__BACKGROUND OF THE INVENTION__
__Field of the Invention__
The present invention relates to a highly nonlinear optical
fiber and an optical device using the optical fiber.

__Related Background Art__
In wavelength conversion or the like using the nonlinear
optical phenomena, a highly nonlinear optical fiber such as a dispersion-shifted
fiber is used as a medium to cause the nonlinear optical phenomena (e.g.
Japanese Patent Application Laid-Open No. 8-95106
). The development of optical fiber in such usage has been focused heretofore
mainly on improvement in nonlinearity and decrease of the dispersion slope. It is
also important to reduce the variation in the zero dispersion wavelength. However,
the decrease of the dispersion slope leads to increase of variation in the zero
dispersion wavelength in the longitudinal direction of the filter. In addition,
no attention has been directed heretofore to the fourth order dispersion &bgr;_{4}
of the fourth derivative &bgr;_{4} of the propagation constant &bgr;
by angular frequency, which is important to improvement in the wavelength conversion
bandwidth.

For example, a reference of "
M. E. Marhic, et al., Optics & Photonics News (September 2004) pp.21-25 (2004
)" describes that the bandwidth in an OPA (optical parametric amplifier)
is expanded by decrease of the fourth order dispersion &bgr;_{4} of optical
fiber. Furthermore, for example, a reference of "
M-C. Ho, et al., J. of Lightwave Technol. Vol. 19, No. 7, pp.977-981 (2001)
" reports wide-band OPA using the optical fiber with the fourth order dispersion
&bgr;_{4} being -5.8 × 10^{-56} s^{4}/m. However,
there is the description "large variation of dispersion" in the section "B. Experimental
Setup for OPA Gain Measurement" on page 978 in this "
M-C. Ho, et al., J. of Lightwave Technol. Vol. 19, No. 7, pp.977-981 (2001)
", and the decrease of the fourth order dispersion &bgr;_{4}
is insufficient. A reference of "
M. Gao, et al., Optics Express, Vol. 12, No. 23, pp.5603-5613 (2004)
" describes execution of optimization of fiber parameters including the
fourth order dispersion &bgr;_{4}, but fails to give consideration to
such phenomena as variation in the zero dispersion wavelength and coupling of orthogonal
polarization mode which must be significant issues in practical fiber.

As discussed above, there were proposals on the fiber parameters
from the viewpoint of use of optical fiber, but there was no study from the aspect
of production of optical fiber; it was thus difficult to produce an optical fiber
with the parameters as proposed. For example, a reference of "
T. Okuno, et al., OFC 2004, MF21
" and other references describe such known fibers as an optical fiber having
the conversion bandwidth of 91.3 nm in the fiber length of 100 m and an optical
fiber having the conversion bandwidth of 110 nm in the fiber length of 100 m, but
they were achieved by simply shortening the optical fibers, without optimization
of the dispersion parameters.

A reference of "
J. Hiroishi, et al., ECOC2002 Post Deadline Papers, PD1 (2002
) " describes an optical fiber with a so-called W-shape index profile including
a center core part, a depressed part, and a cladding part, and shows 1.0 ×
10^{-4} ps^{4}/km (= 1.0 × 10^{-55} s^{4}/m)
as a typical value of the fourth order dispersion &bgr;_{4}. In fact,
the value of the fourth order dispersion &bgr;_{4} can be adjusted even
in the case of the W-shape index profile, but no consideration is given to the significance
of the fourth order dispersion &bgr;_{4}. The wide bandwidth is achieved
by decreasing the dispersion slope to +0.013 ps/nm^{2}/km, but the wavelength
conversion bandwidth by four-wave mixing is limited to below 40 nm, presumably,
because of large fluctuation in the zero dispersion wavelength in the longitudinal
direction in practice.

The Inventor discovered that the fourth order dispersion
&bgr;_{4} could be adjusted in practical optical fibers and that a wider
bandwidth could be achieved actually in the wavelength conversion, OPA, etc. by
decreasing the fourth order dispersion &bgr;_{4} and suppressing the variation
in the zero dispersion wavelength in the length direction of optical fiber, thereby
accomplishing the present invention.

__SUMMARY OF THE INVENTION__
The present invention has been accomplished in order to
solve the above problem, and an object of the invention is to provide an optical
fiber capable of achieving a wider bandwidth in the wavelength conversion, OPA,
etc. and an optical device using the optical fiber.

An optical fiber according to the present invention is
an optical fiber wherein an absolute value of the fourth order dispersion &bgr;_{4}
for the derivative propagation constant &bgr; of with respect to angular frequency
&ohgr; at a mean zero dispersion wavelength &lgr;_{0} in an overall length
is not more than 5 × 10^{-56} s^{4}/m and wherein a fluctuation
of a zero dispersion wavelength along a longitudinal direction is not more than
±0.6 nm. By using the optical fiber as described above, it becomes feasible
to achieve a wider bandwidth in the wavelength conversion, OPA, etc. by four-wave
mixing and to achieve, for example, the wavelength conversion bandwidth of 200 nm.
A method of measuring the zero dispersion wavelength along the longitudinal direction
of optical fiber is described, for example, in Document "
L. F. Mollenauer, et al., Optics Lett., Vol. 21, No. 21, pp.1724-1726 (1996)
." Although the optical fiber may be a holey fiber with holes along the
longitudinal direction, the optical fiber of the present invention can be a solid
one, which facilitates production, fusion splicing with another optical fiber, and
control of the zero dispersion wavelength along the longitudinal direction. The
absolute value of the fourth order dispersion &bgr;_{4} is preferably
not more than 1 × 10^{-56} s^{4}/m and more preferably not
more than 5 × 10^{-57} s^{4}/m.

The optical fiber according to the present invention is
preferably configured so that the mean zero dispersion wavelength &lgr;_{0}
is in the range of 1440 nm to 1640 nm. This wavelength band includes the S-band
(1460 nm-1530 nm), C-band (1530 nm-1565 nm), and L-band (1565 nm-1625 nm), which
are the bands generally used in optical communications, and it is easy to acquire
an inexpensive high-output laser source in the bands.

The optical fiber according to the present invention is
preferably configured so that an effective area at the mean zero dispersion wavelength
&lgr;_{0} is not more than 15 µm^{2}. In this case, the nonlinearity
becomes so significant as to enable efficient wavelength conversion.

The optical fiber according to the present invention is
preferably configured so that a dispersion slope at the mean zero dispersion wavelength
&lgr;_{0} is not less than +0.018 ps/nm^{2}/km. In this case,
it is relatively easy to suppress the variation in the zero dispersion wavelength
along the longitudinal direction. The dispersion slope at the mean zero dispersion
wavelength &lgr;_{0} is more preferably +0.018 to +0.030 ps/nm^{2}/km.

The optical fiber according to the present invention is
preferably configured so that a wavelength derivative of the dispersion slope at
the mean zero dispersion wavelength &lgr;_{0} is in the range of -0.00012
ps/nm^{3}/km to -0.00008 ps/nm^{3}/km. In this case, it is relatively
easy to suppress the variation in the zero dispersion wavelength.

The optical fiber according to the present invention is
preferably configured so that a polarization mode dispersion at the overall length
is not more than 0.2 ps. In this case, it is feasible to make influence of the polarization
mode dispersion relatively small and to exhibit the nonlinear optical phenomena
over a long period of time and on a stable basis. In the case of a non-polarization-maintaining
fiber, the polarization mode dispersion is desirably as small as possible, preferably
not more than 0.1 ps, and more preferably not more than 0.05 ps.

The optical fiber according to the present invention is
preferably configured so that a crosstalk between orthogonal polarization components
of fundamental mode light guided is not more than -15 dB at the overall length.
In this case, where the optical fiber is a polarization-maintaining fiber, the influence
of the polarization mode dispersion can be substantially ignored, and it is feasible
to exhibit the nonlinear optical phenomena over a long period of time with extremely
high stability.

The optical fiber according to the present invention is
preferably configured as follows: it further comprises at least a center core part
having a maximum refractive index N_{1} and an outside diameter 2a, a depressed
part surrounding the center core part and having a minimum refractive index N_{2}
and an outside diameter 2b, and a cladding part surrounding the depressed part and
having a maximum refractive index N_{3}; the refractive indices satisfy
a relation of "N_{1} > N_{3} > N_{2}"; with respect
to the refractive index N_{3} of the cladding part, a relative index difference
of the center core part is defined as &Dgr;_{+} and a relative index difference
of the depressed part as &Dgr;_{-}, and a difference "&Dgr;_{+}-&Dgr;_{-}"
is not less than 2.2%; and a ratio Ra of the respective outside diameters of the
center core part and the depressed part (= 2a/2b) is in the range of 0.2 to 0.7.
When the optical fiber has the so-called W-shape index profile and when the relative
index difference &Dgr;_{+} of the center core part, the relative index
difference &Dgr;_{-} of the depressed part, and the ratio Ra satisfy the
conditions as described above, it becomes easy to adjust the dispersion characteristics
and to reduce the absolute value of the fourth order dispersion &bgr;_{4}.
The difference "&Dgr;_{+}-&Dgr;_{-}" is preferably not less
than 3.1% and in this case, the nonlinear coefficient can be increased to 20/W-km
or more. The relative index difference &Dgr;_{-} of the depressed part
is preferably in the range of -0.1% to -1.1% and in this case, the absolute value
of the fourth order dispersion &bgr;_{4} can be further reduced.

The optical fiber according to the present invention is
preferably configured so that the fiber length is not more than 500 m. This facilitates
expansion of the wavelength conversion bandwidth.

