Two-color photoemission produced by femtosecond laser pulses on copper

Muggli et al. Vol. 12, No. 4/April 1995/J. Opt. Soc. Am. B 553 Two-color photoemission produced by femtosecond laser pulses on copper P. Muggli, R. Brogle, and C. Joshi Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, California 90024 Received July 21, 1994; revised manuscript received December 2, 1994 Single-color illumination of a copper surface by a red or an ultraviolet femtosecond laser pulse yields a threephoton (red) or a two-photon (UV) photoemission process. A multicolor, multiphoton process is generated when the red and the UV pulses overlap both in space and in time on the photocathode. It is shown that this emission process results from the absorption by an electron of one red and one UV photon. It provides a means to correlate ultrashort laser pulses of different wavelengths. Key words: multiphoton processes, photoemission, femtosecond phenomena, beams, electron, correlation 1. INTRODUCTION One-photon (photoelectric effect) 1 and multiphoton photoemission processes from metals, 2,3 semiconductors, 4 and insulators 5 have been extensively studied. For multiphoton photoemission to be observed, the incident light intensity has to be large enough that electrons can absorb n number of photons consecutively to gain enough energy to overcome the material work potential barrier. The signature of such n-photon processes is the nth power dependency of the emitted current density on the incident light intensity. In previous experiments 1 5 each of the n photons had the same energy. However, as observed in this experiment, the absorption by an electron of n photons with different energies can also induce emission and lead to multicolor, multiphoton photoemission. In either case the electron absorbs the n photons simultaneously, i.e., is emitted through coupling to virtual states of lifetime 1 n, where n is the frequency of the absorbed photon. Note that transition through a real state of the metal is also a possible path. Multicolor, multiphoton photoemission through virtual states from a metallic cathode could be used as an alternative to sum-frequency generation for correlating laser pulses of different frequencies. To our knowledge, this paper is the first report of the observation of a two-photon, two-color (2P2C) photoemission process through virtual states. A copper surface is illuminated by a red and an ultraviolet (UV) subpicosecond laser pulse. Measurements of the emitted charge versus the energy of the red and UV pulses show that the emission process requires one red and one UV photon per electron emission, as opposed to two red and one UV photon. This 2P2C photoemission process provides a simple way to cross correlate or overlap two laser pulses in space and time. The total current density J generated by a light beam of intensity I and frequency n, incident upon a metal of work function f, is given by the generalization of the Fowler 6 and DuBridge 7 theory: `P J J n, (1) where n 0! n e J n a n A 1 2 R n I n T 2 hn e F 0 1 @ nhn 2efA, (2) k B Te 2 n is the order of the n-photon process, a n is a material dependent constant, A 120 A cm 2 K 2 is the theoretical Richardson coefficient, e is the electron charge, h is the Planck constant, k B is the Boltzmann constant, and R is the reflection coefficient of the metal surface for the light of frequency n. The Fowler function F x is proportional to the number of electrons available for each process, according to their Fermi Dirac distribution function in the conduction band of the metal, at temperature T e. In the absence of thermal effects (T e room temperature), the order of the dominant n-photon process is given by the integer n such that ef hn # n, 1 1 ef. (3) hn For laser pulses with fixed full width at half-maximum duration s t and full width at full maximum spot size area S r, the total emitted charge Q n R dt R dsj n s t S r J n versus the pulse energy E R dt R dsi s t S r I can be written as [from Eq. (2)] Q n b n E n. (4) Experimentally, the order n is obtained from the slope of Q versus E on a log log plot, and the value of the a n and b n coefficients from the measurement of Q versus E, both in the Q n / E n regime. Expression (2) with n 0 yields the thermionic current density. Expression (3) is an energy absorption requirement for an electron to overcome the metal work potential ef. In general, photoemission processes are observed with the absorption of n photons of the same energy hn. However, the absorption of photons of different energies hn i can lead to the emission of an electron, as long as the energy condition P n i hn i $ ef, n i, i 1,... integers (5) i is satisfied. This leads to the multiphoton, multicolor photoemission. Two-color, two-photon photoemission 0740-3224/95/040553-06$06.00 1995 Optical Society of America

