- Email: [email protected]
Reflection of a Gaussian beam from a saturable absorber
1 February 1996
OPTICS COMMUNICATIONS Optics Communications 123 (1996) 637-641
ELSEVIER
Reflection of a Gaussian beam from a saturable absorber D.V. Petrov ‘, A.S.L. Gomes, Cid B. de Aratijo Departamento
de Ft’sica, Universidade
Federal de Pemambuco,
50670-901 Recife-PE, Brazil
Received 10 July 1995; revised version received 26 September 1995; accepted 28 September 1995
Abstract The modification of a Gaussian beam profile caused by the electronic contribution to the surface nonlinear absorption of a semiconductor doped glass was measured. The reflection Z-scan and transmission Z-scan techniques used allow to observe
differences between the bulk and the surface nonlinear properties.
A laser beam incident on the surface of a nonlinear medium can display characteristic features arising from the light-matter interaction at the surface [ l-51. If the nonlinear effects are strong enough, the intensity profile of the reflected wave may exhibit drastic spatial modifications due to the absorption modulation along the longitudinal direction in the bulk [ 61. This subject was also investigated in Ref. [ 71, where the spatial modification of a Gaussian beam on reflection from a saturable absorber was studied theoretically. The dependence of the reflectivity on the intensity of the incoming optical beam is revealed through the changes that derive mainly from effective aperturing effects in amplitude and phase. More recently, the changes in reflectivity from a medium with the Kerr nonlinearity were studied theoretically in Ref. [ 81. In this work we present experimental results on the modification of a Gaussian beam profile caused by the electronic contribution for the nonlinear optical properties of a surface. The reflection Zscan technique [ 91 (RZ-scan) was used to investigate the spatial modification of a Gaussian beam by reflection on a surface
’ Permanent address: The Institute of Semiconductor Physics, Novosibirsk, 630090, Russia.
of a saturable absorber. As in the conventional transmission Z-scan technique (TZ-scan) [ lo] the beam profile modification is monitored through an aperture placed in the far-field region. Hence, the phase distortion produced in the reflected beam is transformed to amplitude distortion which is easily detected by a photodiode. In the experiment of Ref. [9] a CW mode-locked laser was used as the excitation source and therefore a themlly induced change in the surface properties of a semiconductor doped glass (SDG) resulted in a surface deformation. In the present work we report on the spatial changes of the reflected beam profile induced by the electronic nonlinearity in SDG’s studied exploiting the RZ-scan technique. For the laser wavelength used the sample behaves as a saturable absorber as discussed below. We give first a theoretical analysis of the problem and then describe experimental results for nonlinear absorption (NLA) . Although we analyze here the case of a single nonlinear interface, an extension of the method to study nonlinear thin films is also possible. Let the sample be placed with its front surface at the distance z from the origin which is taken as the position of the incident Gaussian beam waist. The Fresnel
003~4018/%/$12.00 0 1996 Elsevier Science B.V. All rights reserved SSDI 0030-4018(95)00593-5
638
D.V. Petrou er al. / Optics Communications
123 (1996) 637-641
coefficient for the mirror-reflected beam is given by R(r,z)
= [(%r,z)
- l)/(%r,z)
wRo+R~[An(r,z)
+ l)]
+iAK(r,z)]
,
(1)
whereR0= (no+k0-I)/(n0+iK0+1) isthelinear reflection coefficient, n0 and KO are the linearrefractive index and extinction coefficient, An(r, z) = n21E01* and AK(T, z) = ~21EO1*are the nonlinearcontributions to the refractive index and extinction coefficient, EO is the field amplitude of the incident beam at r = 0, 112 and ~2 are the nonlinear refractive index and extinction coefficients, and *
N
=
JWr,z) ~~_-_1~~
2
.JR(r,z)
dn
C?K
(no + 1 +
iK0)
2’
The mirror-reflected field at the interface is described by PO(Z) + ~
kr*
2qo(z)
+ RN(n2 + k2)@ x
exp
I)
[l + (z/z0)*]-’
PO(Z) +p
kr2
2Qo(z)
II’
(2)
whereqo(z) =z+izoandPo(z) =-iln(l-iz/z0) are the complex Gaussian beam parameters, -=--1 Qo(z>
i
1 qotz)
kw(z
)*/4
w(z)* = wi [1 + (z/zo)*] is the beam width, z0 = kwi/2 is the confocal parameter, w0 is the beam waist radius, r is the radial coordinate of the Gaussian beam, and k is the light wavenumber. The first term inside the large parentheses in Eq. (2) describes the linearreflected beam while the second term is due to the sample nonlinearity. The expression for the on-axis reflected intensity in the far-field region (“small aperture” measurement) was given in Ref. [9]. The total reflected intensity (“open aperture” measurement) can be found by integration over r in Eq. (2). Taking into account that ~2 lEoI* < 1, and n21Eoj2 << 1 the normalized expression for the reflectance with open aperture is given by {1
+
(RO/RN)n:!
