Page 353 - Vibrational Spectroscopic Imaging for Biomedical Applications

T issue Imaging with CARS Micr oscopy 327

11.4 CARS by the Numbers

11.4.1 Signal Generation in Focus with Pulsed Excitation
Compared to the linear response of materials to optical fields, the
third order susceptibility of samples is extremely small. Expressed in
3
()
electrostatic units, measured values of χ for condensed phase mate-
()
55
3
rials are on the order of ~10 − 14 esu. The χ related changes to the
2
refractive index are of magnitude 10 −16 cm /W, which implies that an
2
optical field with an intensity of 1 W/cm will modify the material’s
refractive index by only 10 −16 . Clearly, much stronger optical fields
are required to induce a detectable third-order nonlinear signal.
The high-peak powers offered by pulsed excitation provide such
electric field strengths.
Keeping the average power constant, increasingly higher peak
powers are obtained for increasingly shorter pulses. Consequently,
the highest third-order signals are obtained for the shortest pulses.
The purely electronic (nonresonant) CARS response is indeed maxi-
2
mized for the shortest possible pulse, as it scales as ~/τ , where τ is
1
56
the pulse width. Nonetheless, the ratio of the vibrationally resonant
response over the nonresonant signal is decreasing for shorter pulse
widths. This is because not all the frequency components of broader
bandwidth pulses combine to drive the vibrational modes at ω − ω ,
p S
whereas all combinations of the spectral components contribute to
generate the nonresonant response. A balance between maximum sig-
nal generation and an optimized resonant-to-nonresonant signal ratio
33
is found for pulse widths of 2 to 5 ps. For such temporal widths, the
spectral width of the pulses matches the width of the Raman reso-
nances in condensed phase materials, which constitutes the most
favorable excitation condition for CARS imaging based on a single
Raman band.
When a 5 ps, 800 nm pulse of 0.1 nJ is focused by a water immer-
sion microscope objective with a numerical aperture of 1.2, the peak
×
11
2
intensity in focus amounts to 210 W/cm . Optical fields that cor-
respond to these intensities bring about detectable changes to the
refractive index, especially in the phase-matched direction. Under
such conditions, the amount of detected CARS signal generated from
−1
pure water at the OH-stretching vibration (~3300 cm ) can be as high
34
as 500 photons per shot. For sub-micrometer sized objects, such as a
−1
lipid bilayer visualized at the CH -stretching vibration (2845 cm ),
2
the CARS signals are generally substantially smaller, but still detect-
6
able. With similar pulse energies, a bilayer with more than 10 CH
2
modes in the focal volume can be visualized in the phase-matched
forward direction at ~0.1 photons detected per shot. Such photon
detection rates are sufficient to produce good quality images recorded
with sub-ms pixel dwell times and ~80 MHz pulse repetition rates.
For planar lipid membranes detection in the epidirection is similarly