554 J. Opt. Soc. Am. B/Vol. 12, No. 4/April 1995 Muggli et al. through image-potential states has been observed in copper, silver, and nickel. 8 However, in the present experiment, the excited electrons transit via virtual states of lifetime 1 n i before becoming free electrons. 2. EXPERIMENT An ultrafast dye laser is synchronously pumped by a mode-locked, frequency-doubled Nd:YAG laser to produce 2.5-nJ, 200-fs pulses near 650 nm (red, hn e 1.91 ev) at a rate of 76 MHz. A small fraction of the remaining IR beam from the Nd:YAG laser is amplified in a 5-Hz repetition-rate regenerative amplifier. It is frequency doubled to pump a dye amplifier that amplifies the red pulses to 2 mj, with a pulse broadening factor of 1.3 2.0, depending on the pumping fluence. The red pulse is split by a 50% beam splitter; one half is sent through the red delay line, and the other half is frequency doubled (UV, 325 nm; hn e 3.82 ev) in a Type I KDP crystal and sent through the UV delay line. A BG3 filter is placed after the doubling crystal to eliminate the remaining red energy. The red, s-polarized and the UV, p-polarized pulses are combined with a dichroic mirror and collinearly sent to the photocathode. The angle of incidence is chosen to be 45 ±. The spot area S r on the photocathode is 0.085 cm 2 (full width at full maximum), and the pulse width s t is 570 fs (full width at half-maximum) if not otherwise specified. The shot-to-shot energy of the two pulses is monitored by calibrated photodiodes placed behind the delay-line mirrors. The temporal width and the spot size of the two pulses are assumed not to vary from shot to shot, for a given set of measurements. A computer controls the optical delay between two pulses and acquires the data at a 5-Hz rate. No averaging is performed; each point on the figures corresponds to an actual laser shot. The photocathode arrangement consists of a 2.54-cm-diameter flat copper mirror cathode (polished to l 20 at 10.6 mm; ef Cu 4.6 ev) grounded through a 1-MV load resistor and of a rounded-tip anode placed a distance of 3.0 mm away from the cathode and biased to a positive potential (15 kv). The total integrated charge emitted by the photocathode is measured through a capacitor placed in parallel with the 1-MV load resistor. In this experiment the overlap in space and in time of two red pulses (no BG3 filter in the UV line) is achieved by their collinear autocorrelation in the path going to the photocathode. Once the overlap in time of the two quasicw, nonamplified beams is reached, the overlap in space can be improved until no interference fringes are observed on the photocathode. The optical delay corresponding to the overlap of the red and the UV pulses can be calculated from the indices of refraction of the optics placed in the delay lines for the actual experiment. Electron yields from copper illuminated with red light of comparable wavelength leading to three-photon photoemission have been published by Anisimov et al. 9 and Srinivisan- Rao et al. 10 3. RESULTS AND DISCUSSION Figure 1 shows the charge emitted by the photocathode as a function of the red and the UV pulse energies separately. As expected with a copper photocathode (ef Cu 4.6 ev) and at low energies, the slope 2.96 on the log log plot of the charge versus the pulse energy obtained with the red light (hn e 1.91 ev) indicates a three-photon process, and the slope 2.20 for the UV light (hn e 3.82 ev) indicates a two-photon process. At higher energies, leading to charges above 1 pc with an applied electric field of 1.6 MV m, the charge curves deviate from the Q n / E n law [Eq. (4)] and are space-charge limited. All the following results were acquired with total emitted charges below 1 pc, i.e., in the absence of any space-charge influence. The b n coefficients [Eq. (4)] can be deduced from these curves: b 2 0.23 pc mj 2 and b 3 1.21 3 10 26 pc mj 3. These coefficients are used to calculate the expected charge from the energy of the separate red and UV pulses. Figure 2 shows the total emitted charge as a function of the delay Dt between the red and the UV pulses, for different pulse energies. At a delay Dt 0 the traces exhibit a peak riding on the background level. The peak is the result of the overlapping, both in space and in time, of the two pulses on the photocathode. When the two color pulses are sent to the photocathode with a time delay much larger than the sum of their widths jdtj.. s t,red 1s t,uv, the emitted charge is the sum of the charges generated by each pulse independently: Q background Q red 1 Q UV b 3 E 3 red 1 b 2 E 2 UV, jdtj.. s t,red 1s t,uv (6) and forms the background level of Fig. 2. This is assuming that there is no effect present (space charge, thermal, charge depletion,...) other than the two n-photon photoemission processes. When the time delay between the two pulses is comparable with, or smaller than, the sum of the widths of the pulses jdtj #s t,red 1s t,uv, two-color multiphoton processes become possible because they satisfy an energy absorption condition similar to expression (3): or 2hn red 1 1hn UV $ ef Cu (7) 1hn red 1 1hn UV $ ef Cu. (8) Fig. 1. Total charge emitted by the copper photocathode (ef Cu 4.6 ev) as a function of the red (hn e 1.91 ev; squares) and of the UV (hn e 3.82 ev; circles) pulse energy. Open symbols correspond to the space-charge-free regime (Q n / E n ; fitted curve); filled symbols correspond to the space-charge-dominated regime.