Another optical fiber according to the present invention
is an optical fiber wherein a mean zero dispersion wavelength &lgr;_{0}
in an overall length is in the range of 1440 nm to 1640 nm, wherein a fluctuation
of a zero dispersion wavelength along a longitudinal direction is not more than
±0.6 nm, and wherein an absolute value of the fourth order dispersion &bgr;_{4}
of propagation constant &bgr; with respect to frequency &ohgr;, at the mean zero
dispersion wavelength &lgr;_{0} is not more than 5 × 10^{-56}
S^{4}/m, an effective area is not more than 15 µm^{2}, a dispersion
slope is in the range of +0.018 ps/nm^{2}/km to +0.030 ps/nm^{2}/km,
and a wavelength derivative of the dispersion slope is in the range of -0.00012
ps/nm^{3}/km to -0.00008 ps/nm^{3}/km.

An optical device according to the present invention is
an optical device comprising: an optical fiber; a pump light source for generating
a pump light of a wavelength &lgr;_{P}; and a probe light source for generating
a probe light of a wavelength &lgr;_{S}, wherein the pump light and the
probe light are guided through the optical fiber and an idler light of a new wavelength
&lgr;_{I} is generated from the optical fiber by a nonlinear optical phenomenon.
The optical fiber in this optical device is preferably the optical fiber according
to the present invention as described above. This optical device induces wavelength
conversion by four-wave mixing in the optical fiber to generate the idler light
of the new wavelength &lgr;_{I} different from both of the pump wavelength
&lgr;_{P} and the probe wavelength As. Even if the wavelength spacing
is wide between the pump wavelength &lgr;_{P} and the probe wavelength
As, the wavelength conversion can be induced effectively. The pump light may be
a pump of one wavelength, but may be a plurality of pumps of two or more wavelengths.
The probe light may also be a probe of one wavelength, but may be a plurality of
probes of two or more wavelengths. When control pulses are injected as the pump
light into the optical fiber, the optical device can serve as an optical switch
making use of the wavelength conversion, or as an optical demultiplexer. Since the
optical device can generate a new photon with the same information as a certain
photon of signal light and of a wavelength different from that of the photon, it
can also generate a photon pair for quantum encryption communication. Furthermore,
the optical device is able to readily produce light of a wavelength at which there
is no good light source, and thus it can be applied not only in the optical communication
field but also in the other fields.

The optical device according to the present invention is
preferably configured as follows: where P_{P-in} stands for a power of the
pump light injected into the optical fiber, P_{S-in} for a power of the
probe light injected into the optical fiber, and P_{I-out} for a power of
the idler light outputted from the optical fiber, each of the wavelength &lgr;_{P}
and power P_{P-in} of the pump light is kept constant, and a range of the
wavelength As of the probe light where a fluctuation rate of a conversion ratio
r (= P_{I-out}/P_{S-in}) of the respective powers of the idler light
and the probe light with change in the wavelength As of the probe light is not more
than 3 dB, is not less than 100 nm. In this case, the device can achieve the wavelength
conversion in an extremely wide band. The pump light may be pumps of two or more
wavelengths and even in that case no change is necessary for the condition for the
pump light. For example, the optical device is able to collectively convert multi-wavelength
signal light in a band including the C-band and L-band, into light in a band including
the E-band (1360 nm-1460 nm) and S-band. The range of the wavelength As of the probe
light where the fluctuation rate of the conversion ratio r is not more than 3 dB,
is preferably not less than 160 nm, more preferably not less than 200 nm, and still
more preferably not less than 300 nm.

The optical device according to the present invention is
preferably configured as follows: where P_{P-in} stands for a power of the
pump light injected into the optical fiber, P_{S-in} for a power of the
probe light injected into the optical fiber, and P_{I-out} for a power of
the idler light outputted from the optical fiber, each of the wavelength &lgr;_{P}
and power P_{P-in} of the pump light is kept constant, and with respect
to a value of a conversion ratio r (= P_{I-out}/P_{S-in}) of the
respective powers of the idler light and the probe light when an absolute value
of a difference "&lgr;_{P}-&lgr;_{S}" between the respective
wavelengths of the pump light and the probe light is 5 nm, a change rate of the
conversion ratio r when the absolute value of the difference "&lgr;_{P}-&lgr;_{S}"
is not less than 50 nm, is not more than 3 dB. Since the pump wavelength &lgr;_{P}
is approximately equal to the zero dispersion wavelength of the optical fiber, if
the probe light injected is probes of multiple wavelengths and if the probe wavelengths
are close to the pump wavelength, there will arise a problem of four-wave mixing
between the probes. However, if the probe wavelengths are located 50 nm or more
apart from the zero dispersion wavelength (= the pump wavelength), the absolute
value of the dispersion is not less than about 1 ps/nm/km and the four-wave mixing
between probes is considerably suppressed.

The optical device according to the present invention is
preferably configured so that the power P_{S-out} of the probe light outputted
from the optical fiber is larger than the power P_{S-in} of the probe light
injected into the optical fiber. It is feasible to achieve amplification in a wide
band by OPA. In addition to an amplifier, the optical device can also serve as a
switch or as an optical demultiplexer where control pulses are injected as the pump
light.

__BRIEF DESCRIPTION OF THE DRAWINGS__
Fig. 1 is a drawing showing the relationship between power
P_{I-out} of idler &lgr;_{I} emitted from optical fiber, and probe
wavelength &lgr;_{S}.

Figs. 2A and 2B are drawings showing the relationship between
wavelength conversion bandwidth and the wavelength difference &lgr;_{O}
-&lgr;_{P} between zero dispersion wavelength &lgr;_{O} and
pump wavelength &lgr;_{P}.

Fig. 3 is a drawing to illustrate a minimum of the wavelength
conversion bandwidth in a drawing showing the relationship between wavelength conversion
bandwidth and the wavelength difference &lgr;_{O} -&lgr;_{P}
between zero dispersion wavelength &lgr;_{O} and pump wavelength &lgr;_{P}.

Figs. 4A, 4B and 4C are drawings showing tables of wavelength
conversion bandwidths at respective values of the absolute value of the fourth order
dispersion &bgr;_{4} and the fiber length L, for respective values of
variation width of the zero dispersion wavelength &lgr;_{0} of optical
fiber.

Figs. 5A, 5B and 5C are drawings showing tables of wavelength
conversion bandwidths at respective values of the absolute value of the fourth order
dispersion &bgr;_{4} and the fiber length L, for respective values of
variation width of the zero dispersion wavelength &lgr;_{0} of optical
fiber.

Fig. 6 is a drawing showing the relationship between the
wavelength conversion bandwidth and the fourth order dispersion &bgr;_{4}
in an optical fiber with the fiber length of 100 m without variation in the zero
dispersion wavelength &lgr;_{0}.

Fig. 7 is a drawing showing the relationship between the
wavelength conversion bandwidth and the fourth order dispersion &bgr;_{4}
in an optical fiber with the fiber length of 100 m with variation of ±0.05
nm in the zero dispersion wavelength &lgr;_{0}.

Fig. 8 is a drawing showing the relationship between the
wavelength conversion bandwidth and the fourth order dispersion &bgr;_{4}
in an optical fiber with the fiber length of 100 m with variation of ±0.10
nm in the zero dispersion wavelength &lgr;_{0}.

Fig. 9 is a drawing showing the relationship between the
wavelength conversion bandwidth and the fiber length L in an optical fiber with
variation of ±0.10 nm in the zero dispersion wavelength &lgr;_{0}.

Fig. 10 is a drawing showing the relationship between the
wavelength conversion bandwidth and variation amount of zero dispersion wavelength
&lgr;_{0}.

Figs. 11A and 11B are drawings showing a preferred example
of a sectional structure and index profile of optical fiber 10 according to an embodiment
of the invention.

Fig. 12 is a drawing showing a table of the dispersion
slope S, the wavelength derivative of the dispersion slope (dS/d&lgr;), and the
fourth order dispersion &bgr;_{4} for each of values of ratio Ra.

Fig. 13 is a drawing showing a table of the dispersion
slope S, the wavelength derivative of the dispersion slope (dS/d&lgr;), and the
fourth order dispersion &bgr;_{4} for each of values of ratio Ra.

Figs. 14A, 14B, 14C and 14D are drawings showing other
preferred examples of the index profile of optical fiber according to an embodiment
of the invention.

Fig. 15 is a drawing showing a table of the dispersion
slope S, the wavelength derivative of the dispersion slope (dS/d&lgr;), and the
fourth order dispersion &bgr;_{4} for each of values of ratio Ra.

Fig. 16 is a drawing showing a table of the dispersion
slope S, the wavelength derivative of the dispersion slope (dS/d&lgr;), and the
fourth order dispersion &bgr;_{4} for each of values of ratio Ra.

Fig. 17 is a drawing showing a table of the dispersion
slope S, the wavelength derivative of the dispersion slope (dS/d&lgr;), and the
fourth order dispersion &bgr;_{4} for each of values of ratio Ra.

Fig. 18 is a drawing showing the relationship between the
fourth order dispersion &bgr;_{4} and the ratio Ra.

Fig. 19 is a drawing showing a table of the dispersion
slope S, the wavelength derivative of the dispersion slope (dS/d&lgr;), and the
fourth order dispersion &bgr;_{4} for each of values of ratio Ra.

Fig. 20 is a drawing showing the relationship between the
fourth order dispersion &bgr;_{4} and the ratio Ra.

Fig. 21 is a drawing showing the relationship between the
fourth order dispersion &bgr;_{4} and the ratio Ra.

Fig. 22 is a drawing showing the relationship between the
fourth order dispersion &bgr;_{4} and the ratio Ra.

Fig. 23 is a drawing showing the relationship between the
fourth order dispersion &bgr;_{4} and the ratio Ra.

Fig. 24 is a drawing showing the relationship between the
fourth order dispersion &bgr;_{4} and the ratio Ra.

Fig. 25 is a drawing showing the relationship between the
fourth order dispersion &bgr;_{4} and the dispersion slope S.

