Analytical approaches for nano-plasmonic and micro-millimetric antennas

www.ietdl.org Published in IET Microwaves, Antennas & Propagation Received on 25th May 2010 Revised on 28th September 2010 doi: 10.1049/iet-map.2010.0206

ISSN 1751-8725

Analytical approaches for nano-plasmonic and micro-millimetric antennas A. Massaro1 D. Caratelli2 A. Yarovoy2 R. Cingolani3 1

Italian Institute of Technology IIT, Center of Bio-Molecular Nanotechnology, Arnesano 73100, Italy IRCTR, Delft University of Technology TUD, Mekelweg 4, 2628 CD Delft, The Netherlands 3 Italian Institute of Technology IIT, Via Morego 30, 16163 Genova, Italy E-mail: [email protected] 2

Abstract: Antenna modelling approaches, based on suitable spherical harmonic expansions of the radiated electromagnetic field, are addressed and thoroughly investigated. Particular emphasis is put on the simultaneous transverse resonance diffraction (STRD) technique for plasmonic antennas. This method efficiently allows evaluation of the near-field distribution because of the interaction of optical sources, such as surface plasmon waves, with perfectly conducting wedges. The STRD technique based on the multipole expansion of Green’s function (MEG) is particularly suitable for the design and rigorous analysis of wireless nano-systems. On the other hand, the characterisation of electromagnetic radiation processes in millimetric/ micrometric short-pulse electrical antennas can be conveniently carried out by means of the dedicated singularity-expansionmethod(SEM)-based methodology detailed in the second part of this study. Together, the proposed new analytical approaches provide a powerful and complete tool for small antenna design GHz and THz frequency ranges.

1

Introduction

Since the near-field distribution is difficult to evaluate experimentally at optical frequencies, an accurate approach able to model and design a wedge metallic optical antenna is highly desirable. In fact, the electromagnetic field excited in the presence of metal/dielectric discontinuities features a very complex behaviour which makes the adoption of detection principles impossible. To overcome this limitation, the simultaneous transverse resonance diffraction (STRD) method can be conveniently used to evaluate the near-field distribution excited by an infinitely thin metal conductor (Fig. 1). In this way, field singularity issues arising in radiation problems regarding optical antennas can be efficiently handled. The traditional numerical approaches such as the finite-element method (FEM), and finitedifference time-domain (FDTD) technique are computationally expensive when calculating the radiated field in the proximity of a dielectric or metallic discontinuity. To this end, a new approach based on the multipole expansion of Green’s function (MEG) combined with the novel principle of STRD [1] is used. The STRD/ MEG has been applied previously to the evaluation of the electromagnetic field excited near three-dimensional dielectric corners, showing good convergence together with reduced computational burden, the computational time being 15/12 times smaller compared to conventional numerical methods [1]. For the first time in this work the STRD/MEG method is applied to the electromagnetic characterisation of a particular class of antennas suitable for plasmon resonance nano-probe systems [2 – 9], which can IET Microw. Antennas Propag., 2011, Vol. 5, Iss. 3, pp. 349– 356 doi: 10.1049/iet-map.2010.0206

be described in terms of wedge conductors. According to theory [10], a wire antenna, whose length l is l0/5 , l , l0/10 (l0 is the working wavelength), behaves as an infinitesimal dipole (small dipole). In view of this, in the second part of this paper emphasis is put on the electromagnetic characterisation of small dipole-like antennas operating in the GHz-to-THz frequency range. To this end, a semi-analytical methodology [11] for accurate modelling of transient electromagnetic radiation processes is adopted. Using the proposed procedure based on the singularity expansion method (SEM), the radiated field is presented directly in the time domain as the superposition of outgoing propagating non-uniform spherical waves related to the complex resonant processes occurring in the structure under analysis. Any time-domain integral-equation or finite-difference technique can be adopted to carry out the full-wave analysis within a volume surrounding the antenna, and to determine, in step with the numerical simulation, a spherical harmonic expansion of the equivalent electric and magnetic currents excited on a suitable Huygens surface enclosing the radiating structure. Then, a pole/residue representation of the currents is derived by a dedicated time-domain vector fitting procedure [11]. In this way, closed-form expressions of the antenna parameters in the time domain can be obtained in terms of a newly introduced class of incomplete spherical Bessel functions, thus generalising and expanding the methodology in [11]. Also, in this second approach, the suggested method allows for a significant reduction of the computational resources (both in terms of time and memory). Both the novel approaches, based on spherical 349