Muggli et al. Vol. 12, No. 4/April 1995/J. Opt. Soc. Am. B 555 Fig. 2. Charge emitted as a function of the time delay Dt between the red and the UV pulses (upper traces). The UV pulse hits the photocathode before the red pulse for Dt, 0, and the two pulses overlap at Dt 0. The circle plotted at Dt 23.75 ps indicates the charge emitted by the red pulse alone; the square plotted at Dt 23.50 ps indicates the charge emitted by the UV pulse alone. The lower traces are calculated as Q Q total 2 b 3 Ered 3 1 b 2 EUV 2. (a) E red 18 mj, E UV 0.18 mj, Q red Q UV ; (b) E red 18 mj, E UV 0.68 mj, Q red,, Q UV ; (c) E red 40.9 mj, E UV 0.18 mj, Q red.. Q UV ; (d) E red 41.4 mj, E UV 0.66 mj, Q red Q UV. The total emitted charge is then given by Q total Q background 1 Q cross, jdtj #s t,red 1s t,uv, (9) where Q background is given by relation (6), and the cross charge is the sum of the 2-red 1 1-UV (2 1 1) and the 1-red 1 1-UV 1 1 1 photon processes: Q cross Q 211 1 Q 111. (10) For a given time delay Dt the cross charges Q 211 and Q 111 are proportional to! Q 211 Dt / 1 2hn red 1 hn UV 2 ef F hn red k B T e 3 Z ` 2` Q 111 Dt / 3 2hn red F 3 Z ` 2` I 2 red t I UV t 2Dt dt, (11)! hn red 1 hn UV 2 ef k B T e I red t I UV t 2Dt dt. (12) Note that all the possible absorption paths have been taken into account in relations (11) and (12). Relations (11) and (12) show on one hand that, because the argument of the Fowler function F x is the same for the 2 1 1 (or the 1 1 1) photon process as for the 2-UV (or 3-red) photon process, the number of electrons available is the same in each case. More electrons are thus available for the 2 1 1 photon process than for the 1 1 1 photon process. On the other hand, the 2 1 1 photon process is less probable (at given intensities) than the 1 1 1 photon process because it involves the absorption of three photons instead of two. The question thus arises as to which process or which of their combinations contributes to the observed cross charge. Experimentally, the contribution of each crosscorrelation process to the observed charge is determined by a method similar to the one used for the two- and three-photon processes. The time delay is set for the best time overlap of the two pulses: Dt 0. The emitted charge is recorded as a function of the energy of one of the pulses while the energy of the other is kept constant. The cross charge is obtained by subtraction of the expected charge from the UV and red pulses alone, as obtained from their energies and from the b 2 and b 3 coefficients, from the total measured charge (Fig. 1). For a fixed time delay between the two pulses the cross charge can be expressed in a similar fashion as that for the n-photon charges: Q Dt 211 b Dt 211 E 2 rede UV, (13) Q Dt 111 b Dt 111 E red E UV. (14)

556 J. Opt. Soc. Am. B/Vol. 12, No. 4/April 1995 Muggli et al. C E red C E UV É É E UV 0 ) 2b 3 E 3 red b 2E 2 UV, 2Q red Q UV ) C max b 111 3! 1/3 4, b 3 b2e 2 (16) UV 0 ) b 2 EUV 2 b 3 Ered 3, Q UV E red! Q red ) C max b 1/2 111 1. (17) 2 b 2 b 3 E red Fig. 3. Cross charge Q cross versus the UV pulse energy, at Dt 0, calculated from the total emitted charge and the energy of the two pulses [expressions (6) and (9)], for different red pulse energies. The number of red (or UV) photons used for every electron emission is given by the dependency of the cross charge versus the red (or UV) pulse energy: one if linear, two if quadratic. Figure 3 shows that, as expected, the cross charge is a linear function of the UV pulse energy. Only one UV photon can contribute to either of the cross processes. The ratios of the slopes obtained with different red energies are the same as the ratios of the respective red energies, indicating that only one red photon contributes to the observed cross-emission process. This result is confirmed by the linear dependency of the cross charge on the red pulse energy exhibited in Fig. 4. Note that the ratios of the slopes in Fig. 4 are now the same as the ratios of the respective UV pulse energies. The dominant cross process in this experiment is thus the 1-red 1 1-UV photon process: Q cross Q 111, the one requiring the minimum number of photons. The