EIT based tunable metal composite spherical nanoparticles

Ghassem Rostami a, Mahmoud Shahabadi a, Ali Afzali-Kusha a, Ali Rostami b,*a School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran

b School of Engineering-Emerging Technologies, University of Tabriz, Tabriz 51666, Iran

Received 6 August 2010; received in revised form 22 July 2011; accepted 9 August 2011

Available online 16 September 2011

Abstract

Optical polarizability of a composite metal–dielectric and dielectric–metal spherical nanoparticle is investigated in view of

achieving all-optical tunability. In this work, the Electromagnetically Induced Transparency (EIT) implemented in the shell or core

of the nanoparticle is used. For the proposed nanoparticle, we show that EIT phenomenon can be utilized to tune the resonance

frequency in the frequency response of polarizability. We present a quasi-static analysis for determining polarizability of the

nanoparticle. According to our simulation results, all-optical tunability of polarizability can be achieved for reasonable values of

optical pump power. Also, we demonstrate how the extinction quality factor and electric field distribution can be controlled for the

introduced nanoparticle.

# 2011 Elsevier B.V. All rights reserved.

Keywords: EIT; Metal composite nanoparticles; Quasi-static

www.elsevier.com/locate/photonics

Available online at www.sciencedirect.com

Photonics and Nanostructures – Fundamentals and Applications 10 (2012) 102–111

1. Introduction

Composite nanoparticles are key elements for

nanoscale engineering. They are composed of two or

more homogeneous layers. The optical properties of

these particles, especially their nonlinear behavior, can

be engineered using optical and geometrical parameters

[1]. It is well known that for suitable arrangement of

layers desirable optical characteristics can be achieved.

For example these nanoparticles can be used to

implement as basic elements of nanoscale optical

amplifiers in quantum dot semiconductor optical

amplifiers (QD-SOA) [2]. Also, they can be used to

realize array of nanoparticles as optical and quantum

passive elements such as waveguides [3]. The optical

* Corresponding author.

E-mail addresses: gh.rostami@ece.ut.ac.ir, rostami@tabrizu.ac.ir

(A. Rostami).

1569-4410/$ – see front matter # 2011 Elsevier B.V. All rights reserved.

doi:10.1016/j.photonics.2011.08.001

properties of composite nanoparticles have been the

subject of many articles on enhancement of nonlinear

optical properties [4], management of different shapes

and distribution of nanoparticles [5], linear optical

properties of gold nanoparticles [6], effect of incident

frequency changes on nanoparticles’ response [7],

properties of hollow gold nanospheres [8], control of

luminescent host materials by doping of metal nano-

particles [9], investigation of optomechanical properties

of composites [10], electromagnetic field distribution and

manipulation of optical parameters of composite

materials [11,12], temperature dependent optical para-

meters of composite materials [13,14], controlling

efficiency of nonlinear optical phenomenon in composite

materials [15], and polarizability management of nano-

shells [16–20]. Metallic nanoshell structure with a

metallic core is one of the most common structures in

composite nanoparticles. Recently, many researchers

have been focused on the investigation of the linear

optical properties of metal nanoshells [20].

G. Rostami et al. / Photonics and Nanostructures – Fundamentals and Applications 10 (2012) 102–111 103

For implementation of tunable complex frequency

responses, a tunable subsystem is necessary. To this end,

one commonly shapes the geometry of a nanoparticle

[5]. For metal composite nanoparticles, tunability of the

plasmon resonance frequency has been achieved

experimentally using variation of geometrical para-

meters [6–8]. However, all-optical tunability of

composite nanoparticle is not reported so far [14–20].

It is the objective of this work to introduce an optically

tunable nano-structure. Here, Electromagnetically

Induced Transparency (EIT) implemented in spherical

nanoshells is used to achieve tunability. To demonstrate

this property, we make use of a quasi-static analysis to

extract the linear polarizability of spherical nanopar-

ticles composed of various layers. We show how with

the help of EIT the electric field intensity inside the

particle as well as the plasmon resonance frequency can

be tuned over a wide range.

