Nonlinear Fiber Optics - 4 ed. Agrawal

436 Chapter 11. Highly Nonlinear Fibers
Figure 11.7: Microphotographs of (a) the original single-mode fiber, (b) the transition region,
and (c) the central region with a narrow core. (After Ref. [54]; c○2004 OSA.)
11.3 Tapered Fibers with Air Cladding
A simple approach for reducing the core diameter to below 2 μm, while maintaining
the confinement of the optical mode to the fiber core, consists of replacing the cladding
material with air. Since n 2 ≈ 1 for an air cladding, the index step at the core–cladding
interface is about 0.45 for silica-core fibers (Δ = 0.31). Such a large index step keeps
the mode confined to the core even when the core diameter is close to 1 μm.
It is not easy to make narrow-core fibers with air cladding. A technique, used as
early as 1993 to enhance the self-phase nodulation effects [50], tapers a standard fiber
with silica cladding of 125 μm diameter down to 2 μm or so [51]–[55]. Tapering
of optical fibers was first carried out during the 1970s for making fiber couplers by
heating and stretching the fiber [56]. Heating can be accomplished with a flame torch
but the use of a CO 2 laser has become common in recent years [57]–[59]. As the laser
light is absorbed, the heat generated softens the fiber. Suitable weights attached to
the two fiber ends provide the force that pulls the fiber and reduces its diameter. The
fiber diameter is monitored continuously during the stretching process, and the laser is
turned off when the desired diameter has been reached. The end result is a fiber whose
cladding diameter narrows down from 125 μm to about 2 μm in two transition regions
that surround a central region of 20 to 30 cm length. As an example, Figure 11.7 shows
the microphotographs of (a) the fiber before tapering, (b) the transition region, and
(c) the central region with a narrow core [54]. It should be stressed that the core of
the original fiber becomes so thin in the central region that it is unable to confine the
incident light. The cladding of the original fiber acts as a core and confines light, with
the surrounding air acting as a cladding.
The important question is: How large is the nonlinear parameter γ in the central
thin region of a tapered fiber? The standard definition of γ given in Eq. (2.3.29) cannot
be used because n 2 is not the same in the core and the cladding. Rather, as indicated in
Eq. (2.3.20), γ should be defined as
γ = 2π ∫∫ ∞
−∞ n 2(x,y)|F(x,y)| 4 dxdy
(∫∫
λ ∞
−∞ |F(x,y)|2 dxdy ) . (11.3.1)
2
The integrals can be performed analytically if we approximate the mode profile with
a Gaussian shape given in Eq. (2.2.14) and use F(x,y) =exp(−ρ 2 /w 2 ), where ρ is