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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 12 — Jun. 4, 2012
  • pp: 13457–13469
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High-order nonlinear optical response of a polymer nanocomposite film incorporating semiconducotor CdSe quantum dots

Xiangming Liu, Yusuke Adachi, Yasuo Tomita, Juro Oshima, Takuya Nakashima, and Tsuyoshi Kawai  »View Author Affiliations


Optics Express, Vol. 20, Issue 12, pp. 13457-13469 (2012)
http://dx.doi.org/10.1364/OE.20.013457


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Abstract

We report on observation of high-order optical nonlinearities in our recently developed photopolymerizable semiconductor CdSe quantum dot (QD)-polymer nanocomposite films at various volume fractions of CdSe QDs as high as 0.91 vol.% (3.6 wt.%). We performed Z-scan and degenerate multi-wave mixing (DMWM) measurements using a 532-nm picosecond laser delivering single 35 ps pulses at a repetition rate of 10 Hz. Using the uniformly cured polymer nanocomposite films, we observed the third- and fifth-order nonlinear optical effects in closed-aperture Z-scan measurements by which it was found that saturable nonlinear absorption (light-induced transparency) and large negative nonlinear refraction were induced. We also measured dependences of the effective third- and fifth-order nonlinear refraction constants on CdSe QD volume fraction. Based on the Maxwell-Garnett model, we estimated the third- and fifth-order nonlinear optical susceptibilities of CdSe QD and discussed a contribution of the third-order effect to the fifth-order one due to the cascaded (local-field) effect. Coexistence of the third- and fifth-order nonlinear refraction was also confirmed by DMWM.

© 2012 OSA

1. Introduction

Recently, we have developed a new polymer nanocomposite material system, the so-called photopolymerizable nanoparticle-polymer composites, where either inorganic-oxide or organic nanoparticles are uniformly dispersed in photopolymerizable monomer hosts [1

1. Y. Tomita, “Holographic nanoparticle-photopolymer composites,” in H. S. Nalwa, ed., Encyclopedia of Nanoscience and Nanotechnology15 (American Scientific Publishers, Valencia, 2011), 191–205 and references therein.

]. As a result of holographic assembly of nanoparticles in polymer [2

2. Y. Tomita, N. Suzuki, and K. Chikama, “Holographic manipulation of nanoparticle distribution morphology in nanoparticle-dispersed photopolymers,” Opt. Lett. 30(8), 839–841 (2005). [CrossRef] [PubMed]

], dispersed nanoparticles at high volume fractions redistribute and provide a significant increase in refractive index modulation of a recorded volume hologram under holographic exposure. Simultaneously, they improve mechanical/thermal stability of the hologram [3

3. Y. Tomita, T. Nakamura, and A. Tago, “Improved thermal stability of volume holograms recorded in nanoparticle--polymer composite films,” Opt. Lett. 33(15), 1750–1752 (2008). [CrossRef] [PubMed]

]. Nanoparticle-polymer composites possessing these advantages are used for applications such as holographic data storage [4

4. N. Suzuki, Y. Tomita, K. Ohmori, M. Hidaka, and K. Chikama, “Highly transparent ZrO(2) nanoparticle-dispersed acrylate photopolymers for volume holographic recording,” Opt. Express 14(26), 12712–12719 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-26-12712. [CrossRef] [PubMed]

,5

5. E. Hata, K. Mitsube, K. Momose, and Y. Tomita, “Holographic nanoparticle-polymer composites based on step-growth thiol-ene photopolymerization,” Opt. Mater. Express 1(2), 207–222 (2011), http://www.opticsinfobase.org/ome/abstract.cfm?uri=ome-1-2-207. [CrossRef]

] and holographic diffractive elements for neutron quantum beams [6

6. M. Fally, J. Klepp, Y. Tomita, T. Nakamura, C. Pruner, M. A. Ellabban, R. A. Rupp, M. Bichler, I. D. Olenik, J. Kohlbrecher, H. Eckerlebe, H. Lemmel, and H. Rauch, “Neutron optical beam splitter from holographically structured nanoparticle-polymer composites,” Phys. Rev. Lett. 105(12), 123904 (2010). [CrossRef] [PubMed]

,7

7. J. Klepp, C. Pruner, Y. Tomita, C. Plonka-Spehr, P. Geltenbort, S. Ivanov, G. Manzin, K. H. Andersen, J. Kohlbrecher, M. A. Ellabban, and M. Fally, “Diffraction of slow neutrons by holographic SiO2 nanoparticlepolymer composite gratings,” Phys. Rev. A 84(1), 013621 (2011). [CrossRef]