lEOi*/
[I
+
(Z/zO)*]}
.
Fig. 1. Calculated Z-scan traces for on-axis intensity: (a) n:, = 0 and (b) ~2 = 0. The results for open aperture (~2 = 0) are illustrated in (c).
Fig. 1 illustrates the expected behavior of the onaxis reflectance in the case of pure NLA (n2 = 0) (a), pure nonlinear refraction (NLR) (~2 = 0) (b), and for measurements of NLR with open aperture (c) . In the calculations we considered n0 = 1.55 and cu0 = 2kK0 = 220 cm-‘, which are close to the parameters of the studied samples. The wavelength &J is 532 nm. Note that, conversely to the TZ-scan technique, the characteristic dispersion-shaped dependence in the small aperture R&scan measurements is observed for the NLA case. In the open aperture case only the NLR affects the intensity of the reflected beam. Hence, for a single interface, the RZ-scan measure-
D.V. Petrov et d/Optics
Fig. 2. Experimental
set-up for reflection
Communications
123 (1996) 637-641
639
Z-scan measurements.
ments with small and open aperture allow to determine unambiguously the NLA and NLR coefficients, respectively. The measurement with open aperture should be performed as the first step to find the NLR coefficient. Then the small aperture data should be used to fit the theoretical expression (Eq. (3) of Ref. [ 9 1 ) in order to find the NLA coefficient. We performed experiments to determine the NLA coefficient of a semiconductor doped glass (Schott glass RG695). Two slabs of different thickness (sample A with 0.013 cm and sample B with 0.2 cm) were available. For the wavelength used in the experiments (532 nm) the linear absorption coefficient was (~0 = 220 cm-t. The experimental set-up used is shown in Fig. 2. The samples were excited by the second harmonic of a Q-switched and mode-locked Nd:YAG laser. Each Q-switched burst consists of about 20 pulses of 80 ps duration separated by 10 ns. The low repetition rate of the Q-switch (5 Hz) was chosen in order to avoid cumulative thermal index of refraction and absorption changes. The beam was focused by a 15 cm focal distance lens and the incident intensity was changed by a combination of half-wave plate and polarizer. The focused light passed through two beamsplitters: BSt and BS2. The beam splitter BSt deflects part of the beam to the reference photodiode D2 and BS:! compensates the focus aberration produced by BSI in the plane of incidence. The photodiode D3 allows to record the usual TZ-scan traces. The sample was mounted in a translation stage driven by a stepping motor. The light reflected from the sample was deflected by BSt to the aperture and the intensity of light transmitted was measured by the photodiode Dt . To enhance the accuracy of the measurements we used the same aperture dimension and the same distance from the beamsplitter
1.6
-1
0
1
Z(cm) Fig. 3. Transmission Z-scan traces measured with small aperture (a) and with open aperture (b) The average intensity of the beam was 140 nW (sample A).
to the reference diode as for the main channel [ 111. The conventional TZ-scan measurement was first performed using sample A. The results of these measurements with small aperture (S = 0.1) and with open aperture (S = 1) are shown in Fig. 3. Notice that the open aperture measurements reveal a strong saturable absorption in the sample. The average intensity for this measurement was 140 nW, which gives for a 35 pm beam waist diameter, and the laser parameters given above, the on-axis peak intensity la = 1.8 MW/cm2, which corresponds to a fluence of 0.14 mJlcm2. The NLA coefficient, K:! = -4 x lo-t0cm2/W, was found fitting the experimental data to the theoretical dependence for the open aperture measurements [lo]. The NLR index, x lo-” cm2/W, was found from the data n2 = -5 of Fig. 3a. Hence, considering the values of n2 and ~2 we should expect that the saturable absorption gives the main contribution for the modification of the reflected beam profile.
