Propagation of surface polaritons over macroscopic distances at optical frequencies

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Solid State Communications, Vol. 88, Nos. 11/12, pp. 1067-1071, 1993. Printed in Great Britain.

0038-1098/9356.00+.00 Pergamon Press Ltd

PROPAGATION OF SURFACE POLARITONS OVER MACROSCOPIC DISTANCES AT OPTICAL FREQUENCIES* J. Schoenwald, E. Burstein and J.M. Elson • Department of Physics and Laboratory for Research'on the Structure of Matter, University of Pennsylvania, Philadelphia, Pennsylvania 19104

(Accepted 2 November 1972)

We report the propagation of surface polaritons over macroscopic distances along copper-air interfaces at 10.6/am wavelength using a prism coupling technique for generating and detecting the surface modes. The measured propagation length ( ~ 1.6cm) is in agreement with theoretical estimates based on available optical data. The surface polaritons are easily observed visually using Radelin thermographic phosphor paper.

RESEARCH on the nature of surface polaritons (i.e. surface EM waves involving photons coupled to surface electric dipole or magnetic dipole excitations) occurring at the interface of dielectric (or magnetic)media has focussed primarily on their dispersion curves and on their coupling with bulk EM waves. Little attention has been given to the distances which they travel at optical frequencies, although it is well known that the TEM modes of'strip' transmission lines, which are in fact plasmon-type surface polaritons, propagate large distances at microwave frequencies. We present here the results of an investigation of the propagation of surface polaritons along a copperair interface at 10.6 , m using a 'prism coupling' technique to generate and to detect the surface modes. The data obtained indicate a propagation length of ~ 1.6cm. Similar results are expected for optical phonon-type surface polaritons at dielectric-air interfaces. The dispersion relation of the surface polariton at the interface of two semi.infinite, isotropic 'dielectric' media, a_and b, characterized by frequency dependent~ complex dielectric constants e(~o) = e, (co) + ie2 (co) is given by1 * Research supported by the Advanced Research Projects Agency, the National Sdence Foundation, and the U.S. Office of Naval Research.

co 2 e o ( ~ )

~" :

eb(¢o)

c 2 e_o(,~) + e.b(,,,) :

k°2'7'2"(~)

(1) where ks,, and ~7o,,are the frequency dependent wavevector and complex refractive index, respectively, o f the surface polaritons, and ko : ¢o/c. Since we are concerned with surface polaritons excited by bulk radiation of well defined frequency, we consider co real and treat the wavevector as complex, i.e. ks, -- kl + &2. The decay constants ~ and a b which characterize the decay in amplitude with distance from the interface in the two media are functions of e(w) and ks,, and are therefore also complex. 2 The surface polaritons are TM modes. If ks, is along x, and the interface normal is alongy, with medium a occupying the y > 0 space, the time average energy flow vector P(x), representing the average energy passing per unit time through an area having unit width (along z) and length extending fromy = -- oo to y = + oo is given by P(k,x) =

T dy S°.v(k) exp [--2k:x] exp [~:2ae,by] . . . .

~m=m

= P6(x) + Pb(x) ~ -

¢2ao

+

Previotmlypublished in: SolidState Commun. Vol. 12, No. 3, pp. 185-189 (1973)

exp [--2k2x]

(2)

1068

PROPAGATION OF SURFACE POLARITONS C

S°'b(k)-- 8n Re (Ea_,_b× I'll.b)x-o._ _ y-o

(3) where ~.~(k) is the time average Poynting vector in medium a or b_at x = 0, y = 0. The quantity L = 1/2/ci represents the 'propagation length' of the surface mode, i.e. the distance at which the mode intensity decays to l/e of its initial value. We will assume that there is no surface roughnessinduced conversion of the surface polaritons into bulk radiation, and we neglect attenuation due to non-linear interactions. Since we are interested in modes where L is large, we consider modes having Ik2 I< ~ ee(co). Under these circumstances, we obtain from the dispersion relation [equation (I)] the following expression for 2k2 :

+ 2k,--77,, e% L

'

+

+

e_l, + e

J [4(a)]

where we have neglected ea'2(w) and eo~ (w) relative to e.~.1(co) and et=(co) in the denominator and omitted the frequency dependence designations. At frequencies where e~2 < ~1 and e~2 < ~ 1 , equation [4(@] simplifies to

2k2 "" e~,]---~ L~,~'/

~ 2 + eo..2 •

[4(b)] Correspondingly, pa(x) and po(x) are given by

~ ~(x) --

/ea, 1 w 2 el, ] ~..o2 k [~-~-) ps(x) . . 16"n . . c -'F',~. exp [-2k2x] k ~_vl (5)

where E~x is the magnitude of E~ at x = 0 , y = 0, Clearly, the energy flow in b_is smaller than and in the opposite direction to that in a_~.Furthermore the ratio pg(x)/~(x) represents the ratio of the energy in b_to that in g. This follows from the relation p a, b(X) = v& ~ Ue,b(X) > , where us is the velocity of energy transport and < Ua b(x) > is the average energy per unit area.