]. If semiconductor quantum dots (QDs) [8

8. L. Jacak, P. Hawrylak, and A. Wojs, Quantum Dots (Springer, Berlin, 1998).

], also referred to as semiconductor nanocrystals, that confine optically excited electron-hole pairs in all three space dimensions are employed as nanometer-size constituents in nanoparticle-polymer composites, we expect the realization of novel photonic materials being capable of optically constructing multi-dimensional and functional (e.g., nonlinear) photonic lattice structures by the holographic nanoparticle assembling technique. Indeed, we recently demonstrated holographic assembly of semiconductor CdSe QDs (the average size of ~3 nm) in a photopolymerizable monomer host for constructing volume Bragg grating structures with diffraction efficiency near 100% [9

9. X. Liu, Y. Tomita, J. Oshima, K. Chikama, K. Matsubara, T. Nakashima, and T. Kawai, “Holographic assembly of semiconductor CdSe quantum dots in polymer for volume Bragg grating structures with diffraction efficiency near 100%,” Appl. Phys. Lett. 95(26), 261109 (2009). [CrossRef]

].

QDs have interesting characteristics such as fluorescence tunability, enhanced photosensitivity and large optical nonlinearities: The electronic states of QDs are strongly influenced by the quantum confinement effect when the radius of QDs is smaller than approximately three times of the exciton Bohr radius [10

10. Y. Kayanuma, “Quantum-size effects of interacting electrons and holes in semiconductor microcrystals with spherical shape,” Phys. Rev. B Condens. Matter 38(14), 9797–9805 (1988). [CrossRef] [PubMed]

]. The band gap (Eg) of QDs increases with decreasing their size and the quantum confinement effect can strongly enhance the third-order optical nonlinearity [11

11. S. Schumitt-Rink, D. A. B. Miller, and D. S. Chemla, “Theory of the linear and nonlinear optical properties of semiconductor microcrystallites,” Phys. Rev. B 35(15), 8113–8125 (1987). [CrossRef]

12

12. G. P. Banfi, V. Degiorgio, and D. Ricard, “Nonlinear optical properties of semiconductor nanocrystals,” Adv. Phys. 47(3), 447–510 (1998) (and references therein). [CrossRef]

]. The II-VI bulk semiconductor CdSe has the direct band gap Eg = 1.74 eV at 300 K and has the exciton Bohr radius of 5.6 nm [12

12. G. P. Banfi, V. Degiorgio, and D. Ricard, “Nonlinear optical properties of semiconductor nanocrystals,” Adv. Phys. 47(3), 447–510 (1998) (and references therein). [CrossRef]

]. Therefore, the strong quantum confinement effect of CdSe QDs plays an important role in a large enhancement of the optical nonlinearity as compared with that of the bulk CdSe. For this reason it would be of great interest to investigate the nonlinear optical properties of uniformly cured and holographically patterned CdSe QD-polymer composites for their photonic applications such as optical switching/limiting, signal/image processing and nonlinear photonic crystals [13

13. R. E. Slusher and B. J. Eggleton, eds., Nonlinear Photonic Crystals (Springer, Berlin, 2003).

,14

14. Y. Tomita, “Holographic manipulation of nanoparticle-distribution morphology in photopolymers and its applications to volume holographic recording and nonlinear photonic crystals,” OSA Trends Opt. Photonics Ser. 99, 274–280 (2005).

].

Over the past two decades intensive studies have been done to investigate optical nonlinearities in various semiconductor QDs such as CdSe [15

15. N. Peyghambarian, B. Fluegel, D. Hulin, A. Migus, M. Joffre, A. Antonetti, S. W. Koch, and M. Lindberg, “Femtosecond optical nonlinearities of CdSe quantum dots,” IEEE J. Quantum Electron. 25(12), 2516–2522 (1989). [CrossRef]

25

25. H. Song, Y. Zhai, Z. Zhou, Z. Hao, and L. Zhou, “Optical nonlinearity of CdSe and CdSe-C60 quantum dot,” Mod. Phys. Lett. B 22(32), 3207–3213 (2008). [CrossRef]

], CdSxSe1-x [26

26. S. R. Friberg and P. W. Smith, “Nonlinear optical glasses for ultrafast optical switches,” IEEE J. Quantum Electron. 23(12), 2089–2094 (1987). [CrossRef]

32

32. Y. Chen, K. Beckwitt, F. W. Wise, B. G. Aitken, J. S. Sanghera, and I. D. Aggarwal, “Measurement of fifth- and seventh-order nonlinearities of glasses,” J. Opt. Soc. Am. B 23(2), 347–352 (2006). [CrossRef]

], CdS [33

33. N. Venkatram, D. N. Rao, and M. A. Akundi, “Nonlinear absorption, scattering and optical limiting studies of CdS nanoparticles,” Opt. Express 13(3), 867–872 (2005). [CrossRef] [PubMed]

,34

34. J. He, J. Mi, H. Li, and W. Ji, “Observation of interband two-photon absorption saturation in CdS nanocrystals,” J. Phys. Chem. B 109(41), 19184–19187 (2005). [CrossRef] [PubMed]

