## Laser-controlled adsorption of Na atoms in evanescent wave spectroscopy

Optics Express, Vol. 4, Issue 2, pp. 59-66 (1999)

http://dx.doi.org/10.1364/OE.4.000059

Acrobat PDF (306 KB)

### 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

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]

## 2. Theory

*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*. 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

_{s}*ω*, the corresponding amplitude of the surface current density can be found as

**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

*θ*

_{0}is the angle of incidence. In the case of total internal reflection, i.e. if

*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*, Eq. (2) reduces to

_{c}*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.

*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

*J*is the atomic flux to the surface,

*S*is the sticking probability and

*v*a preexponential constant having the dimension of a frequency.

*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

*θ*<< 1), Eq. (11) reduces to the form

## 3. Experimental set up

_{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.

*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.

^{+}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

*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.

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]

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]

*v*. 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

_{z}*v*is dominant near the line peaks and is well reproduced by the theory of Ref.s [5

_{z}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]

*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

_{z}**8**, 1795–1805 (1975). [CrossRef]

**9**, 1221–1235 (1976). [CrossRef]

*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

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]

*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,

*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*= 6.6∙10

_{s}^{-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

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]

## Acknowledgments

## 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 |

3. | C. Delsart and J.-C. Keller, “The optical Autler-Townes effect in Doppler-broadened three-level systems,” J. Phys. (Paris) |

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. |

6. | R. Salomaa and S. Stenholm, “Two-photon spectroscopy II. Effects of residual Doppler broadening,” J. Phys. B: Atom. Molec. Phys. |

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” |

8. | S. Gozzini, G. Nienhuis, E. Mariotti, G. Paffuti, C. Gabbanini, and L. Moi, “Wall effects on light-induced drift,” Optics Commun. |

9. | V.P. Zhdanov, Ya. Pavlichek, and Z. Knor, “”Normal” preexponential factors for elementary physical-chemical processes at a surface,” Surface |

**OCIS Codes**

(240.0240) Optics at surfaces : Optics at surfaces

(240.6690) Optics at surfaces : Surface waves

(300.6280) Spectroscopy : Spectroscopy, fluorescence and luminescence

**ToC Category:**

Focus Issue: Laser controlled dynamics

**History**

Original Manuscript: December 1, 1998

Published: January 18, 1999

**Citation**

V. Bordo and H.-G. Rubahn, "Laser-controlled adsorption of Na atoms in
evanescent wave spectroscopy," Opt. Express **4**, 59-66 (1999)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-4-2-59

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### References

- V.M. Agranovich and D.L. Mills, Eds., Surface Polaritons (North-Holland, Amsterdam, 1982).
- A. Lindinger, M. Verbeek and H.-G. Rubahn, "Adiabatic population transfer by acoustooptically modulated laser beams," Z. Phys. D 39, 93-100 (1997). [CrossRef]
- 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]
- V.G. Bordo and H.-G. Rubahn, "Two-photon evanescent wave spectroscopy of alkali atoms," Phys. Rev. A, submitted.
- 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]
- 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]
- A.M. Bonch-Bruevich, Yu.M. Maksimov and V.V. Khromov, "Variation of the absorption spectrum of sodium atoms when they are adsorbed on a sapphire surface" Optics Spectrosc. 58, 854-856 (1985).
- S. Gozzini, G. Nienhuis, E. Mariotti, G. Pa_uti, C. Gabbanini and L. Moi, "Wall effects on light-induced drift," Optics Commun. 88, 341-346 (1992). [CrossRef]
- 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).

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