Fig. 26 is a drawing showing the relationship between the
fourth order dispersion &bgr;_{4} and the wavelength derivative of the
dispersion slope S (dS/d&lgr;).

Fig. 27 is a drawing showing the relationship between variation
amount of the zero dispersion wavelength &lgr;_{0} and the dispersion
slope S with variation of 1% in the core diameter 2a.

Fig. 28 is a configuration diagram of optical device 1
of an example.

Fig. 29 is a drawing showing the relationship between the
power P_{I-out} of idler &lgr;_{I} emitted from optical fiber
10 of optical device 1 of the example, and the probe wavelength &lgr;_{S}.

Fig. 30 is a drawing showing the relationship between the
power P_{I-out} of idler &lgr;_{I} emitted from optical fiber
10 of optical device 1 of the example, and the probe wavelength &lgr;_{S}.

Fig. 31 is a drawing showing the relationship between the
power P_{I-out} of idler &lgr;_{I} emitted from optical fiber
10 of optical device 1 of the example, and the probe wavelength &lgr;_{S}.

Fig. 32 is a drawing showing the relationship between the
power P_{I-out} of idler &lgr;_{I} emitted from optical fiber
10 of optical device 1 of the example, and the probe wavelength &lgr;_{S}.

Fig. 33 is a drawing showing the relationship between the
power P_{I-out} of idler &lgr;_{I} emitted from optical fiber
10 of optical device 1 of the example, and the probe wavelength &lgr;_{S}.

Fig. 34 is a drawing showing the relationship between the
power P_{I-out} of idler &lgr;_{I} emitted from optical fiber
10 of optical device 1 of the example, and the probe wavelength &lgr;_{S}.

Fig. 35 is a drawing showing the relationship between the
power P_{I-out} of idler &lgr;_{I} and the probe wavelength &lgr;_{S},
where the length of the optical fiber of the example is 1000 m.

Fig. 36 is a drawing showing the relationship between the
wavelength conversion bandwidth and the fiber length in each of optical fibers of
the example and conventional examples.

__DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS__
An embodiment of the present invention will be described
below in detail with reference to the accompanying drawings. In the description
of drawings the same elements will be denoted by the same reference symbols, without
redundant description.

First described are the contents of theoretical study conducted
prior to accomplishment of the present invention. Let us consider a situation in
which pumps (wavelengths &lgr;_{P1}, &lgr;_{P2}) and a probe
(wavelength &lgr;_{S}) are injected into an optical fiber, a nonlinear
optical phenomenon (e.g., four-wave mixing: a kind of parametric process) occurs
in the optical fiber, and an idler of a new wavelength (wavelength &lgr;_{I})
is generated in the optical fiber by the nonlinear phenomenon. The wavelength &lgr;_{P1}
and the wavelength &lgr;_{P2} may be equal to each other and in that case,
these wavelengths are represented by &lgr;_{P}.

Let P_{P1-in} be the power of the pump &lgr;_{P1}
injected into the optical fiber, P_{P2-in} be the power of the pump &lgr;_{P2}
injected into the optical fiber, and P_{S-in} be the power of the probe
&lgr;_{S} injected into the optical fiber. Then the power P_{I-out}
of the idler &lgr;_{I} outputted from the optical fiber is represented
by Eq (1) and Eq (2) below. &Dgr;&bgr; is a phase mismatching amount and is
represented by Eq (3) below. &ggr; is a nonlinear coefficient of the optical fiber
and is represented by Eq (4) below. L_{eff} is an effective length of the
optical fiber and is represented by Eq (5) below. The four wavelengths &lgr;_{P1},
&lgr;_{P2}, &lgr;_{S}, and &lgr;_{I} are assumed to
be close to each other, and these wavelengths &lgr; are approximated by Eq (6)
below. These equations are detailed in Document "
K. Inoue et al., J. of Lightwave Technol., Vol. 10, No. 11, pp.1553-1561,
(1992)
."

Equation 1:
$${P}_{I-\mathit{out}}={\mathit{D\&ggr;}}^{2}{P}_{P1-\mathit{in}}{P}_{P2-\mathit{in}}{P}_{S-\mathit{in}}{{L}_{\mathit{eff}}}^{2}\mathrm{\&eegr;}\cdot \mathrm{exp}\left(-,\mathrm{\&agr;},\begin{array}{}\end{array},L\right)$$

Equation 2:
$$\mathrm{\&eegr;}=\frac{1}{{\mathrm{\&agr;}}^{2}+\mathrm{\&Dgr;}{\mathrm{\&bgr;}}^{2}}\left\{{\mathrm{\&agr;}}^{2},+,4,,\mathrm{exp},\left(-,\mathrm{\&agr;},\begin{array}{}\end{array},L\right),\cdot ,{\mathrm{sin}}^{2},\left(L,\cdot ,\mathrm{\&Dgr;},\begin{array}{}\end{array},\mathrm{\&bgr;},/,2\right),/,{{L}_{\mathit{eff}}}^{2}\right\}$$

Equation 3:
$$\mathrm{\&Dgr;}\begin{array}{}\end{array}\mathrm{\&bgr;}={\mathrm{\&bgr;}}_{P1}+{\mathrm{\&bgr;}}_{P2}-{\mathrm{\&bgr;}}_{S}-{\mathrm{\&bgr;}}_{I}$$

Equation 4:
$$\mathit{\&ggr;}=\frac{2\mathrm{\&pgr;}}{\mathit{\&lgr;}}\frac{{n}_{2}}{{A}_{\mathit{eff}}}$$

Equation 5:
$${L}_{\mathit{eff}}=\frac{1-\mathrm{exp}\left(-,\mathrm{\&agr;},\begin{array}{}\end{array},L\right)}{\mathrm{\&agr;}}$$

Equation 6
$$\mathit{\&lgr;}=\frac{4}{1/{\mathit{\&lgr;}}_{P1}+1/{\mathit{\&lgr;}}_{P2}+1/{\mathit{\&lgr;}}_{S}+1/{\mathit{\&lgr;}}_{I}}$$

L is an optical fiber length. n_{2} is a third-order
nonlinear index of the optical fiber at the wavelength &lgr;. A_{eff}
is an effective area of the optical fiber at the wavelength &lgr;. &agr; is
a transmission loss of the optical fiber at the wavelength &lgr;. &bgr;_{P1}
is a propagation constant of the optical fiber at the wavelength &lgr;_{P1},
&bgr;_{P2} is a propagation constant of the optical fiber at the wavelength
&lgr;_{P2}, &bgr;_{S} is a propagation constant of the optical
fiber at the wavelength &lgr;_{S}, and &bgr;_{I} is a propagation
constant of the optical fiber at the wavelength &lgr;_{I}. D is a degeneracy
factor. The degeneracy factor takes the value of 1 where the wavelength &lgr;_{P1}
and the wavelength &lgr;_{P2} are equal to each other, and the degeneracy
factor takes the value of 4 where the wavelength &lgr;_{P1} and the wavelength
&lgr;_{P2} are different from each other.

Particularly, where the transmission loss &agr; of the
optical fiber at the wavelength &lgr; is negligible small, the aforementioned
Eq (1) can be approximated by Eq (7) below. As seen from this equation, the closer
the phase mismatching amount &Dgr;&bgr; to the value of 0, the larger the power
P_{I-out} of the idler &lgr;_{I} outputted from the optical fiber.
The shorter the fiber length L, the smaller the value of "L&Dgr;&bgr;/2"; therefore,
the power P_{I-out} of the idler &lgr;_{I} outputted from the
optical fiber is less affected by the phase mismatching amount &Dgr;&bgr;.

Equation 7:
$${P}_{I-\mathit{out}}={\mathit{D\&ggr;}}^{2}{L}^{2}{P}_{P1-\mathit{in}}{P}_{P2-\mathit{in}}{P}_{S-\mathit{in}}{\left\{\frac{\mathrm{sin}\left(L,\cdot ,\mathrm{\&Dgr;},\begin{array}{}\end{array},\mathrm{\&bgr;},/,2\right)}{L\cdot \mathrm{\&Dgr;}\begin{array}{}\end{array}\mathrm{\&bgr;}/2}\right\}}^{2}$$

In addition, Eq (8) below holds from the frequency matching
condition. Therefore, Eq (6) above can be transformed into Eq (9) below. In order
to implement high-efficiency wavelength conversion in a wide probe wavelength range
in the optical fiber, it is desirable to make the phase mismatching amount &Dgr;&bgr;
represented by Eq (3) above, nearly null in a wide wavelength range. The wavelength
&lgr; represented by Eq (6) above or by Eq (9) is converted into angular frequency
&ohgr;, as represented by Eq (10) below. In the equation c represents the speed
of light in vacuum.

Equation 8:
$${\mathrm{\&ohgr;}}_{I}={\mathrm{\&ohgr;}}_{P1}+{\mathrm{\&ohgr;}}_{P2}-{\mathrm{\&ohgr;}}_{S}$$
$$\frac{1}{{\mathit{\&lgr;}}_{I}}=\frac{1}{{\mathit{\&lgr;}}_{P1}}+\frac{1}{{\mathit{\&lgr;}}_{P2}}-\frac{1}{{\mathit{\&lgr;}}_{S}}$$

Equation 9:
$$\mathit{\&lgr;}=\frac{2}{1/{\mathit{\&lgr;}}_{P1}+1/{\mathit{\&lgr;}}_{P2}}$$

Equation 10:
$$\mathrm{\&ohgr;}=\frac{2\mathrm{\&pgr;}\begin{array}{}\end{array}c}{\mathit{\&lgr;}}$$

The propagation constant &bgr; is expressed by Eq (11)
below through the Taylor expansion about the angular frequency &ohgr; described
in Eq (10). The n^{th} derivative of the propagation constant &bgr; with
respect to angular frequency &ohgr; is represented by Eq (12) below. There are
relations represented by Eq (13) to Eq (15) below, of the second derivation -----&bgr;_{2},
the third order dispersion &bgr;_{3}, and the fourth order dispersion
&bgr;_{4} with the chromatic dispersion D, the dispersion slope S, and
the wavelength derivative of the dispersion slope (dS/d&lgr;).

