- Email: [email protected]
Anisotropy in the nonlinear absorption of elongated silver nanoparticles in silica, probed by femtosecond pulses
Optics Communications 282 (2009) 1909–1912
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Anisotropy in the nonlinear absorption of elongated silver nanoparticles in silica, probed by femtosecond pulses R. Rangel-Rojo a,*, J. McCarthy b, H.T. Bookey b, A.K. Kar b, L. Rodriguez-Fernandez c, J.C. Cheang-Wong c, A. Crespo-Sosa c, A. Lopez-Suarez c, A. Oliver c, V. Rodriguez-Iglesias c, H.G. Silva-Pereyra c a
Departamento de Optica, Centro de Investigación Científica y de Educación Superior de Ensenada, Apartado Postal 2732, Ensenada BC 22860, Mexico School of Engineering and Physical Sciences, David Brewster Building, Heriot-Watt University, Edinburgh, EH14 4AS Scotland, UK c Instituto de Física, Universidad Nacional Autónoma de México, Circuito de la Investigación Científica S/N Ciudad Universitaria, Distrito Federal, Mexico b
a r t i c l e
i n f o
Article history: Received 30 October 2008 Accepted 20 January 2009
PACS: 42.55.f 42.65.Tg 42.60.Da
a b s t r a c t We present measurements of the anisotropy of the nonlinear absorption of a silica matrix doped with aligned spheroidal silver nanoparticles, produced by a double ion-implantation process of silver nanoparticles followed by an irradiation with Si ions. The nonlinear response was studied using the z-scan technique with fs pulses at 530 nm, which lies very close to the surface-plasmon absorption peak of the sample. The observed saturable absorption is studied for different angles of the input linear polarization of the pulses, showing a strong anisotropy, which is consistent with the fact that the nanorods are aligned. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Nonlinear absorption Nanoparticles Surface-plasmon resonance
1. Introduction Nanostructured materials have attracted a considerable amount of attention for their application in optical systems, and particularly for their nonlinear optical properties. Metallic nanoparticles embedded in dielectric matrices have shown considerably large nonlinearities, with response times in the ps regime [1]. The nonlinearity is enhanced by the presence of a strong absorption band in the visible, that arises from the surface-plasmon resonance. Among the many techniques to generate nanoparticles, metal ion implantation in glass substrates has proven to be a reliable technique for producing samples with well controlled characteristics. Recently, further high energy ion irradiation with different ions, has been shown to produce highly elongated metallic nanoparticles, with a prolate spheroidal shape [2]. Although the position of the nanoparticles is random, the resulting spheroids are aligned in the direction of incidence of the second set of ions. For a sample with aligned particles, a strong birefringence of the linear and nonlinear optical properties can be expected, which can be exploited for different purposes, including the implementation of has been called ‘lab-on-a-chip’ platforms [3]. Only in the last few years there * Corresponding author. Tel.: +52 646 175 0500; fax: +52 646 175 0553. E-mail address: [email protected] (R. Rangel-Rojo). 0030-4018/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2009.01.048
have been some studies of the nonlinear optical response of elongated nanoparticles and nanorods [4–7], but very few of them concern aligned silver [6], and gold nanoparticles [7]. In this work we present a study of the nonlinear optical properties of the aligned spheroidal nanoparticle-containing glass matrix samples produced by this method. The nonlinearity is studied using the z-scan technique with fs pulses at a 527 nm wavelength, and the anisotropy of the nonlinearity is tested by using several linear polarizations. The dependence of the results with the polarization angle is compared with theoretical results. 2. Sample preparation and characterization The samples were produced using high-purity silica glass plates ð20 20 1 mm3 Þ, NSG ED-C (Nippon Silica Glass) as host matrices, and Ag ions were implanted at 2 MeV at room temperature. The silica plates have a total impurity content less than 20 ppm, no individual impurity content greater than 1 ppm, with less of 1 ppm of OH. The implanted samples were thermally annealed at 600°C in a 50%N2 þ 50%H2 reducing atmosphere for 1 h in order to obtain the highest amount of nucleated nanoparticles. Rutherford Backscattering Spectroscopy (RBS) was used to determine both the metal ion fluence of 7 1016 Ag=cm2 , and the ion projected range of 0.9 lm. Afterwards the samples were cut into
