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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 15 — Jul. 20, 2009
  • pp: 12849–12868
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Anisotropic linear and nonlinear optical properties from anisotropy-controlled metallic nanocomposites

Jorge Alejandro Reyes-Esqueda, Vladimir Rodríguez-Iglesias, Héctor-Gabriel Silva-Pereyra, Carlos Torres-Torres, Ana-Laura Santiago-Ramírez, Juan Carlos Cheang-Wong, Alejandro Crespo-Sosa, Luis Rodríguez-Fernández, Alejandra López-Suárez, and Alicia Oliver  »View Author Affiliations


Optics Express, Vol. 17, Issue 15, pp. 12849-12868 (2009)
http://dx.doi.org/10.1364/OE.17.012849


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Abstract

High-energy metallic ions were implanted in silica matrices, obtaining spherical-like metallic nanoparticles (NPs) after a proper thermal treatment. These NPs were then deformed by irradiation with Si ions, obtaining an anisotropic metallic nanocomposite. An average large birefringence of 0.06 was measured for these materials in the 300-800 nm region. Besides, their third order nonlinear optical response was measured using self-diffraction and P-scan techniques at 532 nm with 26 ps pulses. By adjusting the incident light’s polarization and the angular position of the nanocomposite, the measurements could be directly related to, at least, two of the three linear independent components of its third order susceptibility tensor, finding a large, but anisotropic, response of around 10−7 esu with respect to other isotropic metallic systems. For the nonlinear optical absorption, we were able to shift from saturable to reverse saturable absorption depending on probing the Au NP’s major or minor axes, respectively. This fact could be related to local field calculations and NP’s electronic properties. For the nonlinear optical refraction, we passed from self-focusing to self-defocusing, when changing from Ag to Au.

© 2009 OSA

1. Introduction

Very recently, we have reported on the control of the deformation of metallic NPs by Si irradiation, obtaining metallic nanocomposites composed of ellipsoidal NPs aligned along the Si irradiation’s direction and with an aspect ratio dependent on the Si fluence [6

6. A. Oliver, J. A. Reyes-Esqueda, J. C. Cheang-Wong, C. E. Román-Velázquez, A. Crespo-Sosa, L. Rodríguez-Fernández, J. A. Seman, and C. Noguez, “Controlled anisotropic deformation of Ag nanoparticles by Si ion irradiation,” Phys. Rev. B 74(24), 245425 (2006). [CrossRef]

]. We also showed that these anisotropic nanosystems show a large form or optical birefringence of around 0.1 for wavelengths close to their SP resonances [20

20. J. A. Reyes-Esqueda, C. Torres-Torres, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, C. Noguez, and A. Oliver, “Large optical birefringence by anisotropic silver nanocomposites,” Opt. Express 16(2), 710–717 (2008). [CrossRef] [PubMed]

]; now, we are reporting on the birefringence for the 300-800 nm region. However, one of the most promising endowments of these anisotropic systems comes from their nonlinear optical properties, since they have exhibited so far the largest cubic nonlinearities under resonance conditions, which is due to the strengthening of the local field at SP resonance frequencies [21

21. T. He, Z. Cai, P. Li, Y. Cheng, and Y. Mo “Third-order nonlinear response of Ag/methyl orange composite thin films,” J. Mod. Opt. 55(6), 975–983 (2008). [CrossRef]

23

23. K. Tsuchiya, S. Nagayasu, S. Okamoto, T. Hayakawa, T. Hihara, K. Yamamoto, I. Takumi, S. Hara, H. Hasegawa, S. Akasaka, and N. Kosikawa, “Nonlinear optical properties of gold nanoparticles selectively introduced into the periodic microdomains of block copolymers,” Opt. Express 16(8), 5362–5371 (2008). [CrossRef] [PubMed]

], and since they can be implicated in optoelectronics [24

24. R. W. Boyd, “Nonlinear Optics,” Academic Press, San Diego, (1992).

] and quantum-information devices [25

25. Y. Li, S. Zhang, J. Liu, and K. Zhang, “Quantum correlation between fundamental and second-harmonic fields via second-harmonic generation,” J. Opt. Soc. Am. B 24(3), 660–663 (2007). [CrossRef]

32

32. L. J. Klein, H. F. Hamann, Y.-Y. Au, and S. Ingvarsson, “Coherence properties of infrared thermal emission from heated metallic nanowires,” Appl. Phys. Lett. 92(21), 213102 (2008). [CrossRef]

], for example. Nevertheless, a complete understanding of the physical reasons behind the nonlinear optical response of metallic NPs for all the possible scenarios (NPs size and shape, wavelength used, pulse duration, etc.) is still lacking. For instance, although some works have started to clear the path to [33

33. F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys., A Mater. Sci. Process. 47(4), 347–357 (1988). [CrossRef]

35

35. Y. Guillet, M. Rashidi-Huyeh, and B. Palpant, “Influence of laser pulse characteristics on the hot electron contribution to the third-order nonlinear optical response of gold nanoparticles,” Phys. Rev. B 79(4), 045410 (2009). [CrossRef]

], there is not yet an unambiguous trend indicating whether the nanocomposite will show saturable or reverse saturable absorption near resonance [36

36. R. F. Haglund Jr, L. Yang, R. H. Magruder III, J. E. Witting, K. Becker, and R. A. Zuhr, “Picosecond nonlinear optical response of a Cu:silica nanocluster composite,” Opt. Lett. 18(5), 373–375 (1993). [CrossRef] [PubMed]

47

47. R. L. Sutherland, “Handbook of Nonlinear Optics,” Marcel Dekker Inc, New York, (1996).

]. In such a direction, studying the physical contribution of the separate components of the third-order susceptibility tensor would add more information about the physics behind the optical response of metallic nanocomposites. In particular, as it will be shown below for nanoellipsoids, this tensor has only three linear independent components when probing with a fully-degenerate wave mixing and two of them can be associated to the major and minor axes of the ellipsoid, respectively [47

47. R. L. Sutherland, “Handbook of Nonlinear Optics,” Marcel Dekker Inc, New York, (1996).

,48

48. R. P. Davis, A. J. Moad, G. S. Goeken, R. D. Wampler, and G. J. Simpson, “Selection rules and symmetry relations for four-wave mixing measurements of uniaxial assemblies,” J. Phys. Chem. B 112(18), 5834–5848 (2008). [CrossRef] [PubMed]

]. In this way, for the wavelength chosen, we will be near or close to the position of the surface plasmon resonance of the metallic NPs, helping to get more elements in order to identify whether there is a hot electron contribution or not.

