## Abstract

A new spectroscopic technique for studying adsorption of atoms at a transparent dielectric surface is exploited. A quantitative comparison of the Autler-Townes splitting in measured and calculated, surface temperature-dependent two-photon evanescent wave spectra provides values of the adsorption energy, the preexponential factor for the rate of desorption and the polarizability of alkali atoms, adsorbed on a glass surface. It is speculated that this technique could form the basis for future two-photon control of atoms close to dielectric surfaces.

© Optical Society of America

## 1.Introduction

Evanescent wave (EW) spectroscopy has been widely used for studying dynamic processes at surfaces. For this purpose, the origin of the evanescent wave is not important. It might have been excited as a surface plasmon at a metal surface [1] or via total internal reflection at a transparent dielectric surface. Advantages of the EW-technique are based on the fact that the EW field has its field strength maximum at the surface and thus the obtained spectral intensities are sensitive to the surface conditions. For example, the dispersion relation for surface plasmons is significantly modified when a layer of adsorbed atoms or molecules is formed on the metal surface. This, of course, is also true for the surface of a dielectric. In the present paper we exploit the change in evanescent wave intensity and its spectroscopic indicator (Autler-Townes splitting) to deduce a novel two-photon technique for studying adsorption dynamics at a gas-dielectric interface. We note that a quantitative understanding of the two-photon aspect opens up possibilities for future control of both the adsorption-desorption dynamics as well as the electronic excitation process in evanescent waves. The latter prospect implies a coherent two-photon technique, which in fact has already been demonstrated for the present system, albeit in the gas phase [2].

If the EW is resonant to the transition between the ground and excited states of the atoms in the gas and has an amplitude which is large enough to saturate this transition, then the energy levels involved in the transition will be split (“Autler-Townes splitting”) and the value of this splitting will be proportional to the field amplitude [3]. This effect can be observed in the power spectrum of a cascade three-level system when the upper level is connected with the split level by a resonant probe field. The adsorption of gas atoms at the surface alters the EW amplitude and this change is related to the surface coverage. Thus a precise measurement of the Autler-Townes splitting in such a system allows one to extract information about the adsorbed layer. However, one has to keep in mind that the spectrum of atoms excited by an EW shows transit time broadening arising from the finite time that the gas atoms stay in an EW field. If the depth of the EW into the gas is too small, the Autler-Townes splitting will be washed out [4]. In order to reduce transit time broadening in the present work we excite an EW in the vicinity of the critical angle.

## 2. Theory

Let us consider now a system which consists of a medium 1 occupying a half-space *z* < 0 and having the permittivity *ϵ*
_{1} and a gas (medium 2) occupying a half-space *z* > 0 and having the permittivity *ϵ*
_{2}. At the interface *z*=0 a two-dimensional layer of adsorbed atoms exists with the isotropic polarizability as in the plane of the interface and with the surface number density *N _{s}*. Upon irradiation with an external field the Fresnel formulas will be modified because of the induced displacement current. Assuming a harmonic time dependence of the incident wave with the frequency

*ω*, the corresponding amplitude of the surface current density can be found as

where **E**
_{t} is the tangential component of the electric field amplitude at the interface. Taking into account the current given by Eq. (1) in the boundary condition for the tangential component of the magnetic field, one can obtain the amplitude of the wave transmitted into the medium 2, **E**
_{2}, for the case that a wave of the amplitude **E**
_{0} hits the interface from the medium 1. In particular, for s-polarization of the incident wave we get

where

and

are the z-components of the wave vectors of the incident and transmitted waves, respectively, and *θ*
_{0} is the angle of incidence. In the case of total internal reflection, i.e. if ${\theta}_{0}>{\theta}_{c}=\mathrm{arcsin}\sqrt{\frac{{\u03f5}_{2}}{{\u03f5}_{1}}}$, the component *k*
_{2z} is imaginary and Eq. (2) gives the amplitude of the evanescent wave (EW) at the interface. In the vicinity of the critical angle, *θ _{c}*, Eq. (2) reduces to

Note that in the limit *θ*
_{0} → θ_{c}1 the EW amplitude in the case of a p-polarized incident wave does not depend on the surface displacement current at all.

