Optical fiber for frequency conversion

An optical fiber for frequency conversion, has an annular index profile structure for obtaining zero order phase matching and optimum overlap between the fibers's resonant propagation modes, one propagating the wave w and the other the wave kw where 2.ltoreq.k.ltoreq.4 for at least one wavelength lying in the range 0.4 .mu.m to 2.6 .mu.m, with the index step .delta.n in the ring lying in the range 2.times.10.sup.-2 and 5.times.10.sup.-2, the inside radius r.sub.i of the ring lying in the range 0.5 .mu.m to 1.5 .mu.m, and the outside radius r.sub.e of the ring lying in the range 2 .mu.m to 3.5 .mu.m.

The present invention relates to an optical fiber for frequency conversion, 
in particular for frequency doubling and tripling. 
Frequency doubling in a material is a property of the material whereby it 
converts a beam of frequency .omega. into a beam of frequency 2.omega.. If 
.omega. corresponds to a wavelength of 1064 nm, then the harmonic lies in 
the green at 532 nm. This is a non-linear second order effect. 
The doubling phenomenon is forbidden in materials possessing a center of 
inversion, e.g. homogeneous glasses. It is therefore necessary to break 
this symmetry in the fiber in order to observe this conversion. The 
article by M. E. Fermann, L. Li, M. C. Farries and D. N. Payne entitled 
"Frequency-doubling by modal phase matching in poled optical fibers", 
published in Electronics Letters 7/1988, 24 No. 14, p. 894, specifies that 
the fiber must possess active sites such as point defects located on or 
around atoms of germanium or phosphorus which are highly asymmetrical, 
i.e. giving rise to considerable hyperpolarizability. However, these sites 
must be distributed in a manner which is not centro-symmetrical so as to 
ensure that the non-linear susceptibility is not zero. 
The problem that arises is obtaining a high degree of conversion 
efficiency. To do this, it is necessary for the pumping wave and the 
emitted wave to travel at the same speed, i.e. the effective indices of 
the fiber at .omega. and at 2.omega. should be equal. 
At present, known fibers do not satisfy this condition. They satisfy a 
different condition giving rise to less intense conversion: this condition 
is the coefficient of non-linearity being modulated in the z direction by 
a periodic function of period .lambda., where: 
##EQU1## 
(See the article by M. C. Farries, P./ St. J. Russel, M. E. Fermann and D. 
N. Payne entitled "Second harmonic generation in an optical fiber by self 
written X.sup.(2) grating", published in Electronics Letters (1987) 23 
(7), pp. 322-323.) This article describes generating second and third 
harmonics in optical fibers having a step index profile (or a triangular 
profile) obtained by forming such a grating. The breaking of symmetry 
required for doubling is produced spontaneously or artificially by 
interaction of the material with light at 3.omega. or at 2.omega.. Local 
susceptibility at the point (r, .theta., z) is constructed from this 
interaction; its three-dimensional distribution is determined by the 
overlap of the modes that support the waves .omega. and 2.omega.. Since 
the propagation mode of w is imposed, the mode for 2.omega. is free ab 
initio, and is determined by a condition for maximizing overlap. 
Nevertheless, conversion efficiency remains low, about 1%. 
The object of the present invention is to provide an optical fiber whose 
conversion efficiency is much greater than that of optical fibers known in 
the past. 
The present invention provides an optical fiber for frequency conversion, 
characterized by the fact that it has an annular index profile structure 
for obtaining zero order phase matching and optimum overlap between the 
fiber's resonant propagation modes, one propagating the wave .omega. and 
the other the wave k.omega. where 2.ltoreq.k.ltoreq.4 for at least one 
wavelength lying in the range 0.4 .mu.m to 2.6 .mu.m, with the index step 
.delta.n in the ring lying in the range 2.times.10.sup.-2 and 
5.times.10.sup.-2, the inside radium r.sub.i of the ring lying in the 
range 0.5 .mu.m to 1.5 .mu.m, and the outside radius r.sub.e of the ring 
lying in the range 2 .mu.m to 3.5 .mu.m. 
Preferably, for frequency doubling, .delta.n lies in the range 
2.times.10.sup.-2 and 3.times.10.sup.-1. 
Preferably, for frequency tripling, .delta.n lies in the range 
3.times.10.sup.-2 and 5.times.10.sup.-2. 
The present invention also provides a laser that makes use of the 
above-defined fiber.