Vol. 88, Nos. 11/12

Table 1. Propagation length, relaxation time and decay constants for infrared surface polaritons at copper air interfaces ~m

1

5

10

19

--el e2 L

39* 1.61 * 0.15mm 260A

1000t 150? 0.54cm 250A

4000~ 1200t 1.9cm 250A

1/~

25/~

120/~

9000~ "-5700t 6.1cm 320A 290~

6oa = llctoa 6.,r = 1 / a ~

* Bulk, annealed and electropolished (reference 4). ~f Evaporated film (reference 5).

Equation (4) can be used to estimate the propagation length of surface polaritons at various interfaces for which data on ea and eb are available. In the case of metal-air interfaces s u b estimates indicate that L is quite small (L < 10 "4cm) in the visible. However, L increases rapidly with increasing wavelength, a Values of k= and L for copper-air interfaces, which have the largest values of L in the infrared based on data for e bl and e~2 derived from optical measurements,l'~ are given in Table 1, together with the corresponding value o f 6 ~ = 1/o~i and 6cu = 1/at. The corresponding data for silver-air and gold--air interfaces are not appreciably different. Similar considerations apply to optical phonontype surface polaritons at dielectric-air interfaces. As co decreases towards coT, the frequency of the q -~ 0 TO phonons, the fraction of the total energy of the surface polariton within the dielectric decreases rapidly. Thus L increases appreciably, despite the increase in e t l , as co approaches ~ r . In the case of MgO-air interfaces, L ~ 0.5cm at CO~COT= 1.01. Bemuse of its greater flexibility, the prism coupling technique s rather than the grating-coupling technique 7 was used to convert bulk polaritons into surface polaritons and to back convert surface polaritons into bulk radiation for optical detection. These techniques are essentially identical to those used in thin film guided optics, s'e and the factors which determine the interconversion efficiencies are quite similar.

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PROPACATION OF SURFACE POLARITONS

(o)

1069

Right angle input and output prisms were fabricated from infrared window quality single crystals of NaCI. At 10.6/zm, the refractive index of NaCl is 1.49 and the crilical angle 0¢ is 42 °. Because the dielectric constant of the metal at this wavelength is very much larger than that of air, it is evident from equation (1) that ~h, ~ 1, and accordingly, 0 ~ 0e.

• .

_ C / , / / / / / / / / / / / / /

Eb K ' ~ / / / S ~ F A C E ACTIVE/ / "L MIO,UU •

The coupling characteristic of NaCl prisms was confirmed in an ATR measurement, using the experimental configuration of Fig. l(a) with a gapg ~- 15~m. The data [Fig. 2(a)] clearly shows a prominent dip in reflectivity at 0 ~ 42*.

(b)

~

--_2_

. ~ z / / / - z / / / / / /

///

"fY

.~o,u.

Y///;,//V///,

FIG. 1. Experimental configurations for (a) single prism ATR measurements and (b) double prism measurement of propagation length L. Prisms are spaced a variable distance g above metal surface. In the prism-coupling or ATR (attenuated total reflection) technique, a prism of refractive index %, is placed close to the metal surface with one of its polished faces parallel to the metal-air interface [Fig. l(a)]. A bulk polariton mode propagating in the prism, at an angle 0 to the normal of the prism-air interface, couples to a surface polariton mode when rlnke sin 0 = k~, ----%,,ko. e The strength of the coupling between bulk and surface modes is, among other things, dependent upon the 'gap' (g) between the prism and the 'air-metal interface. Two truncated prisms were used - an input prism to convert bulk polaritons into surface polaritons ('generate') and an output prism to back-convert for optical detection. The truncated edges of both prisms faced one another [Fig. l(a)]. The input EM beam was directed at the prism close to the truncated edge. The surface polaritons reaching the output prism back-con. vert into radiation at the coupling angle 0. The 10.6pm output of a 250roW CW COs laser was used as the source of input radiation. At this wavelength, the decay length of the surface polariton in copper 8 ~ = i / a ~ 250A. We therefore used copper films (~-3000A thick) evaporated on standard glass microslides as an effective semi-infinite metal medium.