640
D.V. Petrov et d/Optics
Communications 123 (1996) 637-641
Fig. 4. Reflection Z-scan trace measured through the small aperture ( S = 0.1) for the glass sample B. The average input beam intensity was 400 nW.
The TZ-scan experiment was performed to be sure that the sample used behave as a saturable absorber for the wavelength and intensities used. The RZ-scan experiments, however, were performed using sample B, where CXOD > 1, to reduce the possibility of multiple internal reflections which may affect the interpretation of the results. Indeed, effects due to multiple reflections were observed in our experiments with sample A and organic thin films. However a more elaborated theoretical approach is required for the interpretation of the RZ-scan data. The on-axis reflectance with small aperture exhibits a dependence with the Zcoordinate as shown in Fig. 4, while the open aperture measurement did not show any change as a function of the sample position. This result indicates that the modification of the reflectance is mainly due to the nonlinear absorption at the interface. The value of K2 = -3 x 10m8cm’/W was determined from this experiment. This result is about 75 times larger than the value obtained from the conventional TZ-scan measurement performed with sample A. To discuss the results obtained we first note that the main effect is due to the NLA arising from electronic origin. In order to warrant that the nonlinearity was of electronic origin, the low repetition rate and extremely low fluence used avoided the saturation of the tail states of the semiconductor band edge. The effect of fluence on competing thermal and electronic nonlinearities of semiconductor doped glasses has been studied in detail by Finlayson and co-workers [ 121. Using time-resolved measurements they have clearly
demonstrated that the electronic contribution for the nonlinearity saturates at energy fluences larger than 5 ml/cm2 due to the band-filling effect. The thermal contribution becomes dominant at fluences larger than 10 mJ/cm2. The fluences used in our experiments were more than one order of magnitude less than the saturation fluence for the electronic nonlinearity and the use of 80 ps pulses allowed the peak power to be high enough be able to perform the measurements with a good signal to noise ratio. Our results agree with the theoretical model presented in Ref. [ 131 which predicts that for light frequencies larger than the bandgap frequency of semiconductor doped glasses, the electronic contribution of NLA is larger than the NLR. Accordingly, in the present experiments the small electronic contribution for NLR is below the sensitivity of our detection system. Concerning the small aperture results, we recall that the nonlinear susceptibility of a surface can differ from the bulk susceptibility because of several nonlinear mechanisms inherent to interfaces [ 141. The TZ-scan measurements give information on the nonlinear bulk properties, averaged on the effective propagation length, while in the RZ-scan measurements of a highly absorbing material, the reflectance changes is due to the nonlinear properties of a layer of about (~0’ thickness (in our case LYE’< 50 pm). TO our knowledge, studies of the microscopic mechanisms which contribute to the nonlinear response of the interface air-SDG are not available to allow a better understanding of the surface enhancement observed. We anticipate that a model to explain this enhancement should take into account surface-electric-dipolar effects. Such effects have proven to be dominant in the case of centrosymmetric semiconductors exposed to air [ 151. In the present case the sample nonlinearity is due to the semiconductor crystallites and the second-order susceptibility associated to the surface electric-dipoles would contributes through a cascade mechanism to the effective surface nonlinearity measured. Then, the contribution of the cascade process to the Kerr-like nonlinear properties is expected to be larger for the reflection coefficient than for the transmission coefficient. Because of the smaller interaction length the phase-matching condition required by the cascade mechanism can be easily satisfied for the reflection measurements rather than for the transmission case. However, a detailed explanation regarding the
D.V. Perrov et d/Optics
physical origin of the surface enhancement the SDG is out of the scope of this paper. This work ian Agencies Cientifico e de Estudos e J.P da Silva
Communicarions
effect in
was partially supported by the BrazilConselho National de Desenvolvimento Tecnol6gico (CNPq) and Financiadora Projetos (FINEP) .We thank also Blenio for polishing the samples.
