Three-photon absorption for nanosecond excitation in cadmium selenide quantum dots

We experimentally observe saturable absorption and dra- matic three-photon absorption in various colloidal solutions of cadmium selenide quantum dots, with a strong size dependence witnessed for these properties. We also develop a model for the electronic portion of the nonlinearities that illustrates well the trends exhibited by our experi- mental data. The model incorporates six bands three each in the va- lence and conduction bands. © 2007 Society of Photo-Optical Instrumentation Due to their small size, ability to be embedded in other materials to affect the host's properties, ability to have their own properties easily tuned by slightly varying their size or composition, and the development of standard production techniques, quantum dots are rapidly showing promise in a wide range of applications. The nonlinear optical properties of quantum dots are important for many of these applica- tions. One of these properties is multiphoton absorption. A theoretical model describing two-photon absorption in quantum dots was developed by Fedorov, Baranv, and Inoue, 1 with the effect being recently studied experimentally. 2 The relationship of nonlinearities of the quantum dots to the bulk material has been an issue of some debate. In particular, a recent study of the nonlineari- ties of CdSe quantum dots essentially the same sample types as studied in this work showed that the nonlinear properties were very similar to the bulk properties. 3 Several other studies 2,4,5 show instead that the nonlinear properties of the quantum dots differ greatly from those of the bulk material, and are critically dependent on dot size. The find- ings of this work are in line with these studies, seeing strongly size-dependent nonlinearities. Three-photon ab- sorption has also recently been reported in CdS, 6 ZnO, and ZnS 7,8 quantum dot samples. The studies in ZnO and ZnS, 7 performed with femtosecond pulses to study purely elec- tronic nonlinearities, saw a maximum value for the three- photon absorption of 0.016 cm 3 / GW 2 , with the values seen in CdS being approximately an order of magnitude smaller. 6 While these are relatively large with respect to those witnessed in dyes and other common absorbers, in this study we witnessed effective three-photon absorption values 3 to 7 orders of magnitude larger 4 to 9 orders of magnitude when corrected for volume concentration than those previously reported for quantum dot samples by ex- citing with nanosecond pulses to access nonlinearities be- yond purely electronic. Also, the previous studies were per- formed with long wavelength lasers 720 to 1000 nm, with the three-photon absorption becoming negligible at shorter wavelengths. 7 By identifying samples with ex- tremely large values of three-photon absorption at visible wavelengths 532 nm for the current study, this result is of extreme importance for the development of nonlinear lithography, 9,10 where a key factor is minimizing /N, with N being the order of the absorption. In the current study, we carefully examine three-photon absorption in CdSe quan- tum dots as a function of dot size. We measured extremely large experimental values for the effective three-photon ab- sorption coefficients. We further develop a six-band theo- retical model to explain the relative values observed for the various dot sizes, though the absolute values differ from our results, as the model currently only accounts for the electronic portion of the nonlinearities. A collection of CdSe core-shell quantum dot colloids and composites, 11 each with distinct dot properties and cor- responding linear optical properties, have been provided by Evident Technologies Troy, New York. Using standard open-aperture z-scan measurements, the nonlinear absorp- tions were studied as a function of dot size. For the data reported here, all of the measurements were made at = 532 nm, using the second harmonic of a 10-Hz, 6-ns Nd:YAG laser, with the pulse energies set at 90 J. For future studies, other wavelengths will also be explored us- ing the optical parametric oscillator which is tunable from 420 nm to more than 2 m pumped by the third harmonic of this system. In the results described here, the measure- ments were made on 1-cm-long samples of the pure quan- tum dot colloids in toluene solution. Ongoing phases of the research are exploring how the nonlinearities described here are altered in the composite quantum dot materials. Results of the open-aperture z-scans are shown in Fig. 1. In each case, the absorption coefficient was fit to the model: = o + I + I 2 , 1