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Measurement of third order susceptibility by nonresonant nondegenerate four wave mixing in polymer embedded cadmium sulfide quantum dot systems
Optical Materials 29 (2006) 342–347 www.elsevier.com/locate/optmat
Measurement of third order susceptibility by nonresonant nondegenerate four wave mixing in polymer embedded cadmium sulfide quantum dot systems D. Mohanta *, A. Choudhury Department of Physics, Tezpur University, P.O. Napaam, Assam 784 028, India Received 26 April 2005; accepted 5 November 2005 Available online 3 January 2006
Abstract We report clear evidence of third order nonlinearity v(3) in polymer embedded cadmium sulfide quantum dot system as a result of nonresonant nondegenerate four frequency mixing. We notice thickness dependent enhancement of nonlinear absorption with increase in incident intensity of light. Two pump beams (k = 1064 nm) were oppositely directed into the sample and to receive phase conjugated signal, a probe beam was focused at the point of intersection on the sample. In the conditions satisfying self diffraction phenomena, we have measured change in refractive index as a function of incident power. We have observed very high value of third order susceptibility (v(3) 107 e.s.u.) and predict figure of merit as high as 1.9 for the thinnest quantum dot sample (0.54 lm). Nonlinear susceptibility drops by nearly 10 times for the thickest sample (1.211 lm) due to considerable suppression in nonlinear absorption. 2005 Elsevier B.V. All rights reserved. PACS: 81.05.Dz; 81.07.Ta; 42.65.Hw Keywords: Nonresonant; Nondegenerate; Quantum dots
1. Introduction Low dimensional composites consisting of metallic or semiconducting materials embedded in dielectric hosts have unusual nonlinear optical properties of interest for both scientific and technological reasons. Measurements of nonlinear optical response, in both semiconductor and metal quantum dot composites, indicate complementary but favorable characteristics in terms of switching speed, magnitude of nonlinearity and switching energy. Indeed, there is enough scope for the possible deployment of these materials in photonic devices for optical switching and computing. The nonlinear optical phenomena has been discussed in various general texts [1–3]. In the special case of designing devices, there exists a so-called ‘figure of merit’ to grade the *
Corresponding author. E-mail address: [email protected] (D. Mohanta).
0925-3467/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2005.11.005
optical nonlinearity for application. The concept which generally succeeds is the evaluation of the nonlinear optical properties in terms of nonlinear susceptibility v(3) of respective materials. The mechanism determining nonlinear susceptibility is actually different for various kinds of nanomaterials. In nanoscale devices one has no option to use optical resonators to enhance the nonlinear effects-a trick often exploited when the physical dimensions of a nonlinear device are larger than the wavelength of light. Therefore, one has to rely on the nonlinearity of the medium itself. In composite systems like CdSxSe1x where the host matrix is either a glass or a polymer, exploiting the intensity dependent change in the refraction coefficient, determination of third order nonlinearity has been reported by many different processes. They include third harmonic generation (THG), interferometry (IF), pump probe spectroscopy (PP) and degenerate four wave mixing (DFWM) [4–9]. Measurement of third order susceptibility
D. Mohanta, A. Choudhury / Optical Materials 29 (2006) 342–347
has been reported [10–13] and reviewed [14,15] by various workers using z-scan and FWM techniques. However, all these methods involve resonant excitation which is relatively slow (ns) and there is adequate signal loss due to high value of absorption coefficient (105/cm) where as nonresonant excitation is faster and involves low absorption coefficient value (102/cm). In this report, we highlight contribution to the third order susceptibility by nonresonantly excited polymer embedded cadmium sulfide quantum dots based on nondegenerate four frequency mixing (NDFWM) phenomena. The measured optical nonlinearity involves the principle of self diffraction and an established formula which was verified by Cotter et al. for 3.5–6 nm CdSe–Te clusters dispersed in glass [16]. 2. Theory Semiconductor quantum dots represent unique class of quasi-zero dimensional material systems which reveal large optical nonlinearity and hence are potential candidates for optoelectronic and photonic devices. The nature of the nonlinear optical response to an incident light-field can be profoundly influenced by the dimensionality of the material. Nonlinear optical effects are generally strongest in geometries in which the optical intensity is high in the largest possible volume. The practical application of nonlinear optical effects requires field strength as high as 106 V/m [17,18]. In order to explain nonlinear effects, it is normally assumed that the nuclei and associated electrons of the atoms in the solid form electric dipoles. The electromagnetic radiation interacts with these dipoles causing them to oscillate which, by the classical laws of electromagnetism, results in the formation of dipoles which now act as sources of new electromagnetic radiation. If the amplitude of vibration is small, the dipoles emit radiation of frequency comparable to the incident radiation. While the intensity of the radiation increases, the relationship between intensity and amplitude of vibration becomes nonlinear resulting in the generation of harmonics of the frequency of the radiation emitted by oscillating dipoles. Typically, a nonlinear refraction coefficient n2 is defined by nðxÞ ¼ n0 ðxÞ þ DnðxÞ ¼ n0 ðxÞ þ n2 I
ð1Þ
where n0 is the linear (normal) low intensity refractive index and I being intensity of the light beam. Considering the case due to Yoffe et al. [19] 2p ð3Þ 2 v E n0 ¼ n n0
n ¼ n0 þ Dnvð3Þ
and 2pvð3Þ E2 ¼ n0 2pvð3Þ I ¼ n0
ð2Þ
ð3Þ
343
The result has been verified by Cotter et al. [16] for CdSe– Te nanoclusters dispersed in glass. Further, along with Eq. (1) for solid semiconductors, nonlinear refractive index can be written as [20] n2 ¼ and I¼
16p2 Revð3Þ e.s.u. cn20
cn 0 E2 8p
ð4Þ
ð5Þ