FIG. 1 is a highly diagrammatic representation of index variations in the 
core of a silica optical fiber of the invention having an annular index 
profile. When r lies in the range r=r.sub.i (r interior) to r=r.sub.e (r 
exterior), the index increases by an amount .delta.n. This index 
difference may be obtained by doping using oxides of germanium and/or 
phosphorus. French patent number 87 14 286 filed Oct. 16, 1987 describes a 
method of manufacturing such a fiber. 
FIGS. 2 to 5 are graphs showing variations in the effective index n.sub.eff 
(plotted up the Y axis) as a function of wavelength .lambda. 
(log.sub.10.lambda. plotted along the X axis) for various propagation 
modes in fibers having different .delta.n, r.sub.i, and r.sub.e. 
LP.sub.01, LP.sub.02, LP.sub.03, and LP.sub.04 correspond to zero order 
modes of azimuth 0, 1, or 2; LP.sub.11, LP.sub.12, LP.sub.13, and 
LP.sub.14 correspond to first order modes, LP.sub.21, LP.sub.22, 
LP.sub.23, to second order modes, etc. 
In all of these graphs, the log.sub.10.lambda. difference for two modes 
having the same effective index is log.sub.10 2 (i.e., approximately 0.3) 
for .omega. and 2.omega.. It is log.sub.10 3 l (i.e., approximately 0.5) 
for .omega. and 3 .omega.. 
In all cases, a wave .omega. is injected into the fiber in mode LP.sub.01. 
FIG. 2 also includes a curve showing the variation of the index n of silica 
SiO.sub.2 as a function of .lambda.. 
EXAMPLE I 
A fiber was taken having an outside diameter of 125 .mu.m with a ring 
having an index step .delta.n=3.times.10.sup.-2, an inside ring radius 
r.sub.i equal to 0.66 .mu.m and an outside radius r.sub.2 equal to 2 
.mu.m. By moving along the LP.sub.01 dispersion curve (FIG. 2) it can be 
seen that optimum matching for conversion from .omega. to 2.omega. takes 
place at .lambda.=1.18 .mu.m. Secondary tuning points exist at 0.93 .mu.m 
between LP.sub.01 and LP.sub.22, and at 0.77 .mu.m between LP.sub.01 and 
LP.sub.03. 
EXAMPLE II 
A fiber was taken having an outside diameter 125 .mu.m and a ring having an 
index step .delta.n=3.times.10.sup.-2, the inside radius being equal to 1 
.mu.m and the outside radius being equal to 3 .mu.m. It can be seen in 
FIG. 3, that zero order phase matching and optimum mode overlap for 
.omega. and 2.omega. exist over a very wide range of wavelengths, from 
1.54 .mu.m to 2.07 .mu.m, i.e. about 0.5 .mu.m. 
Such a solution is most advantageous since such a fiber is not selective 
and phase matching is not critical. 
For constant .delta.n, while causing r.sub.i and r.sub.e to vary over the 
ranges specified above, anon-critical range of wavelengths of up to 0.4 
.mu.m can be found. At constant .delta.n, there is always a pair (r.sub.i, 
r.sub.e) within the ranges mentioned above for which a non-critical range 
of wavelengths of up to 0.4 .mu.m can be found for the desired wavelength. 
The non-critical range shifts towards shorter wavelengths as the thickness 
of the ring diminishes. 
Such a non-critical range of wavelengths makes it possible to obtain 
frequency doubling even when pumping sources present a degree of 
dispersion in emission frequency due to manufacturing tolerances. 
EXAMPLE III (see FIG. 4) 
A fiber was used having the same .delta.n=3.times.10.sup.-2, the inside 
radius r.sub.i was equal to 1 .mu.m and the outside radius r.sub.e was 
equal to 2.5 .mu.m. Optimum matching was still obtained between LP.sub.01 
and LP.sub.02 for 1.32 .mu.m, together with secondary matching for 104 
.mu.m, 0.91 .mu.m, and 0.77 .mu.m. 
Examples II and III show that starting from a wavelength such as 1.32 .mu.m 
or 1.54 .mu.m, i.e. within the telecommunications window, there exists a 
fiber structure having a ring and .delta.n=3.times.10.sup.-2 for which it 
is possible to obtain optimum matching for .omega. and 2.omega.. 