The absolute value of the EW amplitude given by Eq. (5) determines the Autler-Townes splitting of the gas atoms. To derive its temperature dependence one has to specify the function *N _{s}*(

*T*), where

*T*is the surface temperature. We assume the Lang-muir model of adsorption,

*i.e*., an atom can be adsorbed only at free adsorption sites which are characterized by the surface number density

*N*

_{0}, and the energy of adsorption,

*Q*. We also suppose that lateral interactions between the adsorbed atoms can be neglected. Then in the steady-state limit the surface coverage

obeys the following equation expressing the equality of the rates of adsorption and desorption

where *J* is the atomic flux to the surface, *S* is the sticking probability and

is the rate of desorption with *v* a preexponential constant having the dimension of a frequency.

Eq. (7) has the solution

where

If *A* >> 1, then in the limit of high surface temperatures, *T* → ∞, the surface coverage tends to zero. Let us normalize the EW intensity to its limiting value at high temperatures. We write the relative EW intensity in the form

where

Note that in the case of low surface coverage (*θ* << 1), Eq. (11) reduces to the form

Thus the quantity

depends linearly on the inverse surface temperature, the slope being determined by the energy of adsorption.

## 3. Experimental set up

The experimental set up is sketched in Fig. 1b. A glass prism is mounted inside a vacuum chamber (p_{0} ≤ 10^{-8}mbar) on a manipulator and is liquid-nitrogen cooled down to 220 K. The prism temperature is measured with an uncertainty of less than Δ*T*=5 K by a Pt100 thermo-resistance. Na atoms from a dispenser (SAES getters, flux *J* about 5∙10^{14}sec^{-1}cm^{-2}) reach the prism surface at an angle of about 60° with respect to the surface normal. At room temperature or even lower surface temperatures the alkali atoms stick with a probability of unity and form a discontinuous film. At low coverage the adsorbate consists of isolated atoms, which start forming islands with increasing coverage.

The atoms are excited within the evanescent wave by two counterpropagating laser beams from the 3*S*
_{1/2} ground state into the 5*S*
_{1/2} excited state (Fig. 1a). The resulting, blue shifted fluorescence light from the 4*P*
_{1/2,3/2} → 3*S*
_{1/2} transitions (30267.28 cm^{-1} and 30272.88 cm^{-1}) is observed as a function of detuning of one of the lasers via a collection lens at normal incidence and is recorded behind a glass (Schott UG5) and an interference filter (Δλ=10nm) by a photomultiplier and photon counting electronics.

The counterpropagating, s-polarized light beams from two Ar^{+} laser pumped single mode ring dye lasers (CR 699-21) irradiate the prism via Brewster angle windows at an angle slightly larger than the angle of total internal reflection. Both beams leave the vacuum apparatus through opposite Brewster angle windows. The frequency of one of the lasers (laser 2) is set at a fixed value close to the resonance with the 3*P*
_{3/2} → 5*S*
_{1/2} transition of Na atoms in the gas phase (16227.30 cm^{-1}), while the other laser (laser 1) is scanned across the 3*S*
_{1/2} → 3*P*
_{3/2} resonance at 16973.35 cm^{-1}. The FWHM of the lasers is 6.7∙10^{-5} cm^{-1} with a drift of far less than 1∙10^{-3} cm^{-1} during a typical wavelength scan. The diameters of the laser beams are 0.5 mm (laser 1) and 2 mm (laser 2), respectively, and their powers can be varied up to 160 mW each.

## 4. Results and discussion

In Fig. 2 we present a typical two-EW fluorescence spectrum of Na atoms. The four lines correspond to the transitions between the hyperfine sublevels of the ground state 3*S*
_{1/2}(*F* = 1,2) and the upper excited state 5*S*
_{1/2}(*F*′ = 1,2). Each line shows the Autler-Townes splitting whose value is proportional to the amplitude of the EW, which pumps the lower transition 3*S*
_{1/2} → 3*P*
_{3/2}. Fig. 3 demonstrates that the line splitting decreases at fixed EW intensity as one decreases the temperature of the prism surface while continuously evaporating Na atoms from the dispenser.