In the thin-grating approximation, d 2K2/k (d thickness of the grating, K the grating constant and k the wavelength of the light) [21]. The efficiency of a thin-grating is correlated with the nonlinear change in the refractive index in the simple approximation 2 I 1 pDnd g¼ ð6Þ k IT where I1 is the intensity of the first order diffraction obtained by photon counts on the reverse side of the sample and away from principal beam corresponding to incident intensity (I0), IT is the transmitted intensity of the pump beam (zeroth order intensity), d the thickness of the grating and k the wavelength of the probe-laser. Instead of incident intensity, use of the transmitted intensity allows one to take absorption losses into account. Both I1 and IT are measured corresponding to different incident intensities I0. In fact, there are two regimes concerned with the nonlinear response, the resonant and the nonresonant cases. The response time for the resonant regime is relatively slow, of the order of a nanosecond, but v(3) values can be enhanced by exciton effects to the order of 109 e.s.u. and even values as high as 106 e.s.u. has been reported for iron nanoparticles in amorphous BaTiO3 [22]. Biexciton contribution to the third order nonlinearity was observed by Spocker et al. [23] in resonantly excited nondegenerate four wave mixing (NDFWM). The penalty for working in the resonant mode is the loss in the transmitted light due to the high a-values (105–106/cm) which limits possible practical applications. On the other hand, nonresonant response time is faster and ideally should be in the order of a picosecond. The additional advantage of concentrating on this regime is the damping factor due to low a-values, thus avoiding attenuation of the signal. Working in this regime therefore, involves only the real part of Dn, and since v(3) value is low, the signal is weaker than for the resonant case. Even then; nonresonant process is interesting due to safe passage of light without degrading quality of the specimen. The nonresonant case is simple to handle, since one is concerned with optical effects far removed from the optical absorption edge, i.e., when the photon energy of the incident light hx is less than the energy gap Eg of the quantum dot material. In other words, absorption coefficient is low, exciton effect and multiple-photon absorption are absent, and the major factors involved are the local field and the anharmonicity of the electronic structure. Reports based on nonresonant
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DFWM methods have shown optical nonlinearity as large as 1011 e.s.u. in CdSxSe1x systems [24–26]. 3. Experimental 10 wt.% polyvinyl alcohol (PVA) (loba-chemie, lmw 22,000) matrix was prepared by stirring (200 rpm) and heating (70 C) arrangement. The transparent viscous PVA matrix as prepared, was kept overnight in an icecold environment. 7.5 wt.% aqueous cadmium chloride was reacted with PVA matrix followed by hydrogen sulfide gas treatment till maximum absorption. Faint yellow coloured CdS quantum dot sample was kept ready for subsequent experiments. A number of films have been casted on laboratory glass slides by putting a few drops of the specimen followed by stretching at once. The films were partly dried naturally and partly in vacuum oven. The average film thickness was measured by conventional Michelson interferometric method and found to be in the range 0.05– 1.2 lm. Specimen films of size 1.5 · 1.5 cm2 were extracted from the original films and put into a dark cavity to investigate nonlinear absorption and four wave mixing phenomena. The Nd-YAG laser operated in Q-switching mode (k = 1064 nm and pulse-width 6 ns) was considered as the source of optical pumping. Initially, to observe intensity dependent absorption response, the pump beam was concentrated close to the sample by lens and slit arrangement. Since, CdS quantum dots (melting point Tm = 1475 C, thermal conductivity K 20 W m1 K1) are embedded in a polymer matrix (Tm = 140 C, K 2 W m1 K1) direct exposure might melt the matrix and hence affect the position of individual quantum dots. Therefore, in order to avoid unwanted heating, care was taken to focus the beam close to the sample (2 mm approx.) and not exactly into the sample. A silicon infrared (IR) sensitive photodetector (SFH 203 FA, UK) having power dissipation 100 mW, kpeak = 900 nm and angle of acceptance 40 was placed at the back of the sample. The detector was interfaced with a 60-MHz digital storage oscilloscope (OS-3060 Philips).
bs1 (50:50)
Nd:YAG ~6 ns Pump laser λ = 1064 nm
Fig. 1 depicts experimental arrangement of FWM. The probe beam (He–Ne; k = 632.8 nm) being different from that of pump beam (Nd:YAG; k = 1064 nm); the case is a nondegenerate four wave mixing (NDFWM). The method is based on self diffraction for analyzing change in refractive index with respect to the incident intensity of light. To estimate refractive index change, the self diffraction was measured in a thin-grating approximation using Eq. (6). The PVA polymer being transparent to IR, the ensemble of embedded quantum dots constitute an ideal grating under pump beams satisfying self diffraction principle. The grating constant is the period determined by the counter propagating Nd:YAG pulses, and is given as: wavelength/2 Æ refractive index (k = 1064 nm and nCdS = 2.336), which turns out to be 228 nm, and is close to the inter dot spacing i.e., 200 nm. Considering average interdot spacing to be the grating constant i.e., K 200 nm and kprobe = 632.8 nm, we determine 2K2/k 0.126 lm. Therefore, validity of self diffraction is complete for the samples having thicknesses 0.054 lm, 0.092 lm and 0.125 lm, respectively where as samples with thickness 0.182 lm, 0.980 lm and 1.211 lm may deviate considerably from the self diffraction principle and hence from contributing large optical nonlinearity. As shown, traversing through nearly equal optical paths the two coherent pump beams produced by a Nd:YAG laser and split by a 50:50 beam splitter are allowed to hit the target quantum dot film which is already put in a dark cavity. The diffracted and transmitted orders are detected by time integrated movable Si-detector. A probe beam (k = 632.8 nm) was directed into the interactive region to receive phase conjugated signal so as to measure pumping induced optical nonlinearity. The silicon photodetector which has been interfaced to the storage oscilloscope was placed at suitable position to receive the phase conjugated signal. In order to receive information only from embedded CdS quantum dots, at first PVA sample was placed as a reference sample and then subsequent CdS/PVA samples were tested. For comparison sake, we have tried with bulk CdS without matrix encapsulation but could not receive adequate phase conjugated signal. We interpret that being
S
1
M1
L 2
S*
M2 He-Ne bs2 (50:50)
Probe laser λ = 632.8 nm
60 MHz Digital Storage Oscilloscope Si Detector Dark room
Fig. 1. Nondegenerate four wave mixing (NDFWM) experimental set-up.
