Time-delayed second-harmonic generation with nanosecond broadband light pulses: Studies of femtosecond dephasing process of a monolayer of adsorbates

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TIME-DELAYED SECOND-HARMONIC GENERATION WITH LIGHT PULSES: STUDIES OF FEMTOSECOND DEPHASING OF A MONOLAYER OF ADSORBATES Jung Yaw HUANG,

Zhongping

15 June 1988

NANOSECOND PROCESS

BROADBAND

CHEN and Aaron LEWIS

Department ofApplied Physics, Clark Hall, Cornell University, Ithaca, NY 14853, USA Received

9 November

1987; revised manuscript

received

14 January

1988

A new technique utilizing a broadband incoherent light source and surface second-harmonic generation is proposed for the measurements of the dephasing process of adsorbates. A broadband Fluorescein 548 dye laser having a correlation time of 112 fs was used to measure the dephasing processes of monolayers of rhodamine 6G and retinal molecules adsorbed on glass surfaces. Our experimental data agree with the results of the theoretical analysis based on a resonant three-level model.

1. Introduction Studies on the relaxation process associated with electronic excited states of materials are very important in understanding the dynamical behavior of the light-matter interaction. In a large molecule with a large number of degrees of freedom, the vibronic structures often smear out and a broad featureless absorption bandshape is observed. In condensed matter, these vibronic dephasing times often lie in the subpicosecond range and are hard to determine. In recent years, the progress in the field of femtosecond lasers have enabled these measurements and significantly increased our knowledge of dynamic properties of matter [ 11. Along with the efforts to get improved time resolution by generating shorter pulses, a new methodology based on time-delayed four-wave mixing (TDFM ) using non-transformlimited broadband light was proposed and demonstrated [ 2-8 ] for the observation of ultrafast phenomena. Although some problems remain to be solved [ 9 1, the high time resolution and simplicity of this method have attracted intensive research interest. Degenerate four-wave mixing (DFWM) spectroscopy using coherent short pulses and incoherent broadband light is based on the third order nonlinear optical process, therefore it is not sensitive enough to reveal surface properties. Recently, the second 152

harmonic generation (SHG) technique has been proven to be a simple but versatile surface probe [ lo]. It is highly sensitive and surface-specific; it is also capable of achieving high temporal, spatial, and spectral resolution. Being an optical technique, it can also be applied to any interface accessible by light. The only drawback conceived is its lack of molecular selectivity. This drawback has been overcome by Hund et al. [ 111 by using infrared-visible sum frequency generation (SFG). In addition to the vibrational spectrum of adsorbates, this technique can also provide information about the vibrational dephasing time of surface adsorbates in the ground electronic state. In this paper, we report our studies of the electronic dephasing processes of monolayers of rhodamine 6G dye and retinal molecules with time-delayed second-harmonic generation (TDSHG) using an incoherent broadband light source. This method possesses both the submonolayer sensitivity and the surface specificity of the SHG and the ultrahigh temporal resolution of a broadband light source. Theoretical analysis of the delay time dependence of the TDSHG intensity using the dephasing time as the parameter is described in section 2. The details of the experimental procedures and the results obtained by TDSHG from monolayers of rhodamine 6G dye and retinal molecules are presented in section 3 and 4 respectively.

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2. Theoretical E(t)=&,(t) Consider two beams which are generated by the same broadband light source incident upon the surface at polar angle, 8, whose planes of incidence have a projection angle, @, in the xy plane. Fig. 1 (a) defines the geometry for this situation. The reflected SH output beam, k,, simply bisects the reflected fundamental beams [ 12 1. The two fundamental beams are delayed with respect to each other and recombined to give the total electronic field on the surface

exp(iki-r)

+ 8, (t-r)

exp(ik**r)

.

For an ensemble of non-interacting molecules, the response of the sample is local in space and depends only upon the electric field strength at that same point in space. According to the energy-level scheme shown in fig. 1 (b ) and the equation of motion for the density operator [ 13 1, the expression for the second-order optical polarization is given by

P(2)(t)=~:~~)exp(--T,,t)

X exp[i(o,, X

a

-

s --m

m)fl

dt’ &$E(

t’ )

exp[(~m,-rn,)fl

dt" p$“E( t” )

x exp[i(w,,-o) MONOLAYER FtLM ON SUBSTRATE

(1)

t”+T,,t”]

,

(2)

where m, n, and g refer to the second and first electronic excited states and the ground electronic state respectively. ~~w,,,~=E~-E~ is the energy separation between states 1m) and Ig), and r,,,,> 0 is the damping, due to all causes, of the off-diagonal element of density matrix. Here pm,, = p;, is the dipole matrix element with the definition of ,u~, = . In the derivation of eq. (2), the polarizations of the electric fields have been suppressed in order to simplify the expression. This equation is applicable to the fully resonant three-level model shown in fig.