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www.ietdl.org and the terms gl (r, r ′ ) are  gl (r, r′ ) =

′ ′ −ikjl (kr)h(2) l (kr ) r , r

−ikjl (kr′ )h(2) l (kr)

r . r′

(i = −j)

(5)

with the following spherical Bessel functions [16, 19] jl jl (u) =

p 1/2 2x

Jl+(1/2) (u)

(6)

and spherical Hankel functions h(2) l [12, 22] h(2) l (u) =

p 1/2 2u

[Jl+(1/2) (u) − iNl−(1/2) (u)]

(7)

that for a distance r ≪ l0 [23, 24] (near-field evaluation) are of the type Fig. 1 Infinitely thin metal conductor excited by a surface plasmon wave

harmonic expansion, provide a powerful tool for the simulation of small antennas operating in a frequency range from RF-THz to optical frequencies.

2 STRD/MEG approach for plasmon antennas The radiated electric field at an external point P of a region with refractive index n, as in Fig. 1, is expressed as [12, 13] E(P) =

1 ∇ × ∇P jv4p1c P    ′ ′ × J i G(r, r ) dVQ + (H × nˆ )G(r, r ) dSQ V

−

1 ∇ × 4p P



S

 J (ˆn × E)G(r, r′ ) dSQ − i j v 1c S

where in spherical coordinates the wedge point is at Q ¼ Q(r ′ , u′ , w′ ), and the field is evaluated at P ¼ P(r, u, w). The permittivity 1c ¼ n 2 indicates the cladding permittivity. The cladding encloses the wedge. In spherical co-ordinates, the Green’s function satisfies the Helmholtz scalar equation and the MEG given by [12 – 19] 

∗ gl (r, r′ )Yl,m (u′ , w′ )Yl,m (u, w)

1 · 3 · 5 · · · · · (2l − 1) ul+1

We observe that (2) presents a discontinuity peak of the first derivative at the point Q (point of singularity). According to this property, the MEG is suitable for near-field evaluation in the proximity of metallic singularities. Moreover, the index l indicates the order of the expansion and represents the accuracy of the solution: the convergence of the nearfield solution can be performed by increasing the order of MEG. A solution of Maxwell’s equations in cylindrical co-ordinates is provided by the following three field components Er = −jvm Ef = jvm

1 ∂F r ∂f

∂F ∂r

(2)

Hr = jv 1

1 ∂F r ∂f

Hf = −jv1 where the functions Yl,m are defined as Yl,m (u, w) =

2l + 1 (l − m)! 4p (l + m)!

(3)

Pm l are the Legendre functions [12, 20, 21] given by l+m (−1)m 2 m/2 d (1 − u ) (u2 −1)l , 2l l! dul+m m = −l, . . . , +l

Pl(m) (u) =

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∂F ∂r

(10)

Ez = k 2 F

1/2 Plm ( cos u) ejmw

(9)

where F is a suitable Hertzian potential that satisfies Helmholtz’ equation. The field in (9) is transverse electric (TE) with respect to the z-direction, denoted by TEz, but it is also transverse magnetic (TM) with respect to the fdirection (thus denoted TMf ). A similar modal analysis can be carried out for TMz (i.e. TEf ) fields characterised by the following components

l,m



(8)

Hz = k 2 F (1)

G(r, r′ ) =

h(2) l (u)  i

(4)

Equations (9) and (10) are used in order to calculate the total electric field (1) near the metallic wedge by using the relationships which convert the cylindrical co-ordinates to spherical co-ordinates. It is well recognised that, in many cases, boundary and radiation conditions alone are not sufficient to determine the solution uniquely [1, 25]. In any case, it is possible to construct several different fields which satisfy these conditions. In particular, by considering the metallic wedge IET Microw. Antennas Propag., 2011, Vol. 5, Iss. 3, pp. 349 –356 doi: 10.1049/iet-map.2010.0206

www.ietdl.org reported in Fig. 2a, the MEG approach adapts the radiation conditions well, especially for the near-field calculation, but an accurate evaluation of the potential F is required. Assuming the potential of the form F(r, f) =

