Dynamics of photoexcitation and stimulated optical emission in conjugated polymers: A multiscale quantum-chemistry and Maxwell-Bloch-equations approach

We present a general microscopic theory of intense optical pulse propagation in conjugated polymers. The multiscale theory is based on a combination of density-functional theory on the molecular level and many-particle vibronic density matrices which act as a source in Maxwell’s equations. The resulting equations are solved nonperturbatively in the light field to study optical amplification and lasing. We illustrate our approach using a polyfluorene material of particular current interest containing a small component of planar ($\beta$-phase) chromophores. Significant reshaping of amplified light pulses is found, stemming from the interplay between light propagation and the excitation of numerous vibrational modes. Furthermore a rich dynamic is observed in the amplified spontaneous emission regime with oscillatory structures rooted in the dynamical population and depopulation of lattice modes.

Figure 1

Molecular structure of a fluorene oligomer in the planar ($\beta$-phase) conformation. Explicitly shown is the primitive unit cell consisting of two fluorene units (gray spheres symbolize carbon atoms and light-gray spheres the hydrogen atoms). Periodic continuation of the structure is indicated.

Figure 2

(Color online) Schematic representation of the ground state, $S_0$, and first excited singlet state, $S_1$. Illustrated are the PESs confining the motion of nuclei and the resulting vibrational ladders in each PES. For simplicity the illustration is reduced to only one vibrational degree of freedom and spatial coordinate. The PES displacement between $S_0$ and $S_1$ is shown, together with the pump-probe excitation scheme.

Figure 3

(a) Calculated low-temperature linear vibronic emission, $-\alpha \left(\omega \right)\cdot {\omega }^2$, of a vibrationally relaxed planar ($\beta$-phase) fluorene octamer in full occupation inversion [solid line with $\alpha \left(\omega \right)$ defined in Eq. (14)]. Dashed line: same as solid line but based on a simplified calculation including three effective vibrational modes as defined in Sec. 2B2. (b) Experimental photoluminescence spectrum of $\beta$-phase polyfluorene at 77 K (for experimental details see Ref. 36).

Figure 4

(Color online) Illustration of the spin-coated organic semiconductor film. In the calculations, the chromophore layers are uniformly spaced and the orientation of the linearly polarized transition dipoles is uniformly distributed about the direction of propagation.

Figure 5

(Color online) Pump-probe excitation of $8.1\mu \text{m}$-thick layer. (a) Average electronic ground (dashed lines), $S_0$, and excited (solid lines), $S_1$, state total occupations and incoming (shaded areas), and transmitted (dotted lines) light pulses. (b) As (a) for $t_{\text{rel}}=20\text{ps}$. [(a) and (b)] Results shown for full vibronic (thick/red) and six-level (thin/blue) calculation.

Figure 6

(Color online) Change in pulse intensity after propagation through a thin (16 nm, dashed line) and a thick ($8.1\mu \text{m}$, solid line) film. Same material and excitation parameters as in Fig. 5a. Shown is the temporally resolved gain in intensity (difference between transmitted pulse intensity with and without the sample) of the pulses for the full vibronic model. For comparison, results are normalized to the sample length. A detailed discussion is given in the text.

Figure 7

(Color online) Effects of amplified spontaneous emission on pumping of a $\approx 50\mu \text{m}$-thick layer. Shown are the temporal shape of the pump (shaded areas) and average total excited electronic state (thick lines), $S_1$, and first vibrationally excited electronic ground state (thin lines), $S_0$, occupations for (a) $t_{\text{rel}}=1\text{ps}$ and (b) $t_{\text{rel}}=10\text{ps}$. Dotted lines show results for four times higher pump intensity.