Therefore, in this work, apart from the birefringence measurements, we obtained, by self-diffraction [49

49. C. Torres-Torres, M. Trejo-Valdez, P. Santiago-Jacinto, and J. A. Reyes-Esqueda, “Stimulated emission and optical third order nonlinearity in Li-doped nanorods,” J. Phys. Chem C , in press.

] and P-scan [50

50. P. P. Banerjee, A. Y. Danileiko, T. Hudson, and D. McMillen, “P-scan analysis of inhomogeneously induced optical nonlinearities,” J. Opt. Soc. Am. B 15(9), 2446–2454 (1998). [CrossRef]

] methods at 532 nm and 26 ps, the real and the imaginary parts of the linear independent components of χ (3) for anisotropic Ag- and Au-nanocomposites, which were obtained by controlled deformation with Si irradiation [6

6. A. Oliver, J. A. Reyes-Esqueda, J. C. Cheang-Wong, C. E. Román-Velázquez, A. Crespo-Sosa, L. Rodríguez-Fernández, J. A. Seman, and C. Noguez, “Controlled anisotropic deformation of Ag nanoparticles by Si ion irradiation,” Phys. Rev. B 74(24), 245425 (2006). [CrossRef]

]. For the nonlinear optical refraction, we passed from self-focusing to self-defocusing, when changing from Ag to Au. In the case of Au, we could shift from saturable to reverse saturable absorption by probing the Au NP’s major or minor axes, respectively. By following local field calculations presented earlier by Lamarre et al. [34

34. J.-M. Lamarre, F. Billard, and L. Martinu, “Local field calculations of the anisotropic nonlinear absorption coefficient of aligned gold nanorods embedded in silica,” J. Opt. Soc. Am. B 25(6), 961–971 (2008). [CrossRef]

], we could also verify the ratio between the measured real and imaginary parts of the components associated with the major and the minor axes. Finally, the electronic contribution from hot electrons to this nonlinear optical response will be discussed accordingly to the pulse duration, the intensity and the position of the wavelength used in our setup, with respect to the SP resonances of the anisotropic nanocomposites.

2. Theoretical analysis

2.1 Birefringence analysis

As it has been shown previously [20

20. J. A. Reyes-Esqueda, C. Torres-Torres, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, C. Noguez, and A. Oliver, “Large optical birefringence by anisotropic silver nanocomposites,” Opt. Express 16(2), 710–717 (2008). [CrossRef] [PubMed]

], we have used an ellipsometric technique to measure the light transmission through our anisotropic samples when placed and rotated between crossed and parallel polarizers. The mathematical details about the analysis of these ellipsometric measurements are given throughout in [9

9. A. L. Gonzalez, J. A. Reyes-Esqueda, and C. Noguez, “Optical properties of elongated noble metal nanoparticles,” J. Phys. Chem. C 112(19), 7356–7362 (2008). [CrossRef]

]. However, we recall the main expressions for the measured intensities when using the experimental setup shown in Fig. 1
Fig. 1 Experimental setup for birefringence measurements with white light. Ein stands for the incident electric field, L for a lens, A for analyzer, P for polarizer, and PD for a photodiode.
, which has been used to obtain the results shown below in Table 1

Table 1. Comparative of the measured birefringence peaks of the anisotropic metallic nanocomposites and the corresponding SP resonance positions.

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.

For the transmitted light, when the axes of the polarizer-analyzer system are aligned, it can be shown [9

9. A. L. Gonzalez, J. A. Reyes-Esqueda, and C. Noguez, “Optical properties of elongated noble metal nanoparticles,” J. Phys. Chem. C 112(19), 7356–7362 (2008). [CrossRef]

] that the detected intensity at a given in-plane polarization α is given by
I(α,λ,0)=As2sin4α+Ap2cos4α+12AsApsin22αcos2πLΔnαλ,
(1)
while when they are crossed, the detected intensity is given by
I(α,λ,π2)=14sin22α[As2+Ap22AsApcos2πLΔnαλ],
(2)
where As and Ap are the measured amplitude transmission factors for each eigenpolarization, L is the interaction length, i.e. the thickness of the NPs layer, and λ is the free-space incident wavelength. We will measure these two intensities, obtainingAp2, As2 and the birefringence of the nanocomposite as explained into the results section.

2.2 Third order nonlinear polarization for anisotropic metallic nanocomposites

According to Ref. 47

47. R. L. Sutherland, “Handbook of Nonlinear Optics,” Marcel Dekker Inc, New York, (1996).

, the third order nonlinear polarization is written in general as
P(3)=χ(3)EEE,
(3)
which can be written for each Cartesian component as
Pi(3)(ω4)=6jklχijkl(3)(ω4;ω1,ω2,ω3)Ej(ω1)Ek(ω2)El(ω3),
(4)
where χijkl(3)(ω4;ω1,ω2,ω3) is the macroscopic third order susceptibility of the material, with ω4=ω1+ω2+ω3 and ωi, i=1,2,3, are the frequencies of the incident beams.