1 n r [Ai sin(nf) − Bi cos(nf)] k02

(11)

where k0 ¼ 2p/l0 is the free-space wave number and l0 is the optical working wavelength, the near field will be characterised by the singularityn which can be calculated by a circuit-based approach. If the metallic wedge is embedded in N dielectric materials (see Fig. 2a), the circuit-based approach takes into account the electromagnetic field propagating along a cascade of transmission lines as illustrated in Fig. 2b. Each transmission line is characterised by an electric length di ¼ nCi (which is a function of the angle Ci related to the dielectric material 1i), and by a characteristic impedance zi [14]. The simultaneous resonance of the transmission lines will provide the singularity n value of the electromagnetic field. The resonance condition is performed by annulling the total impedance of the circuit with respect to a reference plane [1, 14]. If the conductor is embedded in a single dielectric material 1l ¼ 1c ¼ n 2 as depicted in Fig. 3a, the equivalent transmission line circuit of the metallic edge will be a single transmission line enclosed by two short circuits (Fig. 3b). Let us consider for simplicity a TE-polarised (Hz , Er , Ew) field. By defining the following equivalent voltages and currents related to the scheme of Fig. 3a Vi =

1 [A cos(nfi ) + Bi sin(nfi )] 1i i

I i = [Ai sin(nfi ) − Bi cos(nfi )],

(12) i = 1, . . . , N

and by making use of the continuity of Hz and Er components we derive the following transmission matrix (ABCD) representation [26] 

V i+1 I i+1



 =

cos(nfi ) z−1 i sin(nfi )

zi sin(nfi ) cos(nfi )



Vi Ii

 (13)

where zi ¼ 1/1 is the normalised TMf characteristic impedance. By introducing the load impedance Zi ¼ Vi/Ii and Ti ¼ tan(nCi) and by using the standard formula for

Fig. 3 Modelling of a thin metal conductor embedded in one dielectric material a Infinitely thin metal conductor b Equivalent transmission line modelling

the impedance transformation along a transmission line Z i = zi

Z i−1 + jzi T i , zi + jZ i−1 T i

i= 1, 2, . . . , N

(14)

we can calculate the simultaneous resonance condition of the total impedance Z1 + Z2 ¼ 0 in the case of N ¼ 1 (case of Fig. 3a) where Z1 and Z2 are the impedances calculated starting from the reference plane of Fig. 3b. In this case we have that T1 ¼ 0, that is n=

p C1

(15)

Fig. 4a shows the STRD – MEG calculated near-field radiation pattern E(r, f ) of the plasmonic antenna of Fig. 1 for l0 ¼ 0.8 mm: an order l ¼ 3 of expansion (2) is in this case enough in order to obtain a good convergent solution. In order to compare the computational cost of the proposed approach with the traditional ones, we simulate an infinitely thin metal conductor (a 1 mm length of 0.001 mm width is enough in order to launch a surface plasmonic wave (SPW) source) by means of a properly designed FEM tool. As illustrated in Fig. 4b we obtain the same near-field radiation pattern of STRDMEG simulation by using a very fine FEM mesh size. The advantage of the proposed approach is mainly in the computational cost: in fact, we found by using a 1 GHz/512M-RAM PC a CPU time reduction of about 13 times (Table 1). Finally, we observe that the modelling proposed in this section is suitable only for very small antennas with dimensions ranging from the micro- to nano-scale. Moreover, the hypothesis of a perfect conductor represents a good approximation to the near-field calculation for distances r ≪ l0 (near-field region) for nano-probe detection systems.

Fig. 2 Modelling of a thin metal conductor embedded in different dielectric materials a Perfect conducting wedge and N dielectric wedges. The z-axis is along the common wedge and normal to the figure b Equivalent transmission line circuit: di represent the electric lengths and zi the characteristic impedance, respectively IET Microw. Antennas Propag., 2011, Vol. 5, Iss. 3, pp. 349– 356 doi: 10.1049/iet-map.2010.0206

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Fig. 4 Near-field radiation pattern of the thin metal conductor a STRD–MEG b FEM Calculated near-field radiation pattern in proximity of point Q and for r ≪ l0

Table 1

Comparison between the computational (CPU)-time cost between STRDMEG and FEM results of Fig. 4 STRD–MEG