D. Mohanta, A. Choudhury / Optical Materials 29 (2006) 342–347
wavelength of the oppositely directed pump beams too short compared to the interactive length of the medium, no detectable amount of nonlinearity was noticed. For QD samples, laser power of single shot (pulse) was varied and corresponding information was stored. 4. Results and discussion Formation of polymer embedded CdS quantum dots was confirmed by high resolution transmission electron microscopy (Fig. 2). Nearly spherical, isolated quantum dots of size 2–7 nm with 200 nm interdot spacing (figure inset) was observable in the micrograph. Although the size range varies from strong to weak confinement regimes (0.4–1.45 aB) excitonic effects may come to the forefront. However, such effects are of significant interest for resonant cases only. In fact, in the present case, the excitation energy of pulsed laser (1.17 eV) is lower by an amount 1.25 eV to initiate the resonant process in CdS (Eg = 2.42 eV). Fig. 3 represents intensity versus transmitted light obtained from the oscilloscope data. It was found that
345
for the thickest sample (1.21 lm) relative transmission is relatively weak possibly due to proportionately high linear absorption owing to large sample thickness. QD sample with thickness 0.054 lm, show significant lowering of transmission by an amount 23%, while incident power was varied between 0.25 GW/cm2 and 2.65 GW/cm2. This might be due to the local field intensity enhancement by nonlinear absorption as a result of virtual excitation of e–h pairs. There are reports available with respect to local field intensity enhancement characterized by a factor QNF, which has been calculated as a function of R for different pump laser wavelengths [27,28]. Also, based on the field correlation effects, time delayed method had been proposed to suppress the thermal effect, and ultrafast relaxation time was measured even in an absorbing medium [29]. Interactive length li is the region of influence when oppositely directed pump beams interact simultaneously in the specimen (Fig. 4). In case of the 1.21 lm sample, being interactive length smaller than that of the thinnest one (0.054 lm), there is only marginal lowering (6%) of transmission response. Conversely, the interactive length is significant for the later case, for which nonlinear absorption is large and hence should have large optical nonlinearity.
1064 nm (pump)
llii
1064 nm (pump)
d 632.8 nm (probe) Phase conjugated signal
li Fig. 2. TEM image of CdS/PVA quantum dots, inset showing magnified view of two isolated spherical quantum dots.
d=1.211 µm
li
d=0.054 µm Fig. 3. Transmission (T) versus incident power for QD films of thickness ( ) 0.054 lm, ( ) 0.092 lm, ( ) 0.125 lm, ( ) 0.182 lm, ( ) 0.92 lm and ( ) 1.211 lm.
Fig. 4. Schematic of interactive regions in CdS quantum dot films.
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Fig. 5. Change in index of refraction Dn (104) versus incident power for QD films of thickness ( ) 0.054 lm, ( ) 0.092 lm, ( ) 0.125 lm, ( ) 0.182 lm, ( ) 0.92 lm and ( ) 1.211 lm.
Referring to Fig. 5, which depicts change in refractive index Dn (104) versus incident intensity I0 (GW/cm2), it was found that the change in refractive index strongly depends on the incident power as well as on the sample thickness. It displays highly nonlinear dependence of refractive index on the incident intensity while sample thickness is smaller than the wavelength of the pump beams. The quantum dots have large number of surface traps which can hold electrons, when dislodged under the influence of radiation could facilitate dipole formation. These dipoles may now become sources of new electromagnetic radiation. Thus, photon–quantum dot interaction is responsible for strong nonlinear absorption which leads to Dn maximum. However, the samples (0.92 lm and 1.211 lm) which are comparable to the wavelength of the pump beam (1.064 lm) suffer saturation absorption beyond finite intensity as a result of which change in refractive index tend to saturate abruptly which in turn can define optical limiting of the concerned QD sample. For thin samples, saturation is expected to occur at extremely high power value of I0, which was beyond the scope of the Nd:YAG operation. Conversely, self diffraction approach is appreciable for thin samples, which is likely to deviate for thicker ones as a reasonable number of the quantum dots are ignored by pump beams in the later case. The respective slopes d(Dn)/dI0 are obtained from Fig. 5 (which corresponds to the nonlinear refraction coefficient n2) and using Eq. (4), v(3) values were computed for different QD samples (Table 1). Assuming linear refractive index
Table 1 Third order susceptibility measurement of CdS quantum dots cn2
Sample thickness (lm)
2 n2 ¼ dðDnÞ dI 0 (cm /GW)
vð3Þ ¼ n2 16p02 (e.s.u.)