EIT phenomenon is one of the useful optical effects

described by quantum optics. In this phenomenon, a

three-level atom (such as Si/SiO2) becomes transparent

at a certain wavelength (the probe wavelength) once a

strong laser field is applied at the wavelength

corresponding to the second transition of the material.

EIT has been observed in atoms [21], rare-earth-ion

doped crystals [22], semiconductor quantum wells [23],

quantum dots [24] and Bose–Einstein condensates

[25,26]. Basic principles and characteristics of EITwere

introduced in [27]. Some interesting applications of EIT

in optoelectronic systems were introduced in [28,29].

Applications of EIT for design of tunable optical

waveguides were introduced in [30]. In this paper,

exploiting EIT, we propose a nano-structure with

optically tunable characteristics. For this purpose, the

paper is organized as follows.

In Section 2, calculation of polarizability using a

quasi-static approximate analysis is presented. Numer-

ical results generated using this analysis are presented

and described in Section 3. Finally, we bring the paper

to an end with some concluding remarks.

Fig. 1. (a) Structure of the composite spherical nanoparticle and (b) compo

2. Polarizability formulations

In this section, an analysis for calculation of electric

polarizability of a three-layer nanoparticle is presented.

We also take into account EIT properties of the layers

composing this nanoparticle.

2.1. Single spherical metal–dielectric composite

nanoparticles

In this section, electromagnetic properties of a

metal–dielectric and dielectric–metal spherical compo-

site nanoparticle illustrated in Fig. 1(a) will be analyzed

with the help of the method described in [12], and

Chapters 14 [31] and 2 [32]. The particle is exposed to a

linearly polarized incident electric field described by~Eð~r; tÞ ¼ ~Eo expðið~k �~r � vtÞÞ where ~k denotes its

wave-vector. Now, a quasi-static approximation is used.

As shown in Fig. 1, the nano-structure under

investigation is placed in a host material and has a

spherical core of radius a and a spherical shell of radius

b. Following the notations assumed by Neeves and

Birnboim in [12], we denote the complex absolute

permittivity of the core, the shell, and the host material

by eC, eS, and eH, respectively.

Since the outer radius of the nanoparticle under

investigation is much smaller than the wavelength of the

incident plane wave, we can approximately determine

the electric field inside the nanoparticle with the help of

an electrostatic analysis. In this analysis, the nanopar-

ticle is assumed to be in a uniform electric field as

shown in Fig. 1(b). Under this assumption, the electric

field everywhere inside the nanoparticle can be

approximately expressed in terms of the amplitude of

the electric field and the relative permittivity of the

different layers of the nanoparticle. This has been

carried out in [12]. According to electromagnetic

theory, for obtaining response of the material to incident

electric field, at first electric potential and then electric

field must be calculated [12]. Then electric field outside

site spherical nanoparticle exposed to a uniform applied electric field.

G. Rostami et al. / Photonics and Nanostructures – Fundamentals and Applications 10 (2012) 102–111104

the composite spherical nanoparticle resembles the

electric field generated by a dipole whose effective

dipole moment ~p based on classical electromagnetic

theory is given by [12]:

~p ¼ a~EoP; (1-1)

where a denotes the polarizability of the composite

spherical nanoparticles and is expressed by [12]:

a ¼ 4peHb3 eSea � eHeb

eSea þ 2eHeb; (1-2)

where

ea , eC � ð3 � 2 f Þ þ 2 f � eS; (1-3)

eb , eC � f þ eS � ð3 � f Þ; (1-4)

with

f ¼ 1 � a

b

� �3

; (1-5)

in which f can be interpreted as the ratio of the volume

of the shell 4p(b3 � a3)/3 to the volume of composite

particle 4pb3/3 [12]. Using the effective dipole moment

given by (1-1) and (1-2), one can calculate the radiation

intensity of the equivalent dipole Idipole according to the

calculations presented in [31]. The result is

Idipole ¼1

hH

Ed � E�d

¼ nH

n0

� �jaj2ðkÞ6½ðjcj2 þ j’j2Þ � j’j2 sin2ðuÞ

þ 2Reðc � ’Þ cos2ðuÞ� � jE0j2;(1-6)

where k = 2p/l

cðkrÞ ¼ 1

krþ i

ðkrÞ2� 1

ðkrÞ3

!; (1-7a)

fðkrÞ ¼ 1

kr� 3i

ðkrÞ2þ 3

ðkrÞ3

!: (1-7b)

The composite nanoparticle cross sections for

scattering, absorption, and extinction (Csca, Cabs, and

Cext) as well as their quality factors can be obtained

from the relations presented in Chapter 2 of [32].