1910
R. Rangel-Rojo et al. / Optics Communications 282 (2009) 1909–1912
several pieces to be irradiated at room temperature with 8 MeV Si ions at an angle of 45° with respect to the sample surface. The Si ion fluence was 2:3 1016 Si=cm2 . Ion implantation and RBS analysis were performed using the 3 MV Tandem accelerator (NEC 9SDH-2 Pelletron) at UNAM. The resulting sample has a 0.5 lm thick layer containing the elongated nanoparticles, at a 1 lm depth inside the silica matrix, as shown schematically in Fig. 1. The particles are aligned at 45° with respect to the substrate normal, as is also shown in Fig. 1, and when viewed from the front, the projection of the nanoparticles long axes point in the direction we label as x. The HRTEM photographs shown in Fig. 2, demonstrate that the nanoparticles are prolate spheroids with a minor axis diameter of 5 nm, and an aspect ratio of 1.7, and that they are indeed aligned. An Ocean Optics Dual Channel S2000 UV–visible spectrophotometer was used to collect the optical absorption spectra, using linearly polarized light with different polarization orientations. Fig. 3 shows the absorption spectra of the sample recorded at normal incidence and using two mutually orthogonal polarizations, at 0° and 90° which are roughly parallel (labeled Ek ), and perpendicular (labeled E? ) to the long axis of the nanoparticles, respectively. Two different absorption bands are clearly discerned from the spectra, one centered at 365 nm for the spectrum taken with the E? polarization, and a broader one at 517 nm for the Ek polarization. These peaks correspond to the different surface-plasmon
a
x
y
b
y
z E
z
x
Fig. 1. Sample morphology, the side view in (a) shows the thin layer containing the elongated nanoparticles, which are aligned at 45° with the normal to the surface, and (b) the front view showing the projection of the nanoparticles and the geometry chosen for the polarization of the incident light.
2.0
1.5
1.0
0.5
0.0 300
400
500
600
700
800
900
Wavelength [nm] Fig. 3. Absorption spectra of the prolate spheroidal silver nanoparticle sample taken for mutually orthogonal linear polarizations, the continuous line corresponds to a polarization angle h ¼ 0 ðEk Þ, and the dotted line to h ¼ 90 ðE? Þ.
resonances for each polarization, as has been probed by studying the linear birefringence of the sample [8]. From Fig. 3 is easily seen that for the Ek polarization there is a remnant of the 365 nm peak, this can be due to a residual misalignment with respect to the direction of elongation of the particles, or to a fraction of the nanoparticles remaining spherical after the second ion-implantation process. Absorption spectra were also taken at intermediate polarization angles. Fig. 4 shows the values of the linear absorption coefficient extracted from the optical density (OD) measured at 527 nm as function of the polarization angle h ða ¼ OD ln 10=LÞ. This is the wavelength of the laser source employed in the z-scan measurements. For a collection of perfectly aligned anisotropic particles, the linear absorption coefficient aðhÞ can be written as [9]:
aðhÞ ¼ ða0 ap=2 Þ cos2 h þ ap=2 ;
ð1Þ
where a0 is the linear absorption coefficient for h ¼ 0 (Ek polarization), and ap=2 is the one corresponding for h ¼ 90 (E? polarization). Fig. 4 shows a fit to the experimental values of OD using expression (1) with a0 ¼ 2:76 104 cm1 , and ap=2 ¼ 5066 cm1 .
35000
-1 lin [cm ]
30000 25000 20000 15000 10000 5000 0 0
15
30
45
60
75
90
Polarization angle [degrees] Fig. 2. High resolution TEM micrograph of the composite film, showing the elongated Ag nanoparticles aligned in a preferential direction. The inset shows the morphology of a single nanoparticle with higher resolution, which clearly has a prolate spheroidal shape.
Fig. 4. Dependence of the linear absorption coefficient alin of the sample measured as a function of polarization angle h. The dots represent the experimental points, while the line represents a fit made using expression (1).
