Subpicosecond coherent nonlinear optical response of isolated single-walled carbon nanotubes

We report an excitation-energy dependence of ultrafast changes of exciton absorptions in isolated semiconducting single-walled carbon nanotubes. For a photoexcitation far below the exciton transition, a blueshift of exciton absorptions originating from the optical Stark effect due to exciton-photon coupling was observed. Under near-resonant excitation conditions, a broadening of exciton absorptions was discriminated from a blueshift signal in the time and frequency domains. The broadening can be attributed to virtual exciton-real exciton scattering, which is considered to be characteristic of strongly confined excitons in nanotubes.

Figure 1

(Color online) (a) Absorption (OD) spectrum and (b) photoinduced absorption $\left(\text{ΔOD}\right)$ spectra in the SWNT film. The OD spectrum was decomposed into the three Lorentz functions shown by dotted lines. The pump energy is indicated by a solid arrow.

Figure 2

(Color online) (a–c) Time characteristics of $\Delta \text{OD}$. The probe energies are indicated by open arrows in Fig. 1b. The shaded regions show instantaneous responses. (d) The differential $\Delta \text{OD}$ spectra, $\delta \text{OD}\left(t_{\text{d}}\right)=\left[\Delta \text{OD}\left(t_{\text{d}}\right)-\Delta \text{OD}\left(0.3\text{ps}\right)\right]$, for $t_{\text{d}}=-0.1$, 0, and 0.1 ps. The broken and the solid line show the first derivative and the second derivative of the OD spectrum, respectively. The dotted line is a visual guide.

Figure 3

(Color online) (a) The OD spectrum and the pump energies (arrows). (b)–(e) $\Delta \text{OD}$ spectra and their time characteristics around $E_{\text{ex}}$ for pump energies of (b) 0.72, (c) 1.01, (d) 1.25, and (e) 1.33 eV.

Figure 4

(Color online) The differential $\Delta \text{OD}$ spectra, $\delta \text{OD}\left(0.0\text{ps}\right)=\left[\Delta \text{OD}\left(0.0\text{ps}\right)-\Delta \text{OD}\left(0.3\text{ps}\right)\right]$, for pump energies of (a) 0.72, (b) 1.25, (c)1.01, and (d) 1.14 eV. The upper solid lines show the OD spectrum. Broken and dotted lines show the first and second derivatives of the OD spectrum, respectively. Thin solid lines show the sum of the first and second derivatives. (e) Magnitudes of the photoinduced shift $\Delta E_{\text{S}}$ and broadening $\Delta E_{\text{B}}$ as a function of the inverse of the detuning energy $E_{\text{d}}$. The broken line shows the linear relation for $\mu =4.4\left(\text{eÅ}\right)$. The dotted line is a visual guide.