On the other hand, for an uniaxial system, aligned but not oriented (D symmetry) [48

48. R. P. Davis, A. J. Moad, G. S. Goeken, R. D. Wampler, and G. J. Simpson, “Selection rules and symmetry relations for four-wave mixing measurements of uniaxial assemblies,” J. Phys. Chem. B 112(18), 5834–5848 (2008). [CrossRef] [PubMed]

], the susceptibility tensor has only 11 nonzero elements, 10 of which are independent, for a non-degenerate wave mixing. In the case of a single degeneracy, only 8 nonzero elements remain, 7 of which are independent. But, most interestingly, in fully degenerate wave mixing, where ω1=ω2=ω and ω3=ω, it remains only 3 nonzero, independent components, given by χ1111(3), χ1133(3) and χ3333(3) [48

48. R. P. Davis, A. J. Moad, G. S. Goeken, R. D. Wampler, and G. J. Simpson, “Selection rules and symmetry relations for four-wave mixing measurements of uniaxial assemblies,” J. Phys. Chem. B 112(18), 5834–5848 (2008). [CrossRef] [PubMed]

]. In consequence, the nonlinear polarization of a general uniaxial system, for the fully degenerate case, may be written as
P1(ω)=[χ1111(3){3E1(ω)E1(ω)E1*(ω)+2E1(ω)E2(ω)E2*(ω)+E2(ω)E2(ω)E1*(ω)}+χ1133(3){6E1(ω)E3*(ω)+3E3(ω)E1*(ω)}E3(ω)];P2(ω)=[χ1111(3){3E2(ω)E2(ω)E2*(ω)+2E1(ω)E2(ω)E1*(ω)+E1(ω)E1(ω)E2*(ω)}+χ1133(3){6E2(ω)E3*(ω)+3E3(ω)E2*(ω)}E3(ω)];P3(ω)=[χ1133(3){3(E1(ω)E1(ω)+E2(ω)E2(ω))E3*(ω)+6(E1(ω)E1*(ω)+E2(ω)E2*(ω))E3(ω)}+3χ3333(3)E3(ω)E3(ω)E3*(ω)],
(5)
where Ei*(ω)=Ei(ω), such that Ei(ω)Ei*(ω)=Ei(ω)Ei(ω)=|Ei(ω)|2 and Ei(ω)Ei(ω)=Ei2(ω).

Now, in order to determine the components of the susceptibility tensor for an uniaxial material by using the last expression and fully degenerate wave mixing, it is necessary to choose the laboratory coordinate system such that the z-axis is parallel to the optical axis of the nanocomposite. However, such a coincidence it is not obvious for the anisotropic metallic nanocomposites studied in this work, since the metallic nanoparticles are embedded into a SiO2 matrix and then deformed in the direction of a Si ions beam, becoming an unixial system [6

6. A. Oliver, J. A. Reyes-Esqueda, J. C. Cheang-Wong, C. E. Román-Velázquez, A. Crespo-Sosa, L. Rodríguez-Fernández, J. A. Seman, and C. Noguez, “Controlled anisotropic deformation of Ag nanoparticles by Si ion irradiation,” Phys. Rev. B 74(24), 245425 (2006). [CrossRef]

,11

11. V. Rodríguez-Iglesias, H. G. Silva-Pereyra, J. C. Cheang-Wong, J. A. Reyes-Esqueda, L. Rodríguez-Fernández, A. Crespo-Sosa, G. Kellerman, and A. Oliver, “MeV Si ion irradiation effects on the optical absorption properties of metallic nanoparticles embedded in silica,” Nucl. Instrum. Methods B 266(12-13), 3138–3142 (2008). [CrossRef]

,20

20. J. A. Reyes-Esqueda, C. Torres-Torres, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, C. Noguez, and A. Oliver, “Large optical birefringence by anisotropic silver nanocomposites,” Opt. Express 16(2), 710–717 (2008). [CrossRef] [PubMed]

]. In consequence, the electric field of the incident light beam will always make an angle θ to this optical axis. Therefore, the most convenient way of performing the calculations is giving preference to the deformed NP coordinate system, expressing the incident electric field in this frame and then coming back to the laboratory frame. To do this in the simplest manner, one can choose the laboratory and the NP systems such that their x-axes coincide, the y-axis of the laboratory frame be parallel to the wavevector of the incident light, the electric field be parallel to the z-axis of the laboratory, and that this last make an angle θ to the NP z-axis. This choice is shown in detail in Fig. 2
Fig. 2 Reference systems for the laboratory (primed) and the anisotropic metallic nanoparticle (unprimed).
.

