Theory of femtosecond coherent anti-Stokes Raman backscattering enhanced by quantum coherence for standoff detection of bacterial spores

Backscattered signal of coherent anti-Stokes Raman spectroscopy can be an extremely useful tool for remote identification of airborne particles, provided the signal is sufficiently large. We formulate a semiclassical theory of nonlinear scattering to estimate the number of detectable photons from a bacterial spore at a distance. For the first time, the theory incorporates enhanced quantum coherence via femtosecond pulses and a nonlinear process into the classical scattering problem. Our result shows a large backscattered signal in the far field, using typical parameters of an anthrax spore with maximally prepared vibrational coherence. Using train pulses of 1 kHz of repetition rate each with energy of 10 mJ, we estimate that about ${10}^7$ photons can be detected by a 1 m diameter detector placed 1 km away from the spore in the backward scattering direction. The result shows the feasibility of developing a real time remote detection of hazardous microparticles in the atmosphere, particularly biopathogenic spores.

Figure 1

(a) The structure of a bacterial spore with the core which is approximately spherical and contains about $5\times {10}^8$ dipicolinic acid (DPA) molecules. (b) A simple level scheme used to describe the CARS process in a DPA molecule. (c) The time sequence of a pair of Raman pulses for coherence preparation and a probe pulse scatters off the coherence to produce a signal.

Figure 2

(Color online) Typical setup of a femtosecond LIDAR for remote detection of backscattered CARS signal from a distant particle. The size of the spore has been exaggerated.

Figure 3

Ratio of the signal intensity to probe intensity (thick line) plotted using Eq. (17) for (a) inhomogeneous incident fields (thick curve) within the spore due to lensing or focusing by the spore, including internal reflection and refraction. Refractive indices of $n_1=1.6$, $n_2=1.7$, and $n_3=1.8$ are used for the three incident fields and $n_4=1.6$ is used for the anti-Stokes (signal). We have used Eqs. (13, E6, E7, E8) and take $\Phi =0$. (b) For comparison, the result for homogeneous field (thin curve) is plotted using $n_4=1.6$, Eqs. (22, 23).

Figure 4

(a) Schematic in spherical coordinate system used to calculate ${\tilde{\mathbf{E}}}_4$ the signal field at the observation point $(R,\Theta ,\Phi )$ produced from a spore modelled as a sphere. (b) Dimensions and orientation of a cylindrical spore.

Figure 5

(Color online) Absolute values of the geometrical factor $F$ as a function of $x$ for three different geometries, (a) sphere (—) $x={\rho }_0$, (b) cylinder along detection direction $(\cdots )$ $x=H$, and (c) cylinder perpendicular to detection direction (-∙-∙-) $x=r_0$, computed from Eqs. (29, 30, 31), respectively. The sphere radius is ${\rho }_0=0.5\mu \mathrm{m}$, cylinder radius $r_0=0.35\mu \mathrm{m}$, and cylinder length $H=1\mu \mathrm{m}$.

Figure 6

Normalized intensity distributions of the incident fields in a spherical spore computed from the Lorenz-Mie theory. (a) $x$ component $\left({\mid u_{f,x}\mid }^2\right)$ and (b) $z$ component $\left({\mid u_{f,z}\mid }^2\right)$ for $\varphi =0$. The incident field $f$ is polarized along the $x$ axis. Note the high intensity of the $x$ component near the front surface.