1911
R. Rangel-Rojo et al. / Optics Communications 282 (2009) 1909–1912
3. Z-scan experiments The light source employed in the experiments was an OPA (model Spectra Physics OPA-800) which was pumped by a regeneratively amplified Ti:Sapphire laser (Spectra Physics Spitfire) emitting 1 mJ pulses at a 800 nm wavelength with a repetition rate of 1 kHz, and a pulse width of 70 fs. The signal wavelength of the OPA was tuned to around 1290 nm, and the idler output oscillating at 2.1 lm was quadrupled in frequency by two consecutive second harmonic crystals to yield pulses at a 527 nm wavelength. The standard open-aperture z-scan set-up was used to study the nonlinear absorption of the sample, using a lens with focal length f = 20 cm to focus the 233 fs pulses at 527 nm into the sample, resulting on a beam waist w = 33 lm. Fig. 5 shows experimental results obtained for 150 nJ pulses, and two orthogonal polarizations. The data for h ¼ 0 polarization shows the signature of saturable absorption, i.e. increased transmittance with higher irradiance, while the one at h ¼ 90 shows no discernible change, indicating a much weaker nonlinearity, that is, a higher saturation irradiance Is for this polarization. The nonlinear absorption of the sample is thus highly anisotropic, so we make a study of the nonlinearity for different input polarization angles and pulse energies to fully characterize the response. For all the input polarizations and pulse energies studied, the open-aperture results showed a saturating nonlinearity, which can be modeled by an intensity dependent absorption coefficient aðIÞ given by:
aðIÞ ¼
alin 1 þ I=Is
ð2Þ
;
where alin is the linear absorption coefficient, and Is is the saturation irradiance. This model nonlinear absorption corresponds for example to a two-level system near resonance. The z-scan results were analyzed using expression (2) to calcu0 late transmission through the sample (by solving dI=dz ¼ aðIÞI), and the input irradiance was considered as the gaussian at each sample position z, as described in references [10,11] for example. Fig. 6 shows the experimental results obtained for a h ¼ 0 input polarization, and a pulse energy of 30 nJ. Also shown is the fit made using the procedure previously described. The same procedure was performed with all the z-scan traces obtained at the different polarization angles employed, and using the results at the lowest pulse energies where an effect was clearly seen. We used the results for the lowest energies possible, in order to make sure that
Fig. 6. Z-scan result for a h ¼ 0 polarization, and a pulse energy of 30 nJ. The circles represent the experimental data, while the continuous line represent the fit made using the procedure described in the text.
the nonlinear absorption approximates to that in expression (2) as much as possible. For high irradiance values the nonlinear absorption can deviate considerable from that of a two-level saturable absorber, as it has been shown for other materials [11]. For each input polarization angle h, the fit to the open z-scan results yields a value for Is . Fig. 7 shows the values of Is extracted from the fits as a function of h. The figure shows a rapidly growing Is value for h going to 90°. In fact, pulse energies as high as 300 nJ were needed for h ¼ 90 to actually see an effect. In order to understand this dependence we notice that for a two-level saturable absorber, the saturation irradiance is given by:
Is ¼
hx
rs
ð3Þ
;
where hx is the photon energy, r is the absorption cross section of the transition, and s is the lifetime of the excited state. Using the fact that the absorption coefficient can be written as alin ¼ rN with N the number density of the particles, together with expression (1) for aðhÞ, we can write the polarization-angle dependent saturation irradiance Is ðhÞ as:
Is ðhÞ ¼
Nhx ; s½ða0 ap=2 Þ cos2 h þ ap=2
ð4Þ
1.6 1.5
400
1.4
=0o
1.2
Isat [GW/cm2]
1.3 =90o
1.1
300
200
100
1.0 0.9 -60
-40
-20
0
20
40
60
position z [mm]
0 0
15
30
45
60
75
90
Polarization angle [degrees] Fig. 5. Open-aperture z-scan results for the prolate spheroidal nanoparticle sample with fs pulses at 527 nm. The results are shown for a pulse energy of 150 nJ, and for two different input polarizations, which are labeled h ¼ 0 (diamonds), and h ¼ 90 (squares).
Fig. 7. Saturation irradiance extracted from the z-scan data as a function of polarization angle h. The filled circles represent the Is values extracted from the zscan data, an d the line represents a fit made using expression (4).
