtaining the dispersion relation of SPs and thereby the SPPs wavelength is a bottleneck task.Here we use simulation result to determine SP wavelength.According to Eqs. ( 6) and ( 7) maximum light intensity occurs at some specific interspace distance which is corresponds to SP wavelength (λ sp ).The asymmetrical extinction ratio is plotted in Fig. 5 as a function of interspace distance.The periodicity of the plot is equal with SP wavelength, which is about 445 nm.The asymmetrical extinction ratio (r) can be achieved as high as 47 dB (P d /P u = 108) for interspace distance of 1008 nm.For this interspace distance, the structure delivers desirable phase retardation for the incident light and mutual interference of the two SP fields with different relative phases happens.The simulation result reveal that the SP fields generated at the slit exit apertures the magnetic field distribution of silver layer possess a strong spatial distribution orientation.From Figs. 6(a)-6(c) it can be seen the field intensity along the left direction on the metal surface was increased while the field intensity along the right direction because of destructive interference was suppressed, as was predicted.The most important achievement is that by selecting appropriate parameters the magnetic field at undesired direction because of destructive interferes was approximately quenched.Another point worth noting in Figs.6(a) and 6(b) is that the simulated SP intensities along the left side are larger than the intensity calculated for the separate single slit.This increase is attributed to the inter-slit effect, which leads part of SP on illuminated surface couple with SP of remote slit and enhances the SP intensity at the slit exit aperture.The magnetic field intensity along the X-direction under the metallic surface for ON and OFF state and magnetic field distribution are shown in Figs.6(b) and 6(c).There is almost no magnetic field along right interface in ON state; meanwhile the light intensity along left interface because of constructive interference is even higher than OFF state.By calculating the mean value of magnetic field intensity in SIO 2 layer under the metallic layer in Fig. 6(a), and normalizing with magnetic field intensity in free space, the launching efficiency η is obtained 55% that is also superior to previous reported work.
The two parallel electrodes with the EO material sandwiched in between form a capacitor with capacitance of where ε 0 is the permittivity of vacuum, ε EO = 5.3 is the dielectric constant of EO polymer under applied voltage, A is the area of the ITO covering the top and bottom of EO material, and h is the distance between electrodes [34].The power consumption can be estimated by , given V = 8.7V and f = 470 THz (wavelength = 632.8nm), the projected power consumption in the device is on the order of 9 fJ/bit.The energy consumption of optical devices has to be in the order of 10 fJ/bit or lower according to an analysis presented by Miller [51] which our structure meet this requirements.
If the slits fill with inorganic crystals such as BaTiO 2 or polymer electrooptic materials, the required voltage for the same structure will be in the order of 35 V and 100 V, respectively.As a result organic crystals with high Electro-optic coefficient are a good candidate for optoelectronic application.

Conclusions
In summary, for the first time by utilizing electrooptic materials we have designed electrically controlled unidirectional SPPs propagator with higher generation efficiency, extinction ratio and compact size compare to previously reported structures.By choosing proper geometrical parameters to manipulate SPs interference at the exit of slits, higher launching efficiency of 55% and higher extinction ratio of 47 dB at wavelength of 632.8 nm was achieved.The structure is very compact with effective length of 1.2µm that can be integrated easily with other plasmonic components for the application in plasmonic circuitry, such as Bragg grating mirrors to realize selective coupling of SPPs into different ports.Furthermore, it works under low voltage (8.7 V) and low power consumption (9 fJ/bit) which is compatible with silicon electronics.In addition, our proposed unidirectional propagator is achieved for normal incidence that is unavoidable in most applications.Our results may have potential applications in plasmonic integrated circuits and on-chip applications.

Fig. 1 .
Fig. 1. a) Schematic 3D view of the proposed structure.b) 2D view of the structure.D and w stands for interspace distance and slit width, respectively.A, B located at 2µm away from slits are monitors to calculate the SPPs passing along it.The TM polarized light impinges from top with 632.8nm wavelength.The layers thickness is defined in legend.

Fig. 2 .
Fig. 2. The effective index dependence on the slit width for incident light of 632.8 nm wavelength.Solid and starred lines represent the real and imaginary parts of the effective index, respectively.The inset shows the sketch of a MDM structure.

Fig. 3 .
Fig. 3. a) Logarithmic magnetic field distribution in OFF state.b) shows the magnetic field intensity along X-direction along metalSilica interface, which in both directions is identical.

Fig. 4 .
Fig. 4. effective refractive index differences as function of applied voltage obtained by using Eqs.(4) and (5).The inset plot shows the effective refractive index versus applied voltage.

Fig. 5 .
Fig. 5.The asymmetrical extinction ratio as a function of interspace distance.The plot has a periodic nature with the periodicity of SPPs wavelength which has about 445 nm.A big asymmetrical extinction ratio about 47 dB for interspace distance of 1008 nm is achieved

Fig. 6 .
Fig. 6. a) The magnetic field intensity under the metallic layer recorded by two remote monitors.dashed lines are the result of right monitor while solid lines stands for the result of left monitor.b) Light intensity along X-direction, under the metallic layer in both states.c) Logarithmic magnetic field distribution when the voltage takes the value 8.7 V (ON state).