2.2. Resonance condition

From (1-2), it is obvious that the polarizability of the

composite nanoparticle can be maximized if the

denominator of (1-2) meets the resonance condition,

i.e., if the real part of the denominator vanishes. This

condition, which is also used in [12], results in

ReðeSea þ 2eHebÞ ¼ 0: (1-8)

In terms of real and imaginary part of the permittivity

functions, i.e., eC ¼ e0C þ ie00C; eS ¼ e0S þ ie00S , and

eH ¼ e0H þ ie00H , one can exress (1-8) as

ð3 � 2 f Þðe00Ce0S þ e0Ce00SÞ þ 2 f ð2e0Se00S þ e00Ce

0H þ e0Ce

00HÞ

þ 2ð3 � f Þðe0He00S þ e00He0SÞ ¼ 0: (1-9)

The above condition determines the resonance

frequencies for various compositions of the nanopar-

ticle as described below.

2.2.1. First case

In this case, we assume that the core is made of a

metal whose complex permittivity can be expressed as

eC ¼ 1 �v2

p

vðv þ igÞ ; (1-10)

where vp, and g are plasma frquency and free electron

relaxation frequency, respectively. In other words, we

model the core using a Drude model. The above ex-

pression is used in (1-9) to determine the resonance

frequency. For this purpose, a numerical computation is

required; however, in the special case of loss-less shell

and host medium, i.e., e00S ¼ e00H ¼ 0, the resonance

frequency for the system, that is equivalent to zero

imaginary part, is obtained as follows.

vr ¼ v p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið3 � 2 f Þ � e0S þ 2 f � e0H

ð3 � 2 f Þ � e0S þ 2 f � e0H þ 2 f � e0S2

þ2ð3 � f Þ � e0He0S

� g2

v2p

vuuut :

(1-11)

2.2.2. Second case

For metallic shell, the resonance frequencies can be

obtained as follows.

v6 þ b1v4 þ b2v

2 � b3 ¼ 0: (1-12)

In this equation coefficients b1, b2, and b3 defined as

b1 ,

2g2 � ð2 f þ P2Þ � P1 � v2p � 4v2

p � f

P2 þ 2 f

" #;

(1-13a)

;

– Fundamentals and Applications 10 (2012) 102–111 105

b2 ,

g4 � ð2 f þ P2Þ � P1 � v2p � g2 þ 2 f � v4

p

�4 f � v2p � g

P2 þ 2 f

26664

37775;(1-13b)

b3 , �2 f � v4

p � g2

P2 þ 2 f

" #; (1-13c)

P1 , ð3 � 2 f Þ � e0C þ 2ð3 � f Þ � e0H ; (1-14a)

P2 , ð3 � 2 f Þ � e0C þ 2ð3 � f Þ � e0H þ 2 f � e0C � e0H :

(1-14b)

According to Eqs. (1-11) and (1-12) the resonance

frequency can be tuned by applying the pump field.

2.3. Electromagnetically Induced Transparency

(EIT)

In this section, we utilize the EIT phenomenon as an

effective approach for realization of all-optical tuning of

the composite nanoparticles. Atomic systems with three

or more levels which are usually realized by quantum

dots can exhibit EIT. A simple atomic structure for

realization of EIT is illustrated in Fig. 2. In this figure,

we consider Si nanocrystal in SiO2 host to achieve EIT

at frequencies desirable for plasmonic systems. Type

and size of the nanoparticles are determined depending

G. Rostami et al. / Photonics and Nanostructures

Fig. 3. (a) Real and (b) imaginary parts of the susceptibility of the Si/SiO2 EIT

field (Dac = 0). For these figures, the Rabi frequency is set at 0.05 � 101

frequencies are equivalent to an applied field of 3.3 � 103 and 5.28 � 105

Fig. 2. Schematic of EIT atomic system (Si nanocrystal inside SiO2

vac = 5.6019 � 1015 rad/s).

on the plasmonic frequency range of the metal used in

the composite nanoparticles.