0.054 0.092 0.125 0.182 0.920 1.211
1.156 0.945 0.301 0.148 0.142 0.126
1.19 · 107 9.79 · 108 3.12 · 108 1.53 · 108 1.47 · 108 1.31 · 108
of CdS be 2.336 corresponding to k = 1.064 lm, third order susceptibility of the CdS quantum dot samples was estimated, which is of the order 107–108 e.s.u. Such a high value of nonlinearity obtained due to nonresonant excitation drops by substantial amounts when film thickness increases as a result of suppression in the nonlinear absorption. The third order susceptibility of these system is 100 times more than the previous reports [4,26], where third harmonic generation and degenerate four wave mixing methods were considered with respect to our nondegenerate four frequency mixing case. Again, low intensity threshold, high index change nonlinear materials are desired for all optical switching [30]. Transmission based nonlinear devices rely on materials which effect a p-phase shift due to a change in refractive index n before the signal to be processed is attenuated to 1/e of its incident value as a result of absorption aeff. The requirement, is expressed in terms of Stegeman’s figure of merit [31] given by, F ¼
Dnsat L 1 Dnsat . ¼ >1 k La kaeff
ð7Þ
The above expression combines two requirements for optimum nonlinear waveguide device operation. The first term contains the necessary minimum phase shift of the refractive index Dn required for switching the waveguide device (L is the device length, here thickness d of the sample and k is the wavelength of light). The second term is a so-called throughput criterion, ensuring that the damping losses due to absorption fulfill the requirement La < 1. For thin QD samples, since complete saturation in the Dn was not obtained which was beyond the scope of Nd:YAG operation, Dn corresponding to max. I0 can be approximated as Dnsat using saturation trend in Fig. 5. Considering k = 1064 nm, Dnsat 7 · 104 and aeff = 0.34/mm; figureof-merit as high as F = 1.9 is obtained for 0.054 lm QD sample. Note that Dnsat was obtained from the Dn versus I0 plot exhibiting a saturation trend and aeff was measured using Lambert’s established relation (I = I0ead, d being sample thickness). This high value of figure-of-merit observed in a nondegenerate and nonresonant process would find better scope in optical switching over resonant processes, where deterioration of the sample cannot be ignored. Therefore, as far as nonresonant excitation is concerned we are successful in observing appreciable amount of third order nonlinearity in polymer embedded CdS quantum dot system retaining quality of the QD-sample. The probable cause of nonlinear response may be governed by two components, a fast component due to the free carriers (tens of ps) and a slow component due to trapped carriers (tens of ns). Semiconductor doped host matrices contain both types of particles, that is, particles without traps that are responsible for the free carrier component and particles with traps that are responsible for the slow nonlinearity. The two components compete progressively to contribute a resultant nonlinearity.
D. Mohanta, A. Choudhury / Optical Materials 29 (2006) 342–347
5. Conclusion To summarize, based on self diffraction approach, we have measured nonresonant NDFWM led detectable amounts of nonlinear susceptibility in CdS quantum dot systems. The nonresonant process was performed to retain samples’ quality. We have observed strong nonlinear change in refractive index for the thin quantum dot samples where all the quantum dots interact with the counter propagating waves. Saturative nature of refractive index (Fig. 5) predicts optical limiting due to saturation absorption. Third order susceptibility is reduced by a factor of 10 for the thickest quantum dot film (1.211 lm) with respect to 0.054 lm QD sample, thus illustrating deviation from the conditions of self diffraction in the former case. Reasonably high value of the figure of merit 1.9 was calculated for 0.054 lm QD sample, which ensures vital application in optical switching networks and interconnects. Acknowledgements The authors are thankful to the ISRO project under respond. The authors would like to extend sincere thanks to RSIC, Shillong for TEM analysis and Dr. K. Baruah for extending help and support for Nd:YAG operation. References [1] R.W. Boyd, Nonlinear optics, Academic Press, New York, 1982. [2] H.M. Gibbs, Optical bistability: Controlling light with light, Academic press, New York, 1985. [3] P.N. Prasad, D.J. Williams, Introduction to Nonlinear effects in molecules and polymers, Wiley, New York, 1985. [4] L.T. Cheng, N. Herron, Y. Wang, J. Appl. Phys. 66 (1989) 3417. [5] G.R. Olbright, N. Peyghambarian, Appl. Phys. Lett. 48 (1986) 1184.