Equation 11:
$$\begin{array}{ll}\mathrm{\&bgr;}& ={\mathrm{\&bgr;}}_{0}+{\displaystyle \sum _{\mathit{n}=1}^{\mathrm{\infty}}\frac{1}{n!}{\mathrm{\&bgr;}}_{n}{\left(\mathrm{\&ohgr;},-,{\mathrm{\&ohgr;}}_{P1}\right)}^{n}}\\ \phantom{\rule{1em}{0ex}}& ={\mathrm{\&bgr;}}_{0}+{\mathrm{\&bgr;}}_{1}\left(\mathrm{\&ohgr;},-,{\mathrm{\&ohgr;}}_{P1}\right)+\frac{1}{2}{\mathrm{\&bgr;}}_{2}{\left(\mathrm{\&ohgr;},-,{\mathrm{\&ohgr;}}_{P1}\right)}^{2}\\ \phantom{\rule{1em}{0ex}}& +\frac{1}{6}{\mathrm{\&bgr;}}_{3}{\left(\mathrm{\&ohgr;},-,{\mathrm{\&ohgr;}}_{P1}\right)}^{3}+\frac{1}{24}{\mathrm{\&bgr;}}_{4}{\left(\mathrm{\&ohgr;},-,{\mathrm{\&ohgr;}}_{P1}\right)}^{4}+\cdots \end{array}$$

Equation 12:
$${\mathrm{\&bgr;}}_{n}=\frac{{d}^{n}\mathrm{\&bgr;}}{d{\mathrm{\&ohgr;}}^{n}}$$

Equation 13:
$${\mathrm{\&bgr;}}_{2}=-\frac{{\mathit{\&lgr;}}^{2}}{2\mathrm{\&pgr;}\begin{array}{}\end{array}c}D$$

Equation 14:
$${\mathrm{\&bgr;}}_{3}=\frac{{\mathit{\&lgr;}}^{3}}{2{\mathrm{\&pgr;}}^{2}\begin{array}{}\end{array}{c}^{2}}D+\frac{{\mathit{\&lgr;}}^{4}}{4{\mathrm{\&pgr;}}^{2}\begin{array}{}\end{array}{c}^{2}}S$$

Equation 15:
$${\mathrm{\&bgr;}}_{4}=-\frac{3{\mathit{\&lgr;}}^{3}}{4{\mathrm{\&pgr;}}^{3}\begin{array}{}\end{array}{c}^{3}}D-\frac{3{\mathit{\&lgr;}}^{5}}{4{\mathrm{\&pgr;}}^{3}\begin{array}{}\end{array}{c}^{3}}S-\frac{3{\mathit{\&lgr;}}^{6}}{8{\mathrm{\&pgr;}}^{3}\begin{array}{}\end{array}{c}^{3}}\frac{dS}{d\mathit{\&lgr;}}$$

Supposing the wavelength &lgr;_{P1} and the wavelength
&lgr;_{P2} are equal to each other, i.e., to wavelength &lgr;_{p},
relations of "&lgr;=&lgr;_{p}" and "&ohgr;=&ohgr;_{P}" are
derived from Eq (9) and Eq (10) above. Therefore, the foregoing Eq (3) is reduced
to Eq (16) below, using Eq (8) and Eq (11) above.

Equation (16)
$$\mathrm{\&Dgr;\&bgr;}=-{\mathrm{\&bgr;}}_{2}{\left({\mathrm{\&ohgr;}}_{P},-,{\mathrm{\&ohgr;}}_{S}\right)}^{2}-\frac{1}{12}{\mathrm{\&bgr;}}_{4}{\left({\mathrm{\&ohgr;}}_{P},-,{\mathrm{\&ohgr;}}_{S}\right)}^{4}$$

It is seen from this Eq (16) that the absolute value of
the phase mismatching amount &Dgr;&bgr; becomes smaller with decrease in respective
absolute values of the second order dispersion &bgr;_{2} and the fourth
order dispersion &bgr;_{4} at the pump wavelength &lgr;_{P}.
In addition, it is not always preferable to match the pump wavelength &lgr;_{P}
with the zero dispersion wavelength of the optical fiber so as to null the second
order dispersion &bgr;_{2}, and the pump wavelength &lgr;_{P}
should be selected in consideration of the influence of the fourth order dispersion
&bgr;_{4}. Namely, where the fourth order dispersion &bgr;_{4}
is negative, the pump wavelength &lgr;_{P} should be so selected that
the second order dispersion &bgr;_{2} is positive and that the pump wavelength
is thus shorter than the zero dispersion wavelength. Conversely, where the fourth
order dispersion &bgr;_{4} is positive, the pump wavelength &lgr;_{P}
should be so selected that the second order dispersion &bgr;_{2} is negative
and that the pump wavelength is thus longer than the zero dispersion wavelength.

Next described is the result of further specific analysis
based on the result of the analysis described above. Fig. 1 is a drawing showing
the relationship between the power P_{I-out} of the idler &lgr;_{I}
outputted from the optical fiber, and the probe wavelength &lgr;_{S}.
The horizontal axis represents the probe wavelength &lgr;_{S}, and the
vertical axis represents the normalized idler intensity in dB unit. This result
was obtained under the following conditions: the pump injected into the optical
fiber is a pump of one wavelength, the zero dispersion wavelength &lgr;_{0}
of the optical fiber is 1570 nm, the dispersion slope S of the optical fiber at
the zero dispersion wavelength &lgr;_{0} is +0.024 ps/nm^{2}/km,
the fiber length L of the optical fiber is 100 m, and the transmission loss a of
the optical fiber is 0.20/km. The pump wavelength &lgr;_{P} was matched
with the zero dispersion wavelength &lgr;_{0} of the optical fiber. Investigation
was conducted on how the power P_{I-out} of the idler &lgr;_{I}
varied relatively, using the aforementioned Eqs (1) to (6) and Eq (16).

Fig. 1 shows two cases for the fourth order dispersion
&bgr;_{4}, 1 × 10^{-55} s^{4}/m as a general value,
and 1 × 10^{-57} s^{4}/m two figures smaller. As shown in Fig.
1, a width of two probe wavelengths at the power of the idler -3 dB or more smaller
than a peak value (i.e., full width at half maximum), is defined as "wavelength
conversion bandwidth." When the pump wavelength &lgr;_{p} and the zero
dispersion wavelength &lgr;_{0} of the optical fiber are equal to each
other, the second order dispersion &bgr;_{2} of the propagation constant
&bgr; is 0; therefore, as seen from above Eq (16), the wavelength conversion bandwidth
becomes wider with decrease in the fourth order dispersion &bgr;_{4}.

Figs. 2A and 2B are drawings showing the relationship between
the wavelength conversion bandwidth and the pump wavelength &lgr;_{P}.
The horizontal axis represents "zero dispersion wavelength &lgr;_{0} -
pump wavelength &lgr;_{P}," and the vertical axis the wavelength conversion
bandwidth. It is seen from this drawing that the maximum of the wavelength conversion
bandwidth becomes larger with decrease in the absolute value of the fourth order
dispersion &bgr;_{4} and that the absolute value is preferably as small
as possible. Where the fourth order dispersion &bgr;_{4} is negative,
the pump wavelength &lgr;_{P} becomes smaller than the zero dispersion
wavelength &lgr;_{0} so as to make the second order dispersion &bgr;_{2}
positive; where the fourth order dispersion &bgr;_{4} is positive, the
pump wavelength &lgr;_{P} is larger than the zero dispersion wavelength
&lgr;_{0} so as to make the second order dispersion &bgr;_{2}
negative; this is just as indicated by Eq (16). As apparent from a comparison between
Fig. 2A and Fig. 2B, with the fourth order dispersion &bgr;_{4} having
an equal absolute value, the wavelength conversion bandwidths are also approximately
equal.

From these Figs. 2A and 2B, where the fiber length L is
100 m, the wavelength conversion bandwidth becomes wide, not less than 100 nm, and
the tolerances of "zero dispersion wavelength &lgr;_{0} - pump wavelength
&lgr;_{P}" are approximately ±0.6 nm. Where the fourth order dispersion
&bgr;_{4} is -10^{-55} s^{4}/m, the wavelength conversion
bandwidth becomes wide, not less than 100 nm, and the tolerances of "zero dispersion
wavelength &lgr;_{0} - pump wavelength &lgr;_{P}" are also ±0.6
nm. Since the pump wavelength &lgr;_{P} is normally kept constant, it
is said that it is necessary to suppress the variation in the zero dispersion wavelength
&lgr;_{0} of the optical fiber in the range of not more than ±0.6
nm in order to implement the wavelength conversion in a wide band. This optical
fiber as suppressed in the variation of the zero dispersion wavelength &lgr;_{0}
can be substantialized, for example, by measuring the index profile of an optical
fiber preform at each of locations in the longitudinal direction, grinding the contour
of the optical fiber preform so as to obtain the optical fiber with desired characteristics
based on the measurement result, and drawing the optical fiber preform.