], CdTe [35

35. L. A. Padilha, J. Fu, D. J. Hagan, E. W. Van Stryland, C. L. Cesar, L. C. Barbosa, and C. H. B. Cruz, “Two-photon absorption in CdTe quantum dots,” Opt. Express 13(17), 6460–6467 (2005). [CrossRef] [PubMed]

37

37. I. Dancus, V. I. Vlad, A. Petris, N. Gaponik, V. Lesnyak, and A. Eychmüller, “Saturated near-resonant refractive optical nonlinearity in CdTe quantum dots,” Opt. Lett. 35(7), 1079–1081 (2010). [CrossRef] [PubMed]

], GaAs [38

38. M. D. Dvorak, B. L. Justus, and A. D. Berry, “Pump/probe Z-scan studies of GaAs nanocrystals grown in porous glass,” Opt. Commun. 116(1–3), 149–152 (1995). [CrossRef]

] and PbS [39

39. B. Liu, H. Li, C. H. Chew, W. Que, Y. L. Lam, C. H. Kam, L. M. Gan, and G. Q. Xu, “PbS–polymer nanocomposite with third-order nonlinear optical response in femtosecond regime,” Mater. Lett. 51(6), 461–469 (2001). [CrossRef]

,40

40. H. S. Kim, M. H. Lee, N. C. Jeong, S. M. Lee, B. K. Rhee, and K. B. Yoon, “Very high third-order nonlinear optical activities of intrazeolite PbS quantum dots,” J. Am. Chem. Soc. 128(47), 15070–15071 (2006). [CrossRef] [PubMed]

] that were uniformly dispersed in either liquid or solid hosts. Because these semiconductor QDs are randomly dispersed, they possess the inversion symmetry so that they possess optical nonlinearities of the odd orders. Although most of reported experiments with semiconductor QDs discussed the third-order effect, high-order optical nonlinearities in CdSxSe1-x QDs doped glasses [27

27. L. H. Acioli, A. S. L. Gomes, and J. R. Rios Leite, “Measurement of high-order optical nonlinear susceptibilities in semiconductor-doped glasses,” Appl. Phys. Lett. 53(19), 1788–1790 (1988). [CrossRef]

32

32. Y. Chen, K. Beckwitt, F. W. Wise, B. G. Aitken, J. S. Sanghera, and I. D. Aggarwal, “Measurement of fifth- and seventh-order nonlinearities of glasses,” J. Opt. Soc. Am. B 23(2), 347–352 (2006). [CrossRef]

] and colloidal CdTe QDs [37

37. I. Dancus, V. I. Vlad, A. Petris, N. Gaponik, V. Lesnyak, and A. Eychmüller, “Saturated near-resonant refractive optical nonlinearity in CdTe quantum dots,” Opt. Lett. 35(7), 1079–1081 (2010). [CrossRef] [PubMed]

] were also reported. Other nonlinear optical materials exhibiting high-order optical nonlinearities include silver nanoparticles in aqueous solution [41

41. E. L. Falcão-Filho, B. de Araújo, J. J. Rodrigues, and Jr., “High-order nonlinearities of aqueous colloids containing silver nanoparticles,” J. Opt. Soc. Am. B 24(12), 2948–2956 (2007).

,42

42. D. Rativa, R. E. de Araujo, and A. S. L. Gomes, “Nonresonant high-order nonlinear optical properties of silver nanoparticles in aqueous solution,” Opt. Express 16(23), 19244–19252 (2008). [CrossRef] [PubMed]

], organic solutions [43

43. E. Koudoumas, F. Dong, M. D. tzatzadaki, S. Couris, and S. Leach, “High-order nonlinear optical response of C60-toluene solutions in the sub-picosecond regime,” J. Phys. At. Mol. Opt. Phys. 29(20), L773–L778 (1996). [CrossRef]

45

45. K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009). [CrossRef] [PubMed]

], chalcone and its derivatives [46

46. B. Gu, W. Ji, X. Q. Huang, P. S. Patil, and S. M. Dharmaprakash, “Nonlinear optical properties of 2,4,5-Trimethoxy-4-nitrochalcone: observation of two-photon-induced excited-state nonlinearities,” Opt. Express 17(2), 1126–1135 (2009). [CrossRef] [PubMed]

], chalcogenide glasses [47

47. F. Smektala, C. Quemard, V. Couderc, and A. Barthélémy, “Non-linear optical properties of chalcogenide glasses measured by Z-scan,” J. Non-Cryst. Solids 274(1–3), 232–237 (2000). [CrossRef]

] and InN thin films [48

48. Z. Q. Zhang, W. Q. He, C. M. Gu, W. Z. Shen, H. Ogawa, and Q. X. Guo, “Determination of the third- and fifth-order nonlinear refractive indices in InN thin films,” Appl. Phys. Lett. 91(22), 221902 (2007). [CrossRef]

]. Saturation of the cubic Kerr nonlinearity due to such high-order nonlinearities arising at high optical intensities provide interesting nonlinear phenomena such as the formation of stable multi-dimensional optical solitons, but it sometimes causes a detrimental effect in, for example, optical switching applications [32

32. Y. Chen, K. Beckwitt, F. W. Wise, B. G. Aitken, J. S. Sanghera, and I. D. Aggarwal, “Measurement of fifth- and seventh-order nonlinearities of glasses,” J. Opt. Soc. Am. B 23(2), 347–352 (2006). [CrossRef]

]. For this reason it is necessary to investigate the third- and, if any, high-order optical nonlinearities in nanocomposite materials.

In this paper we report on an observation of high-order optical response of photopolymerizable semiconductor CdSe QD-polymer nanocomposite films in the Z-scan [49

49. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]

] and degenerate multi-wave mixing (DMWM) [26

26. S. R. Friberg and P. W. Smith, “Nonlinear optical glasses for ultrafast optical switches,” IEEE J. Quantum Electron. 23(12), 2089–2094 (1987). [CrossRef]

] measurements with a 532-nm picosecond laser at a low repetition rate. We study dependences of effective third- and high-order nonlinear refraction constants on volume fraction of CdSe QDs in the Z-scan measurement, by which, based on the Maxwell-Garnett model, we extract the third- and fifth-order nonlinear susceptibilities of CdSe QD and discuss a cascaded (local-field) contribution to the fifth-order nonlinearity. Coexistence of the third- and fifth-order optical nonlinearities is also examined by the DMWM measurement.

2. Sample preparation

3. Experimental method

A passively and actively mode-locked and frequency-doubled Nd:YAG laser operating at a wavelength of 532 nm and at a repetition rate of 10 Hz was employed. The output laser pulse having the FWHM pulsewidth of 35 ps and the beam diameter of approximately 3 mm was focused on a polymer nanocomposite film sample of 10-μm thickness by a convex lens of a 200-mm focal length, forming a beam spot with the beam waist radius ω0 of approximately 32 µm determined by a commercial beam profiler. The single-beam Z-scan technique was used to measure the nonlinear absorption and refraction of polymer nanocomposite film samples at various volume fractions of CdSe QDs exhibiting the optical nonlinearity. In this setup the polymer nanocomposite film sample placed on a computer-controlled translation stage was moved along the beam propagation direction (z axis). An aperture and a detector placed behind it were set at a distance far away from the diffraction length z0 (≈6 mm) of the focused pulse laser beam, where z0 is given by 02/2 with k being the wavenumber of the incident beam. Linear transmittances of the aperture were set to be unity and 0.06 in the open- and closed-aperture Z-scan measurements, respectively. The normalized transmittance T(z), defined as the ratio of the detected pulse energy to the incident pulse one normalized by the linear transmittance, was evaluated as functions of the sample position z and an incident pulse intensity I0 at the polymer nanocomposite film sample. Individual transmitted pulses at a given pulse energy within ± 10% were selected and used to measure T(z) in order to avoid unwanted intensity fluctuations of the incident laser pulses at a repetition rate of 10 Hz.

The forward DMWM measurement was also performed to study the third- and high-order optical nonlinearities in the polymer nanocomposite film samples of 50-μm thickness since the DMWM setup could spatially separate self-diffracted beams caused by the third- and high-order optical nonlinearities. The experimental setup is shown in Fig. 2
Fig. 2 Experimental setup for forward DMWM. BS, a beam splitter; L, a convex lens; S, a polymer nanocomposite film sample; P, a prism. k3, k5, k3 and k5 indicate wavevetors of self-diffracted beams.
. The same green pulse laser as that used in the Z-scan measurement was employed in this measurement. Either two s-polarized or cross-polarized beams were focused on the polymer nanocomposite film sample by a convex lens of a 700-mm focal length. The angle between two interacting beams was approximately 0.77° in the air. The beam radius in the focal plane was approximately 119 µm. The delay line was used to adjust the zero time delay between two incident beams. Self-diffracted beams were observed in the screen placed away from the polymer nanocomposite film sample.

4. Experimental results and discussions

4.1 Open-aperture Z-scan

Figure 3(a)
Fig. 3 (a) Open-aperture Z-scan T(z) at I0 = 1.8 GW/cm2 as a function of sample position z for a polymer nanocomposite film sample with 0.91 vol.% CdSe QDs. The solid curves are the least-squares fits of the TPA (curve in red), SA1 (curve in blue) and SA2 (curve in brown) models to the data. Best fit values for the TPA, SA1 and SA2 models are β = 107 cm/GW, Is = 0.53 and 0.11 GW/cm2, respectively. (b) Transmittance change ΔT at z = 0 as a function of input intensity I0. The solid curves are the least-squares fits of the TPA (curve in red), SA1 (curve in blue) and SA2 (curve in brown) models to the data.
shows a typical open-aperture Z-scan data for a polymer nanocomposite film sample with 0.91 vol.% CdSe QDs at I0 = 1.8 GW/cm2. It can be seen that T(z) is more or less peaked at the focus (z = 0). A similar trend was observed at other incident pulse intensities up to 2.5 GW/cm2 in our measurement. We also found that a neat polymer film without CdSe QDs did not exhibit any nonlinear absorption. Therefore, the observed light-induced transparency originates from the optical nonlinearity of CdSe QDs. We speculate that the physical origin of the observed nonlinear transparency at a laser wavelength of 532 nm below the exciton bandgap (~480 nm) is attributed to transient bleaching of the excitonic transitions as a result of the state filling effect [52

52. C. Burda, S. Link, T. C. Green, and M. A. El-Sayed, “New transient absorption observed in the spectrum of colloidal CdSe nanoparticles pumped with high-power femtosecond pulses,” J. Phys. Chem. B 103(49), 10775–10780 (1999). [CrossRef]

] in CdSe QDs as observed by pump-probe spectroscopic measurements [53

53. M. G. Bawendi, W. L. Wilson, L. Rothberg, P. J. Carroll, T. M. Jedju, M. L. Steigerwald, and L. E. Brus, “Electronic structure and photoexcited-carrier dynamics in nanometer-size CdSe clusters,” Phys. Rev. Lett. 65(13), 1623–1626 (1990). [CrossRef] [PubMed]

]. The data are fitted better by theoretical models of the open-aperture Gaussian-beam Z-scan for saturable absorption (SA) [54

54. B. Gu, Y. Fan, J. Wang, J. Chen, J. Ding, H. Wang, and B. Guo, “Characterization of saturable absorbers using an open-aperture Gaussian-beam Z scan,” Phys. Rev. A 73(6), 065803 (2006). [CrossRef]

] than by a model for two-photon absorption (TPA) [49

49. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]

] with a negative TPA coefficient β. The two models for SA consider different intensity-dependent absorption coefficients α(I) as given by [54

54. B. Gu, Y. Fan, J. Wang, J. Chen, J. Ding, H. Wang, and B. Guo, “Characterization of saturable absorbers using an open-aperture Gaussian-beam Z scan,” Phys. Rev. A 73(6), 065803 (2006). [CrossRef]

]
α(I)={α01+I/Isforahomogeneousbroadeningsystem(SA1)α01+I/Isforaninhomogeneousbroadeningsystem(SA2),
(2)
where I is the laser pulse intensity inside a medium, Is is the saturation intensity and α equals to α0 under the low-intensity approximation (I << Is). Analytic expressions for the open-aperture Gaussian-beam Z-scan T(z) in these models can be given by means of the Adomian’s decomposition method [54

54. B. Gu, Y. Fan, J. Wang, J. Chen, J. Ding, H. Wang, and B. Guo, “Characterization of saturable absorbers using an open-aperture Gaussian-beam Z scan,” Phys. Rev. A 73(6), 065803 (2006). [CrossRef]

56

56. G. Adomian, “A review of the decomposition method in applied mathematics,” J. Math. Anal. Appl. 135(2), 501–544 (1988). [CrossRef]

]. We confirmed that the summation up to the eighth term in the series expansion for T(z) with the Adomian’s decomposition method was enough to obtain the convergence in our experiment. The SA1 and SA2 models give best fit values for Is to be 0.53 and 0.11 GW/cm2, respectively. Figure 3(b) shows transmittance changes ΔT at z = 0 [defined as T(0)−1] as a function of I0. It can be seen that the SA1 and SA2 models give best fit values for Is to be 0.54 and 0.21 GW/cm2, respectively. We see that the SA1 model gives a consistent result for the parameter fitting of Is in Fig. 3(a) with that in Fig. 3(b). For this reason we consider that the saturable absorption (light-induced transparency) observed in our polymer nanocomposite film samples is well described by the SA1 model. This result implies excellent size uniformity of CdSe QDs in our sample as found by the TEM measurement.

4.2 Closed-aperture Z-scan

Figure 4(a)
Fig. 4 (a) Closed-aperture Z-scan T(z) at I0 = 1.8 GW/cm2 as a function of sample position z for the same polymer nanocomposite film sample with 0.91 vol.% CdSe QDs as that shown in Fig. 3. Solid curves correspond to the least-squares fits of the theoretical formulae for the closed-aperture Gaussian-beam Z-scan T(z) without (curve in red) and with (curve in blue) saturable absorption of the SA1 type. The best-fit values for n2 and n4 are −4.0 × 10−3 cm2/GW and + 1.5 × 10−3 cm4/GW2, respectively. (b) ΔTp-v/I0 as a function of input intensity I0. The solid line is the least-squares linear fit to the data.
shows typical closed-aperture Z-scan data at I0 = 1.8 GW/cm2 for the same cured polymer nanocomposite film sample as that shown in Fig. 3. It can be seen that the Z-scan data exhibit the peak-and-valley configuration, indicating the negative nonlinear refraction. A similar trend was observed in the closed-aperture Z-scan measurement at incident pulse intensities up to 2.5 GW/cm2. It is well known that ΔTp-v [defined as a peak-to-valley difference in T(z)] is proportional to I0 for a material possessing the third-order effect [49

49. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]

]. The ratio for ΔTp-v/I0 is plotted as a function of I0 as shown in Fig. 4(b). It can be seen that ΔTp-v/I0 is not a constant, indicating that the third-order nonlinear refraction is not the sole contribution to the observed optical nonlinearity. It can also be seen that the magnitude of ΔTp-v/I0 more or less linearly decreases with an increase in I0. It means that the third- and fifth-order effects simultaneously contribute to T(z) in the closed-aperture Z-scan measurement.

Ee(z,r,t)=I(L)exp[iΔϕ(z,r,t)].
(5)

When Eq. (5) is decomposed into a summation of many Gaussian beams by a Taylor series expansion as done in the original Z-scan theory [49

49. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]

], an individual Gaussian beam independently propagates along z axis toward an aperture in free space. As a result, the electric field of the laser beam in front of the aperture positioned at the distance d from the medium is obtained by a summation of the propagating individual Gaussian beams such that

Ea(z,r,t)=I(L)m=0[iΔϕ(z,r=0,t)]mm!wm0wmexp(r2wm2ikr22Rm+iθm).
(6)

In Eq. (6) wm02 = w2(z)/(2m + 1) and wm2 = wm02[g2 + (d/dm)2] in which w2(z) = w02(1 + z2/z02), g = 1 + d/[z(1 + z02/z2)], and dm = kwm02/2. Also, Rm = d[1−g/(g2 + d2/dm2)]−1 and θm = tan−1[d/(dmg)]. The normalized Z-scan transmittance T(z) for the nonlinear medium possessing the saturable absorption (SA1) and the simultaneous third- and fifth-order nonlinear refraction in the closed-aperture Z-scan measurement can be found by the following formula [49

49. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]

]:
T(z)=PT(z,t)dtSPi(t)dt,
(7)
where the transmitted pulse power PT(z, t) through the aperture is given by
PT(z,t)=2π0raIa(z,r,t)rdr=cε0n0π0ra|Ea(z,r,t)|2rdr,
(8)
the incident pulse power Pi(t) is given by πw02I0(t)/2, and the linear transmittance of the aperture S is given by 1−exp(−2ra2/wa2) with ra and wa being the aperture radius and the Gaussian beam radius at the aperture, respectively. Also, c and ε0 are the speed of light in vacuum and the vacuum permittivity, respectively. Equation (7), together with Eqs. (4), (5), (6) and (8), was numerically calculated to extract n2 and n4 by the curve fitting to the data shown in Fig. 4(a). Note that IS of 0.53 GW/cm2 found in the open-aperture Z-scan measurement (see Fig. 3) is used for this fitting procedure. It can be seen in Fig. 4(a) that the second model is in good agreement with the data. As a result, the best-fit values for n2 and n4 were found to be −4.0 × 10−3 cm2/GW and + 1.5 × 10−3 cm4/GW2, respectively, at I0 = 1.8 GW/cm2.

Figure 5
Fig. 5 (a) Extracted values for (a) n2 and (b) n4 as a function of input intensity I0 for a polymer nanocomposite film sample doped with 0.91 vol.% CdSe QDs.
shows the extracted best-fit values for n2 [Fig. 5(a)] and n4 [Fig. 5(b)] as a function of I0. It can be seen that n2 and n4 are more or less independent of the input intensityin the measured intensity range; the average values for n2 and n4 are −4.0 × 10−3 cm2/GW and + 1.5 × 10−3 cm4/GW2, respectively. The magnitude of n2 for the polymer nanocomposite film sample with 0.91 vol.% (3.6 wt.%) CdSe QDs is approximately two orders of magnitude larger than that ( = −1.45 × 10−5 cm2/GW) of a bulk CdSe at 1064 nm [58

58. M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of Bound Electronic Nonlinear Refraction in Solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991). [CrossRef]

] and is approximately one order of magnitude larger than that ( + 4.3 × 10−4 cm2/GW) at 794 nm for the polymer CR39 composite film dispersed with 1.5 wt.% CdSe QDs [23

23. C. Gan, Y. Zhang, S. W. Liu, Y. Wang, and M. Xiao, “Linear and nonlinear optical refractions of CR39 composite with CdSe nanocrystals,” Opt. Mater. 30(9), 1440–1445 (2008). [CrossRef]

]. We note that the sign of n2 (also, that of nonlinear absorption) is not necessarily consistent in past literatures [15

15. N. Peyghambarian, B. Fluegel, D. Hulin, A. Migus, M. Joffre, A. Antonetti, S. W. Koch, and M. Lindberg, “Femtosecond optical nonlinearities of CdSe quantum dots,” IEEE J. Quantum Electron. 25(12), 2516–2522 (1989). [CrossRef]

25

25. H. Song, Y. Zhai, Z. Zhou, Z. Hao, and L. Zhou, “Optical nonlinearity of CdSe and CdSe-C60 quantum dot,” Mod. Phys. Lett. B 22(32), 3207–3213 (2008). [CrossRef]

] that were different material parameters and experimental conditions such as the size of QDs, types of host materials (liquid and solid hosts) and operating wavelengths. We also note that a contribution of the third- and fifth-order nonlinear refraction to the nonlinear refractive index change is comparable at I0 of the order of GW/cm2.

The effective fifth-order optical nonlinearity may generally include intrinsic, macroscopic and microscopic cascaded contributions [45

45. K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009). [CrossRef] [PubMed]

]. The intrinsic contribution due to the intrinsic fifth-order nonlinear optical susceptibility of nanoparticles χn(5) is proportional to f and is given by [45

45. K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009). [CrossRef] [PubMed]

]

χeff(5)=f|q|4q2χn(5).
(12)

Figure 7
Fig. 7 Closed-aperture Z-scan T(z) as a function of incident intensity for a polymer nanocomposite film sample doped with 0.91 vol.% CdSe QDs when the sample is placed at the valley (○) and peak (●) positions.
shows the normalized transmittances as a function of incident intensity by means of a variant of the closed-aperture Z-scan technique, the so-called intensity scan technique [64

64. B. Taheri, H. Liu, B. Jassemnejad, D. Appling, R. C. Powell, and J. J. Song, “Intensity scan and two photon absorption and nonlinear refraction of C60 in toluene,” Appl. Phys. Lett. 68(10), 1317–1319 (1996). [CrossRef]

] that measures T(z) for a nonlinear medium placed at either a valley or a peak position away from the beam focus (z = 0) in the closed-aperture Z-scan setup as seen in Fig. 4(a). This technique can be used to determine the sign and the magnitude of effective optical nonlinear constants either when a nonlinear material such as a polymer film has low damage threshold or when a transversal beam quality along the z direction is poor. It can be seen that T(z) decreases (increases) with increasing an incident intensity for the polymer nanocomposite film sample was located at the valley (peak) position. The decreasing trend of the laser power after an aperture with increasing an incident laser intensity can be used for optical power limiting; it would be more effective when a thicker film sample is employed.

4.3 Degenerate multi-wave mixing

2πλL/n0Λ2 (λ is a wavelength of light in vacuum) [65

65. R. Magnusson and T. K. Gaylord, “Diffraction efficiencies of thin phase gratings with arbitrary grating space,” J. Opt. Soc. Am. 68(6), 806–808 (1978). [CrossRef]

] is 0.07. It can be seen that four diffracted beams are newly generated. These diffracted beams correspond to the third- and fifth-order nonlinear optical effects, which is consistent with our Z-scan measurement described earlier. It is indicative of the coexistence of the third- and fifth-order optical nonlinearities in the polymer nanocomposite film samples. Figure 8(b) shows the transmitted and diffracted beams from the dynamic grating at 1 μm that corresponds to Q = 114 (i.e., the Bragg regime). Unlike the case shown in Fig. 8(a) no self-diffraction is seen because the phase mismatching is significant for self-diffracted beams in the Bragg regime. We also performed the DMWM experiment with the cross-polarized input beams. The first-order diffraction was observed due to the third-order effect arising from the off-diagonal element of the third-order nonlinear optical susceptibility tensor χ(3)1212 in isotropic media. Details on these DMWM experiments will be reported elsewhere.

5. Conclusions

We have studied the nonlinear optical properties of uniformly cured semiconductor CdSe QD-polymer nanocomposite films by means of the Z-scan technique and DMWM with a 532-nm picosecond laser at a low repetition rate. Using closed- and open-aperture Z-scan techniques, we have found that the polymer nanocomposite films at the volume fraction of CdSe QDs as high as 0.91 vol.% (3.6 wt.%) exhibit the saturable absorption (light-induced transparency) as well as the negative third-order and the positive fifth-order nonlinear refraction. We have also found that the observed high-order nonlinearity originates mainly from the intrinsic fifth-order effect and partly from the third-order one due to the cascaded contributions. The observed nonlinearity is attributed to the electronic state filling effect. Such coexistence of the third- and fifth-order optical nonlinearities has been also confirmed by DMWM measurements. The observation of cross-polarized DMWM diffraction also supports the electronic origin of the third- and fifth-order nonlinearities. The large third-order nonlinearity, the occurrence of high-order nonlinearities and the capability of holographic nanoparticle assembling make our CdSe QD-polymer nanocomposite system promising for nonlinear photonics applications. For example, let us estimate the materials (one-photon) figure of merit W given by |Δn|/λα [66

66. G. I. Stegeman and R. H. Stolen, “Waveguides and fibers for nonlinear optics,” J. Opt. Soc. Am. B 6(4), 652–662 (1989). [CrossRef]