Using the well-known quantum mechanical density

matrix method [28–30] and assuming a three-level

atomic system like the Si/SiO2 nanoparticles proposed

above, we can obtain the optical susceptibility of the

EIT medium as [28]:

x ¼ x0 þ ix00; (1-15a)

x0 ¼ NajPabj2De0�hZ

g3ðg1 þ g3Þ þ D2 � g1g3 �V2

4

� �� �;

(1-15b)

x00 ¼ NajPabj2

e0�hZD2ðg1 þ g3Þ � g3 D2 � g1g3 �

V2

4

� �� �(1-15c)

Z ¼ D2ðg1 þ g3Þ2 þ D2 � g1g3 �V2

4

� �2

; (1-15d)

where D = vab = vS is the incident signal detuning.

Moreover, we assumed vac = vC. Here, g1 and g3 are

the decay rates for off-diagonal density matrix elements

related to the transitions a–b and a–c, respectively; Na is

the density of nanoparticles; and Pab and V ¼ PabE=�hare the dipole matrix element between a and b and the

Rabi frequency, respectively. In this relation, E is the

amplitude of the pump field. Diagrams of Fig. 3 which

are calculated using (1-15) show the real and imaginary

medium versus probe frequency (vS) (rad/s) in the case of tuned pump0 rad/s (without pump) and 8 � 1010 (with pump) rad/s. These Rabi

V/m, respectively.

host, Eab = 3.74 eV and Eac = 3.7 eV) (vab = 5.6628 � 1015 rad/s,

G. Rostami et al. / Photonics and Nanostructures – Fundamentals and Applications 10 (2012) 102–111106

Fig. 4. (a) Refractive index (refractive index of background medium n0 is 1.48). (b) Absorption coefficient of EIT medium versus pump field (pump

detuning is �10�6vS).

parts of the complex susceptibility. From the complex

susceptibility x, one can compute the refractive index

n ¼ffiffiffiffiffiffiffiffiffiffiffiffiffin2

0 þ xp

, where n0 is the background effective

refractive index. The computation results are given in

Fig. 4. Calculations of Fig. 4 were performed for a

background refractive index of n0 = 1.48, Na = 1023/m3,

Pab = e � 10�10 cm, y1 = 102 GHz, g3 = 100 MHz.

According to Fig. 4, we can tune the medium loss

and the value of the resonance frequency by the ampli-

tude of the pump signal. Note that for the proposed Si/

SiO2 nanocrystal and the parameters assumed above,

the refractive index can be varied from 1.425 to 1.525

for a pump electric field of 2.2 V/m. In the proposed

composite nanostructure, we can employ this 3-level

atomic system in the shell in order to control the

refractive index and absorption coefficient of this layer

as a function of the applied pump signal.

3. Results and discussion

In this section, the computed characteristics of the

proposed composite nanostructure are presented. We

will investigate effect applied pump field on polariz-

ability, resonance frequency, extinction quality factor,

and radiation properties of the composite nanoparticles.

First, we assume that the core of the composite

nanoparticles is made of gold with a radius of 40 nm and

that its shell which is capable of showing EIT has a

thickness of 10 nm which means that the total radius of

the composite nanoparticles amounts to 50 nm. Note

that we have assumed vp = 1.3 � 1016 rad/s and

g = 1.0753 � 1014 rad/s for the core material. In

Fig. 5, the absolute value and phase of the polarizability

of these composite nanoparticles are depicted as a

function of the applied pump field. For these diagrams,

the frequency of operation is set at 5.662797 � 1015 rad/

s. The diagrams are shown for various values of the host

refractive index.

In Fig. 6, we demonstrate the impact of the pump

field on the frequency response of polarizability. The

maximum value of polarizability corresponds to zero

detuning of the incident signal. For increasing pump

field, the refractive index of the shell is also decreased

so the equivalent optical path in the shell is reduced.