As it was established above, Eq. (5) gives the nonlinear polarization of the all system in its main axes; consequently, for the anisotropic metallic nanocomposite, this polarization may be expressed in the NP frame by rewriting the electric field in that system, coming back later to the laboratory frame. Thus, Eq. (5) may be written in the xyz-frame of the NP, as
PNL(3)(ω)=χ1111(3)[{3Ex(ω)|Ex(ω)|2+2Ex(ω)|Ey(ω)|2+Ey2(ω)Ex*(ω)}i^+{3Ey(ω)|Ey(ω)|2+2Ey(ω)|Ex(ω)|2+Ex2(ω)Ey*(ω)}j^]++χ1133(3)[{6Ey(ω)Ez*(ω)+3Ez(ω)Ey*(ω)}Ez(ω)i^+{6Ex(ω)Ez*(ω)+3Ez(ω)Ex*(ω)}Ez(ω)j^+{3(Ex2(ω)+Ey2(ω))Ez*(ω)+6(|Ex(ω)|2+|Ey(ω)|2)Ez(ω)}k^]++3χ3333(3)Ez(ω)|Ez(ω)|2k^,
(6)
where, by using Fig. 2, the components of the electric field can be written in such a frame as
Ex(ω)=Ex*(ω)=0,Ey(ω)=E(ω)sinθEz(ω)=E(ω)cosθ.
(7)
This allows rewriting the third order nonlinear polarization for the anisotropic metallic nanocomposite in terms of the angle between the electric field and the NP’s axis, which defines the optical axis of the nanocomposite, as
PNL(3)(θ;ω)=3|E(ω)|2E(ω)[χ1111(3)sin3θj^+32χ1133(3)sin2θ{cosθj^+sinθk^}+χ3333(3)cos3θk^].
(8)
When the incident electric field is parallel to the x-axis, the nonlinear polarization is trivially given by
PNL(3)(ω)=PNL,lab(3)(ω)=3|E(ω)|2E(ω)χ1111(3)i^.
(9)
When projecting the polarization components given by Eq. (8) on the laboratory frame y’z’, the nonlinear polarization is expressed as
PNL,lab(3)(θ;ω)=3|E(ω)|2E(ω)[χ1111(3)sin3θ(cosθj^'sinθk^')+3χ1133(3)sinθcosθj^'+χ3333(3)cos3θ(sinθj^'+cosθk^')].
(10)
These last two equations, Eqs. (9) and (10), are to an uniaxial, aligned but not oriented, system, what the one typically found in literature [24

24. R. W. Boyd, “Nonlinear Optics,” Academic Press, San Diego, (1992).

,47

47. R. L. Sutherland, “Handbook of Nonlinear Optics,” Marcel Dekker Inc, New York, (1996).

]
PNL(3)(ω)=6EE*Eχ1122(3)+3EEE*χ1221(3),
(11)
is to isotropic systems. Equation (9) determines χ1111(3) directly when measuring with the incident electric field perpendicular to the major axis of the NPs, but all three components are present in Eq. (10). Therefore, in order to determine each of them separately, it becomes necessary performing at least two other measurements as a function of the angle of incidence of the light with respect to the major axis of the NPs, such that we obtain enough equations to determine the other two components of the nanocomposite’s tensor, χ1133(3) and χ3333(3).

From what has been said above, one can rewrite Eq. (8) as
PNL(3)(θ;ω)=|E(ω)|2E(ω)χeff(3),
(12)
where
χeff(3)=3[(χ1111(3)sin3θ+32χ1133(3)sin2θcosθ)j^+(32χ1133(3)sin2θsinθ+χ3333(3)cos3θ)k^],
(13)
is the effective third order susceptibility of the nanocomposite, when measuring at a given tilt of θ between the NP and the incident electric field, after considering light refraction. This last expression allows us finally to write
|χeff(3)|2=9[|χ1111(3)|2sin6θ+|χ3333(3)|2cos6θ+32sin22θ{32|χ1133(3)|2+sin2θ(Reχ1111(3)Reχ1133(3)+Imχ1111(3)Imχ1133(3))+cos2θ(Reχ1133(3)Reχ3333(3)+Imχ1133(3)Imχ3333(3))}].
(14)
In consequence, when measuring according to what has been explained for Fig. 3, cases b) and c), we would obtain |χeff(3)|2=9|χ1111(3)|2 and |χeff(3)|2=9|χ3333(3)|2, respectively; while for case a), we would apply Eq. (14) fully.

3. Experimental

3.1 Synthesis and deformation of metallic nanoparticles

As reported before [6

6. A. Oliver, J. A. Reyes-Esqueda, J. C. Cheang-Wong, C. E. Román-Velázquez, A. Crespo-Sosa, L. Rodríguez-Fernández, J. A. Seman, and C. Noguez, “Controlled anisotropic deformation of Ag nanoparticles by Si ion irradiation,” Phys. Rev. B 74(24), 245425 (2006). [CrossRef]

,11

11. V. Rodríguez-Iglesias, H. G. Silva-Pereyra, J. C. Cheang-Wong, J. A. Reyes-Esqueda, L. Rodríguez-Fernández, A. Crespo-Sosa, G. Kellerman, and A. Oliver, “MeV Si ion irradiation effects on the optical absorption properties of metallic nanoparticles embedded in silica,” Nucl. Instrum. Methods B 266(12-13), 3138–3142 (2008). [CrossRef]

,20

20. J. A. Reyes-Esqueda, C. Torres-Torres, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, C. Noguez, and A. Oliver, “Large optical birefringence by anisotropic silver nanocomposites,” Opt. Express 16(2), 710–717 (2008). [CrossRef] [PubMed]

], high-purity silica glass plates were implanted at room temperature with 2 MeV Ag2+ (or Au2+) ions at a fluence of (4.7 ± 0.4) × 1016 ions/cm2 for Ag, and (2.6 ± 0.2) × 1016 and (5.0 ± 0.4) × 1016 ions/cm2 for Au. The Ag ions were implanted at 45.0° ± 0.5° off normal for the nonlinear measurements and at 0° for the birefringence measurements, while the Au ions were implanted at 0° for both cases. The corresponding metal concentrations for these fluences and these angles of implantation are 0.0379 and 0.0268 for Ag, respectively; while for Au are 0.0312 and 0.06, respectively. The depth of the Ag NPs layer was (0.61 ± 0.03) μm with a FWHM of (0.33 ± 0.03) μm for implantation at 45° and (0.90 ± 0.03) μm with a FWHM of (0.45 ± 0.03) μm for implantation at 0°, while for Au the depth was (0.70 ± 0.02) μm and the FWHM was (0.10 ± 0.02) μm. After implantation, the samples were thermally annealed for 1 hr in a reducing atmosphere 50%H2 + 50%N2 at a temperature of 600°C for Ag. In the case of Au, an oxidizing atmosphere (air) was used for 1 hr at 1100°C. The metal implanted distributions and fluences were determined by Rutherford Backscattering Spectrometry (RBS) measurements using a 3 MeV 4He+ beam for Ag and 2 MeV 4He+ beam for Au. Afterwards, the silica plate was cut into several pieces and each piece was irradiated at room temperature with 8 MeV Si ions for Ag and 10 MeV Si ions for Au. The Si irradiation was performed under an angle off normal of θ = (45.0° ± 0.5°) or of (80.0° ± 0.5°) for both, Ag and Au. Each sample was irradiated at different Si fluences in the range of 1015 Si/cm2 for Ag and of 1016 Si/cm2 for Au, in order to induce a shape deformation of the NPs [3

