Nonlinear Fiber Optics - 4 ed. Agrawal

498 Chapter 12. Novel Nonlinear Phenomena
This technique was proposed in 1962 [173] but has been developed only during the
1990s, mostly for electro-optic materials such as LiNbO 3 . It was used for optical fibers
as early as 1989 and was referred to as electric field-induced SHG [174]. The basic
idea is quite simple. Rather than inducing an internal dc electric field optically, the
dc field is applied externally, resulting in an effective χ (2) . However, a constant value
of χ (2) along the fiber length is not very useful in practice because of the large phase
mismatch governed by Δk p in Eq. (12.5.2).
The technique of quasi-phase matching enhances the SHG efficiency by reversing
the sign of χ (2) along the sample periodically [175]. When this technique is applied
to optical fibers, one needs to reverse the polarity of electric field periodically along
the fiber length. The period should be chosen such that the sign of χ (2) is reversed
before the SHG power reverts back to the pump, i.e., its numerical value should be
2π/Δk p . Quasi-phase matching is commonly used in combination with thermal poling,
a technique that can produce relatively large values of χ (2) of a permanent nature in
silica glasses and fibers [176]–[179]. Although thermal poling has been used since
1991, the exact physical mechanism responsible for producing χ (2) was being debated
even in 2005 [180]–[185].
Thermal poling requires that a large dc electric field be applied across the fiber
core, at an elevated temperature in the range of 250 to 300 ◦ , for a duration ranging
anywhere from 10 minutes to several hours. If one wants to establish a constant value
of χ (2) across the entire fiber length, electrodes can be inserted through two holes
within the cladding of a fiber. The positive electrode should pass quite close to the fiber
core because formation of a negatively charged layer close to this electrode plays an
important role in the charge migration and ionization process thought to be responsible
for inducing χ (2) [179].
The technique of quasi-phase matching requires reversal of the polarity of the electric
field periodically along fiber length during the thermal-poling process. To make
such periodically poled silica fibers, the cladding on one side of the fiber is etched
away to produce a D-shaped fiber. The flat surface of the fiber should be quite close to
the core, 5 μm being a typical distance [186]. A patterned aluminum contact is fabricated
on the flat surface using a standard lithographic technique. The required period
is close to 56.5 μm for a pump wavelength of 1.54 μm. Thermal poling of the fiber
then produces a χ (2) grating with the same period.
Such a quasi-phase-matched fiber (length 7.5 cm) was pumped by using 2-ns pulses
with peak powers of up to 30 kW at a wavelength of 1.532 μm [186]. Second-harmonic
light at 766 nm was generated with an average efficiency of up to 21%. Figure 12.36
shows both the average SHG power and the conversion efficiency as a function of
the average power of the pump beam. Further improvement is possible using longer
fibers and optimizing the thermal-poling process to provide higher χ (2) values. This
experiment shows that quasi-phase-matched fibers represent a viable and potentially
useful nonlinear medium for the second-order parametric processes. The main drawback
of quasi-phase matching is that the period of χ (2) grating depends on the pump
wavelength and should be matched precisely. A mismatch of even 1 nm in the pump
wavelength can reduce the efficiency by 50%. The technique of thermal poling was
applied to microstructured fibers soon after they became available [187]. Their modal