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Optics Communications 279 (2007) 291–297

Surface-plasmon wave at the planar interface of a metal filmand a structurally chiral medium

Akhlesh Lakhtakia *

CATMAS – Computational & Theoretical Materials Science Group, Department of Engineering Science and Mechanics,

Pennsylvania State University, University Park, PA 16802-6812, USA

Received 29 May 2007; received in revised form 10 July 2007; accepted 17 July 2007

Abstract

The solution of a boundary-value problem formulated for a modified Kretschmann configuration shows that a surface-plasmon wave can be excited at the planar interface of a sufficiently thin metal film and a nondissipative structurally chiralmedium, provided the exciting plane wave is p-polarized. An estimate of the wavenumber of the surface-plasmon wave also emergesthereby.� 2007 Elsevier B.V. All rights reserved.

Keywords: Chiral liquid crystal; Kretschmann configuration; Metal optics; Plasmonics; Sculptured thin film; Structural handedness; Surface-plasmon

1. Introduction

The propagation of electromagnetic waves localized toa planar interface of a bulk metal and a bulk dielectricmaterial can be traced back to a hundred years ago [1].Called surface-plasmon waves, they attenuate normallyaway from the interface, and are excited only with eva-nescent waves [2] that are usually generated by launchingnonevanescent waves toward different types of couplers[3].

In the Kretschmann configuration, the bulk metal is inthe form of a thin film of uniform thickness, bounded onone side by a high-refractive-index dielectric material andon the other side by a low-refractive-index dielectric

0030-4018/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.optcom.2007.07.026

* Tel.: +1 814 863 4319; fax: +1 814 863 7967.E-mail address: AXL4@psu.edu

material. A plane wave is launched in the optically den-ser dielectric material towards the metal film, in order toexcite a surface-plasmon wave at the interface of themetal with the optically rarer dielectric material [4].The plane wave must be p-polarized. The telltale signis a sharp peak in absorbance (i.e., a sharp trough inreflectance without a compensatory peak in transmit-tance) as the angle of incidence (with respect to thethickness direction) of the launched plane wave is chan-ged [5]. Because the angle of incidence for exciting thesurface-plasmon wave is a delicate function of the consti-tutive properties of all three materials, surface-plasmonwaves in the visible and the near-infrared regimes areexploited for sensing, imaging, and other applications[6–9].

Generally, the optically rarer medium is homogeneous,normal to its planar interface with the metal film at leastwithin the range of the surface-plasmon field. In thiscommunication, this medium is taken to be continuouslynonhomogeneous in the thickness direction. Specifically,the optically rarer medium is structurally chiral, withthe axis of helicoidal nonhomogeneity oriented parallel

292 A. Lakhtakia / Optics Communications 279 (2007) 291–297

to the thickness direction.1 To my knowledge, the solu-tion of the associated boundary-value problem has neverbeen reported before, and its application should drawboth chiral liquid crystals and chiral sculptured thin filmsinto the plasmonics arena.

The plan of this communication is as follows: Section 2contains a description of a modified Kretschmann configu-ration, with the optically rarer medium replaced by a struc-turally chiral medium (SCM) slab of sufficient thickness.The combination of the metal film and the SCM slab issandwiched between two half-spaces occupied by the sameisotropic dielectric material that is optically denser than thechosen SCM. A brief description of the electromagneticboundary-value problem is also presented. Section 3 con-tains numerical results to show that a surface-plasmonwave can be excited at the planar interface of a metal filmand a structurally chiral medium, provided the incidentplane wave is p-polarized.

In the following sections, an exp(�ixt) time-dependenceis implicit, with x denoting the angular frequency. Thefree-space wavenumber, the free-space wavelength, andthe intrinsic impedance of free space are denoted byk0 ¼ x

ffiffiffiffiffiffiffiffiffi�0l0

p, k0 = 2p/k0, and g0 ¼

ffiffiffiffiffiffiffiffiffiffiffil0=�0

p, respectively,

with l0 and �0 being the permeability and permittivity offree space. Vectors are in boldface, dyadics underlinedtwice; column vectors are in boldface and enclosed withinsquare brackets, while matrixes are underlined twice andsimilarly bracketed. Cartesian unit vectors are identifiedas ux, uy and uz.