b Fig. I. (a) Simplified coordinate system that defines the noncollinear excitation geometry. The projection angle, 4, is the angle between the input fundamental beams in the xy-plane. The reflected second-harmonic output lies in the xz-plane. The transmitted beams have been omitted for clarity. (b) The schematic energy-level diagram which shows the time-delayed second-harmonic generation (TDSHG) process. Here o is the frequency of the two incident noncollinear fundamental beams which are split and time-delayed with respect to each other from the same broadband light source.

l(b). The second-order optical polarization, PC’) (t), radiates a new field Esu( t). The output SH intensity is proportional to lPc2) (t) I*. In the present case, however, because of the stochastic nature of Pc2) (t), we should calculate the statistically averaged value of this quantity [ 31

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1 dt, 1 dt, j dt’, 1 dt;exp( -0z --co --m --m

x exp[i(o,,-o) X ew[i(w,,-o)

X exp[ -i(Wmn-c0) X exp[ -i(w,,-c(,) x

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tween figs. 2(a) and (b) indicates that for a fixed value of the dephasing constant of the second excited state, rmg, the more broadening of the first excited state, the faster the decay in the TDSHG curves. Note that when the correlation time of the excitation light is comparable to the material dephasing time, the effect of the dephasing process is still detectable. This can be demonstrated by comparing the TDSHG trace of the material with the correlation curve of the light obtained from a nonlinear crystal.

-2r,,,,t)

t,]

t2+rngt21 t; +(T,,-r,,)

t;]

t;+mgt;]

(E(t,)E(tz)E*(t;)E*(t;))

9

(3)

where the total electric field E(t) in the above equation consists of two terms which are given in eq. ( 1). Eq. (3) can be evaluated when a reasonable form is given to the correlation function of the electric field which is defined by (e(t) ~f~((t-r))=Zlf(r), and (g!(t) &,(.s))=(&;(t) d;(s))=O. Since our purpose is to examine the effect of the relaxation time of material, this may more clearly be seen by letting f(r) =6(7). In this limit, eq. (3) then has the following form Ll(7)=M7)IMO) =

+[l+exp(-lx]-2y]xl)cos(a]x])]

+

[rexp(-2ylxl)/(1+a2)l

x {l+exp(-lxl)[asin(aIxI) -

co~(~lxl)1~ 3

(4)

where the normalized parameters, (Y,y, and x are defined as follows, T,,,/r,,,, = y, r,, ITI = (xl, and a = Awlr,, = ( W”, - c&l,) jr,,. In figs. 2 (a) and (b), the calculated TDSHG curves of eq. (4) for various values of the normalized parameters, (Y and y, are plotted as a function of the normalized delay time, r,,,,r. Three interesting points are noted. First, as the value of the parameter, CV’, is increased, the TDSHG curve exhibits increasing modulation frequency. This parameter indicates the mismatch in the energy separations given by w,,~ and w,,. For a molecule which has equally separated electronic levels (i.e. Aw=O) or has a ultrafast dephasing process (i.e. rmg= cx, ), the modulation is washed out. Second, the envelopes of the TDSHG curves exhibit multi-exponential decaying tails which arise from the dephasing times of the electronic excited states, I m) and I n). Third, comparison be154

15 June 1988

3. Experimental Laser pulses with duration of 7 ns were generated by a Quanta-Ray PDL-1 pulsed dye laser which was pumped by the second harmonic beam of a QuantaRay DCR-1 Nd: YAG laser. In order to obtain broadband laser light, the grating of the PDL-1 dye laser was set to zeroth order. Exciton Fluorescein 548 was used as the laser dye. The central wavelength of this dye laser is about 546 nm with a spectral bandwidth of 56 A. By rotating the grating to a higher order, this spectral bandwidth can be reduced. However in order to further increase the bandwidth, the grating should be replaced by a high reflector and an appropriate dye mixture used in the dye amplifier stage. The broadband light with average power of 6 mW was linearly polarized with a Glan-Thompson prism polarizer. The polarization direction relative to the plane of incidence was adjusted by a half-wave plate. The polarized light was then split in two beams, k, and k2, by a 50/50 beam splitter. Two optical delay lines, one having fixed length and the other being controlled by a stepping motor, were inserted into the paths of the k, and k2 beams respectively. The motorized delay line had a temporal resolution of 10 fs. The two beams were brought to the sample plane by a lens with a focal length of 25 cm. The reflected SH beam along the direction of k, was spatially liltered through a pinhole with a diameter of 2 mm. The stray light was further blocked by a UG-5 color glass filter and a 0.25 m double monochromator. The SH protons were detected by a cooled RCA C3 1034 photomultiplier tube, and then integrated by a Stanford Research Model SR250 boxcar averager. A total of 300 pulses for every setting of the delay time were averaged.