References [ 11 A.E. Kaplan, Sov. Phys. JETP 45 (1974) 896. 121 W.J. Tomlinson, J.l? Gordon, P.W. Smith and A.E. Kaplan, Appl. Optics 21 (1982) 2041. [ 31 D.R. Andersen and J.J. Regan, J. Opt. Sot. Am. B 6 (1989) 1484. [ 41 Th. Peschel, l? Dannberg, U. Langbein and E Lederer, J. Opt. Sot. Am. B 5 (1988) 29.
123 (1996) 637-641
641
[5] T. Saiki, K. Takeuchi, M. Kuwata-Gonokami, T. Mitsuyu and K. Ohkawa, Appl. Phys. Lett. 60 (1992) 192. I61 L. Roso-France, Phys. Rev. Lett. 55 (1985) 2149. [71 S.R. Hartmann and J.T. Manassah, Optics Lett. 16 ( 1991) 1349. 181 S.D. Kumitsiu, Al? Sukhorukov and V.A. Trofimov. Bull. Rus. Acad. Sci. 56 (1992) 2007. 191 D.V. Petrov, A.S.L. Gomes and Cid B. de Araujo. Appl. Phys. Lett. 65 (1994) 1067. I101 M. Sheik-Bahae, A.A. Said, T.H. Wei, D.J. Hagan and E.W. Van Stryland, IEEE J. Quantum Electron. 26 (1990) 760. 1111 H. Ma, A.S.L. Gomes and Cid B. de Aratijo, Appl. Phys. Lett. 59 (1991) 2666. It21 N. Finlayson, W.C. Banyai, C.T. Seaton, G.I. Stegeman, M. O’Neill, T.J. Cullen and C.N. Ironside, J. Opt. Sot. Am. B 6 (1989) 675. 1131 P Roussignol, D. Ricard and C. Flytzanis, Appl. Phys. A 44 (1987) 285. [I41 Y.R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984). 1151 J.A. Litwin, J.E. Sipe and H.M. van Driel, Phys. Rev. B 31 (1985) 5543.
OPTICS COMMUNICATIONS Optics Communications 123 (1996) 637-641
ELSEVIER
Reflection of a Gaussian beam from a saturable absorber D.V. Petrov ‘, A.S.L. Gomes, Cid B. de Aratijo Departamento
de Ft’sica, Universidade
Federal de Pemambuco,
50670-901 Recife-PE, Brazil
Received 10 July 1995; revised version received 26 September 1995; accepted 28 September 1995
Abstract The modification of a Gaussian beam profile caused by the electronic contribution to the surface nonlinear absorption of a semiconductor doped glass was measured. The reflection Z-scan and transmission Z-scan techniques used allow to observe
differences between the bulk and the surface nonlinear properties.
A laser beam incident on the surface of a nonlinear medium can display characteristic features arising from the light-matter interaction at the surface [ l-51. If the nonlinear effects are strong enough, the intensity profile of the reflected wave may exhibit drastic spatial modifications due to the absorption modulation along the longitudinal direction in the bulk [ 61. This subject was also investigated in Ref. [ 71, where the spatial modification of a Gaussian beam on reflection from a saturable absorber was studied theoretically. The dependence of the reflectivity on the intensity of the incoming optical beam is revealed through the changes that derive mainly from effective aperturing effects in amplitude and phase. More recently, the changes in reflectivity from a medium with the Kerr nonlinearity were studied theoretically in Ref. [ 81. In this work we present experimental results on the modification of a Gaussian beam profile caused by the electronic contribution for the nonlinear optical properties of a surface. The reflection Zscan technique [ 91 (RZ-scan) was used to investigate the spatial modification of a Gaussian beam by reflection on a surface
’ Permanent address: The Institute of Semiconductor Physics, Novosibirsk, 630090, Russia.