2. Theory

In conformance with the Kretschmann configuration forlaunching surface-plasmon waves, the half-space z 6 0 is

1 An object is said to be chiral if it cannot be made to coincide with itsmirror-image by translations and/or rotations. There are two types ofchiral mediums: (i) microscopically or molecularly chiral mediums, and (ii)structurally chiral mediums. The first type of mediums either have chiralmolecules or are composite materials made by embedding electricallysmall helixes (and similar inclusions of chiral shapes) in a host medium.Materials comprising chiral molecules have been known for about twohundred years, as a perusal of an anthology of milestone papers [10] willshow to the interested reader. These materials are generally isotropic [11].Composite materials comprising electrically small chiral inclusions werefirst reported in 1898 [12], and can be either isotropic [13,14] or anisotropic[15]. The first type of chiral mediums can be considered as eitherhomogeneous or nonhomogeneous continuums. In contrast, the secondtype of chiral mediums can only be nonhomogeneous and anisotropiccontinuums at the length-scales of interest, their constitutive parametersvarying periodically in a chiral manner about a fixed axis. Take away thenonhomogeneity of a SCM, and its (macroscopic) chirality will alsovanish. This communication is concerned about the second type of chiralmediums, which are exemplfied by chiral liquid crystals [16, Chap. 4] andchiral sculptured thin films [17, Chap. 9]. Parenthetically, a third type of‘‘chiral’’ medium has recently entered scientific literature [18,19]. Such amaterial is made by depositing spirals (and similar objects) on some flatsurface. Spirals, being essentially two-dimensional objects, cannot bechiral, and ‘‘planar chirality’’ [20] is an infelicitous term that ought to bereplaced by a meaningful term.

occupied by a homogeneous, isotropic, dielectric materialdescribed by the relative permittivity scalar �‘. Dissipationin this material is considered to be negligible and its refrac-tive index n‘ ¼

ffiffiffiffi�‘p

is real-valued and positive. The laminarregion 0 6 z 6 Lmet is occupied by a metal with relativepermittivity scalar �met. A structurally chiral material occu-pies the region Lmet 6 z 6 Lmet + Lscm, the dielectric prop-erties of this material being described in the followingsubsection. Finally, without significant loss of generalityin the present context, the half-space z P Lmet + Lscm istaken to be occupied by the same material as fills thehalf-space z 6 0. All constitutive properties generallydepend on the angular frequency x.

A plane wave, propagating in the half-space z 6 0 at anangle h 2 [0,p/2) to the z axis and at an angle w 2 [0, 2p) tothe x axis in the xy plane, is incident on the metal-coatedSCM slab. The electromagnetic field phasors associatedwith the incident plane wave are represented as

EincðrÞ ¼ ðassþ appþÞeijðx cos wþy sin wÞeik0n‘z cos h

HincðrÞ ¼ n‘g0ðaspþ � apsÞeijðx cos wþy sin wÞeik0n‘z cos h

); z 6 0:

ð1ÞThe amplitudes of the s- and the p-polarized components ofthe incident plane wave, denoted by as and ap, respectively,are assumed given, whereas

j ¼ k0n‘ sin h

s ¼ �ux sin wþ uy cos w

p� ¼ � ux cos wþ uy sin w� �

cos hþ uz sin h

9>=>;: ð2Þ

The reflected electromagnetic field phasors are expressedas

ErefðrÞ ¼ ðrssþ rpp�Þeijðx cos wþy sin wÞe�ik0n‘z cos h

HrefðrÞ ¼ n‘g0ðrsp� � rpsÞeijðx cos wþy sin wÞe�ik0n‘z cos h

); z 6 0;

ð3Þand the transmitted electromagnetic field phasors as

EtrðrÞ ¼ ðtssþ tppþÞeijðxcoswþy sinwÞeik0n‘ðz�LRÞcosh

HtrðrÞ ¼ n‘g0ðtspþ � tpsÞeijðxcoswþy sinwÞeik0n‘ðz�LRÞcosh

); z P LR;

ð4Þwhere LR = Lmet + Lscm. The reflection amplitudes rs and rp,as well as the transmission amplitudes ts and tp, have to bedetermined by the solution of a boundary-value problem.