In practice, the zero dispersion wavelength &lgr;_{0}
of optical fiber varies to some extent in the longitudinal direction and thus the
wavelength conversion bandwidth is reduced. Investigation was conducted as to how
the minimum of the wavelength conversion bandwidth varied with a certain width of
"zero dispersion wavelength &lgr;_{0} - pump wavelength &lgr;_{P},"
to study how the wavelength conversion bandwidth varied with variation in the zero
dispersion wavelength &lgr;_{0}. Fig. 3 is a drawing to illustrate the
minimum of the wavelength conversion bandwidth in a diagram showing the relationship
between the wavelength conversion bandwidth and the pump wavelength &lgr;_{P}.
Each of Figs. 4A and 4B and 5 is a drawing showing tables of wavelength conversion
bandwidths at respective values of the absolute value of the fourth order dispersion
&bgr;_{4} and the optical fiber length L, for each of values of the variation
width of the zero dispersion wavelength &lgr;_{0} of optical fiber.

Fig. 4A shows the wavelength conversion bandwidths assuming
no variation in the zero dispersion wavelength &lgr;_{0}. Fig. 4B shows
the wavelength conversion bandwidths with variation of ±0.05 nm in the zero
dispersion wavelength &lgr;_{0}. Fig. 4 C shows the wavelength conversion
bandwidths with variation of ±0.10 nm in the zero dispersion wavelength &lgr;_{0}.
Fig. 5A shows the wavelength conversion bandwidths with variation of ±0.20
nm in the zero dispersion wavelength &lgr;_{0}. Fig. 5B shows the wavelength
conversion bandwidths with variation of ±0.60 nm in the zero dispersion wavelength
&lgr;_{0}. Fig. 5 C shows the wavelength conversion bandwidths with variation
of ±1.0 nm in the zero dispersion wavelength &lgr;_{0}.

Fig. 4A proves that, without variation in the zero dispersion
wavelength &lgr;_{0}, the wavelength conversion bandwidth increases with
decrease in the fourth order dispersion &bgr;_{4}. For example, the wavelength
conversion bandwidth in the fiber length L of 100 m varies as shown in Fig. 6. Fig.
6 is a drawing showing the relationship between the wavelength conversion bandwidth
and the fourth order dispersion &bgr;_{4} in the optical fiber with the
fiber length of 100 m without variation in the zero dispersion wavelength &lgr;_{0}.
As shown in this figure, when the absolute value of the fourth order dispersion
&bgr;_{4} is 1 × 10^{-55} s^{4}/m, which is equivalent
to the conventional level, the wavelength conversion bandwidth cannot be 200 nm
or more. When the absolute value of the fourth order dispersion &bgr;_{4}
is not more than 5 × 10^{-56} s^{4}/m, the wavelength conversion
bandwidth exceeds 200 nm and is suitable. When the absolute value of the fourth
order dispersion &bgr;_{4} is not more than 1 × 10^{-56}
s^{4}/m, the wavelength conversion bandwidth becomes characteristically
large and more than 300 nm. This wavelength conversion bandwidth is preferably 200
nm because it includes the S-band, C-band, and L-band generally used as wavelengths
of signal light in optical communications.

In fact, the zero dispersion wavelength &lgr;_{0}
often varies in the range of about ±0.05 nm to ±0.10 nm. For example,
in the fiber length of 100 m, the wavelength conversion bandwidth varies as shown
in Figs. 7 and 8. Fig. 7 is a drawing showing the relationship between the wavelength
conversion bandwidth and the fourth order dispersion &bgr;_{4} in the
optical fiber with the fiber length of 100 m with variation of ±0.05 nm in
the zero dispersion wavelength &lgr;_{0}. This figure proves that when
the absolute value of the fourth order dispersion &bgr;_{4} is not more
than 5 × 10^{-56} s^{4}/m, the wavelength conversion bandwidth
becomes characteristically large and not less than about 200 nm and that when the
absolute value of the fourth order dispersion &bgr;_{4} is not more than
1 × 10^{-57} s^{4}/m, the wavelength conversion bandwidth becomes
extremely wide, not less than about 300 nm. Fig. 8 is a drawing showing the relationship
between the wavelength conversion bandwidth and the fourth order dispersion &bgr;_{4}
in the optical fiber with the fiber length of 100 m with variation of ±0.10
nm in the zero dispersion wavelength &lgr;_{0}. As shown in this figure,
when the absolute value of the fourth order dispersion &bgr;_{4} is not
more than 3 × 10^{-56} s^{4}/m, the wavelength conversion bandwidth
can be expanded to about 200 nm or more, which is preferred. More preferably, the
absolute value of the fourth order dispersion &bgr;_{4} is not more than
2 × 10^{-56} s^{4}/m.

As seen from the aforementioned Eq (7), the longer the
length L of optical fiber, the higher the power P_{I-out} of the idler &lgr;_{I}
emitted from the optical fiber, and the higher the efficiency. It is also seen from
Eq (7) that this can be solved by increasing the power P_{P} of the pump
&lgr;_{P} injected into the optical fiber. It is apparent from Figs. 4
and 5 that the wavelength conversion bandwidth is expanded with decrease in the
length L of optical fiber. For example, with variation of about ±0.10 nm in
the zero dispersion wavelength &lgr;_{0}, the wavelength conversion bandwidth
varies as shown in Fig. 9. Fig. 9 is a drawing showing the relationship between
the wavelength conversion bandwidth and the fiber length L in the optical fiber
with variation of ±0.10 nm in the zero dispersion wavelength &lgr;_{0}.
This figure proves that the effect of decrease of the fourth order dispersion &bgr;_{4}
becomes definite when the fiber length L is not more than 500 m. Fig. 10 is a drawing
showing the relationship between the wavelength conversion bandwidth and variation
amount of the zero dispersion wavelength &lgr;_{0}. As seen from this
figure, the wavelength conversion bandwidth becomes narrower with increasing variation
in the zero dispersion wavelength &lgr;_{0}. When the variation in the
zero dispersion wavelength &lgr;_{0} is not less than ±0.6 nm, the
effect of decrease of the fourth order dispersion &bgr;_{4} becomes unclear.

By suppressing the variation in the zero dispersion wavelength
&lgr;_{0} to not more than ±0.6 nm, it becomes feasible to achieve
wavelength conversion in a wide band of not less than 100 nm. From Figs. 4A-Ac,
5A-5C, and 10, when the variation in the zero dispersion wavelength &lgr;_{0}
is not less than ±0.6 nm, the effect of decrease of the fourth order dispersion
&bgr;_{4} is not so significant, and when the variation in the zero dispersion
wavelength &lgr;_{0} is not more than ±0.2 nm, the effect of decrease
of the fourth order dispersion &bgr;_{4} appears apparent to expand the
bandwidth, which is further more preferred.

The following will describe specific configuration examples
of optical fiber capable of reducing the absolute value of the fourth order dispersion
&bgr;_{4} as described above. No investigation has been conducted heretofore
about the optical fiber capable of reducing the absolute value of the fourth order
dispersion &bgr;_{4}, and the Inventor first conducted the research. As
seen from Eq (7) above, the nonlinear coefficient &ggr; of optical fiber is preferably
as high as possible and is particularly preferably not less than 10/W-km. For this
reason, the effective area A_{eff} of optical fiber is desirably not more
than 15 µm^{2}.

Figs. 11A and 11B are drawings showing a preferred example
of a sectional structure and index profile of optical fiber 10 according to the
present embodiment. Fig. 11A shows a cross section normal to the longitudinal direction
of optical fiber 10 and Fig. 11B shows the index profile in the radial direction
of optical fiber 10. The optical fiber 10 comprises at least a center core part
11 having a maximum refractive index N_{1} and outside diameter 2a, a depressed
part 12 surrounding this center core part 11 and having a minimum refractive index
N_{2} and outside diameter 2b, and a cladding part 13 surrounding this depressed
part 12 and having a maximum refractive index N_{3}.

The refractive indices of the center core part 11, depressed
part 12, and cladding part 13 satisfy the relation of "N_{1} > N_{3}
> N_{2}." With reference to the refractive index N_{3} of the
cladding part 13, the relative index difference of the center core part 11 is denoted
by &Dgr;_{+} and the relative index difference of the depressed part 12
by &Dgr;_{-}. A ratio of the respective outside diameters of the center
core part 11 and the depressed part 12 is denoted by Ra (= 2a/2b).

Fig. 12 is a drawing showing a table of the dispersion
slope S, the wavelength derivative of the dispersion slope (dS/d&lgr;), and the
fourth order dispersion &bgr;_{4}, for each of values of the ratio Ra.
In the optical fiber 10 of the structure shown in Fig. 11, the parameters used are
as follows: the &agr; value in the alpha profile of refractive index of the center
core part 11 is 3, the relative index difference &Dgr;_{+} of the center
core part 11 3.2%, the relative index difference &Dgr;_{-} of the depressed
part 12 -0.3%, and the zero dispersion wavelength &lgr;_{0} 1550 nm.

As seen from this figure, the fourth order dispersion &bgr;_{4}
is dependent on Ra, the absolute value of the fourth order dispersion &bgr;_{4}
is not more than 5 × 10^{-56} s^{4}/m with Ra being not less
than 0.4, and the absolute value of the fourth order dispersion &bgr;_{4}
is not more than 1 × 10^{-56} s^{4}/m, particularly, with Ra
being near 0.6. Other characteristics of this optical fiber 10 are as follows: at
the wavelength of 1550 nm, the effective area A_{eff} is 9.8 µm^{2},
the nonlinear coefficient &ggr; 24/W-km (measured by XPM method), the fiber cutoff
wavelength 1400 nm, the transmission loss 0.6 dB/km, the mode field diameter 3.6
µm, and the polarization mode dispersion 0.01-0.1 ps/km^{1/2}. It is
known that a measured value of the nonlinear coefficient &ggr; by CW-SPM method
is as small as approximately 70% of the measured value of the nonlinear coefficient
&ggr; by XPM method.