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[6] Yu.V. Vandyshev, V.S. Dneprovskii, V.I. Klimov, Sov. Phys. JETP 74 (1992) 144. [7] R.K. Jain, R.C. Lind, J. Opt. Soc. Am. 73 (1983) 647. [8] S.M. Saltiel, B. ven Wonterghem, P.M. Rentzepis, Opt. Commun. 77 (1990) 59. [9] V. Sperling, U. Woggon, A. Lohde, T. Haalboom, in: Proc. of Int. Conf. Luminscence, Prag, 1996. [10] M. Sheik-Bahae, A.A. Said, T. Wei, D.J. Hagan, E.W. van Stryland, IEEE J. Quantum Electron. 26 (1990) 760. [11] M. Sheik-Bahae, J. Wang, R. Desalvo, D.J. Hagan, E.W. van Stryland, Opt. Lett. 17 (1992) 258. [12] G.I. Stegeman, C.T. Seaton, J. Chilwell, S.D. Smith, Appl. Phys. Lett. 44 (1984) 830. [13] B. Vaynberg, M. Matusovsky, M. Rosenbluh, E. Kolobkova, A. Lipovskii, Opt. Commun 132 (1996) 307. [14] L.L. Beecroft, C.K. Ober, Chem Mater. 9 (1997) 1302. [15] S. Vijayalakshmi, H. Gebel, Nonlinear optical properties of nanostructures, in: H.S. Nalwa (Ed.), Hand book of Nanostructured Materials and Nanotechnology, vol. 4, 2000. [16] D. Cotter, M.G. Burt, R.J. Manning, Phys. Rev. Lett. 68 (1992) 1200. [17] E.G. Sauter, Nonlinear Optics, John Wiley, New York, 1996. [18] J. Wilson, J.F.B. Hawkes, Optoelectronics: An Introduction, Prentice Hall International Ltd., UK, 1992. [19] A.D. Yoffe, Advances in Physics 42 (2) (1993) 241. [20] A.G. Astill, Thin Solid Films 204 (1991) 1. [21] U. Woggon, Optical Properties of semiconductor quantum dots, Springer-Verlag, Berlin, Heidelberg, 1997, p. 175. [22] W. Wang, G. Yang, Z. Chen, Y. Zhou, H. Lu, G. Yang, J. Appl. Phys. 92 (12) (2002) 7242. [23] H. Spocker, M. Portun, U. Woggon, Opt. Lett. 23 (6) (1998) 427. [24] B. Danielzik, K. Nattermann, D. von der Linde, Appl. Phys. B 38 (1985) 31. [25] L.H. Acioli, A.S.L. Gomes, J.R. Rios Leite, C.B. de Araujo, IEEE J. Quantum Electron. 26 (1990) 1277. [26] H. Shinojima, J. Yumoto, N. Uesugi, Appl. Phys. Lett. 60 (1992) 298. [27] Y. Wang, N. Herron, J. Phys. Chem. 95 (1991) 525. [28] Y. Wang, Acc. Chem. Res. 24 (1991) 133. [29] P. Fu, Q. Jiang, X. Mi, Z. Yu, Phys. Rev. Lett. 88 (11) (2002) 113902. [30] L. Brzozowski, E.H. Sargent, IEEE J. Quantum Electron. 36 (2000) 550. [31] G.I. Stegeman, Nonlinear Opt. Prop. Adv. Mater. SPIE 1852 (1993) 75.
Measurement of third order susceptibility by nonresonant nondegenerate four wave mixing in polymer embedded cadmium sulfide quantum dot systems D. Mohanta *, A. Choudhury Department of Physics, Tezpur University, P.O. Napaam, Assam 784 028, India Received 26 April 2005; accepted 5 November 2005 Available online 3 January 2006
Abstract We report clear evidence of third order nonlinearity v(3) in polymer embedded cadmium sulfide quantum dot system as a result of nonresonant nondegenerate four frequency mixing. We notice thickness dependent enhancement of nonlinear absorption with increase in incident intensity of light. Two pump beams (k = 1064 nm) were oppositely directed into the sample and to receive phase conjugated signal, a probe beam was focused at the point of intersection on the sample. In the conditions satisfying self diffraction phenomena, we have measured change in refractive index as a function of incident power. We have observed very high value of third order susceptibility (v(3) 107 e.s.u.) and predict figure of merit as high as 1.9 for the thinnest quantum dot sample (0.54 lm). Nonlinear susceptibility drops by nearly 10 times for the thickest sample (1.211 lm) due to considerable suppression in nonlinear absorption. 2005 Elsevier B.V. All rights reserved. PACS: 81.05.Dz; 81.07.Ta; 42.65.Hw Keywords: Nonresonant; Nondegenerate; Quantum dots
1. Introduction Low dimensional composites consisting of metallic or semiconducting materials embedded in dielectric hosts have unusual nonlinear optical properties of interest for both scientific and technological reasons. Measurements of nonlinear optical response, in both semiconductor and metal quantum dot composites, indicate complementary but favorable characteristics in terms of switching speed, magnitude of nonlinearity and switching energy. Indeed, there is enough scope for the possible deployment of these materials in photonic devices for optical switching and computing. The nonlinear optical phenomena has been discussed in various general texts [1–3]. In the special case of designing devices, there exists a so-called ‘figure of merit’ to grade the *
Corresponding author. E-mail address: [email protected] (D. Mohanta).
0925-3467/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2005.11.005
optical nonlinearity for application. The concept which generally succeeds is the evaluation of the nonlinear optical properties in terms of nonlinear susceptibility v(3) of respective materials. The mechanism determining nonlinear susceptibility is actually different for various kinds of nanomaterials. In nanoscale devices one has no option to use optical resonators to enhance the nonlinear effects-a trick often exploited when the physical dimensions of a nonlinear device are larger than the wavelength of light. Therefore, one has to rely on the nonlinearity of the medium itself. In composite systems like CdSxSe1x where the host matrix is either a glass or a polymer, exploiting the intensity dependent change in the refraction coefficient, determination of third order nonlinearity has been reported by many different processes. They include third harmonic generation (THG), interferometry (IF), pump probe spectroscopy (PP) and degenerate four wave mixing (DFWM) [4–9]. Measurement of third order susceptibility
D. Mohanta, A. Choudhury / Optical Materials 29 (2006) 342–347