3. A. Tao, P. Sinsermsuksakul, and P. Yang, “Polyhedral silver nanoparticles with distinct scattering signatures,” Angew. Chem. Int. Ed. 45(28), 4597–4601 (2006). [CrossRef]

]. Ion implantation, RBS analysis and Si irradiation were performed using the IFUNAM’s 3 MV Tandem accelerator NEC 9SDH-2 Pelletron facility.

3.2 Optical measurements

Optical absorption and ellipsometric measurements were performed with an Ocean Optics Dual Channel S2000 UV-visible spectrophotometer. For the ellipsometric technique, we used the setup shown in Fig. 1 and measured the birefringence in the range of 300-800 nm.

The third order nonlinear optical response for a thin nonlinear optical media with strong absorptive response can be obtained by identifying the vectorial self-diffraction intensities generated by two incident waves [49

49. C. Torres-Torres, M. Trejo-Valdez, P. Santiago-Jacinto, and J. A. Reyes-Esqueda, “Stimulated emission and optical third order nonlinearity in Li-doped nanorods,” J. Phys. Chem C , in press.

]. In this work, we firstly measured the nonlinear optical absorption using a P-scan technique [50

50. P. P. Banerjee, A. Y. Danileiko, T. Hudson, and D. McMillen, “P-scan analysis of inhomogeneously induced optical nonlinearities,” J. Opt. Soc. Am. B 15(9), 2446–2454 (1998). [CrossRef]

], and later we used these results in order to fit the experimental data obtained by scalar self-diffraction experiments. The measurements were performed at IFUNAM’s Nonlinear Optics laboratory using a Nd-YAG PL2143A EKSPLA system at λ = 532 nm with a pulse duration of 26 ps (FWHM) and linear polarization. The maximum pulse energy in the experiments was 0.1 mJ, while the intensity rate between the two beams of the self-diffraction setup, I 1:I 2, was 1:1. The radius of the beam waist at the focus in the sample was measured to be 0.1 mm. The obtained nonlinear results are the average of enough time-distanced single-pulse measurements, well below the ablation threshold, in order to avoid thermal effects from accumulated pulses and assure reversible and reproducible nonlinear optical effects. Both setups are schematized in Fig. 4
Fig. 4 Experimental setup used for self-diffraction and P-scan measurements (dashed components).
, where RPD represents a photodetector used for monitoring the laser stability; PD1 and PD2 are photodetectors for measuring the optical transmittance of the sample, while PD3 detects the self-diffraction signal. The mirrors were placed in order to obtain the same optical path for the two incident beams. We calibrated the self-diffraction measurements using a CS2 sample, which is a well known nonlinear optical media with |χeff(3)| = 1.9 × 10−12esu [ 26

26. M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438(7069), 837–841 (2005). [CrossRef] [PubMed]

]. For the single beam transmittance measurement in the P-scan experiments, we blocked one of the beams in the same experimental setup, as indicate into the Fig.

4. Results and discussion

4.1 RBS, optical absorption and electron microscopy characterization

Figure 5
Fig. 5 RBS spectra of the implanted samples after the corresponding annealing treatments: a) Ag, and b) Au. Typical optical absorption spectra of the anisotropic nanocomposites: c) Ag, and d) Au.
shows the RBS spectra of the Ag and Au nanocomposites, after the corresponding annealing treatments and before the irradiation with Si ions. We have proceeded routinely in this way, since we have verified before that the metal distributions are not affected by the posterior Si irradiation. From these spectra, we can clearly see that the metallic NPs distribute inside the silica in a Gaussian way, where the position of its maximum gives the depth of the layer of NPs, while its FWHM gives the thickness of it. Typical optical absorption spectra of the Ag and Au anisotropic nanocomposites are also included. They show the SPs corresponding to the minor and the major axis of the Si-deformed NPs.

Figure 6
Fig. 6 a) Z contrast (HAADF) image showing the Ag NPs deformed by Si ion irradiation, obtained with a TEM, at 200 KV, with a point to point resolution of 0.19 nm at IFUNAM. b) HRTEM micrograph of a deformed Au NP in [011] zone axis orientation.
shows the deformation of the Ag NPs after Si ion irradiation. As it has been mentioned earlier, the metal concentrations for the fluences and the angles of implantation described before are 0.0379 and 0.0268 for Ag, respectively; while for Au are 0.0312 and 0.06, respectively. From appropriate HRTEM measurements, performed at the Laboratorio Central de Microscopía from IFUNAM, with a 200 KV JEOL-2010FEG in contrast-Z mode, we sorted out a Gaussian size distribution in the 1-6 nm range, with an average diameter of 3.6 nm and FWHM of 2.25 nm for spherical-like Au NPs; while for spherical-like Ag NPs, the Gaussian size distribution was in the range of 1-12 nm, with an average diameter of 4.4 nm and FWHM of 7.0 nm. On the other hand, for the Si-deformed NPs, we observed that not all the NPs are elongated, that were the smallest NPs that remained spherical-like and it was a large number of them, affecting then the aspect ratio distribution; and that the elongated ones show a prolate spheroid shape, with the major axis aligned along the ion irradiation direction (Fig. 6(a)). Besides, the equivalent diameter distribution is very close to that of the spherical-like NPs, indicating that the NP volume is, in general, conserved. For Au, this equivalent diameter is distributed between 2 and 6 nm, with an average equivalent diameter of 3.8 nm, while the aspect ratio distribution goes from 1 to 2 centered at 1.37. For Ag, the equivalent diameter distributes between 1 and 12 nm, with an average of 5.4 nm; while the aspect ratio is between 1 and 3 centered at 2 [51

