Reflection Z-scan technique for measurements of

Reflection Z-scan technique of surfaces

for measurements

of optical properties

D. V. Petrov,a) A. S. L. Gomes, and Cid B. de Arabjo Departamento de Fisica, Universidade Federal de Pernambuco, 50670-910 Recife, PE, Brazil

(Received 21 March 1994; accepted for publication 27 June 1994) . Spatial modification of a Gaussian beam by reflection on a surface of a high-absorbing material is investigated experimentally. A theoretical description in a geometrical-optics approach is given. The usefulness and sensitivity of the method for applications in measuring laser induced surface deformation and Kerr-like nonlinear coefficients is discussed.

A high-power light beam incident on the surface of a medium causes changes in its optical properties. These changes are due to nonlinear optical effects and different energy transformation processes. A consequence of heating is a lattice deformation with a subsequent thermal expansion of the surface. For detection of the thermal expansion, the photothermal displacement spectroscopyl,” is used. This method does not allow, however, for distinguishing between the surface deformation and the nonlinear response of the interface. A technique which can probe in a direct way the nonlinear optical properties of an interface and distinguish between different mechanisms is thus desirable. In this letter we present results which illustrate the modifications of the spatial intensity distribution suffered by a Gaussian beam reflected from a highly absorbing material. Since we scan the sample in the direction normal to its surface (the 2 direction), this reflection Z-scan @Z-scan) technique is implemented as a further extension of transmission Z scan.3-g Similar to what is done in the conventional Z-scan technique, the spatial profile modification of the incident beam upon reflection by the nonlinear material is monitored through an aperture placed in the far-field region. In this way the phase distortion produced in the reflected beam is transformed to amplitude distortion which is detected by a photodiode. A model is given to explain the results and the application of the new method to measure nonlinear parameters and the surface expansion of highly absorptive materialsactually opaque-is discussed.

Consider an incident Gaussian beam propagating along the z axis, with its waist located at z=O (see Fig. 1). The distance between the beam waist and the sample’s surface is z and the aperture plane is placed at the distance d from the beam waist. The Fresnel coefficient for the mirror-reflected beam includes the changes of refractive index and extinction coefficient due to nonlinear effects and the phase change of the reflected wave due to possible thermal expansion of the surface.” Hence, the effective reflection coefficient is given by R(z,r) ={[ii(z,r)-

l]/[S(z,r)

+ l]}exp[i2kUIE(z,r)j2], (1)

where iz(z,r)=nofn~~E(z,r)~2+i[~o+~~~E(~,~)~2] is the complex refractive index, n,, and ~0 the linear refractive index and the extinction coefficient, n2 and ~~ the nonlinear refractive index and the nonlinear extinction coefficient, E(z,r) the transmitted wave field at the interface, r the radial coordinate of a Gaussian beam, UIE(z,r)12=H the surface expansion amplitude, and k the optical wave number. Thus Eq. (1) shows that the phase change of the reflected wave is caused by the surface absorptive nonlinearity and by a surface expansion. On the other hand, the surface refractive nonlinearity is responsible for the amplitude modulation of the reflected wave.” Taking into account the light induced reflection change, the mirror-reflected wave field distribution at the interface air sample is given by

I

exp[

exp(ikz)

-i@(z)-&]

Xexp[-3r”/w”(z)]+ROC

[

R,, exp[-r”/w2(z)]+R~(n2fiK2)IE”(t)[2[11+(z/zo)2]-1

m {2ik~IEo(t)12[1+(z/zo)21-1}m exp~-~2m+l~r2,W2~Z~l Ill=1

m!

2

“‘Permanent address: The Institute of Semiconductor Physics, Novosibirsk, 630090, Russia.

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where E,,(t) is the electriofield amplitude at r=O (inside the sample), w,, the waist radius, w(z)= wO[l +(z/z~)‘]~‘~ the beah radius, zO= kw$2 the diffraction length of the beam, R(z)=z(l -l-&z”) the wave-front radius of curvature at z, the linear reflection &=(fZ,-l+iKo)/(Tl,+l+iKo) X1=2(ao+ 1-2iKo)l(nof1)3, and Q(z) coefficient, =tan-‘(z/zo). The first term inside large parentheses in Eq. (2) describes the linear-reflected beam, the second term includes

contributions of the real and imaginary parts of the nonlinear susceptibility, and the last term is the contribution due to the surface expansion. To calculate the far-field pattern of the beam at the aperture plane we applied the “Gaussian decomposition methog.‘> Using the properties of a Gaussian beam,‘” the on-axis (r =0) intensity distribution at the aperture plane as a function of the surface position z is given by I

I(

IR(z)=Io

m (RoG~1(z)+R,(n2+i~2)~o[~+(~/~O)2]-1G;1(~)f~O~

X(l-iiz/zo)-l

m=l 2

.