has been reported [10–13] and reviewed [14,15] by various workers using z-scan and FWM techniques. However, all these methods involve resonant excitation which is relatively slow (ns) and there is adequate signal loss due to high value of absorption coefficient (105/cm) where as nonresonant excitation is faster and involves low absorption coefficient value (102/cm). In this report, we highlight contribution to the third order susceptibility by nonresonantly excited polymer embedded cadmium sulfide quantum dots based on nondegenerate four frequency mixing (NDFWM) phenomena. The measured optical nonlinearity involves the principle of self diffraction and an established formula which was verified by Cotter et al. for 3.5–6 nm CdSe–Te clusters dispersed in glass [16]. 2. Theory Semiconductor quantum dots represent unique class of quasi-zero dimensional material systems which reveal large optical nonlinearity and hence are potential candidates for optoelectronic and photonic devices. The nature of the nonlinear optical response to an incident light-field can be profoundly influenced by the dimensionality of the material. Nonlinear optical effects are generally strongest in geometries in which the optical intensity is high in the largest possible volume. The practical application of nonlinear optical effects requires field strength as high as 106 V/m [17,18]. In order to explain nonlinear effects, it is normally assumed that the nuclei and associated electrons of the atoms in the solid form electric dipoles. The electromagnetic radiation interacts with these dipoles causing them to oscillate which, by the classical laws of electromagnetism, results in the formation of dipoles which now act as sources of new electromagnetic radiation. If the amplitude of vibration is small, the dipoles emit radiation of frequency comparable to the incident radiation. While the intensity of the radiation increases, the relationship between intensity and amplitude of vibration becomes nonlinear resulting in the generation of harmonics of the frequency of the radiation emitted by oscillating dipoles. Typically, a nonlinear refraction coefficient n2 is defined by nðxÞ ¼ n0 ðxÞ þ DnðxÞ ¼ n0 ðxÞ þ n2 I
ð1Þ
where n0 is the linear (normal) low intensity refractive index and I being intensity of the light beam. Considering the case due to Yoffe et al. [19] 2p ð3Þ 2 v E n0 ¼ n n0
n ¼ n0 þ Dnvð3Þ
and 2pvð3Þ E2 ¼ n0 2pvð3Þ I ¼ n0
ð2Þ
ð3Þ
343
The result has been verified by Cotter et al. [16] for CdSe– Te nanoclusters dispersed in glass. Further, along with Eq. (1) for solid semiconductors, nonlinear refractive index can be written as [20] n2 ¼ and I¼
16p2 Revð3Þ e.s.u. cn20
cn 0 E2 8p
ð4Þ
ð5Þ
In the thin-grating approximation, d 2K2/k (d thickness of the grating, K the grating constant and k the wavelength of the light) [21]. The efficiency of a thin-grating is correlated with the nonlinear change in the refractive index in the simple approximation 2 I 1 pDnd g¼ ð6Þ k IT where I1 is the intensity of the first order diffraction obtained by photon counts on the reverse side of the sample and away from principal beam corresponding to incident intensity (I0), IT is the transmitted intensity of the pump beam (zeroth order intensity), d the thickness of the grating and k the wavelength of the probe-laser. Instead of incident intensity, use of the transmitted intensity allows one to take absorption losses into account. Both I1 and IT are measured corresponding to different incident intensities I0. In fact, there are two regimes concerned with the nonlinear response, the resonant and the nonresonant cases. The response time for the resonant regime is relatively slow, of the order of a nanosecond, but v(3) values can be enhanced by exciton effects to the order of 109 e.s.u. and even values as high as 106 e.s.u. has been reported for iron nanoparticles in amorphous BaTiO3 [22]. Biexciton contribution to the third order nonlinearity was observed by Spocker et al. [23] in resonantly excited nondegenerate four wave mixing (NDFWM). The penalty for working in the resonant mode is the loss in the transmitted light due to the high a-values (105–106/cm) which limits possible practical applications. On the other hand, nonresonant response time is faster and ideally should be in the order of a picosecond. The additional advantage of concentrating on this regime is the damping factor due to low a-values, thus avoiding attenuation of the signal. Working in this regime therefore, involves only the real part of Dn, and since v(3) value is low, the signal is weaker than for the resonant case. Even then; nonresonant process is interesting due to safe passage of light without degrading quality of the specimen. The nonresonant case is simple to handle, since one is concerned with optical effects far removed from the optical absorption edge, i.e., when the photon energy of the incident light hx is less than the energy gap Eg of the quantum dot material. In other words, absorption coefficient is low, exciton effect and multiple-photon absorption are absent, and the major factors involved are the local field and the anharmonicity of the electronic structure. Reports based on nonresonant
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DFWM methods have shown optical nonlinearity as large as 1011 e.s.u. in CdSxSe1x systems [24–26]. 3. Experimental 10 wt.% polyvinyl alcohol (PVA) (loba-chemie, lmw 22,000) matrix was prepared by stirring (200 rpm) and heating (70 C) arrangement. The transparent viscous PVA matrix as prepared, was kept overnight in an icecold environment. 7.5 wt.% aqueous cadmium chloride was reacted with PVA matrix followed by hydrogen sulfide gas treatment till maximum absorption. Faint yellow coloured CdS quantum dot sample was kept ready for subsequent experiments. A number of films have been casted on laboratory glass slides by putting a few drops of the specimen followed by stretching at once. The films were partly dried naturally and partly in vacuum oven. The average film thickness was measured by conventional Michelson interferometric method and found to be in the range 0.05– 1.2 lm. Specimen films of size 1.5 · 1.5 cm2 were extracted from the original films and put into a dark cavity to investigate nonlinear absorption and four wave mixing phenomena. The Nd-YAG laser operated in Q-switching mode (k = 1064 nm and pulse-width 6 ns) was considered as the source of optical pumping. Initially, to observe intensity dependent absorption response, the pump beam was concentrated close to the sample by lens and slit arrangement. Since, CdS quantum dots (melting point Tm = 1475 C, thermal conductivity K 20 W m1 K1) are embedded in a polymer matrix (Tm = 140 C, K 2 W m1 K1) direct exposure might melt the matrix and hence affect the position of individual quantum dots. Therefore, in order to avoid unwanted heating, care was taken to focus the beam close to the sample (2 mm approx.) and not exactly into the sample. A silicon infrared (IR) sensitive photodetector (SFH 203 FA, UK) having power dissipation 100 mW, kpeak = 900 nm and angle of acceptance 40 was placed at the back of the sample. The detector was interfaced with a 60-MHz digital storage oscilloscope (OS-3060 Philips).
