We performed the Z-scan measurement of InN thin film at wavelength 800 nm and 1550 nm. The Z-scan traces of OA and CA measured at 800 nm and 1550 nm are separately shown in Fig. 4-1 and Fig. 4-2. In order to make sure there is no contribution from the substrate (GaN 300nm, AlN300nm, sapphire), we repeated the same measurement on the substrate. As shown in Fig. 4-3, no signal was found in both wavelengths. Previous Z-scan result of the InN film in Figure 4-4 shows that there is no nonlinear absorption and the nonlinear refractive index is negative at wavelength 800 nm. We use eq. (2-19) to fit InN OA Z-scan traces and get nonlinear absorption β.
For calculating 𝐧𝟐, we set ∆𝚽𝟎, Z0 as fitting parameters and use eq. (2-13) to fit CA Z-scan traces. Then 𝐧𝟐 can be calculated from ∆𝚽𝟎(𝐭) = 𝐤𝐧𝟐𝐈𝟎𝐋𝐞𝐟𝐟, where effective length Leff=(1-e-αL)/α can be calculated as Leff=40nm at wavelength 800nm, Leff=47nm at wavelength 1550nm. The CA fitting results are listed in Table 4. The results of the Z-scan measurement can be affected by the high repetition rate of the laser source, which induces local thermal effects in the sample during the measurement. With the strong thermal effect, the sample behaves like an optical lens which may lead to an overestimation of nonlinear parameters obtained by the Z-scan method. The thermal contribution to the measured change in the refractive index, can be estimated by calculating the average on-axis refractive index change at focus given by[4-2],
∆n0 ≅dn dT
0.5 0α Cv
where 𝐧 is thermal optical coefficient, F0 is the flounce at focus point, ρ is the density, Cv is the specific heat, α is absorption coefficient. F0 in our experiment is calculated . 𝟎 × 𝟎− / 𝟐. InN density ρ is 6.1 g/cm3 [4-3] , specific heat is
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0.31 J/g.K [4-3], linear absorption coefficient α of InN is . × 𝟎 − at 790nm[4-4]. Thermal optical coefficient of InN is estimated to be ~ 𝟎− − [4-5],[4-6]
. And the change in refractive index caused by thermal effect can be estimated to be
∆𝐧𝟎= 𝟐. × 𝟎− . Compared with the value ∆𝐧 = 𝐧𝟐𝐈= 𝟎. 𝟐 obtained from the fitting of Fig. 4-1, the contribution of thermal effect is negligibly small. The same process was done at wavelength 1550nm and thermal effect also can be neglected too.
The comparison between our experimental results and thermal effect is listed in Table 5.The nonlinear absorption coefficient of InN measured by Tsai et al.[4-7] at different repetition rates is consistent with our result of ∆𝐧. Our results measured at 800 nm shows the absorption saturation (β<0) and self-focusing (𝐧𝟐 𝟎), while at 1550nm the results shows reverse saturable absorption (β>0) and self-focus (𝐧𝟐 𝟎). The numbers of β and 𝐧𝟐 are listed in Table 6. The listed errors in Table 6 are fitting errors. And β is power-independent as shown figure 4-5, figure 4-6.
Table 4 CA Z-scan traces fitting results.
Wavelength(nm) ∆𝚽𝟎 Z0 (cm) n2 (cm2⁄ ) W
800 0.038 0.11 (5.84) × 10−11
1550 0.0183 0.27 (1.86) × 10−10
Table 5 Comparison between our experimental results and thermal effect.
Wavelength(nm) Δn =n2I(from our experimental data)
Δn0(thermal effect contribution)
800 0.12 2.4×10-4
1550 0.096 9.1×10-5
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Table 6 Nonlinear optical parameters of InN film
Wavelength(nm) β(cm/W) n2(cm2⁄ ) W
800 −(2.12 ± 0.06) × 10−6 (5.84 ± 0.2) × 10−11
1550 (1.65 ± 0.01) × 10−5 (1.86 ± 0.1) × 10−10
The saturable absorption behavior of the InN sample can be explained by the band filling effect. When an InN sample is irradiated by a laser pulse with a wavelength of 800 nm, free carriers are generated through the linear absorption. As the photon-induced free carriers occupy the conduction band, they prevent more electrons from entering to the conduction band and lead to the reduction of absorption. The direct interband absorption coefficient at energy ℏω can be written as[4-8]
where μ = mcmv/(mc+mv) is the reduced mass (mc and mv are the conduction- and valence-band effective masses, respectively) and P = −(iℏ/me)〈S|pz|Z〉momentum matrix element. me is the static electron mass and n0 and Eg are the linear refractive index and the band gap, respectively. ΔN is the photoexcited free electron density.