This optical fiber 10 is very resistant to bending and,
even when wound in the diameter of 30 ϕ, an increase of loss is not more than
0.01 dB/km. This optical fiber 10 can be spliced with an ordinary single-mode optical
fiber, with a splice loss of about 0.5 dB by use of a popular splicer, and the splice
loss can be reduced to 0.2 dB or less by use of a method of expanding the mode field
diameter.

Fig. 13 is also a drawing showing a table of the dispersion
slope S, the wavelength derivative of the dispersion slope (dS/d&lgr;), and the
fourth order dispersion &bgr;_{4}, for each of values of the ratio Ra.
In the optical fiber 10 of the structure as shown in Figs. 11A and 11B, the parameters
used herein are as follows: the a value in the alpha profile of refractive index
of the center core part 11 is 3, the relative index difference A_{+} of
the center core part 11 3.5%, the relative index difference &Dgr;_{-}
of the depressed part 12 -0.35%, and the zero dispersion wavelength &lgr;_{0}
1540 nm.

As seen from this figure, this optical fiber 10 generally
has the small fourth order dispersion &bgr;_{4} and signs thereof change
near each ratio Ra of 0.45 and 0.75. This means that when the optical fiber 10 is
fabricated with the ratio Ra near either of these values, it is feasible to substantialize
the optical fiber 10 with the extremely small fourth order dispersion &bgr;_{4}
of not more than 5 × 10^{-57} s^{4}/m. The other characteristics
of this optical fiber 10 are as follows: at the wavelength of 1550 nm, the effective
area A_{eff} is 9.1 µm^{2}, the nonlinear coefficient &ggr;
26/W-km (measured by XPM method), the fiber cutoff wavelength is 1450 nm, the transmission
loss is 0.9 dB/km, the mode field diameter is 3.4 µm, and the polarization
mode dispersion is 0.01-0.1 ps/km^{1/2}.

This optical fiber 10 is also very resistant to bending
and, even when wound in the diameter of 30 ϕ, an increase of loss is not more
than 0.01 dB/km. This optical fiber 10 can also be spliced with an ordinary single-mode
optical fiber, with a splice loss of about 0.5 dB by use of a popular splicer, and
the splice loss can be reduced to 0.2 dB or less by use of a method of expanding
the mode field diameter.

As described above, the fourth order dispersion &bgr;_{4}
can be adjusted in the optical fiber of the structure having the center core part
11 and the depressed part 12. Figs. 14A-14D are drawings showing other preferred
examples of the index profile of optical fiber according to the present embodiment.
As shown in Fig. 14A, the optical fiber may have still another region 14 outside
the depressed part 11; as shown in Fig. 14 B, the optical fiber may have still another
region 15 outside the region 14; as shown in Fig. 14 C, the optical fiber may have
another region 16 between the center core part 11 and the depressed part 12; as
shown in Fig. 14 D, a dip may exist in the center core part 11. In any of these
cases, the fourth order dispersion &bgr;_{4} can be adjusted, so that
the absolute value of the fourth order dispersion &bgr;_{4} can be made
smaller.

The polarization mode dispersion is preferably as small
as possible because the wavelength conversion bandwidth becomes wider by that degree.
The polarization mode dispersion at the overall length of optical fiber is preferably
not more than 0.2 ps. When the optical fiber is of a polarization maintaining type
(e.g., the PANDA type), it is feasible to suppress coupling between orthogonal polarization
components of fundamental mode light guided through the optical fiber, and it is
more preferred. The coupling between orthogonal polarization components can be made
not more than -15 dB even in the fiber length of 1 km, and can be further reduced
in practically used fiber lengths.

The optical fiber may be wound, for example, in a small
coil with the minimum bend diameter of about 40 ϕ. At this time, the coil
can be made smaller as the covering outside diameter of optical fiber becomes thiner,
not more than 150 µm. When the outside diameter of the glass part 11 of optical
fiber is thin, not more than 100 µm, winding stress is small in a compact winding
state to reduce a probability of breakage and it becomes feasible to suppress deterioration
of the polarization mode dispersion due to bend-induced birefringence.

Optical fibers satisfying the characteristics as described
above were fabricated actually. All the optical fibers had the structure as shown
in Fig. 11. An optical fiber fabricated had the following values of the respective
parameters: the &agr; value in the alpha profile of refractive index of the center
core part 11 was 3, the relative index difference &Dgr;_{+} of the center
core part 11 was 2.5%, the relative index difference &Dgr;_{-} of the
depressed part was 12 -0.5%, the ratio Ra was 0.6, and the core diameter 2a was
4.7 µm. This optical fiber had the zero dispersion wavelength of 1440 nm. The
optical fiber was a highly nonlinear optical fiber with the fourth order dispersion
&bgr;_{4} reduced and with the following characteristics: at the zero
dispersion wavelength of 1440 nm, the dispersion slope was +0.0466 ps/nm^{2}/km,
the wavelength derivative of the dispersion slope was 1.66 × 10^{-4}
ps/nm^{3}/km, the fourth order dispersion &bgr;_{4} was -3.8 ×
10^{-56} s^{4}/m, the effective area A_{eff} was 11 µm^{2},
the nonlinear coefficient &ggr; was 21/W-km, the mode field diameter was 3.8 µm,
the cutoff wavelength was 1.37 µm, and the polarization mode dispersion in
the C-band was 0.02 ps/km^{1/2}.

Another optical fiber produced had the following values
of the respective parameters: the a value in the alpha profile of refractive index
of the center core part 11 was 1.9, the relative index difference &Dgr;_{+}
of the center core part 11 was 3.0%, the relative index difference &Dgr;_{-}
of the depressed part 12 was -0.6%, the ratio Ra was 0.6, and the core diameter
2a was 4.5 µm. This optical fiber had the zero dispersion wavelength of 1640
nm. This optical fiber was a highly nonlinear optical fiber with the fourth order
dispersion &bgr;_{4} reduced and with the following characteristics: at
the zero dispersion wavelength of 1640 nm, the dispersion slope was +0.0231 ps/nm^{2}/km,
the wavelength derivative of the dispersion slope was -9.63 × 10^{-5}
ps/nm^{3}/km, the fourth order dispersion &bgr;_{4} was -3.4 ×
10^{-56} s^{4}/m, the effective area A_{eff} was 11 µm^{2},
the nonlinear coefficient &ggr; was 18/W-km, the mode field diameter was 3.9 µm,
the cutoff wavelength was 1.31 µm, and the polarization mode dispersion in
the C-band and L-band was 0.03 ps/km^{1/2}.

The following will describe a more general design example
of optical fiber capable of reducing the absolute value of the fourth order dispersion
&bgr;_{4} as described above. The optical fiber herein was also one having
the structure as shown in Fig. 11, and having the following values of the respective
parameters: the &agr; value in the alpha profile of refractive index of the center
core part 11 was 4 and the zero dispersion wavelength was 1550 nm.

Fig. 15 is a drawing showing a table of the dispersion
slope S, the wavelength derivative of the dispersion slope (dS/d&lgr;), and the
fourth order dispersion &bgr;_{4}, for each of values of the ratio Ra,
where the relative index difference &Dgr;_{+} of the center core part
11 is 2.5% and the relative index difference &Dgr;_{-} of the depressed
part 12 is -0.1%. In this case, the absolute value of the fourth order dispersion
&bgr;_{4} is as large as about 7 × 10^{-56} s^{4}/m,
and this is not a preferred example. The core diameter 2a is about 4 µm, the
cutoff wavelength about 1400 nm, the effective area A_{eff} at the wavelength
of 1.55 µm is approximately 12 µm^{2}, and the nonlinear coefficient
&ggr; is about 17/W-km.

Fig. 16 is a drawing showing a table of the dispersion
slope S, the wavelength derivative of the dispersion slope (dS/d&lgr;), and the
fourth order dispersion &bgr;_{4}, for each of values of the ratio Ra,
where the relative index difference &Dgr;_{+} of the center core part
11 is 2.5% and the relative index difference &Dgr;_{-} of the depressed
part 12 is -0.2%. In this case, the absolute value of the fourth order dispersion
&bgr;_{4} is as large as about 4 × 10^{-56} s^{4}/m
and this is preferable. The core diameter 2a is about 4 µm, the cutoff wavelength
is about 1400 nm, the effective area A_{eff} at the wavelength of 1.55 µm
is about 12 µm^{2}, and the nonlinear coefficient &ggr; is about
18/W-km.

Fig. 17 is a drawing showing a table of the dispersion
slope S, the wavelength derivative of the dispersion slope (dS/d&lgr;), and the
fourth order dispersion &bgr;_{4}, for each of values of the ratio Ra,
where the relative index difference &Dgr;_{+} of the center core part
11 is 2.5% and the relative index difference &Dgr;_{-} of the depressed
part 12 -0.3%. Fig. 18 is a drawing showing the relationship between the fourth
order dispersion &bgr;_{4} and the ratio Ra in this example. In this case,
the absolute value of the fourth order dispersion &bgr;_{4} can take the
value of 0 and this is a preferred example. In addition, in the range of the ratio
Ra of about 0.5 to about 0.65, the absolute value of the fourth order dispersion
&bgr;_{4} becomes not more than 1 × 10^{-56} s^{4}/m,
and thus structure tolerances are wide in the fabrication of fiber, which is very
preferred. The core diameter 2a is about 4 µm, the cutoff wavelength is about
1400 nm, the effective area A_{eff} at the wavelength of 1.55 µm is
about 12 µm^{2}, and the nonlinear coefficient &ggr; about is 18/W-km.