bs1 (50:50)
Nd:YAG ~6 ns Pump laser λ = 1064 nm
Fig. 1 depicts experimental arrangement of FWM. The probe beam (He–Ne; k = 632.8 nm) being different from that of pump beam (Nd:YAG; k = 1064 nm); the case is a nondegenerate four wave mixing (NDFWM). The method is based on self diffraction for analyzing change in refractive index with respect to the incident intensity of light. To estimate refractive index change, the self diffraction was measured in a thin-grating approximation using Eq. (6). The PVA polymer being transparent to IR, the ensemble of embedded quantum dots constitute an ideal grating under pump beams satisfying self diffraction principle. The grating constant is the period determined by the counter propagating Nd:YAG pulses, and is given as: wavelength/2 Æ refractive index (k = 1064 nm and nCdS = 2.336), which turns out to be 228 nm, and is close to the inter dot spacing i.e., 200 nm. Considering average interdot spacing to be the grating constant i.e., K 200 nm and kprobe = 632.8 nm, we determine 2K2/k 0.126 lm. Therefore, validity of self diffraction is complete for the samples having thicknesses 0.054 lm, 0.092 lm and 0.125 lm, respectively where as samples with thickness 0.182 lm, 0.980 lm and 1.211 lm may deviate considerably from the self diffraction principle and hence from contributing large optical nonlinearity. As shown, traversing through nearly equal optical paths the two coherent pump beams produced by a Nd:YAG laser and split by a 50:50 beam splitter are allowed to hit the target quantum dot film which is already put in a dark cavity. The diffracted and transmitted orders are detected by time integrated movable Si-detector. A probe beam (k = 632.8 nm) was directed into the interactive region to receive phase conjugated signal so as to measure pumping induced optical nonlinearity. The silicon photodetector which has been interfaced to the storage oscilloscope was placed at suitable position to receive the phase conjugated signal. In order to receive information only from embedded CdS quantum dots, at first PVA sample was placed as a reference sample and then subsequent CdS/PVA samples were tested. For comparison sake, we have tried with bulk CdS without matrix encapsulation but could not receive adequate phase conjugated signal. We interpret that being
S
1
M1
L 2
S*
M2 He-Ne bs2 (50:50)
Probe laser λ = 632.8 nm
60 MHz Digital Storage Oscilloscope Si Detector Dark room
Fig. 1. Nondegenerate four wave mixing (NDFWM) experimental set-up.
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wavelength of the oppositely directed pump beams too short compared to the interactive length of the medium, no detectable amount of nonlinearity was noticed. For QD samples, laser power of single shot (pulse) was varied and corresponding information was stored. 4. Results and discussion Formation of polymer embedded CdS quantum dots was confirmed by high resolution transmission electron microscopy (Fig. 2). Nearly spherical, isolated quantum dots of size 2–7 nm with 200 nm interdot spacing (figure inset) was observable in the micrograph. Although the size range varies from strong to weak confinement regimes (0.4–1.45 aB) excitonic effects may come to the forefront. However, such effects are of significant interest for resonant cases only. In fact, in the present case, the excitation energy of pulsed laser (1.17 eV) is lower by an amount 1.25 eV to initiate the resonant process in CdS (Eg = 2.42 eV). Fig. 3 represents intensity versus transmitted light obtained from the oscilloscope data. It was found that
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for the thickest sample (1.21 lm) relative transmission is relatively weak possibly due to proportionately high linear absorption owing to large sample thickness. QD sample with thickness 0.054 lm, show significant lowering of transmission by an amount 23%, while incident power was varied between 0.25 GW/cm2 and 2.65 GW/cm2. This might be due to the local field intensity enhancement by nonlinear absorption as a result of virtual excitation of e–h pairs. There are reports available with respect to local field intensity enhancement characterized by a factor QNF, which has been calculated as a function of R for different pump laser wavelengths [27,28]. Also, based on the field correlation effects, time delayed method had been proposed to suppress the thermal effect, and ultrafast relaxation time was measured even in an absorbing medium [29]. Interactive length li is the region of influence when oppositely directed pump beams interact simultaneously in the specimen (Fig. 4). In case of the 1.21 lm sample, being interactive length smaller than that of the thinnest one (0.054 lm), there is only marginal lowering (6%) of transmission response. Conversely, the interactive length is significant for the later case, for which nonlinear absorption is large and hence should have large optical nonlinearity.
1064 nm (pump)
llii
1064 nm (pump)
d 632.8 nm (probe) Phase conjugated signal
li Fig. 2. TEM image of CdS/PVA quantum dots, inset showing magnified view of two isolated spherical quantum dots.
d=1.211 µm
li
d=0.054 µm Fig. 3. Transmission (T) versus incident power for QD films of thickness ( ) 0.054 lm, ( ) 0.092 lm, ( ) 0.125 lm, ( ) 0.182 lm, ( ) 0.92 lm and ( ) 1.211 lm.
Fig. 4. Schematic of interactive regions in CdS quantum dot films.
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Fig. 5. Change in index of refraction Dn (104) versus incident power for QD films of thickness ( ) 0.054 lm, ( ) 0.092 lm, ( ) 0.125 lm, ( ) 0.182 lm, ( ) 0.92 lm and ( ) 1.211 lm.