2.1. Constitutive relations of the SCM

The frequency-domain electromagnetic constitutive rela-tions of the SCM slab can be written as [17]

DðrÞ ¼ �0�¼scmðzÞ � EðrÞ

BðrÞ ¼ l0HðrÞ

); Lmet 6 z 6 LR: ð5Þ

The frequency-dependent relative permittivity dyadic�¼scmðzÞ is factorable as

A. Lakhtakia / Optics Communications 279 (2007) 291–297 293

�¼scmðzÞ ¼ S

¼zðz� LmetÞ � S¼yðvÞ � �¼refscm � S¼

Ty ðvÞ � S¼

Tz ðz� LmetÞ;

Lmet 6 z 6 LR;

where the reference relative permittivity dyadic

�¼

refscm ¼ �auzuz þ �buxux þ �cuy uy : ð6Þ

The dyadic function

S¼zðzÞ¼ ðuxuxþ uy uyÞcos

pzX

� �þhðuy ux� uxuyÞsin

pzX

� �þ uzuz;

ð7Þ

K¼

h i¼

� sin w � cos w cos h � sin w cos w cos h

cos w � sin w cos h cos w sin w cos h

� n‘g0

� �cos w cos h n‘

g0

� �sin w n‘

g0

� �cos w cos h n‘

g0

� �sin w

� n‘g0

� �sin w cos h � n‘

g0

� �cos w n‘

g0

� �sin w cos h � n‘

g0

� �cos w

2666664

3777775: ð10Þ

B¼scm

h i¼

cosðpLscm=XÞ �h sinðpLscm=XÞ 0 0

h sinðpLscm=XÞ cosðpLscm=XÞ 0 0

0 0 cosðpLscm=XÞ �h sinðpLscm=XÞ0 0 h sinðpLscm=XÞ cosðpLscm=XÞ

26664

37775 ð11Þ

P¼met

h i¼

0 0 0 xl0

0 0 �xl0 0

0 �x�0�met 0 0

x�0�met 0 0 0

26664

37775þ j2

x�0�met

0 0 cosw sinw � cos2 w

0 0 sin2 w � cosw sinw

0 0 0 0

0 0 0 0

26664

37775þ j2

xl0

0 0 0 0

0 0 0 0

� cosw sinw cos2 w 0 0

� sin2 w cosw sinw 0 0

26664

37775:

ð12Þ

contains 2X as the structural period and h = ±1 as thestructural-handedness parameter; thus, the SCM is helicoi-dally nonhomogeneous along the z axis. The tilt dyadic

S¼yðvÞ ¼ ðuxux þ uzuzÞ cos vþ ðuzux � uxuzÞ sin vþ uy uy ð8Þ

involves the angle v 2 [0,p/2]. The superscript T denotes thetranspose.

2.2. Boundary-value problem

The procedure to determine the amplitudes rs, rp, ts, andtp in terms of as and ap is standard [17, Chap. 10], as indeedis true of problems involving other types of multilayeredstructures [21,22]. Interested readers are referred also tothe detailed procedure provided earlier in this journal[23]. It suffices to state here that the following set of fouralgebraic equations emerges (in matrix notation):

ts

tp

0

0

2666437775¼ K

¼

h i�1

� B¼scm

h i� M¼0scm

h i�exp i P

¼met

h iLmet

� �� K¼

h i�

as

ap

rs

rp

26664

37775:

ð9ÞThe procedure to compute the 4 · 4 matrix M

¼0scm

h iis far

too cumbersome for reproduction here, the interested read-

er being referred to [17, Sec. 9.2.2]. The 4 · 4 matrix K¼

h idepends on the refractive index n‘ as well as the angles hand w as follows:

The remaining two matrixes appearing in (9) are

and

The solution of (9) yields the reflection and transmissioncoefficients that appear as the elements of the 2 · 2 ma-trixes in the following relations:

rs

rp

� �¼

rss rsp

rps rpp

� �as

ap

� �;

ts

tp

� �¼

tss tsp

tps tpp

� �as

ap

� �: ð13Þ

Co-polarized coefficients have both subscripts identical,but cross-polarized coefficients do not. The square of themagnitude of a reflection or transmission coefficient is thecorresponding reflectance or transmittance; thus,Rsp = jrspj2 is the reflectance corresponding to the reflectioncoefficient rsp, and so on. The principle of conservation ofenergy mandates the constraints Rss + Rps + Tss + Tps 6 1and Rpp + Rsp + Tpp + Tsp 6 1, the inequalities turning toequalities only in the absence of dissipation in the region0 < z < LR.