1912
R. Rangel-Rojo et al. / Optics Communications 282 (2009) 1909–1912
Table 1 Fitted nonlinear optical coefficients.
4. Conclusions
h (°)
alin ðcm1 Þ 104
Is ðGW=cm2 Þ
b ðcm=GWÞ
Imvð3Þ ðm2 =V2 Þ 1018
0 15 30 45 60 75 90
3.20 3.16 2.54 1.80 1.20 0.844 0.648
12.2 21.0 25.6 36.7 56.9 178 353
2610 1510 994 489 211 47.5 18.4
6.55 3.78 2.49 1.23 0.528 0.119 0.046
Fig. 7 shows the fit obtained using this expression, together with the data extracted from the z-scan results. Given the fit for aðhÞ shown in Fig. 6, the only fitting parameter is the constant N hx=s. As it can be seen from the figure, the fit reproduces the observed angle dependence of the saturation irradiance reasonably well, for a N hx=s ¼ 9:5 105 GW=cm3 value. To get a better fit, it is probably necessary to consider a more realistic nonlinear absorption model, such as the three-level model described in [11]. Although a saturating nonlinearity is not strictly a thirdorder one, for small values of I=Is expression (2) can be approximated as:
aðIÞ ¼
I ’ alin 1 : Is 1 þ I=Is
alin
ð5Þ
When this is compared with the usual expression for a third-order nonlinearity, aðIÞ ¼ alin þ bI, with b the two-photon absorption coefficient, we can make b ¼ alin =Is . Since b is related to Imvð3Þ through Imvð3Þ ¼ ke0 n20 cb=4p (in SI units), we can use the fitted Is ðhÞ values to calculate angle dependent b and Imvð3Þ values, which are contained in Table 1. From the table, it can be seen that jImvð3Þ j takes values as large as 6:55 1018 m2 =V2 ð4:7 1010 esuÞ.
We have shown results for the nonlinear absorption observed in a silica substrate containing a layer of aligned prolate spheroidal silver nanoparticles. The nonlinear absorption mechanism is saturable absorption from the broad surface-plasmon resonance band, and we have found it to be highly anisotropic. We have also shown that the dependence of the linear absorption, and saturation irradiance with the polarization angle observed, can be reasonably well explained by a simple two-level saturation model. Acknowledgements We want to acknowledge CONACYT-Mexico for partial funding for this work through Grant No. 46492 and Scholarship No. 164778, and UNAM for grant DGAPA-UNAM IN119706-3. R. Rangel-Rojo also acknowledges The Royal Society for sponsoring a short visit to the UK. References [1] H. Inouye, K. Tanaka, I. Tanahashi, T. Hattori, H. Nakatsuka, Jpn. J. Appl. Phys. 39 (2000) 5132. [2] A. Oliver et al., Phys. Rev. B 74 (2006) 245425. [3] X.D. Hoa, A.G. Kirk, M. Tabrizian, Biosens. Bioelectron. 23 (2007) 151. [4] H.I. Elim, J. Yang, J.Y. Lee, J. Mi, W. Ji, Appl. Phys. Lett. 88 (2006) 083107. [5] H.E. Ruda, A. Shik, J. Appl. Phys. 101 (2007) 034312. [6] M. Kyoung, M. Lee, Opt. Commun. 171 (1999) 145. [7] J.M. Lamarre, F. Billard, C.H. Kerboua, M. Lequime, S. Roorda, L. Martinus, Opt. Commun. 281 (2008) 331. [8] J.A. Reyes-Esqueda, C. Torres-Torres, J.C. Cheang-Wong, A. Crespo-Sosa, L. Rodrı´guez-Fernández, C. Noguez, A. Oliver, Opt. Express 16 (2008) 710. [9] R.W. Boyd, Nonlinear Optics, Academic Press, San Diego, 1992 (Chapter 4). [10] R. Rangel-Rojo, A.K. Kar, B.S. Wherrett, M. Carroll, G.H. Cross, D. Bloor, Rev. Mex. Fis. 41 (1995) 832. [11] R. Rangel-Rojo, S. Yamada, H. Matsuda, H. Kasai, H. Nakanishi, A.K. Kar, B.S. Wherrett, J. Opt. Soc. Am. B 15 (1998) 2937.
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Anisotropy in the nonlinear absorption of elongated silver nanoparticles in silica, probed by femtosecond pulses R. Rangel-Rojo a,*, J. McCarthy b, H.T. Bookey b, A.K. Kar b, L. Rodriguez-Fernandez c, J.C. Cheang-Wong c, A. Crespo-Sosa c, A. Lopez-Suarez c, A. Oliver c, V. Rodriguez-Iglesias c, H.G. Silva-Pereyra c a
Departamento de Optica, Centro de Investigación Científica y de Educación Superior de Ensenada, Apartado Postal 2732, Ensenada BC 22860, Mexico School of Engineering and Physical Sciences, David Brewster Building, Heriot-Watt University, Edinburgh, EH14 4AS Scotland, UK c Instituto de Física, Universidad Nacional Autónoma de México, Circuito de la Investigación Científica S/N Ciudad Universitaria, Distrito Federal, Mexico b
a r t i c l e
i n f o
Article history: Received 30 October 2008 Accepted 20 January 2009
PACS: 42.55.f 42.65.Tg 42.60.Da
a b s t r a c t We present measurements of the anisotropy of the nonlinear absorption of a silica matrix doped with aligned spheroidal silver nanoparticles, produced by a double ion-implantation process of silver nanoparticles followed by an irradiation with Si ions. The nonlinear response was studied using the z-scan technique with fs pulses at 530 nm, which lies very close to the surface-plasmon absorption peak of the sample. The observed saturable absorption is studied for different angles of the input linear polarization of the pulses, showing a strong anisotropy, which is consistent with the fact that the nanorods are aligned. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Nonlinear absorption Nanoparticles Surface-plasmon resonance
1. Introduction Nanostructured materials have attracted a considerable amount of attention for their application in optical systems, and particularly for their nonlinear optical properties. Metallic nanoparticles embedded in dielectric matrices have shown considerably large nonlinearities, with response times in the ps regime [1]. The nonlinearity is enhanced by the presence of a strong absorption band in the visible, that arises from the surface-plasmon resonance. Among the many techniques to generate nanoparticles, metal ion implantation in glass substrates has proven to be a reliable technique for producing samples with well controlled characteristics. Recently, further high energy ion irradiation with different ions, has been shown to produce highly elongated metallic nanoparticles, with a prolate spheroidal shape [2]. Although the position of the nanoparticles is random, the resulting spheroids are aligned in the direction of incidence of the second set of ions. For a sample with aligned particles, a strong birefringence of the linear and nonlinear optical properties can be expected, which can be exploited for different purposes, including the implementation of has been called ‘lab-on-a-chip’ platforms [3]. Only in the last few years there * Corresponding author. Tel.: +52 646 175 0500; fax: +52 646 175 0553. E-mail address: [email protected] (R. Rangel-Rojo). 0030-4018/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2009.01.048
have been some studies of the nonlinear optical response of elongated nanoparticles and nanorods [4–7], but very few of them concern aligned silver [6], and gold nanoparticles [7]. In this work we present a study of the nonlinear optical properties of the aligned spheroidal nanoparticle-containing glass matrix samples produced by this method. The nonlinearity is studied using the z-scan technique with fs pulses at a 527 nm wavelength, and the anisotropy of the nonlinearity is tested by using several linear polarizations. The dependence of the results with the polarization angle is compared with theoretical results. 2. Sample preparation and characterization The samples were produced using high-purity silica glass plates ð20 20 1 mm3 Þ, NSG ED-C (Nippon Silica Glass) as host matrices, and Ag ions were implanted at 2 MeV at room temperature. The silica plates have a total impurity content less than 20 ppm, no individual impurity content greater than 1 ppm, with less of 1 ppm of OH. The implanted samples were thermally annealed at 600°C in a 50%N2 þ 50%H2 reducing atmosphere for 1 h in order to obtain the highest amount of nucleated nanoparticles. Rutherford Backscattering Spectroscopy (RBS) was used to determine both the metal ion fluence of 7 1016 Ag=cm2 , and the ion projected range of 0.9 lm. Afterwards the samples were cut into
1910
R. Rangel-Rojo et al. / Optics Communications 282 (2009) 1909–1912
several pieces to be irradiated at room temperature with 8 MeV Si ions at an angle of 45° with respect to the sample surface. The Si ion fluence was 2:3 1016 Si=cm2 . Ion implantation and RBS analysis were performed using the 3 MV Tandem accelerator (NEC 9SDH-2 Pelletron) at UNAM. The resulting sample has a 0.5 lm thick layer containing the elongated nanoparticles, at a 1 lm depth inside the silica matrix, as shown schematically in Fig. 1. The particles are aligned at 45° with respect to the substrate normal, as is also shown in Fig. 1, and when viewed from the front, the projection of the nanoparticles long axes point in the direction we label as x. The HRTEM photographs shown in Fig. 2, demonstrate that the nanoparticles are prolate spheroids with a minor axis diameter of 5 nm, and an aspect ratio of 1.7, and that they are indeed aligned. An Ocean Optics Dual Channel S2000 UV–visible spectrophotometer was used to collect the optical absorption spectra, using linearly polarized light with different polarization orientations. Fig. 3 shows the absorption spectra of the sample recorded at normal incidence and using two mutually orthogonal polarizations, at 0° and 90° which are roughly parallel (labeled Ek ), and perpendicular (labeled E? ) to the long axis of the nanoparticles, respectively. Two different absorption bands are clearly discerned from the spectra, one centered at 365 nm for the spectrum taken with the E? polarization, and a broader one at 517 nm for the Ek polarization. These peaks correspond to the different surface-plasmon
a
x
y
b
y
z E
z
x
Fig. 1. Sample morphology, the side view in (a) shows the thin layer containing the elongated nanoparticles, which are aligned at 45° with the normal to the surface, and (b) the front view showing the projection of the nanoparticles and the geometry chosen for the polarization of the incident light.
2.0
1.5
1.0
0.5
0.0 300
400
500
600
700
800
900
Wavelength [nm] Fig. 3. Absorption spectra of the prolate spheroidal silver nanoparticle sample taken for mutually orthogonal linear polarizations, the continuous line corresponds to a polarization angle h ¼ 0 ðEk Þ, and the dotted line to h ¼ 90 ðE? Þ.
resonances for each polarization, as has been probed by studying the linear birefringence of the sample [8]. From Fig. 3 is easily seen that for the Ek polarization there is a remnant of the 365 nm peak, this can be due to a residual misalignment with respect to the direction of elongation of the particles, or to a fraction of the nanoparticles remaining spherical after the second ion-implantation process. Absorption spectra were also taken at intermediate polarization angles. Fig. 4 shows the values of the linear absorption coefficient extracted from the optical density (OD) measured at 527 nm as function of the polarization angle h ða ¼ OD ln 10=LÞ. This is the wavelength of the laser source employed in the z-scan measurements. For a collection of perfectly aligned anisotropic particles, the linear absorption coefficient aðhÞ can be written as [9]:
aðhÞ ¼ ða0 ap=2 Þ cos2 h þ ap=2 ;
ð1Þ
where a0 is the linear absorption coefficient for h ¼ 0 (Ek polarization), and ap=2 is the one corresponding for h ¼ 90 (E? polarization). Fig. 4 shows a fit to the experimental values of OD using expression (1) with a0 ¼ 2:76 104 cm1 , and ap=2 ¼ 5066 cm1 .
35000
-1 lin [cm ]
30000 25000 20000 15000 10000 5000 0 0
15
30
45
60
75
90
Polarization angle [degrees] Fig. 2. High resolution TEM micrograph of the composite film, showing the elongated Ag nanoparticles aligned in a preferential direction. The inset shows the morphology of a single nanoparticle with higher resolution, which clearly has a prolate spheroidal shape.
Fig. 4. Dependence of the linear absorption coefficient alin of the sample measured as a function of polarization angle h. The dots represent the experimental points, while the line represents a fit made using expression (1).
1911
R. Rangel-Rojo et al. / Optics Communications 282 (2009) 1909–1912
3. Z-scan experiments The light source employed in the experiments was an OPA (model Spectra Physics OPA-800) which was pumped by a regeneratively amplified Ti:Sapphire laser (Spectra Physics Spitfire) emitting 1 mJ pulses at a 800 nm wavelength with a repetition rate of 1 kHz, and a pulse width of 70 fs. The signal wavelength of the OPA was tuned to around 1290 nm, and the idler output oscillating at 2.1 lm was quadrupled in frequency by two consecutive second harmonic crystals to yield pulses at a 527 nm wavelength. The standard open-aperture z-scan set-up was used to study the nonlinear absorption of the sample, using a lens with focal length f = 20 cm to focus the 233 fs pulses at 527 nm into the sample, resulting on a beam waist w = 33 lm. Fig. 5 shows experimental results obtained for 150 nJ pulses, and two orthogonal polarizations. The data for h ¼ 0 polarization shows the signature of saturable absorption, i.e. increased transmittance with higher irradiance, while the one at h ¼ 90 shows no discernible change, indicating a much weaker nonlinearity, that is, a higher saturation irradiance Is for this polarization. The nonlinear absorption of the sample is thus highly anisotropic, so we make a study of the nonlinearity for different input polarization angles and pulse energies to fully characterize the response. For all the input polarizations and pulse energies studied, the open-aperture results showed a saturating nonlinearity, which can be modeled by an intensity dependent absorption coefficient aðIÞ given by:
aðIÞ ¼
alin 1 þ I=Is
ð2Þ
;
where alin is the linear absorption coefficient, and Is is the saturation irradiance. This model nonlinear absorption corresponds for example to a two-level system near resonance. The z-scan results were analyzed using expression (2) to calcu0 late transmission through the sample (by solving dI=dz ¼ aðIÞI), and the input irradiance was considered as the gaussian at each sample position z, as described in references [10,11] for example. Fig. 6 shows the experimental results obtained for a h ¼ 0 input polarization, and a pulse energy of 30 nJ. Also shown is the fit made using the procedure previously described. The same procedure was performed with all the z-scan traces obtained at the different polarization angles employed, and using the results at the lowest pulse energies where an effect was clearly seen. We used the results for the lowest energies possible, in order to make sure that
Fig. 6. Z-scan result for a h ¼ 0 polarization, and a pulse energy of 30 nJ. The circles represent the experimental data, while the continuous line represent the fit made using the procedure described in the text.
the nonlinear absorption approximates to that in expression (2) as much as possible. For high irradiance values the nonlinear absorption can deviate considerable from that of a two-level saturable absorber, as it has been shown for other materials [11]. For each input polarization angle h, the fit to the open z-scan results yields a value for Is . Fig. 7 shows the values of Is extracted from the fits as a function of h. The figure shows a rapidly growing Is value for h going to 90°. In fact, pulse energies as high as 300 nJ were needed for h ¼ 90 to actually see an effect. In order to understand this dependence we notice that for a two-level saturable absorber, the saturation irradiance is given by:
Is ¼
hx
rs
ð3Þ
;
where hx is the photon energy, r is the absorption cross section of the transition, and s is the lifetime of the excited state. Using the fact that the absorption coefficient can be written as alin ¼ rN with N the number density of the particles, together with expression (1) for aðhÞ, we can write the polarization-angle dependent saturation irradiance Is ðhÞ as:
Is ðhÞ ¼
Nhx ; s½ða0 ap=2 Þ cos2 h þ ap=2
ð4Þ
1.6 1.5
400
1.4
=0o
1.2
Isat [GW/cm2]
1.3 =90o
1.1
300
200
100
1.0 0.9 -60
-40
-20
0
20
40
60
position z [mm]
0 0
15
30
45
60
75
90
Polarization angle [degrees] Fig. 5. Open-aperture z-scan results for the prolate spheroidal nanoparticle sample with fs pulses at 527 nm. The results are shown for a pulse energy of 150 nJ, and for two different input polarizations, which are labeled h ¼ 0 (diamonds), and h ¼ 90 (squares).
Fig. 7. Saturation irradiance extracted from the z-scan data as a function of polarization angle h. The filled circles represent the Is values extracted from the zscan data, an d the line represents a fit made using expression (4).