FEM

 12 min

 2 h and 39 min

3 SEM-based methodology for micro/millimetric antennas In this section, attention is focused on a novel semi-analytical formulation, based on the SEM and the spherical mode expansion, which is useful for analysing the time-domain radiation properties of complex micro/millimetric antennas. Consider a general antenna operating in free space and driven through a transmission line by a matched voltage generator vg(t) having internal resistance Rg (see Fig. 5). Denoting by Sh a spherical surface of radius Rh enclosing the structure, the relevant time-domain electromagnetic field radiated in the Fraunhofer region can be readily obtained as the vector slant-stack transform (SST) of the equivalent electric and magnetic current densities IS(u, w, t) ¼ [ Js(u, w, t) Ms(u, w, t)] excited along Sh [27]. At any time, IS(u, w, t) can be conveniently approximated as a finite superposition of spherical harmonics I S (q, w, t) =

+1  n 

cn,m (t)Ynm (q, w)

where sn,m,k ¼ 2 sn.m,k + jvn,m,k , cn,m,k ¼ [an,m,k bn,m,k] denote the complex poles and vector residues, respectively, of the exponential terms accounting for the natural resonant processes occurring in the antenna. According to [10], the transient electric field radiated by the antenna can be expressed as the following vector SST of the surface equivalent currents IS(u, w, t) 1 E(r, t)  r× 4prc0

  Sh

  Rh ′ ˙ h0 r × J S q, w , t + cos g c0

  ˙ S q′ , w′ , t + Rh cos g dS ′ +M c0 (18) where cosg ¼ sin u sinu′ cos(w 2 w′ ) + cos u cos u′ , and t ¼ t 2 r/c0 is the spherical-wave time delay. Hence,

(16)

n=0 m=−n

Therefore provided that the considered antenna is excited by a finite-duration pulse, the following modified SEM-based representation of the vector current expansion coefficients in (16) can be adopted

cn,m (t) 

K 

cn,m,k esn,m,k t u(t)

(17)

k=1

with u(t) being the usual Heaviside unit-step distribution, and 352 & The Institution of Engineering and Technology 2011

Fig. 5 Antenna enclosed by a spherical Huygens surface Sh The radiating structure is assumed to be connected to a uniform transmission line excited by a real voltage generator vg(t) with internal resistance Rg . The reference system adopted to express the field quantities is also shown IET Microw. Antennas Propag., 2011, Vol. 5, Iss. 3, pp. 349 –356 doi: 10.1049/iet-map.2010.0206

www.ietdl.org equivalent representation immediately reads

substituting (16) and (17) into (18) yields N  n  K R2h  s esn,m,k t en,m,k E(r, q, w, t) ≃ 4prc0 n=0 m=−n k=1 n,m,k  × e(sn,m,k /c0 )Rh cos g Ynm (q′ , w′ ) sin q′ dq′ dw′ Vh

(19) where en,m,k ¼ 2 h0an,m,k + r × bn,m,k is the general spherical-wave modal vector, and Vh ¼ {(u′ , w′ ):cos g . 2c0 t/Rh} denotes the angular domain of the equivalent currents on Sh contributing, at the normalised time t, to the radiated electromagnetic field excited at the observation point {r, u, w}. Using the Laplace integral representation of the Heaviside unit-step function, and exploiting some advanced analytical properties of the surface harmonics, the radiation integrals in (19) can be evaluated in closed form as 

e(sn,m,k /c0 )Rh cos g Ynm (q′ , w′ ) dV′ Vh



= 4pin

    sn,m,k c0 t c0 t m R , min 1, Yn (q, w) u 1 + c0 h Rh Rh (20)

having defined the incomplete modified spherical Bessel function of order n 1 in (j, w) = 2

1 −w

ejz Pn (z) dz

(21)

Pn(z) denoting the Legendre polynomial of order n. The newly introduced class of special functions is particularly useful in the description of complex wave phenomena regarding electromagnetic diffraction and radiation from truncated spherical structures. Upon combining (20) with (21), and setting for shortness ˆin (j, w) = in (j, min{1, w})

(w [ R)

(22)

the time-domain electric field radiated by the antenna in the Fraunhofer region is obtained as the following superposition of outgoing propagating non-uniform spherical waves attenuating along with the radial distance and time according to the real part of complex poles sn,m,k

E(r, q, w, t) 

N  n  K R2h  s esn,m,k t i n rc0 n=0 m=−n k=1 n,m,k     s c t c t × n,m,k Rh , 0 Ynm (q, w)u 1 + 0 en,m,k c0 Rh Rh (23)

Using (23) and the shifting properties of the unilateral Laplace transform, the complex frequency-domain IET Microw. Antennas Propag., 2011, Vol. 5, Iss. 3, pp. 349– 356 doi: 10.1049/iet-map.2010.0206