In order to obtain a value of the EW amplitude at a given surface temperature we use the theory of two-photon absorption developed for non-evanescent waves [5,6]. This is justified since the angles of incidence of the laser beams are close to the critical angle and hence the transit time broadening is small. Then the EW amplitude corresponding to a given line splitting is determined by fitting the experimental fluorescence line shape with the theoretical spectrum (Fig. 4).

The small deviations between experiment and theory can be understood qualitatively as follows. The two-photon theory of Ref.s [5,6] predicts that the width of each split component is determined by the homogeneous widths of the transitions involved, whereas the whole fluorescence line is power broadened. In our case the fluorescence line shape can be represented by a superposition of spectral contributions from the gas atoms having different velocity components along the normal to the prism surface, *v _{z}*. The transit time broadening should be added to the homogeneous width, and the power broadening is determined by an effective field amplitude taking into account the evanescent character of the exciting field. The contribution of the atoms with small

*v*is dominant near the line peaks and is well reproduced by the theory of Ref.s [5,6]. This is also valid for the value of the line splitting. The contribution of the atoms with the larger normal velocity components is characterized by the larger linewidth of the split components due to the transit time broadening and also by the smaller effective field amplitude due to the short residence time in the EW field. The latter feature leads to the smaller Autler-Townes splitting and to the smaller power broadening as compared with the case of small

_{z}*v*. Thus, the experimentally observed fluorescence line has broadened components and supressed line wings as compared with the two-photon line shape predicted by the theory [5,6]. However, here we are only interested in the value of the splitting, not in the exact line shape (for quantitative line shape comparisons see [4]).

_{z}The dependence of pump EW intensity on the surface temperature, deduced from a comparison with the experimental spectra and normalized to the value at high surface temperatures, *η*(*T*), is shown in Fig. 5a. We use the points at the slope of this curve which are most sensitive to the surface temperature to plot the quantity *μ*(*T*) (Eq. (14)) as a function of inverse temperature (Fig. 5b). The points which result in a negative argument of the logarithm have been omitted in plotting *μ*(*T*). Also, the points corresponding to the minimum temperature (221 K) which do not lie on the straight line have not been accounted for in the linear fitting routine. Apparently Eq. (13), which has been derived for low surface coverages, is no longer strictly valid at high coverages. From the slope of the linear fit in Fig. 5b obtained by means of the least-squares method the adsorption energy of Na atoms at a glass surface is calculated to be *Q* = 0.80 ± 0.16 eV. This value correlates well with the energy of Na atom adsorption at a sapphire surface, 0.75 ± 0.25 eV [7] and at a pyrex surface, 0.71 ± 0.02 eV [8].

In the following *Q* in Eqs. (9) and (11) has been used as a constant and the quantities *A* and *B* have been considered as fitting parameters. The result for *A* = 4∙10^{17} and *B* = 0.7 is shown in Fig. 5a. The experimental conditions are consistent with the following values of the parameters: *J* = 5∙10^{14}
*sec*
^{-1}∙*cm*
^{-2}, *S* = 1, $\frac{\omega}{c}=2\pi \xb716973:35{\mathit{cm}}^{-1}$ and √*ϵ*
_{1} = 1.5. The surface nubmer density of the adsorption sites on a real glass surface cannot be obtained from our measurements. We accept for it a typical value which follows from the Langmuir model of adsorption and is determined by the lattice constant: *N*
_{0} ≈ 10^{15}
*cm*
^{-2}. As a result, the preexponential factor in the rate of desorption is found to be *v* = 2∙10^{17}
*sec*
^{-1} and the polarizability of adsorbed Na atoms is *α _{s}* = 6.6∙10

^{-22}

*cm*

^{3}. Note that the obtained value of

*v*falls into the range of “ordinary” preexponential factors for desorption [9]. Obviously, the obtained values of

*A*and

*Q*can be used to plot the surface coverage as a function of prism temperature, given by Eq. (9). The resulting curve is displayed in Fig. 6.