coefficient b Dt 0 111 can be determined from the slopes in Figs. 3 and 4; it is found to be b Dt 0 111 6.60 6 0.29 3 10 23 pc mj 2. This value is 2 orders of magnitude lower than the value of b 2. Note that the coefficient b Dt 111 depends on the polarization of the two pulses and includes a space overlapping dependency of the two laser spots on the photocathode. This dependency can be expressed in the same way as for the time overlap [integrals in relations (11) and (12)] but is not considered here. The contrast ratio of the cross charge to the background charge can be defined as C E red, E UV Q cross Q background b 111E red E UV b 3 E 3 red 1 b 2 E 2 UV. (15) With one of the energies fixed, the function C E red, E UV has maxima The maximum contrast is obtained when the two singlecolor charges are equal (for all materials) and increases with decreasing charges. The maximum contrast ratios observed in this experiment C, 3.0 are limited by the noise of the charge detection system. When the energy that is varied becomes large, the contrast ratio becomes small and the measurement of the cross charge noisy [Figs. 2(d) and 5]. This low ideal contrast ratio at high energy limits the range of measurement of the cross charge (Figs. 3 and 4). The contrasts obtained in the experiment are in good agreement with the calculated values (Fig. 5). Experimental results have been published 11,12 that show 2P2C photoemission through image-potential states (IPS). The absorption of an UV photon is needed first to populate the IPS, and the ionization is obtained with a second UV or a red photon. The IPS are labeled by the quantum number m, their binding energy E B follows a 1 m 2 Rydberg-like sequence 13 below the vacuum level. In metals the lowest IPS m 1 binding energy is 0.8 ev (relative to the vacuum level). The contribution of these states to photoemission yields has been observed only from surfaces with a well-defined Fig. 4. Cross charge Q cross versus the red pulse energy, at Dt 0, calculated from the total emitted charge and the energy of the two pulses [expressions (6) and (9)], for different UV pulse energies.

Muggli et al. Vol. 12, No. 4/April 1995/J. Opt. Soc. Am. B 557 on the right-hand side of the peak (Dt. 0; the red pulse reaches the photocathode before the UV pulse) the higher background level corresponds to an excess of charge. This excess is measured to disappear linearly with the time delay Dt in approximately 80 ps. The asymmetry could never be reversed, which indicates that the excess charge results from the absorption of a red photon first. The relatively long delay for which the excess charge is observed suggests the coupling to a copper oxide level located 0.8 1.9 ev above the Fermi level. This excess of charge could account for approximately 30% of the measured cross-correlation peak. The degree of dependency of the asymmetry on the pulses energy could not be measured because of the pulse-to-pulse intensity variations of the laser pulse. The small-charge excess signals ride on top of a background-charge signal that varies as the sum of the third and fourth powers of the red pulse intensity. It is unlikely that this asymmetry is due to thermal effects arising from high electron temperature, because of the low intensities (I, 2 3 10 8 W cm 2 ) used in this experiment. Moreover, the electron thermal energy has been measured to relax in the copper lattice within a few picoseconds with incident intensities comparable with the ones used in this experiment. 14 A more detailed investigation of this asymmetry is currently under way. Fig. 5. Contrast of the cross-correlation peak, calculated from expression (15), with b Dt 0 111 6.60 3 10 23 pc mj 2 ; with (a) the average red pulse energy (E red 14.8 mm), corresponding to the middle curve of Fig. 3, and with (b) the UV pulse energy corresponding to the lower curve of Fig. 4 (curves) and with the actual red and UV pulse energies (triangles). The cross-correlation charge is also shown (circles). crystallographic orientation, from samples prepared in situ under ultrahigh vacuum. In copper IPS have been observed on the (011) surface [f Cu 100 4.63 ev] with a binding