of a saturable absorber. As in the conventional transmission Z-scan technique (TZ-scan) [ lo] the beam profile modification is monitored through an aperture placed in the far-field region. Hence, the phase distortion produced in the reflected beam is transformed to amplitude distortion which is easily detected by a photodiode. In the experiment of Ref. [9] a CW mode-locked laser was used as the excitation source and therefore a themlly induced change in the surface properties of a semiconductor doped glass (SDG) resulted in a surface deformation. In the present work we report on the spatial changes of the reflected beam profile induced by the electronic nonlinearity in SDG’s studied exploiting the RZ-scan technique. For the laser wavelength used the sample behaves as a saturable absorber as discussed below. We give first a theoretical analysis of the problem and then describe experimental results for nonlinear absorption (NLA) . Although we analyze here the case of a single nonlinear interface, an extension of the method to study nonlinear thin films is also possible. Let the sample be placed with its front surface at the distance z from the origin which is taken as the position of the incident Gaussian beam waist. The Fresnel
003~4018/%/$12.00 0 1996 Elsevier Science B.V. All rights reserved SSDI 0030-4018(95)00593-5
638
D.V. Petrou er al. / Optics Communications
123 (1996) 637-641
coefficient for the mirror-reflected beam is given by R(r,z)
= [(%r,z)
- l)/(%r,z)
wRo+R~[An(r,z)
+ l)]
+iAK(r,z)]
,
(1)
whereR0= (no+k0-I)/(n0+iK0+1) isthelinear reflection coefficient, n0 and KO are the linearrefractive index and extinction coefficient, An(r, z) = n21E01* and AK(T, z) = ~21EO1*are the nonlinearcontributions to the refractive index and extinction coefficient, EO is the field amplitude of the incident beam at r = 0, 112 and ~2 are the nonlinear refractive index and extinction coefficients, and *
N
=
JWr,z) ~~_-_1~~
2
.JR(r,z)
dn
C?K
(no + 1 +
iK0)
2’
The mirror-reflected field at the interface is described by PO(Z) + ~
kr*
2qo(z)
+ RN(n2 + k2)@ x
exp
I)
[l + (z/z0)*]-’
PO(Z) +p
kr2
2Qo(z)
II’
(2)
whereqo(z) =z+izoandPo(z) =-iln(l-iz/z0) are the complex Gaussian beam parameters, -=--1 Qo(z>
i
1 qotz)
kw(z
)*/4
w(z)* = wi [1 + (z/zo)*] is the beam width, z0 = kwi/2 is the confocal parameter, w0 is the beam waist radius, r is the radial coordinate of the Gaussian beam, and k is the light wavenumber. The first term inside the large parentheses in Eq. (2) describes the linearreflected beam while the second term is due to the sample nonlinearity. The expression for the on-axis reflected intensity in the far-field region (“small aperture” measurement) was given in Ref. [9]. The total reflected intensity (“open aperture” measurement) can be found by integration over r in Eq. (2). Taking into account that ~2 lEoI* < 1, and n21Eoj2 << 1 the normalized expression for the reflectance with open aperture is given by {1
+
(RO/RN)n:!
lEOi*/
[I
+
(Z/zO)*]}
.
Fig. 1. Calculated Z-scan traces for on-axis intensity: (a) n:, = 0 and (b) ~2 = 0. The results for open aperture (~2 = 0) are illustrated in (c).
Fig. 1 illustrates the expected behavior of the onaxis reflectance in the case of pure NLA (n2 = 0) (a), pure nonlinear refraction (NLR) (~2 = 0) (b), and for measurements of NLR with open aperture (c) . In the calculations we considered n0 = 1.55 and cu0 = 2kK0 = 220 cm-‘, which are close to the parameters of the studied samples. The wavelength &J is 532 nm. Note that, conversely to the TZ-scan technique, the characteristic dispersion-shaped dependence in the small aperture R&scan measurements is observed for the NLA case. In the open aperture case only the NLR affects the intensity of the reflected beam. Hence, for a single interface, the RZ-scan measure-
D.V. Petrov et d/Optics
Fig. 2. Experimental
set-up for reflection
Communications
123 (1996) 637-641
639
Z-scan measurements.