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

Tsp

Rsp

Ap

Tpp

Rpp

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

00

00

00

00

00

(a) L = 0 nmmet

(b) L = 5 nmmet

(c) L = 10 nmmet

(d) L = 15 nmmet

(e) L = 20 nmmet

Angle of incidence θ (deg)

Ref

lect

ance

, Tra

nsm

ittan

ce, o

r A

bsor

banc

e

55.98 deg

52.33 deg

51.13 deg

50.75 deg

Fig. 1. Reflectances (Rpp and Rsp), transmittances (Tpp and Tsp), and theabsorbance as functions of h when w = 0�, k0 = 633 nm, and the incidentplane wave is p-polarized. The SCM is described by the followingparameters: �a = 2.7, �b = 3.0, �c = 2.72, v = 30�, X = 200 nm, h = ±1,and Lscm = 2X. The relative permittivity of the metal is �met = �56 + i21,and that of the ambient medium is �‘ = 5. (a) Lmet = 0, (b) Lmet = 5 nm, (c)Lmet = 10 nm, (d) Lmet = 15 nm, and (e) Lmet = 20 nm. The values of h formaximum Ap are identified for different non-zero values of Lmet in the plots.

294 A. Lakhtakia / Optics Communications 279 (2007) 291–297

3. Numerical results and discussion

All eight reflectances and transmittances at the free-space wavelength k0 = 633 nm were computed as func-tions of the angles h and w. The SCM was chosen to pos-sess the following parameters: �a = 2.7, �b = 3.0, �c = 2.72,v = 30�, X = 200 nm, and h = ±1. These representativevalues have often been used for theoretical works on chi-ral sculptured thin films. The relative permittivity of theambient medium was chosen to be �‘ = 5, and that ofthe metal (typ. aluminum) as �met = �56 + i21. For thechosen constitutive parameters, the constraintsRss + Rps + Tss + Tps = 1 and Rpp + Rsp + Tpp + Tsp = 1hold in the absence of the metal film, which was satisfiedto within ±0.01% error for all results provided here.Also, when the SCM was metamorphosed into an isotro-pic and homogeneous material (by setting �a = �b = �c),the computer program yielded the same results as pub-lished by Mansuripur and Li [25].

Fig. 1 shows the variations of the reflectances (Rpp andRsp), transmittances (Tpp and Tsp), and the absorbance

Ap ¼ 1� ðRpp þ Rsp þ T pp þ T spÞ ð14Þwith h, when w = 0� and the incident plane wave is p-polar-ized. The SCM is 1-period thick (i.e., Lscm = 2X), whereasthe thickness of the metal film varies from 0 to 20 nm insteps of 5 nm. A rapid increase in the absorbance Ap indi-cates the excitation of a surface-plasmon wave [25]. Thevalues of h for maximum Ap are identified for differentnon-zero values of Lmet in Fig. 1. For instance, the absor-bance equals 0.93 at h = 52.33�, when Lmet = 10 nm. AsLmet increases, the maximum-absorbance value of hdecreases slightly, whereas the maximum absorbance de-creases as well after peaking.

The calculations for Fig. 1 were repeated for higher val-ues of Lscm/X. As the thickness of the SCM slab wasincreased, the maximum-Ap value of h for a specific valueof Lmet began to converge. This is exemplified by the plotsof Ap vs. h in Fig. 2 for Lscm/X = 4 and Fig. 3 for Lscm/X = 10. Thus, the maximum value of Ap is 0.975 ath = 51.87� in Fig. 2b and also at h = 51.81� in Fig. 3b, bothfor Lmet = 10 nm.