51. V. Rodríguez-Iglesias, “Characterization and optical properties of elongated nanoclusters of Au and Ag embedded in silica,” Ph. D. thesis (2008).

]. Although the actual deformation mechanism is still under discussion, what we have argued before [6

6. A. Oliver, J. A. Reyes-Esqueda, J. C. Cheang-Wong, C. E. Román-Velázquez, A. Crespo-Sosa, L. Rodríguez-Fernández, J. A. Seman, and C. Noguez, “Controlled anisotropic deformation of Ag nanoparticles by Si ion irradiation,” Phys. Rev. B 74(24), 245425 (2006). [CrossRef]

] and nowadays is that, following the D’Orleans scheme [52

52. C. D’Orléans, J. P. Stoquert, C. Estournès, C. Cerruti, J. J. Grob, J. L. Guille, F. Haas, D. Muller, and M. Richard-Plouet, “Anisotropy of Co nanoparticles induced by swift heavy ions,” Phys. Rev. B 67(22), 220101 (2003). [CrossRef]

], the embedded NPs under study in this work fall in a size range such that, when irradiating with Si ions, they melt and flow into the ion track, therefore being deformed as a result of the Si irradiation, according to a thermal spike model. Besides, we have corroborated that, in general, spherical and deformed NPs have a fcc symmetry (Fig. 6(b)) [53

53. H. G. Silva-Pereyra, J. Arenas-Alatorre, L. Rodríguez-Fernández, A. Crespo-Sosa, J. C. Cheang-Wong, J. A. Reyes-Esqueda, and A. Oliver, “High stability of the crystalline configuration of Au nanoparticles embedded in silica under ion and electron irradiation,” submitted to J. Nanopart. Res. May (2009).

], which will be an important fact regarding the discussion below for the nonlinear optical results.

4.2 Birefringence results

We have performed the birefringence measurements in the range of 300-800 nm, i.e. in the visible region, mainly. Figures 7
Fig. 7 Typical intensities measurement obtained in the range of 300-800 nm with setup shown in Fig. 1. Ag NPs (x ions/cm2 fluence) deformed at 80° by a Si fluence of 0.5 × 1015 ions/cm2. Discontinuous curves are the theoretical calculations given for Eqs. (1) and (2) by taking the birefringence calculated with Eq. (15) for selected wavelengths. a) parallel and b) perpendicular polarizers.
and 8
Fig. 8 Typical intensities measurement obtained in the range of 300-800 nm with setup shown in Fig. 1. Au NPs (x ions/cm2 fluence) deformed at 45° by a Si fluence of 1.25 × 1016 ions/cm2. Discontinuous curves are the theoretical calculations given for Eqs. (1) and (2) by taking the birefringence calculated with Eq. (15) for selected wavelengths. a) parallel and b) perpendicular polarizers.
show typical measurements in such a range for Ag and Au, respectively. For α = 0 and α = π/2, we obtain from Eq. (1), for each of the wavelengths, Ap2 and As2, respectively. While, on the other hand, from Eq. (2), with α = π/4, we get the maximum measured birefringence for each wavelength as

Δnmax(λ)=λ2πLcos1[As2+Ap22AsAp2ImeasmaxAsAp].
(15)

In Fig. 9
Fig. 9 Typical birefringence in the range of 300-800 nm for Ag NPs deformed at 45 and 80°, and for Au NPs deformed at 80°, altogether with their absorption spectra, which are two curves for each case since they show the absorption for the minor and the major axes, respectively.
we show typical birefringences computed with Eq. (15) as a function of wavelength for the nanocomposites studied in this work, that is, Ag NPs deformed at 45 and 80°, and Au NPs deformed at 45°, as well as their absorption spectra. As it can be seen, in general, these anisotropic metallic nanocomposites exhibit a large birefringence from 0.04 to 0.07 in the optical region, being bigger for Ag than for Au nanocomposites. However, when comparing the peak positions to the SP positions for each case, it is evident that there is not a match between them. This fact is resumed in Table 1, where we show the corresponding nanocomposite’s angle of deformation, including the SP resonance positions for each case, and the birefringence peak positions. In Ref. 20

20. J. A. Reyes-Esqueda, C. Torres-Torres, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, C. Noguez, and A. Oliver, “Large optical birefringence by anisotropic silver nanocomposites,” Opt. Express 16(2), 710–717 (2008). [CrossRef] [PubMed]

, we had argued that the physical reason behind this birefringence was a dichroism effect. In this work, we still argue the same since, from our measurements, the birefringence for pure SiO2 matrix, not deformed NPs and outside the 300-800 nm region for deformed NPs is null. But we recognize that something not clearly understood is happening according to what is presented in Fig. 9 and Table 1. According to local field calculations performed with the extended Maxwell-Garnett theory, for the nanocomposite parameters presented in Section 4.1 (metal concentrations of 0.0268 for Ag and 0.0312 for Au, aspect ratios of 2 for Ag and 1.37 for Au, matrix dielectric permittivity from standard data for fused silica, Ag and Au dielectric permittivities from [54

54. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

]), one can obtain curves for Δn and Δk, for both Ag and Au, showing the same mismatching between their maxima as that observed in Fig. 9, i.e. in general, the birefringence maxima are red-shifted with respect to the absorption maxima. Theoretical calculations concerning near field considerations around the deformed NPs might give some insight on this mismatching. Besides, from these same calculations, but for the dispersion relations, we found that, at 532 nm, for Ag, the slope is negative for both kx and kz, but also for both nx and nz. On the other hand, for Au the slope is negative for kx but positive for kz, while it is positive for both nx and nz, indicating anomalous dispersion. In particular, these facts for ki can be observed in Fig. 9 for Ag NPs deformed at 45° and for Au, or even in Figs. 5(c) and 5(d).