G,(z) = {g(z) - i Here g(z) = 1 + (z + d)z/(zi + z2), X(2m+l)(z+d)/[kw”(z)/2]}, and ~,,~l~~(t)l~. Figure 2(a) illustrates the behavior of IR(z) for the case of linear material (n,=O, K~=O) suffering a surface expansion. Similar type of curves apply to the case of pure absorbing nonlinearity of a flat surface (&=O, V=O). In Fig. 2(b) we show the dependence of IR(z) for the case of pure refractive nonlinearity of a flat interface (K~=O, U=O). Different values of the nonlinear parameters (12~and K~) were considered and the calculated intensities are normalized to 1,(2==3). Notice that, conversely to the transmission Z scan, the characteristic dispersion-shaped dependence is observed for the absorptive type of nonlinearity and/or for the thermal surface expansion case. The numerical evaluation of Eq. (3) showed that if the experimental apparatus is capable of resolving reflectance changes of al%, nonlinearities corresponding to the values n,Io=7X low3 and ~2;l~= 1.1 X 10m2 are detectable. Thus, for a peak irradiance of I,= 1 GW/cm2, refractive nonlinearities

(3)

higher than nz=7X10-14 cm’/W and nonlinear absorption coefficients higher than 2kfc2=5X10p8 cm/W can be measured using the RZ-scan technique. In the case of a material with the linear absorption coefficient cr, the ratio of sensitivities of RZ scan and transmission Z scan for the refractive type of nonlinearity is equal to where Lee= [l-exp(-&)]/a is the effective We&‘, length of light penetration and L the length of the sample.

FIG. 2. The calculatedz dependenceof the on-axis reflected beam intensity FIG. 1. Experimental scheme for the reflection Z-scan technique.

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Appl. Phys. Lett., Vol. 65, No. 9, 29 August 1994

for (a) n2=0, U=O or n2=0, K~=O; and (bj K~=O, U=O.

Petrov, Gomes, and de Araljjo

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8 3.0 z d2 2.5 !s 2.0 w 1.5 Q 2 1.0 z g 0.5 Z(m)

FIG. 3. Normalized reflectance as a function of sample position for an incident average power of 120 mW. Solid line is the theoretical dependence obtained from Eq. (3) for na=O, K~=O, and H=80 run. The inset shows the transmission spectra of the sample (thickness: 3 mm).

Hence, the sensitivities could be comparable for highabsorbing materials or for thin film with thickness of the order of k-l. The experimental scheme is shown in Fig. 1. The excitation source was the second harmonic of a cw and modelocked Nd-YAG laser that delivers pulses of -100 ps at 100 MHz. The laser beam was focused by the 16 cm focal distance lens and the beam waist measured at the sample position was -40 pm. The reflected light was deflected by the beam splitter BS to the aperture and photodetector D. An optical chopper modulated the laser intensity and provided light pulses of 2 ms duration with the duty cycle of 70%. The reflection from a Schott-glass filter RG-695 was studied. Due to the quasi-cw regime of illumination, the spatial modification of the reflected beam is attributed to a thermal change in the surface properties resulting from the high linear absorption. The temporal evolution of the signal showed that it achieves its steady-state value in about 1.8 ms. This value agrees well with the thermal relaxation time calcuIated for the given beam diameter and the thermal parameters of borosilicate glasses.13,r4 The Z dependence of the beam intensity measured through the small aperture reveals a dispersion-shaped curve (Fig. 3). The background variation of the signal can be corrected for by recording a signal at very low power and substracting its contribution. To analyze the measurements we apply the theoretical results presented above. First we notice that the values of thermal n2 and fez are unknown for the glass used in the experiment. A reasonable estimative for the order of magnitude of the refractive nonlinearity of this glass is to assume nz-10-8 cm?W; that is the same value as obtained for other glass filters measured near the edge of the transmission band.r3*14 In our experiments 1a=+104 W/cm’ and therefore the observed changes of reflectance cannot be explained by a thermal refractive nonlinearity of the sample. Assuming that the absorbing nonlinearity is responsible for the observed reflectance changes, we can fit the experiment and Eq. (3) by &,=1.7 which gives 2kK2=+40 cm/W. However, to our knowledge, there is no mechanism of absorbing nonlinearity in glasses that can provide so large a value and thus this possibility has to be ruled out. Finally, we suppose that thermal expansion of the sur-

face is responsible for the observed reflectance changes. In this case, according to Ref. 1, the amplitude of the surface expansion can be estimated using the expression H=&TLeff, where & is the thermal-expansion coefficient and T is the average rise in temperature over Leff. For highly absorbing materials we may consider that the distribution of temperature in depth is governed mainly by the thermal diffusion processes at the region without a heat source. In this case it is reasonable to assume that LeE=Lth (the thermal diffusion length) and T can be calculated using the expression T=E/(~I@,~,~C,), where E is the total energy absorbed during the steady-state regime (1.8 ms), da the beam radius in the focus, p the density, and C, the specific heat. Therefore, for the present experimental conditions with an incident average power of 120 mW and repetition frequency of 100 MHz, we have E=216 ,vJ and using pC,=2.5 J/cm3 “C and &=5X1O-7 “C-l (Ref. 15) we obtain H=35 nm. The best fitting of Eq. (3) to the experimental points gives in this case H=80 nm (see Fig. 3). Because of the large uncertainty in the values of the phenomenological thermal constants the agreement between theory and experiment is reasonable. We conclude that the thermal surface expansion is the main source of the spatial modification observed in the reflected Gaussian beam intensity distribution. This work was supported by the Brazilian Agencies Conselho National de Desenvolvimento Cienttico e Tecnologico (CNPq) and Financiadora National de Estudos e Projetos (FINEP). One of us (D.V.P.) thanks the International Science Foundation for partial support.

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Petrov, Gomes, and de Araljjo Appl. Phys. Lett., No.to 9,150.161.3.106. 29 August 1994 1069 Downloaded 05 Vol. Jan 65, 2004 Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp