## High-order nonlinear optical response of a polymer nanocomposite film incorporating semiconducotor CdSe quantum dots |

Optics Express, Vol. 20, Issue 12, pp. 13457-13469 (2012)

http://dx.doi.org/10.1364/OE.20.013457

Acrobat PDF (984 KB)

### 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

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*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]

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]

*E*) of QDs increases with decreasing their size and the quantum confinement effect can strongly enhance the third-order optical nonlinearity [11

_{g}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. 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]

*E*= 1.74 eV at 300 K and has the exciton Bohr radius of 5.6 nm [12

_{g}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]

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. H. Song, Y. Zhai, Z. Zhou, Z. Hao, and L. Zhou, “Optical nonlinearity of CdSe and CdSe-C_{60} quantum dot,” Mod. Phys. Lett. B **22**(32), 3207–3213 (2008). [CrossRef]

_{x}Se

_{1-x}[26

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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]

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]

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]

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_{x}Se

_{1-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. 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]

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]

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]

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. 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]

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]

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]

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]

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]

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]

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]

## 2. Sample preparation

50. T. Nakashima, T. Sakakibara, and T. Kawai, “Highly luminescent CdTe nanocrystal-polymer composites based on ionic liquid,” Chem. Lett. **34**(10), 1410–1411 (2005). [CrossRef]

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]

*D*) and the linear refractive index (

*n*) of a CdSe QD as given by [51

_{CdSe}51. L. W. Wang and A. Zunger, “Pseudopotential calculations of nanoscale CdSe quantum dots,” Phys. Rev. B Condens. Matter **53**(15), 9579–9582 (1996). [CrossRef] [PubMed]

*ε*is the relative dielectric constant of the bulk CdSe at high frequencies, which is set 6.2 to equal the experimental value [51

51. L. W. Wang and A. Zunger, “Pseudopotential calculations of nanoscale CdSe quantum dots,” Phys. Rev. B Condens. Matter **53**(15), 9579–9582 (1996). [CrossRef] [PubMed]

*D*is measured in Å. When we used

*n*of 2.318 at 546.1 nm measured by an Abbe refractometer, the calculated value for

_{CdSe}*D*was found to be 3 nm, consistent with our TEM measurement. To make photo-cured solid film samples for nonlinear optical measurements, we mixed the CdSe QD dispersed ionic liquid monomer with 1 wt.% titanocene photoinitiator (Irgacure 784, Ciba) and a comonomer, aliphatic urethane hexaacrylate monomer (Ebecryl 8301, Cytec), for high crosslinking photopolymerization under green light illumination. The volume concentration of the comonomer was chosen to be 9 vol.% since it gave the high refractive index modulation when a plane-wave volume hologram was recorded in this film sample [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]

*α*

_{0}for cured polymer nanocomposite film samples measured at room temperature. It can be seen that the polymer nanocomposite film samples clearly exhibit excitonic absorption peaks at approximately 480 nm, independently of concentrations of CdSe QDs. These peaks correspond to the lowest quantum-confined electron-hole transition of CdSe QDs. A value for

*α*

_{0}with the highest CdSe QD volume fraction of 0.91 vol.% was 88 cm

^{−1}at a measurement wavelength of 532 nm, implying that the skin depth of the film sample was approximately 114 μm. This depth was thicker than the sample thicknesses (10 μm and 50 μm), so that the linear absorption did not cause any negative effect on our measurement.

## 3. Experimental method

*ω*

_{0}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

*z*

_{0}(≈6 mm) of the focused pulse laser beam, where

*z*

_{0}is given by

*kω*

_{0}

^{2}/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

*I*

_{0}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.

## 4. Experimental results and discussions

### 4.1 Open-aperture Z-scan

*I*

_{0}= 1.8 GW/cm

^{2}. 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/cm

^{2}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]

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]

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]

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]

*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]

*I*is the laser pulse intensity inside a medium,

*I*is the saturation intensity and

_{s}*α*equals to

*α*

_{0}under the low-intensity approximation (

*I*<<

*I*). Analytic expressions for the open-aperture Gaussian-beam Z-scan

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

*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

*I*

_{s}to be 0.53 and 0.11 GW/cm

^{2}, respectively. Figure 3(b) shows transmittance changes Δ

*T*at z = 0 [defined as

*T*(0)−1] as a function of

*I*

_{0}. It can be seen that the SA1 and SA2 models give best fit values for

*I*

_{s}to be 0.54 and 0.21 GW/cm

^{2}, respectively. We see that the SA1 model gives a consistent result for the parameter fitting of

*I*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.

_{s}### 4.2 Closed-aperture Z-scan

*I*

_{0}= 1.8 GW/cm

^{2}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/cm

^{2}. It is well known that Δ

*T*[defined as a peak-to-valley difference in

_{p-v}*T*(

*z*)] is proportional to

*I*

_{0}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]

*T*/

_{p-v}*I*

_{0}is plotted as a function of

*I*

_{0}as shown in Fig. 4(b). It can be seen that Δ

*T*/

_{p-v}*I*

_{0}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 Δ

*T*/

_{p-v}*I*

_{0}more or less linearly decreases with an increase in

*I*

_{0}. It means that the third- and fifth-order effects simultaneously contribute to

*T*(

*z*) in the closed-aperture Z-scan measurement.

**26**(4), 760–769 (1990). [CrossRef]

*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

*w*

_{m0}^{2}=

*w*

^{2}(

*z*)/(2

*m*+ 1) and

*w*

_{m}^{2}=

*w*[

_{m0}^{2}*g*

^{2}+ (

*d*/

*d*)

_{m}^{2}] in which

*w*

^{2}(

*z*) =

*w*

_{0}

^{2}(1 +

*z*

^{2}/

*z*

_{0}

^{2}),

*g*= 1 +

*d*/[

*z*(1 +

*z*

_{0}

^{2}/

*z*

^{2})], and

*d*=

_{m}*kw*

_{m}_{0}

^{2}/2. Also,

*R*=

_{m}*d*[1−

*g*/(

*g*

^{2}+

*d*

^{2}/

*d*

_{m}^{2})]

^{−1}and

*θ*= tan

_{m}^{−1}[

*d*/(

*d*)]. The normalized Z-scan transmittance

_{m}g*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

**26**(4), 760–769 (1990). [CrossRef]

*P*(

_{T}*z*,

*t*) through the aperture is given bythe incident pulse power

*P*(

_{i}*t*) is given by

*πw*

_{0}

^{2}

*I*

_{0}(

*t*)/2, and the linear transmittance of the aperture

*S*is given by 1−exp(−2

*r*

_{a}^{2}/

*w*

_{a}^{2}) with

*r*and

_{a}*w*being the aperture radius and the Gaussian beam radius at the aperture, respectively. Also,

_{a}*c*and

*ε*

_{0}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

*n*

_{2}and

*n*

_{4}by the curve fitting to the data shown in Fig. 4(a). Note that

*I*of 0.53 GW/cm

_{S}^{2}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

*n*

_{2}and

*n*

_{4}were found to be −4.0 × 10

^{−3}cm

^{2}/GW and + 1.5 × 10

^{−3}cm

^{4}/GW

^{2}, respectively, at

*I*

_{0}= 1.8 GW/cm

^{2}.

*n*

_{2}[Fig. 5(a)] and

*n*

_{4}[Fig. 5(b)] as a function of

*I*

_{0}. It can be seen that

*n*

_{2}and

*n*

_{4}are more or less independent of the input intensityin the measured intensity range; the average values for

*n*

_{2}and

*n*

_{4}are −4.0 × 10

^{−3}cm

^{2}/GW and + 1.5 × 10

^{−3}cm

^{4}/GW

^{2}, respectively. The magnitude of

*n*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

_{2}^{−5}cm

^{2}/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]

^{−4}cm

^{2}/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]

*n*(also, that of nonlinear absorption) is not necessarily consistent in past literatures [15

_{2}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. H. Song, Y. Zhai, Z. Zhou, Z. Hao, and L. Zhou, “Optical nonlinearity of CdSe and CdSe-C_{60} quantum dot,” Mod. Phys. Lett. B **22**(32), 3207–3213 (2008). [CrossRef]

*I*

_{0}of the order of GW/cm

^{2}.

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]

*χ*

_{n}^{(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]

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 C_{60} in toluene,” Appl. Phys. Lett. **68**(10), 1317–1319 (1996). [CrossRef]

*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

*L*/

*n*

_{0}Λ

^{2}(

*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]

*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

*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. 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]

*Δn*is the nonlinear refractive index change. Using

*Δn*( =

*n*

_{2}

*I*+

*n*

_{4}

*I*

^{2}) = −2.5 × 10

^{−3}at

*I*= 1 GW/cm

^{2}and

*α*= 30 cm

^{−1}with

*I*= 0.53 GW/cm

_{s}^{2}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]

*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. 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]

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]

**95**(26), 261109 (2009). [CrossRef]

## Acknowledgment

## References and links

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**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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