1912
R. Rangel-Rojo et al. / Optics Communications 282 (2009) 1909–1912
Table 1 Fitted nonlinear optical coefficients.
4. Conclusions
h (°)
alin ðcm1 Þ 104
Is ðGW=cm2 Þ
b ðcm=GWÞ
Imvð3Þ ðm2 =V2 Þ 1018
0 15 30 45 60 75 90
3.20 3.16 2.54 1.80 1.20 0.844 0.648
12.2 21.0 25.6 36.7 56.9 178 353
2610 1510 994 489 211 47.5 18.4
6.55 3.78 2.49 1.23 0.528 0.119 0.046
Fig. 7 shows the fit obtained using this expression, together with the data extracted from the z-scan results. Given the fit for aðhÞ shown in Fig. 6, the only fitting parameter is the constant N hx=s. As it can be seen from the figure, the fit reproduces the observed angle dependence of the saturation irradiance reasonably well, for a N hx=s ¼ 9:5 105 GW=cm3 value. To get a better fit, it is probably necessary to consider a more realistic nonlinear absorption model, such as the three-level model described in [11]. Although a saturating nonlinearity is not strictly a thirdorder one, for small values of I=Is expression (2) can be approximated as:
aðIÞ ¼
I ’ alin 1 : Is 1 þ I=Is
alin
ð5Þ
When this is compared with the usual expression for a third-order nonlinearity, aðIÞ ¼ alin þ bI, with b the two-photon absorption coefficient, we can make b ¼ alin =Is . Since b is related to Imvð3Þ through Imvð3Þ ¼ ke0 n20 cb=4p (in SI units), we can use the fitted Is ðhÞ values to calculate angle dependent b and Imvð3Þ values, which are contained in Table 1. From the table, it can be seen that jImvð3Þ j takes values as large as 6:55 1018 m2 =V2 ð4:7 1010 esuÞ.
We have shown results for the nonlinear absorption observed in a silica substrate containing a layer of aligned prolate spheroidal silver nanoparticles. The nonlinear absorption mechanism is saturable absorption from the broad surface-plasmon resonance band, and we have found it to be highly anisotropic. We have also shown that the dependence of the linear absorption, and saturation irradiance with the polarization angle observed, can be reasonably well explained by a simple two-level saturation model. Acknowledgements We want to acknowledge CONACYT-Mexico for partial funding for this work through Grant No. 46492 and Scholarship No. 164778, and UNAM for grant DGAPA-UNAM IN119706-3. R. Rangel-Rojo also acknowledges The Royal Society for sponsoring a short visit to the UK. References [1] H. Inouye, K. Tanaka, I. Tanahashi, T. Hattori, H. Nakatsuka, Jpn. J. Appl. Phys. 39 (2000) 5132. [2] A. Oliver et al., Phys. Rev. B 74 (2006) 245425. [3] X.D. Hoa, A.G. Kirk, M. Tabrizian, Biosens. Bioelectron. 23 (2007) 151. [4] H.I. Elim, J. Yang, J.Y. Lee, J. Mi, W. Ji, Appl. Phys. Lett. 88 (2006) 083107. [5] H.E. Ruda, A. Shik, J. Appl. Phys. 101 (2007) 034312. [6] M. Kyoung, M. Lee, Opt. Commun. 171 (1999) 145. [7] J.M. Lamarre, F. Billard, C.H. Kerboua, M. Lequime, S. Roorda, L. Martinus, Opt. Commun. 281 (2008) 331. [8] J.A. Reyes-Esqueda, C. Torres-Torres, J.C. Cheang-Wong, A. Crespo-Sosa, L. Rodrı´guez-Fernández, C. Noguez, A. Oliver, Opt. Express 16 (2008) 710. [9] R.W. Boyd, Nonlinear Optics, Academic Press, San Diego, 1992 (Chapter 4). [10] R. Rangel-Rojo, A.K. Kar, B.S. Wherrett, M. Carroll, G.H. Cross, D. Bloor, Rev. Mex. Fis. 41 (1995) 832. [11] R. Rangel-Rojo, S. Yamada, H. Matsuda, H. Kasai, H. Nakanishi, A.K. Kar, B.S. Wherrett, J. Opt. Soc. Am. B 15 (1998) 2937.