Multiphoton Imaging - Biomedical Optical Imaging Technologies: Design and Applications - page 239

of x, y,and z . The induced polarization is at 3! that produces a new radiation at
three times the frequency of the incident wave. Cubic nonlinearities are responsible
optical processes like self-focusing and self-defocusing of optical beams and also
give rise to interesting effects, such as optical bistability, phase conjugation, and
optical spatial and temporal solitons.
The phase-matching condition for THG can be written as 3 k 1 k 3 D 0,where
k 3 and k 1 are the wave vectors of the third harmonic field and the fundamental field,
respectively. When a laser beam is focused, THG from a homogenous bulk medium
is canceled out when the phase-matching condition is satisfied. This interesting
phenomenon has been explained on the basis of Gouy phase shift (a phase change
of pi within the Rayleigh range for a focused Gaussian beam), across the focus of
the excitation beam [ 47 ].
Since THG is a coherent process, amplitude of the emitted optical field from
all the molecules is added in contrast with the addition of intensities as in the
case of an incoherent process like fluorescence. When the phases of the interacting
optical fields are properly matched, a condition termed as phase-matching, the total
signal intensity is proportional to the square of the number of scattering molecules
[ 48 ]. When phase-matching is not right, the generated signal is significantly low
in magnitude. Since the condition of phase-matching is dependent on the relative
geometry of the illuminating beam, the signal and the medium, signals generated by
a coherent process are typically small [ 47 ].
Third harmonic signals can be effectively generated from an interface or from
an object with a size comparable to the FWHM of the axial excitation intensity
profile. The signal from a bulk medium is canceled by a wave-vector mismatch
associated with the Gouy phase shift of the focused excitation field. This permits
THG imaging of small features with a high signal-to-background ratio. The THG
radiation from a small object or an interface perpendicular to the optical axis exhibits
a sharp radiation pattern along the optical axis in the forward direction. For an
interface parallel to the optical axis, the role of the Gouy phase shift is to deflect
the phase-matching direction, that is, the THG radiation maximum direction, off the
optical axis.
Third harmonic light is produced by a laser beam tightly focused at an interface.
It is possible to image both biological and nonbiological specimens with inherent
optical sectioning of THG microscopy. Third harmonic light in a material is
produced given that the axial focal symmetry can be broken by a change in
the material properties like interfaces and boundaries due to refractive index
or nonlinear susceptibility changes. This localized production of third harmonic
light at material interfaces provides the inherent optical sectioning desired in a
three-dimensional imaging at higher axial resolution. It is possible to produce three-
dimensional images by THG from different planes perpendicular to the axis of beam
propagation. Compared to other modes of single or multiphoton laser fluorescence
microscopy, no exogenous fluorophores are needed in THG microscopy.
It was demonstrated by Tsang that under tight focusing conditions, THG can
be generated through an interface within the focal volume of the excitation beam
(Tsang 1995) [ 69 ]. Later, it was shown that whenever there is either a change