A comparison of the three figures indicates that the 5-period-thick SCM slab is sufficiently thick as to be equiva-lent to a SCM half-space, which would be required in theusual theoretical treatment of the (unmodified) Kretsch-mann configuration [2]. Parenthetically, the planewaveresponse of a SCM half-space cannot be obtained unlessthe wavevector of the incident plane wave is aligned paral-lel to the z axis [24], because a sufficiently general eigenmo-dal decomposition of the electromagnetic fields isunavailable [17, Chap. 9].

When �a = �b = �c = 2.81 (the average of the three eigen-values of �

¼refscm) were set, along with Lscm = 10X, the maxi-

mum value of Ap changed from 0.9623 at h = 50.66� inFig. 3d to 0.9639 at h = 51.00�. This could indicate thatthe surface-plasmon wavenumber j is not very sensitive

to the structural chirality of the SCM; however, the wave-fields in the SCM slab must display a structurally chiralnature.

A. Lakhtakia / Optics Communications 279 (2007) 291–297 295

Were the SCM to be replaced by an isotropic dielectricmaterial of relative permittivity �iso and the metal film wereabsent, total internal reflection would occur forh P sin�1

ffiffiffiffiffiffiffiffiffiffiffiffi�iso=�‘

p. Then, sin�1

ffiffiffiffiffiffiffiffiffiffiffiffi�iso=�‘

pis the critical angle

and k0ffiffiffiffiffiffi�isop

is an estimate of the wavenumber of the sur-face-plasmon wave [25]. But a simple formulation of a‘‘critical angle’’ is not possible with the SCM. A useful esti-mate can, however, be made, by setting �iso = max

00

(a) L = 0 nmmet

Angle of incidence θ (deg)

Ref

lect

ance

, Tra

nsm

ittan

ce, o

r A

bsor

banc

e

00

00

00

00

(b) L = 5 nmmet

(c) L = 10 nmmet

(d) L = 15 nmmet

(e) L = 20 nmmet

51.87 deg

50.68 deg

50.33 deg

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

Tsp

Rsp

Ap

Tpp

Rpp

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

55.76 deg

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

Fig. 2. Same as Fig. 1, except that Lscm = 4X.

(�a, �b, �c), whereby the ‘‘critical angle’’ equalssin�1

ffiffiffiffiffiffiffiffiffiffi�c=�‘

p¼ 50:77� for the chosen parameters. Fig. 2b–

e and Fig. 3b–e indicate that the surface-plasmon wave isindeed excited in the neighborhood of this estimate of this‘‘critical angle’’, which is also ratified by the plots forLmet = 0 in Fig. 2a and Fig. 3a. Although further researchappears necessary when �a, �b, and �c are all significantlydifferent from each other, it is clear that a surface-plasmon

00

(a) L = 0 nmmet

Ref

lect

ance

, Tra

nsm

ittan

ce, o

r A

bsor

banc

e

00

00

00

(b) L = 5 nmmet

(c) L = 10 nmmet

(e) L = 15 nmmet

(d) L = 20 nmmet

Angle of incidence θ (deg)

51.81 deg

50.66 deg

50.30 deg

Tsp

Rsp

Ap

Tpp

Rpp55.76 deg

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

00

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

Fig. 3. Same as Fig. 1, except that Lscm = 10X.

(a) L = 0 nmmet

(b) L = 5 nmmet

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

0.2

0.4

0.6

0.8

1

Tps

Rps

As

Tss

Rss

00

296 A. Lakhtakia / Optics Communications 279 (2007) 291–297

wave can be excited in the present configuration, providedthat �‘ exceeds the maximum eigenvalue of �

¼refscm.

The surface-plasmon wavenumber j is also sensitive tothe choice of the metal, provided of course that the realpart of �met is negative. Calculations for Fig. 3d wererepeated with one-half of the relative permittivity of alumi-num. The maximum value of Ap changed from 0.9623 ath = 50.66� in Fig. 3d to 0.9192 at h = 53.90�, as could beexpected from the standard treatment for the planar inter-face of a metal and a homogeneous, isotropic dielectricmaterial [25].