Fig. 19 is a drawing showing a table of the dispersion
slope S, the wavelength derivative of the dispersion slope (dS/d&lgr;), and the
fourth order dispersion &bgr;_{4}, for each of values of the ratio Ra,
where the relative index difference &Dgr;_{+} of the center core part
11 is 2.5% and the relative index difference &Dgr;_{-} of the depressed
part 12 is -0.6%. Fig. 20 is a drawing showing the relationship between the fourth
order dispersion &bgr;_{4} and the ratio Ra in this example. In this case,
the absolute value of the fourth order dispersion &bgr;_{4} can take the
value of 0 and this is a preferred example. However, when the fourth order dispersion
&bgr;_{4} is small near 0, the fourth order dispersion &bgr;_{4}
largely varies even with small variation in the ratio Ra, and thus the structure
tolerances are not so high in the fabrication of fiber. The core diameter 2a is
about 4 µm, the cutoff wavelength is about 1300 nm, the effective area A_{eff}
at the wavelength of 1.55 µm is about 11 µm^{2}, and the nonlinear
coefficient &ggr; is about 20/W-km.

The following will describe the relationship between the
fourth order dispersion &bgr;_{4} and the ratio Ra with change in the
relative index difference &Dgr;_{-} of the depressed part 12.

Fig. 21 is a drawing showing the relationship between the
fourth order dispersion &bgr;_{4} and the ratio Ra, where the relative
index difference &Dgr;_{+} of the center core part 11 is 2.5%. Here is
the relationship between the fourth order dispersion &bgr;_{4} and the
ratio Ra, for each of values of the relative index difference &Dgr;_{-}
of the depressed part 12. When &Dgr;_{+} is 2.5%, if &Dgr;_{-}
is not more than about -0.2% and if the difference "&Dgr;_{+}-&Dgr;_{-}"
is not less than about 2.7%, the absolute value of the fourth order dispersion &bgr;_{4}
becomes not more than 5 × 10^{-56} s^{4}/m. It is seen that
the fourth order dispersion &bgr;_{4} takes a minimum near the ratio Ra
of 0.5-0.6. When the absolute value of the fourth order dispersion &bgr;_{4}
is small near this range, the fabrication tolerances become high and with &Dgr;_{-}
of -0.4% to -0.2% the fabrication is easy. Even in the cases where &Dgr;_{-}
is -0.5% to -1.1% and the ratio Ra 0.2-0.3, the absolute value of the fourth order
dispersion &bgr;_{4} is always small and the fabrication is easy.

Fig. 22 is a drawing showing the relationship between the
fourth order dispersion &bgr;_{4} and the ratio Ra, where the relative
index difference &Dgr;_{+} of the center core part 11 is 2.0%. Here is
also the relationship between the fourth order dispersion &bgr;_{4} and
the ratio Ra for each of values of the relative index difference &Dgr;_{-}
of the depressed part 12. The other characteristics are as follows: the core diameter
2a is about 4.5 µm, the effective area A_{eff} at the wavelength of
1.55 µm is about 13-15 µm^{2}, the nonlinear coefficient &ggr;
is 13-15/W-km, and the cutoff wavelength is about 1200-1300 nm. When &Dgr;_{+}
is 2.0%, if &Dgr;_{-} is not more than about -0.2% and if the difference
"&Dgr;_{+}-&Dgr;_{-}" is not less than about 2.2%, the absolute
value of the fourth order dispersion &bgr;_{4} becomes not more than 5
× 10^{-56} s^{4}/m. It is seen that the fourth order dispersion
&bgr;_{4} takes a minimum near the ratio Ra of 0.4-0.6. When the absolute
value of the fourth order dispersion &bgr;_{4} is small near this range,
the fabrication tolerances become high and the fabrication is easy if &Dgr;_{-}
is -0.4 to -0.25%. Even in the cases where &Dgr;_{-} is not more than
-0.5% and the ratio is between Ra 0.2 and 0.3, the absolute value of the fourth
order dispersion &bgr;_{4} is always small and the fabrication is easy.

Fig. 23 is a drawing showing the relationship between the
fourth order dispersion &bgr;_{4} and the ratio Ra, where the relative
index difference &Dgr;_{+} of the center core part 11 is 3.0%. Here is
also the relationship between the fourth order dispersion &bgr;_{4} and
the ratio Ra for each of values of the relative index difference &Dgr;_{-}
of the depressed part 12. The other characteristics are as follows: the core diameter
2a is about 4.0 µm, the effective area A_{eff} at the wavelength of
1.55 µm is about 9-10 µm^{2}, the nonlinear coefficient &ggr;
is 22-26/W-km, and the cutoff wavelength is about 1500-1300 nm. When &Dgr;_{+}
is 3.0%, if &Dgr;_{-} is not more than about -0.10% and if the difference
"&Dgr;_{+}-&Dgr;_{-}" is not less than about 3.1%, the absolute
value of the fourth order dispersion &bgr;_{4} becomes not more than 5
× 10^{-56} s^{4}/m. It is seen that the fourth order dispersion
&bgr;_{4} takes a minimum near the ratio Ra of 0.4-0.6. When the absolute
value of the fourth order dispersion &bgr;_{4} is small near this range,
the fabrication tolerances become high and the fabrication is easy if &Dgr;_{-}
is -0.4 to -0.15%. Even in the cases where &Dgr;_{-} is -1.0% to -0.2%
and the ratio Ra is between 0.2 and 0.3, the absolute value of the fourth order
dispersion &bgr;_{4} is always small and the fabrication is easy.

Fig. 24 is a drawing showing the relationship between the
fourth order dispersion &bgr;_{4} and the ratio Ra, where the relative
index difference &Dgr;_{+} of the center core part 11 is 3.5%. Here is
also the relationship between the fourth order dispersion &bgr;_{4} and
the ratio Ra for each of values of the relative index difference &Dgr;_{-}
of the depressed part 12. The other characteristics are as follows: the core diameter
2a is about 4.0 µm, the effective area A_{eff} at the wavelength of
1.55 µm is about 8-9 µm^{2}, the nonlinear coefficient &ggr;
is 28-31/W-km, and the cutoff wavelength is about 1600-1400 nm. When &Dgr;_{+}
is 3.5%, if &Dgr;_{-} is not more than about -0.10% and if the difference
"&Dgr;_{+}-&Dgr;_{-}" is not less than about 3.6%, the absolute
value of the fourth order dispersion &bgr;_{4} becomes not more than 5
× 10^{-56} s^{4}/m. It is seen that the fourth order dispersion
&bgr;_{4} takes a minimum near the ratio Ra of 0.4-0.7. When the absolute
value of the fourth order dispersion &bgr;_{4} is small near this range,
the fabrication tolerances become high and the fabrication is easy if &Dgr;_{-}
is -0.3 to -0.1%. Even in the cases where &Dgr;_{-} is -0.7% to -0.1%
and the ratio Ra is between 0.2 and 0.4, the absolute value of the fourth order
dispersion &bgr;_{4} is always small and the fabrication is easy.

The above is summarized as follows: preferably, the difference
"&Dgr;_{+}-&Dgr;_{-}" between the relative index difference
&Dgr;_{+} of the center core part 11 and the relative index difference
&Dgr;_{-} of the depressed part 12 is not less than 2.2%, the relative
index difference &Dgr;_{-} of the depressed part 12 is -0.1 to -1.1%,
and the ratio Ra is 0.2-0.7. More preferably, the difference "&Dgr;_{+}-&Dgr;_{-}"
is not less than 3.1%, &Dgr;_{-} is -0.1 to -1.1%, and the ratio Ra is
0.2-0.7 because the effective area A_{eff} becomes small, not more than
11 µm^{2}, and the nonlinear coefficient &ggr; becomes large, not
less than about 20/W-km.

From the above calculation results, the relationship between
the fourth order dispersion &bgr;_{4} and the dispersion slope S is illustrated
as shown in Fig. 25, and the relationship between the fourth order dispersion &bgr;_{4}
and the wavelength derivative of the dispersion slope S (dS/d&lgr;) is illustrated
as shown in Fig. 26. As seen from Fig. 25, the dispersion slope S is preferably
about +0.018 to +0.030 ps/nm^{2}/km. Furthermore, the dispersion slope S
is more preferably about +0.022 to +0.028 ps/nm^{2}/km because the absolute
value of the fourth order dispersion &bgr;_{4} can be further decreased.
As seen from Fig. 26, the wavelength derivative of the dispersion slope S (dS/d&lgr;)
is preferably about -0.00012 to -0.00008 ps/nm^{3}/km. Furthermore, the
wavelength derivative (dS/d&lgr;) of the dispersion slope S is more preferably
about -0.00011 to -0.00009 ps/nm^{3}/km because the absolute value of the
fourth order dispersion &bgr;_{4} can be further reduced.

In a highly nonlinear optical fiber, where the dispersion
slope S is small, variation in the zero dispersion wavelength &lgr;_{0}
becomes large. Fig. 27 is a drawing showing the relationship between variation amount
of the zero dispersion wavelength &lgr;_{0} and the dispersion slope S,
where the variation of the core diameter 2a is 1%. As seen from this figure, the
wavelength conversion bandwidth becomes narrower as the variation of the zero dispersion
wavelength &lgr;_{0} increases. Particularly, the dispersion slope S is
preferably not less than +0.018 ps/nm^{2}/km because the variation of the
zero dispersion wavelength &lgr;_{0} is large in the dispersion slope
range of less than +0.018 ps/nm^{2}/km.

An example of an optical fiber and an optical device according
to the present invention will be described below. Fig. 28 is a configuration diagram
of optical device 1 of the example. This optical device 1 comprises the above-described
optical fiber 10, and further comprises a pump light source 21, an optical amplifier
22, a band-pass filter 23, a polarization controller 24, a probe light source 31,
a polarization controller 34, an optical coupler 40, and a spectrum analyzer 50.

