Anisotropy and polarization dependence of multiphoton charge carrier generation rate in diamond

Anisotropy of multiphoton carrier generation in monocrystalline IIa diamond and its dependence on the polarization state of excitation light (near-infrared few-cycle laser pulses) are investigated using photoluminescence and nonlinear absorption measurements. We observe anisotropy between multiphoton transition rates for light linearly polarized along the 〈100〉 and 〈110〉 crystallographic directions of diamond and a strong intensity-dependent decrease of the transition rate for circularly polarized light. Measured results are compared with numerical simulations using time-dependent density functional theory and with an analytical model assuming a parabolic two-band system and the Houston function as the time-dependent wave function of the valence and conduction bands.

Figure 1

(a) Measured peak excited carrier density as a function of maximum field amplitude $F_0$ of few-cycle pulses for linear polarization along the 〈100〉 (squares) and 〈110〉 (circles) crystallographic directions of diamond compared to numerical simulations using time-dependent density functional theory (TDDFT, dotted curves) and time-dependent Schrödinger equation (TDSE, dashed curves). Inset shows photoluminescence (PL) spectrum of free exciton. The main peak FE+TO corresponds to exciton recombination with emission of transverse optical phonon. (b) Measured ratio between excited carrier populations with linear polarization of excitation light along the 〈110〉 and 〈100〉 directions (squares) compared to TDDFT (dotted curve) and TDSE (dashed curve) calculations. Inset shows the two linear polarizations with respect to the diamond crystal structure.

Figure 2

(a) Photoluminescence yield of free excitons in diamond as a function of the time delay $\mathrm{\Delta }t$ between two laser pulses with parallel polarizations along the 〈110〉 crystallographic direction. (b) Photoluminescence yield of free excitons for pulses with perpendicular polarizations along 〈100〉 and 〈010〉. Insets show the excitation pulse sequences in a simplified layout of the experiment.

Figure 3

Measured (points) and calculated (dashed curve) excited carrier population as a function of light ellipticity defined as $I^{\langle 110\rangle }/\phantom{I^{\langle 110\rangle }{I}^{\langle 1-10\rangle }}{I}^{\langle 1-10\rangle }$ for peak intensity $I_0=0.65\times {10}^{13}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. Data were normalized for clarity.

Figure 4

Multiphoton transition rates for linear polarization along the 〈100〉 crystallographic direction of diamond (black curve), 〈110〉 direction (red curve), and circular polarization (blue curve) calculated using Eqs. (3) and (4). The inset shows the ratio between calculated transition rates for linear polarizations along 〈110〉 and 〈100〉 (black dashed curve) and linear polarization along 〈110〉 and circular polarization (blue dashed curve) compared to measured data (points).

Figure 5

(a) Total number of excited carriers N as a function of the peak intensity of the excitation light $I_0$ obtained from nonlinear absorption measurements for linear polarizations along 〈110〉 (black squares) and 〈100〉 (red circles) crystallographic directions of diamond. Full lines correspond to fits by a dependence $N=I_0^x$ with fitting parameters $x_{\langle 110\rangle }=4.61$ and $x_{\langle 100\rangle }=4.68$. (b) Exciton photoluminescence intensity η (squares) measured in the same setup as the results in (a) with a fitted curve (full). Dashed lines in (a), (b) correspond to the dependence $\approx I_0^5$.

Figure 6

(a) Exciton photoluminescence intensity η at low temperature of $T=50\mathrm{K}$ for linear polarizations along the 〈110〉 (black squares) and 〈100〉 (red circles) crystallographic directions of diamond and circular polarization (blue triangles). Dashed line corresponds to the dependence $\approx I_0^5$. (b) Ratio ${\eta }_{\mathrm{lin}}^{\langle 110\rangle }/\phantom{{\eta }_{\mathrm{lin}}^{\langle 110\rangle }{\eta }_{\mathrm{lin}}^{\langle 100\rangle }}{\eta }_{\mathrm{lin}}^{\langle 100\rangle }$ between exciton photoluminescence intensity at 50 K excited by linear polarizations along 〈110〉 and 〈100〉 (black squares) and ${\eta }_{\mathrm{lin}}^{\langle 110\rangle }/\phantom{{\eta }_{\mathrm{lin}}^{\langle 110\rangle }{\eta }_{\mathrm{circ}}}{\eta }_{\mathrm{circ}}$ between linear polarization along 〈110〉 and circular polarization (red circles).