4.3 Nonlinear optical results

|χeff(3)|, Re(χeff(3)) and Im(χeff(3)) values obtained for each sample, for each angular position, according to what has been described in Section 3.2, are shown in Tables 2 and 3 for Ag and in Tables 4 and 5 for Au. According to Eq. (13), since the refraction was not a problem for Au case, the two last columns of Table 4 correspond actually to |χ1111(3)| and |χ3333(3)|, respectively. Similarly, the two last columns of Table 5 correspond to the imaginary and the real parts of these same components, respectively It is worth remarking, that the self-diffraction and the P-scan signals were measured also for isotropic metallic nanocomposites, i.e. spherical-like Ag and Au NPs not deformed with Si, for each angular position as mentioned before, finding practically the same value for the nonlinear response, respectively.

Following with the discussion, let us undertake first the local field calculations. According to Ref. 34

34. J.-M. Lamarre, F. Billard, and L. Martinu, “Local field calculations of the anisotropic nonlinear absorption coefficient of aligned gold nanorods embedded in silica,” J. Opt. Soc. Am. B 25(6), 961–971 (2008). [CrossRef]

, the real and the imaginary parts of the third order nonlinear susceptibility, for an anisotropic metallic nanocomposite, depend on the metal volume concentration as
Reχeff,j(3)=pεd41(A02+B02)(Ap2+Bp2)2((Ap2Bp2)Reχm(3)+2ApBpImχm(3))
(16)
and
Imχeff,j(3)=pεd41(A02+B02)(Ap2+Bp2)2(2ApBpReχm(3)+(Ap2Bp2)Imχm(3)),
(17)
where p is the metal volume concentration, reaching a maximum value of 20 vol. % to respect the limit of validity of the extended Maxwell-Garnett theory, εd is the matrix dielectric permittivity, χm(3) is the metal third order susceptibility, A0=εd+Lj(Reεmεd), B0=LjImεm, Ap=εd+Lj(1p)(Reεmεd), Bp=Lj(1p)Imεm, εm is the metal dielectric permittivity, Lz=1e2e2(12eln(1+e1e)1) and Lx=Ly=1Lz2 are the corresponding depolarization factors for the major and the minor axes, respectively; and, finally, e2=1(b2/a2) is the ellipticity of the deformed NPs, with b and a being the length of the minor and the major axes, respectively. These Eqs. may be thought as similar to Eq. (13), just in the sense that they distinguish the anisotropy of the nanocomposite, the first one by considering its symmetry arguments, and the last two by considering the anisotropic enhancement of the nonlinear susceptibility due to local field effects. Given this context, as Lamarre et al. have done [34

34. J.-M. Lamarre, F. Billard, and L. Martinu, “Local field calculations of the anisotropic nonlinear absorption coefficient of aligned gold nanorods embedded in silica,” J. Opt. Soc. Am. B 25(6), 961–971 (2008). [CrossRef]

], the best way of comparing this theoretical formalism to the experimental results, and be then able to quantify the anisotropy of the nonlinear susceptibility, is calculating the ratio between the real (imaginary) part of the third order susceptibility along both, the major and the minor axes, as well as the ratio between the real (imaginary) part along the major axis and those measured for the spherical-like NPs. We consider that Au anisotropic nanocomposites are the most interesting case of this work because of the angle of deformation, 80° in this case, which allows us to measure directly the third order susceptibilities corresponding to the major and the minor axes of the deformed NPs; and because of the change of sign for the nonlinear absorption when scanning one or the other axis. In consequence, we used the following parameters for the theoretical formalism given by Eqs. (16) and (17). εd = 2.1316, Reεm=6.508, Imεm=1.71 [34

34. J.-M. Lamarre, F. Billard, and L. Martinu, “Local field calculations of the anisotropic nonlinear absorption coefficient of aligned gold nanorods embedded in silica,” J. Opt. Soc. Am. B 25(6), 961–971 (2008). [CrossRef]

]. We justify this choice since the Au parameters were obtained for samples prepared in a similar way as ours; the shapes are the same, spherical-like and prolate spheroids; and because, despite the difference in sizes, the absorption spectra are quite similar [37

37. J.-M. Lamarre, F. Billard, C. H. Kerboua, M. Lequime, S. Roorda, and L. Martinu, “Anisotropic nonlinear optical absorption of gold nanorods in a silica matrix,” Opt. Commun. 281(2), 331–340 (2008). [CrossRef]

]. For the metal third order susceptibility, we also take the considerations made at [33

33. F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys., A Mater. Sci. Process. 47(4), 347–357 (1988). [CrossRef]

,60

60. D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, “Z-scan measurement of the nonlinear absorption of a thin gold film,” J. Appl. Phys. 86(11), 6200–6205 (1999). [CrossRef]

], where a positive imaginary part is deduced [33

33. F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys., A Mater. Sci. Process. 47(4), 347–357 (1988). [CrossRef]

] and measured [60

60. D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, “Z-scan measurement of the nonlinear absorption of a thin gold film,” J. Appl. Phys. 86(11), 6200–6205 (1999). [CrossRef]