energy E B 0.57 6 0.02 ev and on the (111) surface [f Cu 111 4.88 ev] with a binding energy E B 0.83 6 0.03 ev. 11 These states are thus located 4.06 and 4.05 ev above the Fermi level. It is highly unlikely that 2P2C photoemission through IPS contributes to the yields measured in the present experiment because the 1.9- and 3.8-eV photons cannot couple the electron from the Fermi level (or below) to the IPS. Moreover, it has been shown that lifetime quenching of the IPS resulting from the oxidation of the surface strongly reduces the electron yield of 2P2C photoemission by means of IPS. 12 The copper cathode used in this experiment was exposed to air during setup and was held under a 10 7 10 6 T vacuum. Similarly cross-charge peaks have been observed from the following lower quantum efficiency materials with lower contrasts, with the same photon energies: gold (f Au 5.6 ev; coupling to IPS is impossible), molybdenum (f Mo 4.6 ev), and n-type doped silicon wafers (5.7 ev # f doped silicon # 7.6 ev). The background signal in Fig. 2 is asymmetric around the cross-charge peak. On the left-hand side of the peak (Dt, 0; the UV pulse reaches the photocathode before the red pulse) the background charge is the sum of the charges produced by both pulses separately. We verify this by measuring the two charges independently and by calculating the expected charges [Eq. (4)]. In contrast, Fig. 6. (a) Intensity autocorrelation trace of the nonamplified (thin curve) and amplified (thick curve) red pulses in a b-barium borate crystal. Assuming a sech 2 pulse, the full width at half-maximum of the autocorrelation trace has to be multiplied by 0.648 to yield the real pulse width. (b) Cross-correlation charge signal Q 111 obtained with the red (E red 12.48 mj) and the UV (E UV 0.15 mj) pulses in a copper photocathode.

558 J. Opt. Soc. Am. B/Vol. 12, No. 4/April 1995 Muggli et al. Intensity autocorrelation of laser pulses in nonlinear doubling crystals (harmonic generation, two-photon process) is a commonly used technique to measure the shapes and widths of laser pulses. 15 Cross correlation of two pulses of different wavelengths gives information about the characteristics of one of the pulses if the characteristics of the other pulse are known. 16 In both techniques the background signal obtained when the two pulses do not overlap in time is given by the sum of the signals generated by the two pulses independently. The correlation signal that appears on top of the background when the time delay between the two pulses is comparable with or smaller than the two pulse widths results from the nonlinear character of the process used for the correlation. Correlation in nonlinear crystals can be made background-free by the use of noncollinear beams. 17 The cross-charge peak results from the two-photon cross correlation of the red and the UV pulses. Its width is observed to be less than the autocorrelation width of the red pulse in a b-barium borate crystal (Fig. 6) and depends on the energy of the two pulses. The UV pulse, obtained by the frequency doubling of a red pulse identical to the one used for the measurement, is expected to be narrower than the red pulse, especially at low red-to-uv conversion efficiency. At higher conversion efficiency broadening may happen in the KDP crystal. Measurement of the two-photon photoemission autocorrelation of a red pulse has been shown to give the same pulse width as the one obtained by second-harmonic generation. 18 However, in that experiment three-photon photoemission autocorrelation failed to show the narrowing of the autocorrelation trace expected with a higherorder process. The measurement of the autocorrelation or the cross-correlation width of the cross-charge peak could provide a sensitive means to probe the electron temperature as a function of the red pulse energy. 