Biomedical Engineering Reference
In-Depth Information
that the momentum conservation is satisfied with its intensity on the propagation axis being minimum
[20]. The angle between the lobes increases at high numerical aperture.
4.2.2 tPeF Photophysics
When resonantly enhanced SHG occurs, another nonlinear process, two-photon induced fluorescence
(TPEF), occurs concurrently, both leading to photon emission at wavelengths shorter than the applied
optical wave. Owing to the Stokes shift in fluorescence, the TPEF emission must lie to the red of the SHG
wavelength. Typically, fluorescence will be characterized by a broader spectrum ~30-100 nm FWHM,
and can be readily separated from the SHG, allowing concurrent detection. Figure 4.2 shows a typical
situation where the emission spectrum was measured when 880 nm light was used to excite the dye
Di-6-ASPBS [21]. The sharp peak at 440 nm (twice the excitation frequency) is the photon emission due
to SHG. The SHG bandwidth will be 1/√2 of the fundamental laser, or for typical 100 femtosecond laser
pulses, about 7 nm FWHM. The broad spectrum to the red of the SHG emission is the TPEF spectrum.
Figure 4.1 compares the energetics of TPEF to that of SHG. Whereas for SHG the upper state is gener-
ally a virtual state (it is a real state in the resonant enhancement scenario) and the emission photon carries
away the total input photon energy (2
ħ
ω), for TPEF, the instantaneously excited state is a real excited state
S
*
(
n
≥ 1), from which the molecule then relaxes to the lowest excited state
S
1
before it transits to a vibra-
tionally excited ground state
S
*
. Figure 4.1 shows that the fluorescence emission photon energy (
ħ
ω
21
) is
less than the total excitation energy (2
ħ
ω
1
), and the difference is due to the relaxation both from
S
*
to
S
1
and from
S
*
to
S
0
, which ultimately results in heat dissipation into the surrounding environment. This
is also revealed by Figure 4.2 where the total excitation energy (2
ħ
ω
1
), which corresponds to the SHG
wavelength at 440 nm, is higher than the TPEF emission photon energy (
ħ
ω
2
) corresponding to the broad
band centered around 580 nm [21]. Regardless of the excitation energy or photon absorption order, the
molecules always relax to the lowest excited singlet state,
S
1
, from which fluorescence emission occurs. As
a consequence, the TPEF spectrum must be identical to that of one-photon fluorescence. Moreover, for the
case of resonance SHG, the SHG and TPE excitation spectrum would be essentially identical.
While photon emission of TPEF is not a coherent process, the initial two-photon absorption (TPA),
however, is coherent. Nonintuitively, the absorption (excitation) process is actually a third-order non-
linear process (χ
(3)
), even though only two photons are absorbed. This is because it involves coherent
interaction of two optical waves and a material wave (polarization) [8], in contrast to the second-order
1.0
1.0
SHG
0.5
0.5
0.0
430
435
440
445
450
0.
400
450
500
Wavelength (nm)
550
600
650
FIgurE 4.2
SHG and TPEF spectrum of Di-6-ASPBS excited by 880 nm. (Reproduced from Moreaux. et al.
2000., Membrane imaging by simultaneous second-harmonic generation and two-photo microscopy.
Opt. Lett.
25:320-322. With permission of Optical Society of America.)