In order to confirm the excitation of a surface-plasmonwave at the interface of the metal and the SCM, the time-averaged Poynting vector P(z) = (1/2)Re [E(z) · H*(z)] wasplotted against z 2 (0,Lmet) for all calculations reported inthe previous three figures. Shown in Fig. 4 are the cartesiancomponents of P(z) vs. z in the metal film, when h = 51.81�,Lmet = 10 nm, Lscm = 10X, and all other parameters are thesame as for Fig. 3. The magnitude of Pz decreases and thatof Px increases, both monotonically, as one traverses themetal film from the interface with the medium of incidence

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

z/Lmet

zP

0 0.2 0.4 0.6 0.8 1

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 0.2 0.4 0.6 0.8 1

-0.0025

0

0.0025

0.005

0.0075

0.01

0.0125

z/Lmet

z/Lmet

xPyP

Fig. 4. Cartesian components of the time-averaged Poynting vector P(z)in the metal film vs. z 2 (0,Lmet) when a surface-plasmon wave has beenexcited. The conditions are the same as for Fig. 3c, except that h = 1. Forh = �1, the y-directed component of P(z) is different in sign but not inmagnitude.

(z = 0) to the interface with the SCM (z = Lmet). Clearlythus, the presence of the surface-plasmon wave localizedto the interface z = Lmet is confirmed.

00

00

00

(c) L = 10 nmmet

(d) L = 15 nmmet

(e) L = 20 nmmet

Angle of incidence θ (deg)

Ref

lect

ance

, Tra

nsm

ittan

ce, o

r A

bsor

banc

e

10 20 30 40 50 60 70 80 90

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

00

Fig. 5. Reflectances (Rss and Rps), transmittances (Tss and Tps), and theabsorbance as functions of h when w = 0�, k0 = 633 nm, and the incidentplane wave is s-polarized. The SCM is described by the followingparameters: �a = 2.7, �b = 3.0, �c = 2.72, v = 30�, X = 200 nm, h = ±1,and Lscm = 2X. The relative permittivity of the metal is �met = �56 + i21,and that of the ambient medium is �‘ = 5. (a) Lmet = 0, (b) Lmet = 5 nm,(c) Lmet = 10 nm, (d) Lmet = 15 nm, and (e) Lmet = 20 nm.

A. Lakhtakia / Optics Communications 279 (2007) 291–297 297

Fig. 4 also shows the effects of the anisotropy and thestructural handedness of the SCM. These effects are mani-fested in the y-directed component of P(z) in the metal film.Were the SCM to be replaced by an isotropic material, thiscomponent of P(z) would be identically zero for all z. Also,the sign of this component depends on whether h = 1 orh = �1.

Although all numerical results presented were calculatedfor w = 0�, calculations were made for other values of w aswell. No significant effect of w on the maximum-Ap value ofh was detected, possibly because �a and �c were taken to bequite close to each other.

Fig. 5 shows the variations of the relevant reflectancesand transmittances, and of the absorbance

As ¼ 1� ðRss þ Rps þ T ss þ T psÞ; ð15Þ

with h for the same parameters as for Fig. 1, except that theincident plane wave is s-polarized. Evidence of the excita-tion of a surface-plasmon wave is absent from this figure,just as it would be if the SCM slab were to be replacedby a slab made of a homogeneous, isotropic dielectricmaterial [25]. Calculations for higher values of the ratioLscm/X also did not reveal the existence of a surface-plas-mon wave for s-polarized incidence.

To conclude, the solution of a boundary-value problemformulated for a modified Kretschmann configurationshows that a surface-plasmon wave can be excited at theplanar interface of a sufficiently thin metal film and a non-dissipative structurally chiral medium, provided that (i) theincident plane wave is p-polarized, and (ii) the wavenumber(i.e., j) of the surface-plasmon wave roughly equalsk0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffimaxð�a; �b; �cÞ

p. An estimate of the wavenumber of the

surface-plasmon wave may have to be obtained graphically(by setting Lmet = 0), if �a,b,c are very different from eachother. Future work will be focused on exploring the depen-dence of the surface-plasmon wave on the morphology ofthe SCM slab [26], as well as on applications for sensingfluids absorbed in porous SCM slabs [27].

Acknowledgement

This work was supported in part by the Charles GodfreyBinder Endowment.

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