The experimental configuration used to 'transmit' (generate) and 'receive' (detect) propagating surface polaritons is shown in Fi~ l(b). The gaps for both prisms were in the "range of 3-5#m. No effort was made to adjust the input prism gap for maximum 'generation' efficiency. An a.c. pyroelectric detector and beam chopper were used to observe and measure the intensity of the bulk EM radiation at the output prism, and the ATR. The propagating surface polaritons were also observed visually using Radelin thermographic phosphor paper, x° whose yellow luminescence under ultraviolet illumination is thermally quenched by infrared radiation. When a sheet section of phosphor paper was placed above the output prism, a dark spot appeared where the output beam was incident. When a second sheet section of paper was placed between the two prisms in contact with the film surface and normal to the direction of propagation a darkened fan-like pattern appeared along the lower edge of the paper and the dark spot on the sheet above the output prism disappeared. The dark spot also disappeared when a line was scratched on the metal film across the path of propagation at a point between the two prisms due to mode conversion at the scratch. Using a polarized input beam, we were able to observe a dark spot at the output prism only when the input beam wasp-polarized (parallel to the plane of incidence), in agreement with the fact that surface polafitons at the interface of two isotropic media are polarized in the sagittal plane and can therefore only prism-couple to the p-component of bulk radiation.

1(

PROPAGATION OF SURFACE POLARITONS

Voi. 88, Nos. 11/12

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DISTANCE 8[TWE[N PRISMS (=r~}

FIG. 2. Normalized intensity obtained (a) vs. angle of incidence 0 in single prism ATR measurement and (b) vs. the distance between the input and output prisms in determining the propagation length L. The intensity of the output beam, normalized to that of the input beam, was measured as the distance between the input and output prism was changed. A semi-logarithmic plot of output intensity versus prism separation is given in Fig. 2(b). From the slope, which corresponds to - 2 k 2 , we obtain the value L = 1/2k2 = 0.3cm for the propagation length. This value is appreciably smaller that the value (L = 1.9cm) estimated from optical data (Table 1). The relatively large discrepancy between the two values is tentatively ascribed to: radiative decay induced by surface roughness and by inhomogeneities in the evaporated copper film, losses in the oxide layer formed on the copper film in air, and neglecting non-uniformity and wave. vector dependence in the dielectric constant of the metal. ' Our experiments demonstrate that surface polaritons at semi4nfmite metal-air interfaces propagate macroscopic distances at optical frequencies. Macroscopic propagation should also occur for surface polaritons at dielectric-air interfaces which involve photons

coupled to surface optical phonons. In the absence of surface roughness and bulk inhomoganeity induced conversion of surface to bulk modes, the propagation length is governed by the imaginary part of the dielectric constants of the adjacent media and the fraction of the surface polariton energy within each of the two media. 11 The ability to transmit surface polaritons over" macroscopic distances at the interface of two semiinfinite media provides one with the opportunity to investigate the non-linear interactions of surface polaritons with one anotheror with other surface and bulk excitations, i.e. scattering, diffraction, parametric mixing, second harmonic generation, etc. x2 Such investigations and the corresponding investigation of the linear optics of surface polaritons (reflection, refraction, interference, etc.) are now under way. Acknowledgements - The authors with-to acknowledge useful discussions with L. Kuhn and the assistance of R. Amundson in the experiments.

REFERENCES I.

We assume the dielectric constant to be independent of wavevector and therefore make no distinction between transverse and longitudinal dielectric constants.

2.

Surface polaritons occur provided eb(w)leo.(~o) = -c~(,,.,)l~(w).

3.

L is proportional to 1/co2 for metals whose electronic properties can be approximated by a simple Drude model with a scattering time independent of frequency.

4.

BEATTIE J.R. and CONN G.K.T., Phil. Mag. 46, 989 (1955).

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PROPAGATION OF SURFACE POLARITONS

5.

LENHAMA.P. andTREHERNED.M.,J. Opt. S o c A ~ $6,683(1966).

6.

OTTO A., Z. Phys. 216, 398 (1968).

7.

RITCHIE ILH., ARAKAWA E.T., COWAN J.J. and HAMM ILN., Phy~ Rev. Lett. 21, 1530 (1968).

8.

TIEN P.K.,AppL Optics 10, 2395 (1971).

9.

DAKSS M.L., KLH-INL., HEIDRICH P.F. and SCOTT B.A.,Appl. Phys. Lett. 16,523 (1970).

1071

10.

U.S. Radium Corporation, blorristown, New Jersey.

11.

It should be possible, by combining data on the propagation length of surface polaritons at metal-air interfaces with ATR data to obtain information about the dielectric constants of the surface active medium at optical frequencies and Rs spatial variation in the immediate vicinity of the surface.

12.

BURSTEIN E., SCHOENWALD J.. ELSON J.M., HARTSTEIN A., WALLIS R.F. and MILLS D.L, Non-linear Interactions of Surface Polarit ons, Conference, Surface Properties and Surface States o1"Electronic Materials, University o[Missouri - Rolla, June 19-21 (1972).

Nous reportons la propagation des polaritons de surface ~i traverse des distances macroscopiques le long des interfaces cuivre-air ~ 10.6pm en employant un technique de couplage des prismes pour la g~neration et detection des modes de surface. Le longueur (l.6crn) de propagation mesurd est en accord qualitative avec les estimations theoretiques basdes sur rdsultats des mesures optiques disponibles. On observe visuellement les polaritons de surfaces avec papier de phosphor thermographique.