ments with small and open aperture allow to determine unambiguously the NLA and NLR coefficients, respectively. The measurement with open aperture should be performed as the first step to find the NLR coefficient. Then the small aperture data should be used to fit the theoretical expression (Eq. (3) of Ref. [ 9 1 ) in order to find the NLA coefficient. We performed experiments to determine the NLA coefficient of a semiconductor doped glass (Schott glass RG695). Two slabs of different thickness (sample A with 0.013 cm and sample B with 0.2 cm) were available. For the wavelength used in the experiments (532 nm) the linear absorption coefficient was (~0 = 220 cm-t. The experimental set-up used is shown in Fig. 2. The samples were excited by the second harmonic of a Q-switched and mode-locked Nd:YAG laser. Each Q-switched burst consists of about 20 pulses of 80 ps duration separated by 10 ns. The low repetition rate of the Q-switch (5 Hz) was chosen in order to avoid cumulative thermal index of refraction and absorption changes. The beam was focused by a 15 cm focal distance lens and the incident intensity was changed by a combination of half-wave plate and polarizer. The focused light passed through two beamsplitters: BSt and BS2. The beam splitter BSt deflects part of the beam to the reference photodiode D2 and BS:! compensates the focus aberration produced by BSI in the plane of incidence. The photodiode D3 allows to record the usual TZ-scan traces. The sample was mounted in a translation stage driven by a stepping motor. The light reflected from the sample was deflected by BSt to the aperture and the intensity of light transmitted was measured by the photodiode Dt . To enhance the accuracy of the measurements we used the same aperture dimension and the same distance from the beamsplitter
1.6
-1
0
1
Z(cm) Fig. 3. Transmission Z-scan traces measured with small aperture (a) and with open aperture (b) The average intensity of the beam was 140 nW (sample A).
to the reference diode as for the main channel [ 111. The conventional TZ-scan measurement was first performed using sample A. The results of these measurements with small aperture (S = 0.1) and with open aperture (S = 1) are shown in Fig. 3. Notice that the open aperture measurements reveal a strong saturable absorption in the sample. The average intensity for this measurement was 140 nW, which gives for a 35 pm beam waist diameter, and the laser parameters given above, the on-axis peak intensity la = 1.8 MW/cm2, which corresponds to a fluence of 0.14 mJlcm2. The NLA coefficient, K:! = -4 x lo-t0cm2/W, was found fitting the experimental data to the theoretical dependence for the open aperture measurements [lo]. The NLR index, x lo-” cm2/W, was found from the data n2 = -5 of Fig. 3a. Hence, considering the values of n2 and ~2 we should expect that the saturable absorption gives the main contribution for the modification of the reflected beam profile.
640
D.V. Petrov et d/Optics
Communications 123 (1996) 637-641
Fig. 4. Reflection Z-scan trace measured through the small aperture ( S = 0.1) for the glass sample B. The average input beam intensity was 400 nW.
The TZ-scan experiment was performed to be sure that the sample used behave as a saturable absorber for the wavelength and intensities used. The RZ-scan experiments, however, were performed using sample B, where CXOD > 1, to reduce the possibility of multiple internal reflections which may affect the interpretation of the results. Indeed, effects due to multiple reflections were observed in our experiments with sample A and organic thin films. However a more elaborated theoretical approach is required for the interpretation of the RZ-scan data. The on-axis reflectance with small aperture exhibits a dependence with the Zcoordinate as shown in Fig. 4, while the open aperture measurement did not show any change as a function of the sample position. This result indicates that the modification of the reflectance is mainly due to the nonlinear absorption at the interface. The value of K2 = -3 x 10m8cm’/W was determined from this experiment. This result is about 75 times larger than the value obtained from the conventional TZ-scan measurement performed with sample A. To discuss the results obtained we first note that the main effect is due to the NLA arising from electronic origin. In order to warrant that the nonlinearity was of electronic origin, the low repetition rate and extremely low fluence used avoided the saturation of the tail states of the semiconductor band edge. The effect of fluence on competing thermal and electronic nonlinearities of semiconductor doped glasses has been studied in detail by Finlayson and co-workers [ 121. Using time-resolved measurements they have clearly
