Biophotonics_Concepts_to_Applications

applied electromagneticfield is nonlinear with respect to thisfield. For example,
doubling the optical input intensities does not simply result in a doubling of the
output intensities. In a generalfour-wave-mixing(FWM) process, three laserfields
with frequenciesω 1 ,ω 2 , andω 3 generate a fourthfield with a frequency

xFWM¼x 1 x 2 x 3 ð 9 : 8 Þ

If the frequency differenceω 1 −ω 2 of two of the laserfields is tuned to the
vibrational resonance of a Raman mode of the nonlinear medium, the FWM process

xFWM¼x 1 x 2 þx 3 ¼xCARS ð 9 : 9 Þ

results in coherent anti-Stokes Raman scattering.
Thus the CARS process requires the use of at least two coherent input laser pulses,
which have a frequency difference equal to that of the Raman mode being investigated.
Basically a CARS setup consists of two stimulated Raman scattering steps, as shown in
Fig.9.19. First two separate laser beams emit a pump photon offrequencyωpumpand a
Stokes photon of frequencyωStokes, respectively. These two photons then resonantly
excite a Raman oscillator of vibrational frequencyωvib=ωpump−ωStokes, which is an
excited vibrational state of the molecule. This step is known asstimulated Stokes
emissionbecause the pump photon is inelastically scattered into the Stokes photon
along the direction of the Stokes beam. This action sets up a periodic modulation of the
refractive index of the material. In the second step, which is known asstimulated anti-
Stokes emission, the index modulation can be probed with a laser beam of photon
frequencyωprobe. The interaction of the probe beam with the Raman oscillator produces
the CARS anti-Stokes photon of frequencyωCARS=ωprobe+ωvib=ωprobe+ωpump
−ωStokes, which is the measurement photon.
The CARS method enables label-free imaging of many types of molecular
assemblies by examining their resonant vibrational spectra. Similar to Raman
spectroscopy, there are many variants of CARS. Although Raman spectroscopy and
CARS spectroscopy are equally sensitive because they use the same molecular
transitions, the CARS technique often produces imaging signals that are orders of
magnitude stronger than those obtained using conventional Raman scattering
spectroscopy. This factor allows the CARS signal from a single molecular transition
to be collected by a factor of about 10^5 faster than a Raman signal in practical
situations.

ωprobe ωCARS

ωpump ωStokes

ωvib

Virtual states

Ground state

Fig. 9.19 Basic CARS setup
consists of two stimulated
Raman scattering steps

9.8 Coherent Anti-stokes Raman Scattering Spectroscopy 281