E(r, q, w, p) ≃

N  n  K sn,m,k R2h e−jk0 r  i c0 r n=0 m=−n k=1 p − sn,m,k n   p × Rh Ynm (q, w) en,m,k c0

(24)

where k0 ¼ – jp/c0 is the free-space complex wave number. The considered approach has been validated by application to a dipole-like antenna with total length ld ¼ 300 mm. The near-field full-wave analysis of the considered radiating structure has been performed by means of a locally conformal FDTD scheme [28]. The antenna has been meshed on a uniaxial-perfectly matched layer (PML)backed non-uniform grid with maximum spatial increment Dhmax ¼ lc/20  15 mm, where lc is the free-space wavelength at the upper 210 dB cut-off frequency of the excitation voltage signal, f0 ¼ 1 THz. It has been numerically found that the considered radiating structure is well matched to the feeding line in the frequency band around f0  440 GHz. The central resonant frequency f0 of the antenna can be conveniently controlled by exploiting the piezoelectric properties of the material forming the radiating flairs. Using the developed SEM-based approach, the time-variant spherical harmonic expansion vector coefficients of the surface equivalent currents excited on the Huygens sphere Sh with radius Rh ¼ 200 mm have been computed on-the-fly in step with the numerical FDTD simulation. To this end, a suitable local inverse distance weighting interpolation technique [29] has been adopted to derive a cardinal series (CS) representation of the electromagnetic field distribution over Sh [30]. Truncation errors arise when limiting the order of CS expansion to a finite discrete angular bandwidth N. To mitigate this problem, the parameter N is selected, according to the theory of the optimal interpolation of the radiated electromagnetic fields over a sphere [30], as

2pxRh N= c0 Tg

 (25)

In (25), the excess bandwidth factor x is used to control the approximation error which decreases more than exponentially with x 2 1 [30]. So, upon assuming x ¼ 1.2 and Tg ¼ 5tg  2.4 ps the optimal spherical expansion order is found to be N ¼ 3. The time-varying current coefficients have then been fitted to the modified pole/residue expansion (17) with order K ¼ 10 selected heuristically in such a way as to guarantee an adequate degree of accuracy in the modelling of the natural resonant processes occurring in the structure. The presented non-uniform spherical wave representation (23) and (24) has been applied to evaluate the transient and frequency-domain behaviour of the radiated electromagnetic field excited at a distance R0 ¼ 800 mm along the broadside direction. As it appears in the example of Fig. 6, the antenna response peaks at f0  440 GHz, where the electrical length of the radiating flair is about p/2. It is worth noting from Figs. 6a and b the excellent agreement between the numerical results obtained using the proposed methodology and the reference FDTD solution. However, it is worth stressing that the computational times and memory usage required to carry out the pole/residue spherical harmonic expansion are 353

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www.ietdl.org input field of the antenna a SPW generated by the plasmonic waveguide of Fig. 7a. Assuming that the source is an electric field E0 parallel polarised to the plane of incidence (according with the p-polarised light which is able to excite electronic surface plasmons), the resulting surface electromagnetic wave will have the following general form A1 = A10 ei(kz1 z+kx,EW x−vt) ,

z,0

A2 = A20 ei(kz2 z+kx,SPW x−vt) ,

z.0

(26)

where A stands for E and H, kz1 and kz2 are the wavevectors in the z-direction, kx,EW and kx,SPW are those in the x-direction and v is the angular frequency. The incident light coming from the dielectric material reflects at the metallic interface and localised light, called the evanescent wave (EW), occurs. The EW excites the surface plasmon wave reported in Fig. 7b which is propagating along the surface of the metal film and thus part of the incident light is absorbed. The light intensity of the reflected ray will depend on the incidence angle u. The propagation constant of the EW is expressed as kx,EW =

2p √ 1c sin u l0

(27)

where l0 is the working wavelength. The propagation constant of the SPW wave is given by the following expression [31, 32]   2p 1a 1m 1/2 l0 1a + 1m     2 1a 1m 3/2 4pd 1m kr = −kd exp i l0 (1a + 1m )1/2 1a − 1m 1a + 1m

kd = Fig. 6 Comparison methodology

between

FDTD

and

proposed

SEM

a Transient b Frequency-domain Behaviour of the co-polarised electric field component excited by the dipolelike antenna at a distance R0 ¼ 800 mm along the broadside direction

negligible in comparison with those relevant to the FDTD numerical simulation for computing the far-field distribution. Furthermore, by using the presented approach, one can gain a meaningful insight into the physical mechanisms which are responsible for the electromagnetic behaviour of complex radiating structures. Such information can be usefully exploited to optimise the performance of micro/millimetric antennas for a wide variety of applications. Finally, the SEM approach requires a computational cost of one order lower when compared with the FDTD CPU consumption time.