This results in a blue shift of the polarizability as can be

seen in Fig. 6(a). Further increase of the pump field will

increase the shell refractive index as a result of which a

red shift of the polarizability is observed. Also the

polarizability phase is influenced by the pump field as

can be seen in Fig. 6(b).

Fig. 7(a) illustrates the extinction quality factor of the

proposed composite nanostructure as a function of both

the host refractive index and applied pump field whereas

Fig. 7(b) is the frequency response of the extinction

quality factor for different values of the pump field.

According to Fig. 7, the extinction quality factor behaves

similar to the polarizability. Also, because of small

resonance frequency and large incident frequency the

input energy cannot absorbed by the cavity made by

nanoparticle and then extinction quality factor is large

enough.

Now, we assume that the core of the proposed

nanostructure is made of a medium capable of showing

EIT whereas the shell of the nanostructure is a metal.

The radius of the core and the thickness of the metallic

shell are 40 nm and 10 nm, respectively. Fig. 8

illustrates the calculated extinction quality factor for

this case. According to this figure, increasing the host

refractive index enhances optical coupling into the core

through metallic shell, consequently the extinction

quality factor increases. Note that the quality factor of

the present configuration of the nanoparticles is smaller

than that of the previous case. Fig. 8(a) also depicts the

G. Rostami et al. / Photonics and Nanostructures – Fundamentals and Applications 10 (2012) 102–111 107

Fig. 5. (a) Absolute value and (b) phase (b) of the polarizability of proposed composite spherical nanoparticles with metal (Au) core (radius = 40 nm

and dielectric shell with radius = 50 nm) (vp = 1.3 � 1016 rad/s, g = 1.0753 � 1014 rad/s) for various values of pump field and host refractive index

for incident frequency v = 5.662797 � 1015 rad/s [33].

impact of the pump field on the extinction quality factor

of the nanoparticles. In Fig. 8(b), the extinction quality

factor is shown as a function of frequency. As can be

seen, the resonance frequency increases by increasing

pump field. Furthermore, we observed that additional

increase of the pump field reduces the resonance

frequency. In comparison with the previous case, the

present configuration of the nanoparticles exhibits a

larger amount of frequency shift for the same pump

field. Based on displacement of the resonance frequency

small extinction quality factor can be described too. In

this case the resonance frequency increased because of

the selected geometry, so, the coupling of incident

frequency that is near to the resonance frequency is

increased too. So, the extinction quality factor must be

decreased that is illustrated in this figure.

G. Rostami et al. / Photonics and Nanostructures – Fundamentals and Applications 10 (2012) 102–111108

Fig. 6. (a) Magnitude and (b) phase of the polarizability as a function of frequency when the core is made of metal. Metal core (Au) (radius = 40 nm

and dielectric shell with radius = 50 nm) (vp = 1.3 � 1016 rad/s, g = 1.0753 � 1014 rad/s), for host refractive index n = 1.44 and incident frequency

v = 5.662797 � 1015 rad/s.

Fig. 7. Extinction quality factor of the proposed composite nanoparticles versus (a) pump field and host refractive index and (b) frequency. Metal

core (Au) (radius = 40 nm and dielectric shell with radius = 50 nm) (vp = 1.3 � 1016 rad/s, g = 1.0753 � 1014 rad/s).

G. Rostami et al. / Photonics and Nanostructures – Fundamentals and Applications 10 (2012) 102–111 109

Fig. 8. Extinction quality factor of the composite nanoparticles with EIT core and metallic shell versus (a) pump field and host refractive index and

(b) frequency dielectric core and metal shell (Au) (core radius = 40 nm and shell radius = 50 nm) (vp = 1.3 � 1016 rad/s, g = 1.0753 � 1014 rad/s).

For the present configuration of the nanoparticles,

Fig. 9(a) and (b) represents the magnitude and phase of

particle polarizability as a function of frequency and

applied pump field. These diagrams can be compared

with their counterparts, i.e., Fig. 6(a) and (b).

