Stimulated-emission pumping enabling sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering microscopy

We present a theoretical investigation of stimulated emission pumping to achieve sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering (CARS) microscopy. A pair of control light fields is used to prepopulate the Raman state involved in the CARS process prior to the CARS signal generation. Efficient prepopulation is achieved by employing a path via an electronic or vibrational state. Thereby, the buildup of a coherence between the ground and Raman state during irradiation by the light fields for CARS signal generation is prevented, resulting in the suppression of the CARS intensity by more than 99.8$\%$. Two-dimensional spatial excitation profiles have been calculated using donut-shaped spatial profiles for the control light fields, thus, an intensity-dependent narrowing of the CARS excitation profiles below the diffraction limit. Using computer-generated test images we demonstrate a resolution beyond the diffraction limit for CARS microscopy, which is scalable by the control light field intensity, similar to stimulated emission depletion microscopy.

Figure 1

Energy diagram of the CARS process and involved states: $|1\rangle$ is the ground state which is initially fully occupied. State $|2\rangle$ is a vibrational state involved in the CARS process which we refer to as the Raman state. $|3\rangle$ is the upper electronic state acting as a control state. An additional control state is added by incorporating a second vibrational state $|4\rangle$. The population distribution is manipulated by a pair of control light fields (${\omega }_{c1,\text{el}}+{\omega }_{c2,\text{el}}$ or ${\omega }_{c1,\text{vib}}+{\omega }_{c2,\text{vib}}$) transferring population from the ground state to the Raman state $|2\rangle$ and thus preventing CARS intensity generation (${\omega }_{\text{CARS}}$) by the pump (${\omega }_p$), Stokes (${\omega }_{\text{St}}$), and probe (${\omega }_{\text{pr}}$) light fields.

Figure 2

Population distribution of the states as a function of the intensity of the control light fields for (a) the electronic state $|3\rangle$ and (b) the vibrational state $|4\rangle$ acting as the control state. (c) Resulting CARS intensity as function of the intensity of the control light fields for the case in which the vibrational state acts as the control state (red dashed curve) or in which the electronic state acts as the control state (black solid curve).

Figure 3

(a) CARS intensity as a function of the intensity of the control pulses for a delay of the control pulses of $\tau =0\text{ps}$ and $\tau =-30\text{ps}$. (b) Time of the maximum coherence ${\rho }_{21}$ generated by the control pulses as a function of the intensity of the control pulses for different delays $\tau$.

Figure 4

Cross sections of the spatial beam profiles of the pump (red solid curve), Stokes (blue dotted curve), probe (green solid curve), control (black dashed curve), and diffraction-limited CARS (solid black curve) light fields in the focal plane. The inset shows the phase plate used to create the donut-shaped beam profile of the control light fields.

Figure 5

A donut-shaped spatial profile of the control light field pair narrows the CARS excitation profile below the diffraction limit. For different peak intensities of the donut the resulting CARS excitation profiles have been calculated. (a) Cross section of excitation profiles for donut peak intensities of $I_c=0,2\times {10}^6,2\times {10}^7,2\times {10}^8,4\times {10}^8\mathrm{W}/{\mathrm{cm}}^2$. Two-dimensional illustrations are shown for (b) $I_c=0\mathrm{W}/{\mathrm{cm}}^2$ [black dashed curve in (a)] and (c) $I_c=4\times {10}^8\mathrm{W}/{\mathrm{cm}}^2$ [red dashed curve in (a)]. (d) FWHM of the excitation profiles as a function of the donut peak intensity.

Figure 6

Two test images have been created to simulate CARS images. (a) A dendritic line structure depicting, e.g., brain tissue is shown and (d) an ensemble of randomly located nanobeads (each 40 nm in diameter). (b) and (e) When no control light fields are applied a calculated CARS image does not contain any structure of the test images. (c) and (f) If the control light fields are applied the excitation profile is narrowed down to a FWHM of 17.6 nm and the CARS images reveal the original test images.