], and a 5 times smaller, negative real part is calculated [60

60. D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, “Z-scan measurement of the nonlinear absorption of a thin gold film,” J. Appl. Phys. 86(11), 6200–6205 (1999). [CrossRef]

]; therefore, we take the normalized values, Imχm(3)=5 and Reχm(3)=1, to perform our calculations. However, we will come back to this later, when discussing the electron dynamics, since this fact would have also implications about the role played by the hot electrons of metallic NPs. Taking the metal concentrations given above for Au, i.e. 0.0312 and 0.06 for the two fluences used, respectively. Figure 10
Fig. 10 a) Real and b) imaginary parts of the third order nonlinear susceptibility of the Au anisotropic nanocomposites, for each volume concentration, as a function of the aspect ratio.
shows the real (Fig. 10(a)) and the imaginary (Fig. 10(b)) parts of the nonlinear optical susceptibility for these parameters, for these filling factors and for the minor and the major axes, according with Eqs. (16) and (17), with respect to the aspect ratio, a/b.

5. Conclusions

The ensemble of results obtained throughout this work show the control we have achieved in designing anisotropic metallic nanocomposites, which present large and anisotropic linear and nonlinear optical responses, adding to them supplementary value for potential technological applications. For the linear part, we have measured a large birefringence in the region going from 300 to 800 nm. Concerning the nonlinear optical response, we have first contributed to the tensor analysis of the third order nonlinear optical response for an anisotropic uniaxial nanocomposite. Subsequently, we showed how the third-order nonlinear optical response varies, and even shifts from saturable to reverse saturable absorption in the case of Au, when modifying the angular position of the sample with respect to the incident beams and their polarization. Furthermore, self-focusing was detected in the case of Ag, while the opposite, self-defocusing, was observed for Au. We showed also how the nonlinear optical anisotropy is maximized for just a small deformation of the metallic NP. Finally, these measurements could be associated with the different nonzero components of the third-order susceptibility tensor of the metallic nanocomposite, which are only three in the degenerate case, allowing besides to establish the inequality |χeff(3)|minor axis<|χeff(3)|isotropic<|χeff(3)|major axis, which could be associated with near-field enhancement considerations.

Acknowledgments

We acknowledge the partial financial supports from DGAPA-UNAM, through grants No. IN108807-3, No. IN119706-3 and No. IN108407; and CONACyT-Mexico, through grants No. 80019, No. 82708, No. 79152 and No. 50504. V. Rodríguez-Iglesias and H.-G. Silva-Pereyra acknowledge specially the support from CONACyT and DGEP-UNAM for their Ph. D. scholarships. We are very grateful to the reviewers’ comments since they helped to a great improvement of the discussion of our results.

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53.

H. G. Silva-Pereyra, J. Arenas-Alatorre, L. Rodríguez-Fernández, A. Crespo-Sosa, J. C. Cheang-Wong, J. A. Reyes-Esqueda, and A. Oliver, “High stability of the crystalline configuration of Au nanoparticles embedded in silica under ion and electron irradiation,” submitted to J. Nanopart. Res. May (2009).

54.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

55.

F. Sanchez, “Two-wave mixing in thin nonlinear local-response media: a simple theoretical model,” J. Opt. Soc. Am. B 9(12), 2196–2205 (1992). [CrossRef]

56.

A. López-Suárez, C. Torres-Torres, R. Rangel-Rojo, J. A. Reyes-Esqueda, G. Santana, J. C. Alonso, A. Ortiz, and A. Oliver, “Modification of the nonlinear optical absorption and optical Kerr response exhibited by nc-Si embedded in a silicon-nitride film,” Opt. Express 17(12), 10056–10068 (2009). [CrossRef] [PubMed]

57.

Y.-F. Chau, M. W. Chen, and D. P. Tsai, “Three-dimensional analysis of surface plasmon resonance modes on a gold nanorod,” Appl. Opt. 48(3), 617–622 (2009). [CrossRef] [PubMed]

58.

U. Gurudas, E. Brooks, D. M. Bubb, S. Heiroth, T. Lippert, and A. Wokaun, “Saturable and reverse saturable absorption in silver nanodots at 532 nm using picosecond laser pulses,” J. Appl. Phys. 104(7), 073107 (2008). [CrossRef]

59.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, “Optical third order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica,” J. Appl. Phys. 104(1), 014306 (2008). [CrossRef]

60.

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, “Z-scan measurement of the nonlinear absorption of a thin gold film,” J. Appl. Phys. 86(11), 6200–6205 (1999). [CrossRef]

OCIS Codes
(160.1190) Materials : Anisotropic optical materials
(160.4330) Materials : Nonlinear optical materials
(190.0190) Nonlinear optics : Nonlinear optics
(190.4720) Nonlinear optics : Optical nonlinearities of condensed matter
(190.7070) Nonlinear optics : Two-wave mixing
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(160.4236) Materials : Nanomaterials

ToC Category:
Nonlinear Optics

History
Original Manuscript: May 14, 2009
Revised Manuscript: June 20, 2009
Manuscript Accepted: June 21, 2009
Published: July 13, 2009

Citation
Jorge Alejandro Reyes-Esqueda, Vladimir Rodríguez-Iglesias, Héctor-Gabriel Silva-Pereyra, Carlos Torres-Torres, Ana-Laura Santiago-Ramírez, Juan Carlos Cheang-Wong, Alejandro Crespo-Sosa, Luis Rodríguez-Fernández, Alejandra López-Suárez, and Alicia Oliver, "Anisotropic linear and nonlinear optical properties from anisotropy-controlled metallic nanocomposites," Opt. Express 17, 12849-12868 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12849


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