This equation shows that the laser-induced absorption coefficient change Δα (=α − α0=β×I0) is negative (β < 0), which means that higher laser intensity leads to lower absorption and results in higher transmission. It is consistent with our results at 800nm.
The increase of absorption in the Z-scan measurement can be often observed for the photoexcitation below the bandgap energy through the reverse saturation absorption attribute to two-photon absorption. Since the photon energy of 1550 nm laser pulses is
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larger than the bandgap energy of InN, the reverse saturation absorption due to two-photon absorption can be excluded for our experiment. Meanwhile, when the carrier density photogenerated during the Z-scan measurement is high, the carrier screening of the internal electric field may occur near the bottom of the conduction band. The injected electrons will occupy states at the bottom of the conduction band.
If the electron concentration is large enough, the electron wave function will overlap, forming a gas of interacting particles. The electrons will repel one another by Coulomb forces. In addition, electrons with the same spin will avoid one another for statistical reasons. The net result is a screening of electrons and a decrease in their energy, lowering the energy of the conduction band edge. Band-gap renormalization usually dominate at high photoexcited carrier density N which can be obtained by the relation of,
where α is linear absorption coefficient, R is reflectivity, F is irradiance at focus.
α = 2.23 × 104cm−1, R=25%, F=7.73 × 10−5 J/cm2, this is properties of InN measured at 1550nm, photoexcited free electron density can be calculated N=1.01 × 1019 cm−3. The ultrafast carrier relaxation time of InN is in the range of picosecond and at 1550 nm, InN displays close to resonant behavior. Highly photoexcited carriers quickly gather near the bottom of the conduction band as they cool down and the significant carrier screening can be observed at 1550 nm. Therefore, the nonlinear absorption at 1550nm may be caused by band-gap renormalization.
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Fig. 4-1 (a) Open-aperture Z-scan traces at 800nm. (b) Close-aperture Z-scan traces at 800nm.
Fig. 4-2 (a) Open-aperture Z-scan traces at 1550nm. (b) Close-aperture Z-scan traces at 1550nm.
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Fig. 4-3 (a) Z-scan traces of substrate at 800nm. (b) Z-scan traces of substrate at 1550nm.
Fig. 4-4 Z-scan Measurement of GaN thin films at 800 nm.[4-1] Hollow-square is close-aperture Z-scan traces which indicates self-defocus (n2<0). Our close-aperture Z-scan traces in [Fig. 4-1] and [Fig. 4-2] which indicate self-focus (n2>0) is opposite to this results, so nonlinear effect of GaN is negligible in our measurement. The number of n2=−7.3 × 10−14 reported from reference 4-1. The noise of our measurement is too large so we can‟t observe nonlinearity of GaN in [Fig. 4-3].
-1.0 -0.5 0.0 0.5 1.0
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Fig. 4-5 InN nonlinear absorption coefficient at 800nm.
Fig. 4-6 InN nonlinear absorption coefficient at 1550nm which is plotted with optical intensity shows power-independent.
0.1 0.2 0.3 0.4 0.5
1.3 1.4 1.5 1.6 1.7 1.8 1.9
*105(cm/GW)
(GW/cm2)
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1
-3.0 -2.5 -2.0 -1.5 -1.0
*106(cm/GW)
GW/cm2
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Chapter 5 Results of 3D Au nanoparticle supercrystal
According to Fig. 3-8, the L-mode of Au nanoparticle supercrystal has a resonance at near 800 nm and its effect gets stronger as the layer number increases. By employing the Z-scan method, we investigated the nonlinear properties of Au nanoparticle supercrystal. Up to now the optical properties of 2D Au nanostructures has been intensely studied mainly due to the difficulty of fabrication of 3D structures. We measured the nonlinear coefficients of Au nanoparticles as a function of layer number and laser fluence. We found that the thermal effect which prevents the accurate determination of the nonlinear properties of material by the Z-scan method is exceptionally strong for Au nanoparticls. In this chapter, we present the results of the Z-scan measurement excited by two lasers with the repetition rate of 80 MHz and 1 kHz, respectively.