Fig. 9. Absolute value (a) and phase (b) of polarizab

In this section, we evaluated the proposed core–shell

structure as well as EIT for management of optical

properties of composite materials implemented by these

nanoparticles. We illustrated that by numerical simula-

tion considering EIT lets us tune optical properties of

ility versus frequency for different pump fields.

G. Rostami et al. / Photonics and Nanostructures – Fundamentals and Applications 10 (2012) 102–111110

medium implemented by these nanoparticles. We

considered two cases including core metal and shell

EIT and inverse. Our simulation show that the first case

lets the applied pump field change effectively the

refractive index of the medium than the second case.

This comes back to inherent properties of metals. In

shell metal pump light absorbed more and cannot

effectively change the refractive index.

4. Conclusion

In this paper, EIT phenomenon has been utilized to

introduce composite metal nanoparticles whose polar-

izability can be controlled using an optical pump signal.

We have shown that EIT can be used to tune optical

properties of the nanoparticles such as its extinction

quality factor. Also the resonance frequency of

polarizability can be controlled by the applied pump

signal. The first configuration investigated had a

metallic core and an EIT shell whereas the second

case has an EIT core and a metallic shell. The presented

computational results show that the first configuration

has a more acceptable performance as far as all-optical

tunability is concerned.

References

[1] J.P. Huang, K.W. Yu, Enhanced nonlinear optical response of

materials: composite effects, Phys. Rep. 431 (2006) 87–172.

[2] S.A. Maier, Plasmonic: Fundamentals and Applications, first

ed., Springer, 2007.

[3] S.A. Maier, Nanoparticle plasmon waveguides, in: S.I. Bozhe-

volnyi (Ed.), Plasmonic Nanoguides and Circuits, Pan Stanford,

2009.

[4] D. Prot, D.B. Stout, J. Lafait, N. Pincon, B. Palpant, S. Debrus,

Local electric field enhancements and large third-order optical

nonlinearity in nanocomposite materials, J. Opt. A: Pure Appl.

Opt. 4 (2002) S99–S102.

[5] T.S. Ahmadi, Z.L. Wang, T.C. Green, A. Henglein, M.A. El-

Sayed, Shape-controlled synthesis of colloidal platinum nano-

particles, Science 272 (January (5270)) (1996) 1924–1926.

[6] R.D. Averitt, S.L. Westcott, N.J. Halas, Linear optical properties

of gold nanoshells, J. Opt. Soc. Am. B 16 (October (10)) (1999)

1824–1832.

[7] S.J. Oldenburg, J.B. Jackson, S.L. Westcott, N.J. Halas, Infrared

extinction properties of gold nanoshells, Appl. Phys. Lett. 75

(November (19)) (1999) 2897–2899.

[8] A.M. Schwartzberg, T.Y. Olson, Ch.E. Talley, J.Z. Zhang, Syn-

thesis, characterization, and tunable optical properties of hollow

gold nanospheres, J. Phys. Chem. B 110 (40) (2006) 19935–

19944.

[9] G.D. Hale, J.B. Jackson, O.E. Shmakova, T.R. Lee, N.J. Halas,

Enhancing the active lifetime of luminescent semiconducting

polymers via doping with metal nanoshells, Appl. Phys. Lett. 78

(11) (2001) 1502–1504.

[10] S. Sershen, S.L. Westcott, J.L. West, N.J. Halas, An opto-

mechanical nanoshell–polymer composite, Appl. Phys. B 73

(2001) 379–381.

[11] D. Ricard, P. Roussignol, C. Flytzanis, Surface mediated en-

hancement of optical phase conjugation in metal colloids, Opt.

Lett. 10 (1985) 511–513.

[12] A.E. Neeves, M.H. Birnboim, Composite structures for the

enhancement of nonlinear-optical susceptibility, J. Opt. Soc.

Am. B 6 (April (4)) (1989) 787–796.

[13] S. Sershen, S.L. Westcott, N.J. Halas, J.L. West, Temperature-

sensitive polymer–nanoshell composites for photothermally

modulated drug delivery, J. Biomed. Mater. Res. 51 (2000)

293–298.