Referring to Fig. 5, which depicts change in refractive index Dn (104) versus incident intensity I0 (GW/cm2), it was found that the change in refractive index strongly depends on the incident power as well as on the sample thickness. It displays highly nonlinear dependence of refractive index on the incident intensity while sample thickness is smaller than the wavelength of the pump beams. The quantum dots have large number of surface traps which can hold electrons, when dislodged under the influence of radiation could facilitate dipole formation. These dipoles may now become sources of new electromagnetic radiation. Thus, photon–quantum dot interaction is responsible for strong nonlinear absorption which leads to Dn maximum. However, the samples (0.92 lm and 1.211 lm) which are comparable to the wavelength of the pump beam (1.064 lm) suffer saturation absorption beyond finite intensity as a result of which change in refractive index tend to saturate abruptly which in turn can define optical limiting of the concerned QD sample. For thin samples, saturation is expected to occur at extremely high power value of I0, which was beyond the scope of the Nd:YAG operation. Conversely, self diffraction approach is appreciable for thin samples, which is likely to deviate for thicker ones as a reasonable number of the quantum dots are ignored by pump beams in the later case. The respective slopes d(Dn)/dI0 are obtained from Fig. 5 (which corresponds to the nonlinear refraction coefficient n2) and using Eq. (4), v(3) values were computed for different QD samples (Table 1). Assuming linear refractive index
Table 1 Third order susceptibility measurement of CdS quantum dots cn2
Sample thickness (lm)
2 n2 ¼ dðDnÞ dI 0 (cm /GW)
vð3Þ ¼ n2 16p02 (e.s.u.)
0.054 0.092 0.125 0.182 0.920 1.211
1.156 0.945 0.301 0.148 0.142 0.126
1.19 · 107 9.79 · 108 3.12 · 108 1.53 · 108 1.47 · 108 1.31 · 108
of CdS be 2.336 corresponding to k = 1.064 lm, third order susceptibility of the CdS quantum dot samples was estimated, which is of the order 107–108 e.s.u. Such a high value of nonlinearity obtained due to nonresonant excitation drops by substantial amounts when film thickness increases as a result of suppression in the nonlinear absorption. The third order susceptibility of these system is 100 times more than the previous reports [4,26], where third harmonic generation and degenerate four wave mixing methods were considered with respect to our nondegenerate four frequency mixing case. Again, low intensity threshold, high index change nonlinear materials are desired for all optical switching [30]. Transmission based nonlinear devices rely on materials which effect a p-phase shift due to a change in refractive index n before the signal to be processed is attenuated to 1/e of its incident value as a result of absorption aeff. The requirement, is expressed in terms of Stegeman’s figure of merit [31] given by, F ¼
Dnsat L 1 Dnsat . ¼ >1 k La kaeff
ð7Þ
The above expression combines two requirements for optimum nonlinear waveguide device operation. The first term contains the necessary minimum phase shift of the refractive index Dn required for switching the waveguide device (L is the device length, here thickness d of the sample and k is the wavelength of light). The second term is a so-called throughput criterion, ensuring that the damping losses due to absorption fulfill the requirement La < 1. For thin QD samples, since complete saturation in the Dn was not obtained which was beyond the scope of Nd:YAG operation, Dn corresponding to max. I0 can be approximated as Dnsat using saturation trend in Fig. 5. Considering k = 1064 nm, Dnsat 7 · 104 and aeff = 0.34/mm; figureof-merit as high as F = 1.9 is obtained for 0.054 lm QD sample. Note that Dnsat was obtained from the Dn versus I0 plot exhibiting a saturation trend and aeff was measured using Lambert’s established relation (I = I0ead, d being sample thickness). This high value of figure-of-merit observed in a nondegenerate and nonresonant process would find better scope in optical switching over resonant processes, where deterioration of the sample cannot be ignored. Therefore, as far as nonresonant excitation is concerned we are successful in observing appreciable amount of third order nonlinearity in polymer embedded CdS quantum dot system retaining quality of the QD-sample. The probable cause of nonlinear response may be governed by two components, a fast component due to the free carriers (tens of ps) and a slow component due to trapped carriers (tens of ns). Semiconductor doped host matrices contain both types of particles, that is, particles without traps that are responsible for the free carrier component and particles with traps that are responsible for the slow nonlinearity. The two components compete progressively to contribute a resultant nonlinearity.
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5. Conclusion To summarize, based on self diffraction approach, we have measured nonresonant NDFWM led detectable amounts of nonlinear susceptibility in CdS quantum dot systems. The nonresonant process was performed to retain samples’ quality. We have observed strong nonlinear change in refractive index for the thin quantum dot samples where all the quantum dots interact with the counter propagating waves. Saturative nature of refractive index (Fig. 5) predicts optical limiting due to saturation absorption. Third order susceptibility is reduced by a factor of 10 for the thickest quantum dot film (1.211 lm) with respect to 0.054 lm QD sample, thus illustrating deviation from the conditions of self diffraction in the former case. Reasonably high value of the figure of merit 1.9 was calculated for 0.054 lm QD sample, which ensures vital application in optical switching networks and interconnects. Acknowledgements The authors are thankful to the ISRO project under respond. The authors would like to extend sincere thanks to RSIC, Shillong for TEM analysis and Dr. K. Baruah for extending help and support for Nd:YAG operation. References [1] R.W. Boyd, Nonlinear optics, Academic Press, New York, 1982. [2] H.M. Gibbs, Optical bistability: Controlling light with light, Academic press, New York, 1985. [3] P.N. Prasad, D.J. Williams, Introduction to Nonlinear effects in molecules and polymers, Wiley, New York, 1985. [4] L.T. Cheng, N. Herron, Y. Wang, J. Appl. Phys. 66 (1989) 3417. [5] G.R. Olbright, N. Peyghambarian, Appl. Phys. Lett. 48 (1986) 1184.
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