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0

-3.00

-2.00

Normalized 0 T-

1 .oo

0.00

-1.00

Delayed

2.00

3.00

2.00

3.00

Time

r

oLo

2

-3.00

-2.00

-1.00 Normalized

0.00

1 .oo

Delayed

Time

Fig. 2. The time-delayed second harmonic generation (TDSHG) curves are calculated from eq. (4) with (a) y=O.5, and (b) y=2. The x-axis indicates the normalized delay time, f,n,r. The parameter, (Y, (see text for the interpretation) is chosen to be 1 (shown in the dashed-dot-dot line), 10 (the curves with solid circles), and 50 (solid lines) respectively.

Monolayer samples of rhodamine 6G and retinal adsorbed on glass surfaces were used for our measurements. They were prepared by using the spin-

coating method as detailed by Heinz et al. [ 14 1. The monolayer samples were mounted on a rotating DC motor during measurement in order to minimize the 155

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effect of the laser-induced desorption. With this arrangement the observed SH signal is found to be stable during the data accumulation period. The contribution from the glass substrate to the surface susceptibility could be neglected since the second-order nonlinearities of rhodamine 6G [ 141 and retinal [ 15 ] are at least two orders of magnitude larger than that of glass.

4. Results and discussion

15 June 1988

ple is much longer than the correlation time, 7,, of the exciting light. A typical correlation trace of a broadband Fluorescein 548 dye laser is shown in fig. 3 where the 1/e full-width of the trace is found to be 158 fs. Based on eq. (5), the correlation time of this light source is estimated to be 112 fs. A factor of 2 for the peak-to-background ratio of the trace agrees with eq. (5) very well. The time-delayed four-wave mixing (TDFM) signal from rhodamine 6G dye dissolved in pure water is shown in fig. 4(a). With the broadband Fluores-

The correlation time of an incoherent broadband light source was first characterized by using a simple pump-probe intensity correlation technique developed by Tomita et al. [ 7 1. In brief, the excitation beam was divided into two parts, and the one used for the pump was about 10 times stronger than that used for the probe. The beams were focused to a point on a sample of protonated retinylidene butylamine Schiff base [ 16 ] at an angle of 10’. The transmitted intensity change in the probe beam induced by the pump beam can be expressed as a function of the delay time z by AT(r)/AT(O)cc[l+exp(-22t2/r,2)].

(5)

Eq. (5 ) is applicable under the condition that the longitudinal relaxation time, T,, of the excited sam-

3

.

.

I

I

6

-0.50

Fig. 3. The intensity correlation of a Fluorescein 548 broadband dye laser is made with a methanolic solution of protonated retinylidene butylamine Schiff base. The solid line which is generated by a cubic spline fitting to the experimental data (open circles) is drawn to guide the reader.

156

-0.25

0.00

0.25

0.50

Delay Time (psec) Fig. 4. (a) The time-delayed four-wave mixing signal is plotted as a function of the delay time for rhodamine 6G dye dissolved in pure water. The excitation broadband Pluorescein 548 dye laser has a correlation time of 112fs as shown in fig. 3. (b) The surface optical second-harmonic generation signal obtained from rhodamine 6G dye (the diamonds) and retinal (the open circles) adsorbed on glass surfaces are plotted as a function of the delay time. The excitation broadband light is the same as the one used in (a). The solid and the dashed lines which are generated by cubic spline fittings are drawn to guide the reader.