4. SUMMARY AND CONCLUSIONS In conclusion, a multiphoton, multicolor photoemission process has been observed from a variety of materials. In copper it has been identified as a 1-red 1 1-UV photon process. It is better observed at low red and UV energies because it is a lower-order photon process than the red (1- instead of 3-) and the UV (1- instead of 2-) n-photon processes. This two-photon, two-color process provides a simple way to overlap in space and time two laser pulses of markedly different wavelengths. The measurement of the cross-charge peak could yield the width of one of the pulses if the width of the other one is known. The photoemission process does not suffer from the shortwavelength detection problem or bandwidth limitation that the nonlinear crystals may suffer from, provided that the sum of the energy of the n absorbed photons significantly exceeds the photocathode work potential. Limitations may come from the peak contrast and from space-charge effects. The cross-charge peak is being used to synchronize two laser pulses on the photocathode in a current pump probe experiment aiming at observing the effect of high electron temperature on photoemission processes. ACKNOWLEDGMENTS This research is supported by U.S. Department of Energy grants DE-FG03-91-ER12114 and DE-FG03-92-ER40727 and by U.S. Office of Naval Research grant N0014-90-J- 1952. P. Muggli thanks the Fonds National Suisse de la Recherche Scientifique for partial support. REFERENCES 1. R. A. Millikan, A direct photoelectric determination of Planck s h, Phys. Rev. 7, 355 388 (1916). 2. E. M. Logothetis and P. L. Hartman, Laser induced emission from solids: many-photon photoelectric effects and thermionic emission, Phys. Rev. 187, 460 474 (1969). 3. P. L. Bechtel, W. L. Smith, and N. Bloembergen, Twophoton photoemission from metals induced by picosecond laser pulses, Phys. Rev. B 15, 4557 4563 (1977). 4. See, for example, T. Maruyama, E. L. Garwin, R. A. Mair, R. Prepost, J. S. Smith, and J. D. Walker, Electron-spin polarization in photoemission from thin Al x GA 12x As, J. Appl. Phys. 73, 5189 5192 (1993), and references therein. 5. W. J. Siekhaus, J. H. Kinney, D. Milam, and L. L. Chase, Electron emission from insulator and semiconductor surfaces by multiphoton excitation below the damage threshold, Appl. Phys. A 39, 163 166 (1986). 6. R. H. Fowler, The analysis of photoelectric sensitivity curves for clean metals at various temperatures, Phys. Rev. 38, 45 56 (1931). 7. L. E. DuBridge, Theory of the energy distribution of photoelectrons, Phys. Rev. 43, 727 741 (1933). 8. R. W. Schoenlein, J. G. Fujimoto, G. L. Eesley, and T. W. Capehart, Femtosecond studies of image-potential dynamics in metals, Phys. Rev. Lett. 61, 2596 2599 (1988), and references therein. 9. S. I. Anisimov, V. A. Benderskii, and G. Farkas, Nonlinear photoelectric emission from metals induced by a laser radiation, Sov. Phys. Usp. 20, 467 488 (1977). 10. T. Srinivisan-Rao, J. Fisher, and T. Tsang, Role of optical field in photoemission from copper, Nucl. Instrum. Meth. Phys. Res. A 340, 186 189 (1994). 11. K. Giesen, F. Hage, F. J. Himpsel, H. J. Riess, and W. Steinmann, Binding energy of image-potential states: dependence on crystal structure and material, Phys. Rev. B 35, 971 974 (1987), and references therein. 12. R. W. Schoenlein, J. G. Fujimoto, G. L. Eesley, and T. W. Caperhart, Femtosecond relaxation dynamics of imagepotential states, Phys. Rev. B 43, 4688 4698 (1991). 13. D. Straub and F. J. Himpsel, Spectroscopy of imagepotential states with inverse photoemission, Phys. Rev. B 33, 2256 2262 (1986). 14. H. E. Elsayed-Ali, T. B. Norris, M. A. Pessot, and G. A. Mourou, Time-resolved observation of electron phonon relaxation in copper, Phys. Rev. Lett. 58, 1212 1215 (1986). 15. M. Maier, W. Vaiser, and J. A. Giordmaine, Intense light bursts in the stimulated Raman effect, Phys. Rev. Lett. 17, 1275 1277 (1966); H. P. Weber, Method for pulsewidth measurement of ultrashort light pulses generated by phaselocked lasers using nonlinear optics, J. Appl. Phys. 38, 2231 2234 (1966). 16. G. Albrecht, A. Antonetti, and G. Mourou, Temporal shape analysis of Nd 3+ :YAG active passive mode-locked pulses, Opt. Commun. 40, 59 62 (1981). 17. J.-C. Diels, J. J. Fontaine, and W. Rudolph, Ultrafast diagnostics, Rev. Phys. Appl. 22, 1605 1611 (1985). 18. T. Tsang, T. Srinivisan-Rao, and J. Fisher, Surface-plasmon field-enhanced multiphoton photoelectric emission from metal films, Phys. Rev. B 43, 8870 8878 (1991).