(28) where kd is the dispersion relation of the surface plasmon wave of a metal – vacuum interface in a single -sharpboundary model, kr is the perturbation to kd because of the physical volume of the metal defined by the thickness d, and the complex dielectric function of a metallic film can be expressed in the following form 1m (v) = 1′m (v) + i1′′m (v)

When (29) and (30) satisfy the following equation, surface plasmon resonance occurs and a part of incident light is absorbed kz,SPW = kd + kr

4 Main difference between STRD – MEG and SEM approach: spherical wave expansions with different kinds of excitation sources According to (2) and (16) both the STRD – MEG and SEM methods are based on the expansion of spherical harmonics which allows one to obtain a very accurate solution regarding radiation problems. These functions must be matched with the source in order to improve the exact solution of the physical problem. For this purpose, we use the same expansion approach by differentiating the kind of application by means of the source implementation. In particular for the STRD – MEG approach we select as the 354 & The Institution of Engineering and Technology 2011

(29)

(30)

At the resonance condition the infinite metal conductor placed at the end of the waveguide will be coupled and will radiate as explained in Section 2. A different kind of source is considered in the detailed SEM approach. In this method the spherical wave expansion is related to a Gaussian pulse excitation which is totally different from the plasmon wave source defined in (26). In particular, the Gaussian pulse is defined by ⎡  2 ⎤ t − t0 ⎦ vg (t) = Vg exp⎣− u(t) tg

(31)

IET Microw. Antennas Propag., 2011, Vol. 5, Iss. 3, pp. 349 –356 doi: 10.1049/iet-map.2010.0206

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Fig. 7 Plasmonic antenna and coupled evanescent wave a Plasmon waveguide and evanescent field E (surface plasmon waves) propagating along the z-direction and coupled with the thin plasmon metallic antenna b Evanescent field distribution in air region (z , 0) for a particular time-step. The waveguide used for the antenna excitation is characterised by a gold (1m ¼ 220 + i0.8) metallic layer at z ¼ 0 with d ¼ 100 nm. The working wavelength is l0 ¼ 0.8 mm, 1c ¼ 3.1 and 1a ¼ 1

where Vg ¼ 1 mV, t0 ¼ 10tg in the presented numerical simulations, and the time constant tg has been selected in such a way as to have the source significant energy in the frequency band up to fc ¼ 1 THz, namely tg =

√ ln 10 ≃ 0.48 ps pfc

(32)

The source pulse is coupled into the finite-difference equations used to update the time-domain electric-field distribution within the antenna driving point, and models with reasonable accuracy the millimetric/micro metallic probe used to excite the structure under analysis.

5

Conclusion

The proposed novel STRD/MEG and SEM-based analytical approaches represent a combined powerful tool for the design and analysis of electrically small radiation systems. The STRD/MEG formulation is developed in the frequency domain and is particularly suitable for handling field singularity issues arising in radiation problems regarding wireless optical detection systems based on nano-probes. On the other hand, the presented SEM methodology provides a powerful unified time- and frequency-domain IET Microw. Antennas Propag., 2011, Vol. 5, Iss. 3, pp. 349– 356 doi: 10.1049/iet-map.2010.0206

tool especially useful in the characterisation of millimetric/ micro antennas. Both techniques are based on the spherical harmonic expansion of the radiated electromagnetic field. Different types of excitation mechanisms are used to carry out the field computation for the GHz/THz and optical frequency bands. In particular, surface plasmon waves are used to excite the considered optical antenna within the STRD/MEG method, whereas a suitable wideband Gaussian pulse source is employed in the SEM-based technique. The proposed methodology represents a novel multi-disciplinary approach, involving applied mathematics, physics and electromagnetics, to the design of small antennas for wireless optical detection systems.

6

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IET Microw. Antennas Propag., 2011, Vol. 5, Iss. 3, pp. 349 –356 doi: 10.1049/iet-map.2010.0206