,67

67. Y. Lin, J. Zhang, E. Kumacheva, and E. H. Sargent, “Third-order optical nonlinearity and figure of merit of CdS nanocrystals chemically stabilized in spin-processable polymer films,” J. Mater. Sci. 39(3), 993–996 (2004). [CrossRef]

] for our CdSe QD-polymer nanocomposites, where Δn is the nonlinear refractive index change. Using Δn ( = n2I + n4I2) = −2.5 × 10−3 at I = 1 GW/cm2 and α = 30 cm−1 with Is = 0.53 GW/cm2 for the polymer nanocomposite film with 0.91 vol.% CdSe QDs, we find W to be 1.5. [Thanks to the light-induced transparency, the linear value for α ( = 88 cm−1) is reduced to 30 cm−1. See Fig. 3.] This value is close to 2, the threshold value required for complete all-optical switching for nonlinear guided-wave devices [66

66. G. I. Stegeman and R. H. Stolen, “Waveguides and fibers for nonlinear optics,” J. Opt. Soc. Am. B 6(4), 652–662 (1989). [CrossRef]

]. We expect that the further enhancement of W is possible if the large nonlinearity of the CdSe QD-polymer nanocomposite system is combined with electromagnetic nonlinear feedback mechanisms [68

68. D. Pelinovsky, J. Sears, L. Brozozowski, and E. H. Sargent, “Stable all-optical limiting in nonlinear periodic structures. I. Analysis,” J. Opt. Soc. Am. B 19(1), 43–53 (2002). [CrossRef]

, 69

69. W. N. Ye, L. Brozozowski, E. H. Sargent, and D. Pelinovsky, “Stable all-optical limiting in nonlinear periodic structures. III. Nonsolitonic pulse propagation,” J. Opt. Soc. Am. B 20(4), 695–705 (2003). [CrossRef]

] by constructing photonic lattice structures [2

2. Y. Tomita, N. Suzuki, and K. Chikama, “Holographic manipulation of nanoparticle distribution morphology in nanoparticle-dispersed photopolymers,” Opt. Lett. 30(8), 839–841 (2005). [CrossRef] [PubMed]

,9

9. X. Liu, Y. Tomita, J. Oshima, K. Chikama, K. Matsubara, T. Nakashima, and T. Kawai, “Holographic assembly of semiconductor CdSe quantum dots in polymer for volume Bragg grating structures with diffraction efficiency near 100%,” Appl. Phys. Lett. 95(26), 261109 (2009). [CrossRef]

,14

14. Y. Tomita, “Holographic manipulation of nanoparticle-distribution morphology in photopolymers and its applications to volume holographic recording and nonlinear photonic crystals,” OSA Trends Opt. Photonics Ser. 99, 274–280 (2005).

]. Our study in this direction is currently under way.

Acknowledgment

This work was supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan under grant 23360030.

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64.

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65.

R. Magnusson and T. K. Gaylord, “Diffraction efficiencies of thin phase gratings with arbitrary grating space,” J. Opt. Soc. Am. 68(6), 806–808 (1978). [CrossRef]

66.

G. I. Stegeman and R. H. Stolen, “Waveguides and fibers for nonlinear optics,” J. Opt. Soc. Am. B 6(4), 652–662 (1989). [CrossRef]

67.

Y. Lin, J. Zhang, E. Kumacheva, and E. H. Sargent, “Third-order optical nonlinearity and figure of merit of CdS nanocrystals chemically stabilized in spin-processable polymer films,” J. Mater. Sci. 39(3), 993–996 (2004). [CrossRef]

68.

D. Pelinovsky, J. Sears, L. Brozozowski, and E. H. Sargent, “Stable all-optical limiting in nonlinear periodic structures. I. Analysis,” J. Opt. Soc. Am. B 19(1), 43–53 (2002). [CrossRef]

69.

W. N. Ye, L. Brozozowski, E. H. Sargent, and D. Pelinovsky, “Stable all-optical limiting in nonlinear periodic structures. III. Nonsolitonic pulse propagation,” J. Opt. Soc. Am. B 20(4), 695–705 (2003). [CrossRef]

OCIS Codes
(160.4330) Materials : Nonlinear optical materials
(160.5470) Materials : Polymers
(160.6000) Materials : Semiconductor materials
(190.4400) Nonlinear optics : Nonlinear optics, materials
(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW
(190.4223) Nonlinear optics : Nonlinear wave mixing
(160.4236) Materials : Nanomaterials
(160.5335) Materials : Photosensitive materials

ToC Category:
Nonlinear Optics

History
Original Manuscript: April 3, 2012
Revised Manuscript: April 30, 2012
Manuscript Accepted: April 30, 2012
Published: May 31, 2012

Citation
Xiangming Liu, Yusuke Adachi, Yasuo Tomita, Juro Oshima, Takuya Nakashima, and Tsuyoshi Kawai, "High-order nonlinear optical response of a polymer nanocomposite film incorporating semiconducotor CdSe quantum dots," Opt. Express 20, 13457-13469 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-12-13457


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References

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