## 5. Conclusions

The present work provides first data and a theoretical analysis of a new spectroscopic technique for studying adsorption of atoms at a transparent dielectric surface. The method, which utilizes two evanescent wave excitation in total internal reflection, has been applied to the case of Na adsorption at a glass surface. Values of the adsorption energy, the preexponential factor for the rate of desorption and the polarizability of the adsorbed Na atoms have been obtained. It has been demonstrated that measuring the Autler-Townes splitting in the fluorescence spectrum of Na atoms in the gas phase allows one to monitor the surface coverage of adsorbed Na atoms. The advantage of the present all-optical approach over non-optical surface techniques such as thermal desorption spectroscopy is that it avoids strong perturbation or even destruction of the investigated system by the measuring procedure and that it allows one to deduce values of additional parameters such as the polarizability of the adsorbates. As compared to optical methods such as ellipsometry or second harmonic generation the present approach facilitates a much more direct evaluation of the parameters of interest without the necessity of elaborate corrections or reference measurements.

The proposed technique uses a quantitative correlation between the intensity of the EW amplitude and the surface coverage. Obviously, this idea can be applied to other optical surface dynamics techniques, which are sensitive to the exciting field amplitude, as well. For example, it has recently been demonstrated that coherent two-photon optical population transfer (STIRAP) in the present Na ladder system becomes possible in a gaseous environment if one acoustooptically (AOM) modulates the continuous wave laser beams [2]. If one would be able to quantitatively understand the two-photon evanescent wave spectra and their relation to the morphological properties of the thin film adsorbates, then AOM-STIRAP in an evanescent wave set up and thus coherent control of atoms close to dielectric surfaces should become feasible. The work of the present paper is believed to be an important first step in this direction.

## Acknowledgments

We are most grateful to C.Henkel for his skillful experimental assistance in the course of this work. We also thank J.P.Toennies for generous support and the European Community (network “Laser controlled dynamics of molecular processes and applications”) for partial financial support.

## References

**1. **V.M. Agranovich and D.L. Mills, Eds., Surface Polaritons (North-Holland, Amsterdam, 1982).

**2. **A. Lindinger, M. Verbeek, and H.-G. Rubahn, “Adiabatic population transfer by acoustooptically modulated laser beams,” Z. Phys. D **39**, 93–100 (1997). [CrossRef]

**3. **C. Delsart and J.-C. Keller, “The optical Autler-Townes effect in Doppler-broadened three-level systems,” J. Phys. (Paris) **39**, 350–360 (1978). [CrossRef]

**4. **V.G. Bordo and H.-G. Rubahn, “Two-photon evanescent wave spectroscopy of alkali atoms,” Phys. Rev. A, submitted.

**5. **R. Salomaa and S. Stenholm, “Two-photon spectroscopy: effects of a resonant intermediate state,” J. Phys. B: Atom. Molec. Phys. **8**, 1795–1805 (1975). [CrossRef]

**6. **R. Salomaa and S. Stenholm, “Two-photon spectroscopy II. Effects of residual Doppler broadening,” J. Phys. B: Atom. Molec. Phys. **9**, 1221–1235 (1976). [CrossRef]

**7. **A.M. Bonch-Bruevich, Yu.M. Maksimov, and V.V. Khromov, Optics Spectrosc. “Variation of the absorption spectrum of sodium atoms when they are adsorbed on a sapphire surface” **58**, 854–856 (1985).

**8. **S. Gozzini, G. Nienhuis, E. Mariotti, G. Paffuti, C. Gabbanini, and L. Moi, “Wall effects on light-induced drift,” Optics Commun. **88**, 341–346 (1992). [CrossRef]

**9. **V.P. Zhdanov, Ya. Pavlichek, and Z. Knor, “”Normal” preexponential factors for elementary physical-chemical processes at a surface,” Surface **10**, 41–46 (1986) (in Russian).