The optical fiber 10 used herein has the structure as shown
in Fig. 11, which had the following characteristics: the relative index difference
&Dgr;_{+} of the center core part 11 3.41%, the relative index difference
&Dgr;_{-} of the depressed part 12 of -0.14%, the ratio Ra of 0.56, the
core diameter 2a of 3.78 µm, and the length L of 100 m. This optical fiber
10 had the zero dispersion wavelength &lgr;_{0} of 1562.3 nm, the transmission
loss of 1 dB/km at the wavelength of 1.55 µm, the effective area A_{eff}
of 9.4 µm^{2}, the mode field diameter of 3.51 µm, the nonlinear
coefficient &ggr; of 25/W-km measured by XPM method, and the polarization mode
dispersion of 0.03 ps/km^{1/2}. This optical fiber 10 had the following
characteristics at the zero dispersion wavelength: the dispersion slope S +0.024
ps/nm^{2}/km, the wavelength derivative of the dispersion slope S (dS/d&lgr;)
-0.00010 ps/nm^{3}/km, the third order dispersion &bgr;_{3} of
the propagation constant &bgr;4 × 10^{-41} s^{3}/m, and the
fourth order dispersion &bgr;_{4} +2 × 10^{-56} s^{4}/m.

The pump light source 21 generates a pump light of wavelength
&lgr;_{P}. The probe light source 31 generates a probe light of wavelength
&lgr;_{S}. In the present example the pump wavelength &lgr;_{P}
is set near the zero dispersion wavelength of the optical fiber 10. The probe wavelength
&lgr;_{S} was swept in an output range (1440-1653 nm) of the wavelength-tunable
light source. The optical amplifier 22 optically amplifies the pump light outputted
from the pump light source 21, and outputs the amplified pump. The band-pass filter
23 selectively transmits light of the wavelength &lgr;_{P} out of the
light emitted from the optical amplifier 22, and outputs the transmitted light.
The polarization controller 24 controls the polarization state of the pump &lgr;_{P}
outputted from the band-pass filter 23, and outputs the resultant pump. The polarization
controller 34 controls the polarization state of the probe &lgr;_{S} outputted
from the probe light source 31, and outputs the resultant probe.

The optical coupler 40 receives the pump &lgr;_{P}
outputted from the polarization controller 24 and also receives the probe &lgr;_{S}
outputted from the polarization controller 34, couples these pump &lgr;_{P}
and probe &lgr;_{S}, and outputs the coupled lights. The optical fiber
10 receives the pump &lgr;_{P} and probe &lgr;_{S}. In the present
example, the power P_{P1-in} of the pump &lgr;_{P} injected into
the optical fiber 10 was set to +3 dBm and the power P_{S-in} of the probe
&lgr;_{S} injected into the optical fiber 10 to -5 dBm, thereby generating
an idler &lgr;_{I} by four-wave mixing in this optical fiber 10. The idler
wavelength &lgr;_{I} is represented by the equation of "&lgr;_{I}
= (2/&lgr;_{P} - 1/&lgr;_{S})^{-1}." The spectrum analyzer
50 receives the light outputted from the optical fiber 10 and measures a spectrum
of the light. Particularly, in the present example, the spectrum analyzer 50 measured
the power P_{I-out} of the idler &lgr;_{I} emitted from the optical
fiber 10.

Fig. 29 is a drawing showing the relationship between the
power P_{I-out} of the idler &lgr;_{I} emitted from the optical
fiber 10 of the optical device 1 of the example, and the probe wavelength &lgr;_{S}.
The vertical axis of this drawing is normalized while the maximum of the power P_{I-out}
of the idler &lgr;_{I} is defined as 0 dB. This drawing shows the relationship
between the idler power P_{I-out} and the probe wavelength &lgr;_{S},
for each of the values of the pump wavelength &lgr;_{P}, 1562.0 nm, 1562.3
nm, and 1562.6 nm. Since the fourth order dispersion &bgr;_{4} of the
optical fiber 10 is positive, the wavelength conversion bandwidth is expected to
become wide where the pump wavelength &lgr;_{P} is longer than the zero
dispersion wavelength &lgr;_{0} of the optical fiber 10.

In fact, as shown in Fig. 29, the wavelength conversion
bandwidth was 126 nm at the pump wavelength &lgr;_{P} of 1562.0 nm, the
wavelength conversion bandwidth was 168 nm at the pump wavelength &lgr;_{P}
of 1562.3 nm, and the wavelength conversion bandwidth was 220 nm at the pump wavelength
&lgr;_{P} of 1562.6 nm. Namely, the wavelength conversion bandwidth was
widest when the pump wavelength &lgr;_{P} was 1562.6 nm, which is 0.3
nm longer than the zero dispersion wavelength &lgr;_{0}.

In the example, however, no evaluation was possible with
the probe &lgr;_{S} on the longer wavelength side than 1653 nm, by virtue
of the limit of the output wavelength range of the wavelength-tunable light source
actually used as the probe light source 31. Therefore, the power P_{I-out}
of the idler &lgr;_{I} emitted from the optical fiber 10 was calculated
from the aforementioned Eqs (1) to (6) and Eq (16).

Fig. 30 is a drawing showing the relationship between the
power P_{I-out} of the idler &lgr;_{I} emitted from the optical
fiber 10 of the optical device 1, and the probe wavelength &lgr;_{S},
where the pump wavelength &lgr;_{P} is 1562.0 nm. Fig. 31 is a drawing
showing the relationship between the power P_{I-out} of the idler &lgr;_{I}
emitted from the optical fiber 10 of the optical device 1, and the probe wavelength
&lgr;_{S}, where the pump wavelength &lgr;_{P} is 1562.3 nm.
Fig. 32 is a drawing showing the relationship between the power P_{I-out}
of the idler &lgr;_{I} emitted from the optical fiber 10 of the optical
device 1, and the probe wavelength &lgr;_{S}, where the pump wavelength
&lgr;_{P} is 1562.6 nm. In these drawings, solid lines indicate calculated
values of the power P_{I-out} of the idler &lgr;_{I} emitted from
the optical fiber 10.

As seen from Figs. 30 and 31, the calculated values and
actually measured values demonstrate extremely good agreement with each other, where
the pump wavelength &lgr;_{P} is 1562.0 nm and 1562.3 nm. On the other
hand, as seen from Fig. 32, where the pump wavelength &lgr;_{P} is 1562.6
nm, the calculated values and actually measured values agree well with each other,
but agreement is not so good on the short wavelength side of the probe &lgr;_{S}.

Then the idler intensity was again calculated with variation
of ±0.1 nm in the zero dispersion wavelength &lgr;_{0} in the longitudinal
direction of optical fiber 10, and the result is as shown in Fig. 33. As shown in
this drawing, where the variation in the zero dispersion wavelength &lgr;_{0}
is ±0.1 nm, the calculated values and actually measured values demonstrate
extremely good agreement with each other. In this optical fiber 10, therefore, the
wavelength conversion bandwidth is wide, not less than 100 nm, even if the pump
wavelength &lgr;_{P} is not optimized, and the wavelength conversion bandwidth
is extremely wide, 220 nm, if the pump wavelength &lgr;_{P} is optimized.
The variation in the zero dispersion wavelength &lgr;_{0} can be estimated
as approximately ±0.1 nm. This result doubles the conversion bandwidth of 90-110
nm conventionally known.

Fig. 34 is a drawing showing the relationship between the
power P_{I-out} of the idler &lgr;_{I} emitted from the optical
fiber 10 of the optical device 1, and the probe wavelength &lgr;_{S},
where the pump wavelength &lgr;_{P} is 1562.7 nm. When the probe wavelength
&lgr;_{S} is made further longer to 1562.7 nm as in this example, the
wavelength conversion band is not continuous but is divided into two bands. However,
high wavelength conversion efficiency is achieved even if the probe wavelength &lgr;_{S}
is far from the pump wavelength &lgr;_{P}. Although the wavelength conversion
bandwidth defined within 3 dB becomes narrower, optical devices such as OPA and
switches can avoid the problem of four-wave mixing or the like between probes because
the probe wavelength &lgr;_{S} is so far from the pump wavelength &lgr;_{P}
as to make the dispersion at the probe wavelength relatively large.

Fig. 35 is a drawing showing the relationship between the
power P_{I-out} of the idler &lgr;_{I} and the probe wavelength
&lgr;_{S}, where the length of the optical fiber of the example is 1000
m. Fig. 36 is a drawing showing the relationship between the wavelength conversion
bandwidth and the fiber length of optical fiber for each of the example and the
conventional examples. As seen from the aforementioned Eq (7) and shown in Fig.
9, the wavelength conversion bandwidth becomes narrower with increasing fiber length
L. In the case of the ordinary optical fibers not being polarization-maintaining
fibers, there arises the additional problem of coupling between two polarization
modes, and thus the conventional fibers never had the wavelength conversion bandwidth
of not less than 50 nm in the length of not less than 500 m and the wavelength conversion
bandwidth of about 20 nm in the length of 1000 m. In contrast to it, the optical
fiber of the example experimentally made had the significant effect of decrease
of the fourth order dispersion &bgr;_{4} and the significantly expanded
wavelength conversion bandwidth of 64 nm even in the fiber length of 1000 m.

As described above, it is seen that the optical fiber of
the present invention comes to have the extremely wide wavelength conversion bandwidth
of not less than 100 nm (preferably not less than 150 nm and more preferably not
less than 200 nm) by controlling the absolute value of the fourth order dispersion
&bgr;_{4} to not more than 5 × 10^{-56} s^{4}/m and
controlling the variation of the zero dispersion wavelength &lgr;_{0}
to not more than ±0.6 nm. Since the parametric process efficiently occurs in
the extremely wide wavelength range, it becomes feasible to readily substantialize
optical fiber type devices and applications, such as wavelength conversion and OPA,
optical switches, optical demultiplexers, and sampling oscilloscopes in communication
and non-communication uses.

The above embodiments according to the present invention
enables achievement of a wider bandwidth in the wavelength conversion, OPA, and
so on.