Four-wave mixing enhanced white-light cavity

We discuss bandwidth enhancement of a cavity without reducing its maximum intensity buildup in a regime where the light propagation dynamics is crucial. The enhancement relies on a frequency-dependent phase compensation via negative dispersion provided by a coherently prepared atomic medium in the cavity. We analyze the spatiotemporal dynamics in such a white-light cavity with a full simulation of the field propagation. We find that the probe field dispersion is in addition changed by a coherent field which is generated within the medium via four-wave mixing. Counterintuitively, this in-medium dynamics leads to a further enhancement of the cavity bandwidth.

Figure 1

(Color online) (a) The considered double-$\Lambda$ level scheme. Thick solid blue lines indicate strong continuous-wave driving fields. The probe field is shown as a dashed red arrow. The dotted blue arrow represents a field generated within the medium via four-wave mixing. ${\Omega }_{jk}$ are Rabi frequencies. The spontaneous decays with rates ${\gamma }_{jk}$ are denoted by the wiggly green lines ($j∊\{3,4\}$, $k∊\{1,2\}$). (b) Attenuation or amplification of the control fields (solid blue line), probe field (dashed red line), and generated field (dotted blue line) over the medium. The generated field is scaled to the initial value of the probe field. (c) Peak of a probe field pulse for successive times (i)–(vi), scaled to the respective maximum in time. The peak leaves the medium before it enters and runs through the medium in reversed direction.

Figure 2

(Color online) (a) Group index of a Gaussian probe pulse with bandwidth of $2\gamma$ (dotted line) and $\gamma ∕2$ (solid line). The dashed line shows the bandwidth $\gamma ∕2$, but with field generation via 4WM suppressed. Bandwidth narrowing below $\gamma ∕2$ does not change the group index significantly. (b) Real part ${\chi }^{\prime }$ (upper blue lines) and imaginary part ${\chi }^{″}$ (lower red lines) of the effective probe field susceptibility with (solid lines) and without (dashed lines) 4WM.

Figure 3

(Color online) Intensity buildup for an $\mathcal{F}=1000$ cavity without medium (i) and with the proposed WLC medium (iv). Curve (iii) shows the corresponding medium result with four-wave mixing artificially suppressed. The other three profiles show the general case with 4WM and a 2% (ii), a $-2\%$ (v), and a $-4\%$ (vi) mismatch of the cavity length with respect to the WLC condition. For better visibility the different profiles have been shifted by multiples of 0.25 with respect to each other. Profiles (iii) and (iv) have the same shift.

Figure 4

(Color online) (a) Cavity bandwidth throughout a Gaussian transverse control field intensity profile with width ${\sigma }_c$ (solid line). Shaded areas indicate probe beam intensity profiles with widths ${\sigma }_c∕3$ and ${\sigma }_c∕10$. (b) Enhancement factor with (solid line) and without (dashed line) the in-medium generated 4WM field against empty cavity bandwidth ${\gamma }_0$.