[14] Y. Sun, Y. Xia, Increased sensitivity of surface Plasmon reso-

nance of gold nanoshells compared to that of gold solid colloids

in response to environmental changes, Anal. Chem. 74 (October

(20)) (2002) 5297–5305.

[15] J.B. Jackson, S.L. Westcott, L.R. Hirsch, J.L. West, N.J. Halas,

Controlling the surface enhanced Raman effect via the nanoshell

geometry, Appl. Phys. Lett. 82 (January (2)) (2003) 257–259.

[16] E. Prodan, A. Lee, P. Nordlander, The effect of a dielectric core

and embedding medium on the polarizability of metallic nano-

shells, Chem. Phys. Lett. 360 (2002) 325–332.

[17] E. Prodan, P. Nordlander, N.J. Halas, Effects of dielectric

screening on the optical properties of metallic nanoshells, Chem.

Phys. Lett. 368 (2003) 94–101.

[18] E. Prodan, P. Nordlander, Structural tunability of the Plasmon

resonances in metallic nanoshells, Nano Lett. 3 (4) (2003) 543–

547.

[19] C. Noguez, Optical properties of isolated and supported metal

nanoparticles, Opt. Mater. 27 (2005) 1204–1211.

[20] O. Pena, U. Pal, L. Rodriguez-Fernandez, A. Crespo-Sosa, Linear

optical response of metallic nanoshells in different dielectric

media, J. Opt. Soc. Am. B 25 (August (8)) (2008) 1371–1379.

[21] S.E. Harris, Electromagnetically induced transparency, Phys.

Today 50 (July (7)) (1997) 36.

[22] K.J. Boller, A. Imamoglu, S.E. Harris, Observation of electro-

magnetically induced transparency, Phys. Rev. Lett. 66 (May

(20)) (1991) 2593–2596.

[23] B.S. Ham, P.R. Hemmer, M.S. Shahriar, Efficient electromag-

netically induced transparency in a rare-earth doped crystal, Opt.

Commun. 144 (1997) 227–230.

[24] G.B. Serapiglia, E. Paspalakis, C. Sirtori, K.L. Vodopyanov, C.C.

Phillips, Laser-induced quantum coherence in a semiconductor

quantum well, Phys. Rev. Lett. 84 (January (5)) (2000) 1019.

[25] S. Marcinkevicius, A. Gushterov, J.P. Reithmaier, Transient

electromagnetically induced transparency in self-assembled

quantum dots, Appl. Phys. Lett. 92 (2008) 041113.

[26] L.V. Hau, S.E. Harris, Z. Dutton, C.H. Behroozi, Light speed

reduction to 17 meters per second in an ultra cold atomic gas,

Nature 397 (February) (1999).

[27] M. Fleischhauer, A. Imamoglu, J.P. Marangos, Electromagneti-

cally induced transparency: optics in coherent media, Rev. Mod.

Phys. 77 (2005) 633.

[28] M.O. Scully, M.S. Zubairy, Quantum Optics, Cambridge Univ.

Press, Cambridge, UK, 1997.

[29] A. Neogi, T. Mozume, H. Yoshida, O. Wada, Intersubband

transition at 1.3 and 1.55 mm in novel coupled InGaAs/AlAsSb

quantum well structures, IEEE Photon. Technol. Lett. 11 (Janu-

ary (6)) (1999) 632–634.

[30] M. Davanco, P. Holmstrom, D.J. Blumenthal, L. Thylen, Direc-

tional coupler wavelength filters based on waveguides exhibiting

G. Rostami et al. / Photonics and Nanostructures – Fundamentals and Applications 10 (2012) 102–111 111

electromagnetically induced transparency, IEEE J. Quantum

Electron. 39 (April (4)) (2003) 608–613.

[31] J. David Jackson, Classical Electrodynamics, third ed., John

Wiley and Sons Press, 1999 (Chapter 14).

[32] C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light

by Small Particles, Wiley, 1983 (Chapter 2).

[33] P.B. Johnson, R.W. Christy, Optical constants of the noble

metals, Phys. Rev. B 6 (1972) 4370.