demonstrated that the electronic contribution for the nonlinearity saturates at energy fluences larger than 5 ml/cm2 due to the band-filling effect. The thermal contribution becomes dominant at fluences larger than 10 mJ/cm2. The fluences used in our experiments were more than one order of magnitude less than the saturation fluence for the electronic nonlinearity and the use of 80 ps pulses allowed the peak power to be high enough be able to perform the measurements with a good signal to noise ratio. Our results agree with the theoretical model presented in Ref. [ 131 which predicts that for light frequencies larger than the bandgap frequency of semiconductor doped glasses, the electronic contribution of NLA is larger than the NLR. Accordingly, in the present experiments the small electronic contribution for NLR is below the sensitivity of our detection system. Concerning the small aperture results, we recall that the nonlinear susceptibility of a surface can differ from the bulk susceptibility because of several nonlinear mechanisms inherent to interfaces [ 141. The TZ-scan measurements give information on the nonlinear bulk properties, averaged on the effective propagation length, while in the RZ-scan measurements of a highly absorbing material, the reflectance changes is due to the nonlinear properties of a layer of about (~0’ thickness (in our case LYE’< 50 pm). TO our knowledge, studies of the microscopic mechanisms which contribute to the nonlinear response of the interface air-SDG are not available to allow a better understanding of the surface enhancement observed. We anticipate that a model to explain this enhancement should take into account surface-electric-dipolar effects. Such effects have proven to be dominant in the case of centrosymmetric semiconductors exposed to air [ 151. In the present case the sample nonlinearity is due to the semiconductor crystallites and the second-order susceptibility associated to the surface electric-dipoles would contributes through a cascade mechanism to the effective surface nonlinearity measured. Then, the contribution of the cascade process to the Kerr-like nonlinear properties is expected to be larger for the reflection coefficient than for the transmission coefficient. Because of the smaller interaction length the phase-matching condition required by the cascade mechanism can be easily satisfied for the reflection measurements rather than for the transmission case. However, a detailed explanation regarding the
D.V. Perrov et d/Optics
physical origin of the surface enhancement the SDG is out of the scope of this paper. This work ian Agencies Cientifico e de Estudos e J.P da Silva
Communicarions
effect in
was partially supported by the BrazilConselho National de Desenvolvimento Tecnol6gico (CNPq) and Financiadora Projetos (FINEP) .We thank also Blenio for polishing the samples.
References [ 11 A.E. Kaplan, Sov. Phys. JETP 45 (1974) 896. 121 W.J. Tomlinson, J.l? Gordon, P.W. Smith and A.E. Kaplan, Appl. Optics 21 (1982) 2041. [ 31 D.R. Andersen and J.J. Regan, J. Opt. Sot. Am. B 6 (1989) 1484. [ 41 Th. Peschel, l? Dannberg, U. Langbein and E Lederer, J. Opt. Sot. Am. B 5 (1988) 29.
123 (1996) 637-641
641
[5] T. Saiki, K. Takeuchi, M. Kuwata-Gonokami, T. Mitsuyu and K. Ohkawa, Appl. Phys. Lett. 60 (1992) 192. I61 L. Roso-France, Phys. Rev. Lett. 55 (1985) 2149. [71 S.R. Hartmann and J.T. Manassah, Optics Lett. 16 ( 1991) 1349. 181 S.D. Kumitsiu, Al? Sukhorukov and V.A. Trofimov. Bull. Rus. Acad. Sci. 56 (1992) 2007. 191 D.V. Petrov, A.S.L. Gomes and Cid B. de Araujo. Appl. Phys. Lett. 65 (1994) 1067. I101 M. Sheik-Bahae, A.A. Said, T.H. Wei, D.J. Hagan and E.W. Van Stryland, IEEE J. Quantum Electron. 26 (1990) 760. 1111 H. Ma, A.S.L. Gomes and Cid B. de Aratijo, Appl. Phys. Lett. 59 (1991) 2666. It21 N. Finlayson, W.C. Banyai, C.T. Seaton, G.I. Stegeman, M. O’Neill, T.J. Cullen and C.N. Ironside, J. Opt. Sot. Am. B 6 (1989) 675. 1131 P Roussignol, D. Ricard and C. Flytzanis, Appl. Phys. A 44 (1987) 285. [I41 Y.R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984). 1151 J.A. Litwin, J.E. Sipe and H.M. van Driel, Phys. Rev. B 31 (1985) 5543.