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548 dye laser as the excitation source the observed TDFM signal is found to be 105 fs between the peak and the l/e point of the signal intensity. The nearly symmetric nature of the curve implies that the electronic dephasing time of rhodamine 6G dye molecules, T,, is smaller than the correlation time of the excitation broadband light [ 5 1. Note that for cresyl violet and Nile Blue which have a similar size as rhodamine 6G, T, have been found to be 75 and 85 fs respectively by using the time-resolved abborption spectroscopy with a time resolution of 10 fs and an excitation wavelength of 6 18 nm [ 17 1. A typical curve obtained by the time-delayed surface optical second-harmonic generation (TDSHG) from a monolayer of rhodamine 6G dye molecules which are adsorbed on a glass surface is shown by the dashed line in fig. 4 (b). The 2 : 1 contrast ratio agrees with the theoretical result shown in fig. 2. Based on the result of the TDFM measurement which is shown in fig. 4(a), the decaying tail induced by the electronic dephasing and the ultrafast modulation generated by the energy mismatch of the electronic levels are not expected to be resolved because the correlation time of the excitation light is longer than the dephasing time of rhodamine 6G. In fig. 4(b) the TDSHG trace of retinal monolayer (the solid line) is also included for comparison. For retinal, the fundamental and the second-harmonic photon energies are outside the one-photon 7crt* absorption band (&I,, = 380 nm). Considering the large detunings of the photon energies, the damping constants, r,,, and r,ng, can be neglected. Therefore only the effect of the finite correlation time of the broadband excitation light source appears in the TDSHG curve of retinal. The decrement of the l/e half widths of the TDSHG curves in fig. 4(b) reveals the broadening effect of the electronic dephasing process of rhodamine 6G. By comparing fig. 4 (b ) with 4 (a), it is noted that the spectrum of the output SH light is not affected by the adsorbates. This is different from the result reported by Kwok et al. [ 181. In their experiment, the spectrum of the SH beam generated in a KDP crystal which was excited with a broadband dye-laser source having a 14 A bandwidth was found to be as narrow as 2.1 A. Based on their interpretation, the similar spectral bandwidth observed in our expericein

15 June 1988

ment indicates that in the TDSHG the simple doubling of frequency is the major process and hence the assumption which is used in our theoretical formulation is supported.

4. Conclusion In conclusion, we have proposed and demonstrated a simple technique for the measurement of the electronic dephasing time of adsorbates. Our experimental data obtained from monolayers of rhodamine 6G and retinal adsorbed on glass surfaces indicate that this technique is capable of achieving femtosecond time resolution and submonolayer sensitivity. Assume the damaging threshold of a monolayer is 0.1 J/cm2, then the second-harmonic signal generated by a nanosecond light source is about two orders of magnitude smaller than that using an amplified femtosecond laser #I. However in view of the high time resolution and the insensitivity to the group velocity dispersion of optical medium [ 81, the TDSHG is attractive since the non-transform-limited broadband light is rather easy to generate in various spectral regions. We believe that with appropriate improvement this method can serve as a useful probe for the observation of ultrafast relaxation process of adsorbates in various spectral regions where femtosecond laser systems are still not available.

References For review, see, the special issue on Femtosecond optical interaction, ed. D. Grischkowsky, J. Opt. Sot. Am. B2 (1985) 584. A. Asaka, H. Nakatsuka, M. Fujiwara and M. Matsuoka, Phys. Rev. A29 (1984) 2286. N. Morita and T. Yajima, Phys. Rev. A30 (1984) 2525. R. Beach, D. Debeer and S.R. Hartmann, Phys. Rev. A32 (1985) 3467. M. Fujiwara, R. Kuroda and H. Nakatsuka, J. Opt. Sot. Am. B2 (1985) 1634. J.E. Golub and J.W. Mossberg, J. Opt. Sot. Am. B3 ( 1986) 554.

” In this calculation, we take 5 mJ/pulse in 10 ns at 10 Hz as a typical nanosecond light source and 1 uJ/pulse in 100 fs at 5 kHz for an amplified femtosecond laser.

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[7] M. Tomita and M. Matsuoka, J. Opt. Sot. Am. B3 (1986) 560. [ 81 N. Morita, T. Tokizaki and T. Yajima, J. Opt. Sot. Am. B4 (1987) 1269. [9] M.T. Portella, P. Montelmacher, A. Bourdon, P. Eresque and J. Duran, J. Phys. Chem. 91 (1987) 3715. [lo] Y.R. Shen, Ann. Rev. Mater. Sci. 16 (1986) 69. [ 111J.H. Hund, P. Guyot-Sionnest and Y.R. Shen, Chem. Phys. Lett. 133 (1987) 189. [ 12 ] R.E. Muenchausen, R.A. Keller and N.S. Nogar, J. Opt. Sot. Am. 84 (1987) 237.

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] 13 I B. Dick and R.M. Hochstrasser, J. Chem Phys. 78 ( 1983) 3398. [ 14 I T.F.Heinz, C.K. Chen, D. Ricard and Y.R. Shen, Phys. Rev. Lett. 48 (1982) 478. [ 15I J.Y. Huang, A. Lewis and Th. Rasing, J. Phys. Chem., to be published. [ 161 M.A. Marcus, A.T. Lemley and A. Lewis, J. Raman Spec trosc. 8 (1979) 22. [ 171 C.H. Brito Cruz, R.L. Fork, W.H. Knox and C.V. Shank Chem. Phys. Lett. 132 (1986) 341. [ 181 H.S. Kwok and P.H. Chiu, Optics Lett. 10 ( 1985) 28.