EXAMPLE IV 
Returning to the fiber of Example II and the graph of FIG. 3, such a fiber 
may provide matching enabling conversions in cascade: a first conversion 
from 1.82 .mu.m to 0.91 .mu.m (LP.sub.01 to LP.sub.02), followed by energy 
transfer at 0.91 .mu.m from LP.sub.02 to LP.sub.01, followed by conversion 
from 0.91 .mu.m to 0.45 .mu.m (LP.sub.01 to LP.sub.03). 
EXAMPLE V 
A fiber was used having .delta.n=5.times.10.sup.-2, with an inside radius 
r.sub.i of 1 .mu.m and an outside radius r.sub.e of 3 .mu.m. .delta.n of 
this value may be obtained using oxides of germanium or phosphorus as 
dopants (see the article by R. B. Dyott, J. R. Cozens, D. G. Morris 
entitled "Preservation of polarization in optical fiber waveguides with 
elliptical cores" published in Electroncis Letters 21/1979, 15, No. 13, 
pp. 380-382). The graph of FIG. 5 shows a matching optimum between .omega. 
and 3.omega. for .lambda.=1.64 .mu.m and for .lambda.=0.546 .mu.m. It may 
be observed that there is simultaneous matching between .omega. and 
2.omega. and between .omega. and 3.omega. for 1.52 .mu.m, and secondary 
matching between .omega. and 2.omega. for 1.19 .mu.m. 
In all of the preceding examples, conversion efficiency for 2.omega. is not 
less than 50% with a pumping wave of about 400 watts and a fiber that is a 
few meters long. 
An additional feature of fibers of the invention should also be observed. 
These fibers always have large .delta.n, of not less than 
2.times.10.sup.-2. In such cases, a small degree of ellipticity nearly 
always appears in practice during manufacture as can be measured by 
birefringence, and this ellipticity turns out to be advantageous for 
facilitating phase matching. The fiber has slightly different effective 
indices along two orthogonal axes and this provides a little latitude in 
the wavelength values. 
In general, for all annular fibers of the invention, there always exists a 
wavelength lying in the range 0.4 .mu.m to 2.6 .mu.m for which there is a 
matching optimum between .omega. and 2.omega.. conversely, if the 
wavelength is specified, then it is always possible to find at least one 
fiber of the invention for which optimum matching occurs between .omega. 
and 2.omega.. 
A most advantageous application of fibers of the invention lies in 
converting the optical frequencies used in optical telecommunications 
windows (800 nm, 1300 nm, 1550 nm, and 2550 nm) so as to facilitate 
detection thereof. 
A fiber of the invention is particularly advantageous in an optical fiber 
autocorrelator. 
The technique of optical autocorrelation for evaluating the duration of 
ultra-short light pulses emitted in the infrared is described, in 
particular, in the article by U. Osterberg and W. Margulis, entitled 
"Autocorrelation of short pulses using a single mode fiber" published in 
IEEE J. Quant. Electroncis, QE-24, October 1988, pp. 2127-2129. 
There follows a description of a laser making use of an optical fiber of 
the invention. Optical fiber lasers are already known. They include fibers 
doped with various rare earths. Table I below shows the ions already in 
use and the corresponding emission wavelengths. 
TABLE I 
______________________________________ 
Ion Laser .lambda. (.mu.m) 
______________________________________ 
Nd.sup.3+ 0.94/1.06-1.09/1.4 
Er.sup.3+ 1.54 
Tm.sup.3+ 1.8 
Pr.sup.3+ 1.07 
Sm.sup.3+ 0.65 
Yb.sup.3+ 1.02-1.14 
______________________________________ 
When a doped fiber laser of this type is operated under mode locked 
triggered conditions, for example, the peak power inside the cavity at the 
laser wavelength may be as much as 6 kW to 7 kW (see the article by I. N. 
Duling, L. Goldberg, J. F. Weller published in Electronics Letters, 24 
(1988), p. 1333). 
In the past, if an emission wavelength was desired in the visible spectrum, 
a frequency doubler device was placed outside the cavity. 
In a laser making use of a fiber of the invention, the fiber is used both 
as a laser amplifier medium and as an intracavity frequency doubler. 
The block diagram of FIG. 6 shows a segment of fiber 11 of the invention 
doped with a lanthanide ion, two mirrors 12 and 13 defining an optimum 
resonator, a pumping source 14 matching the doping in the fiber under 
consideration, with injection taking place into the segment of fiber 11 by 
means of a focusing device 17. The cavity may optionally contain a trigger 
15, a mode locking device 16, and collimating optics 18. The transmittance 
of the inlet mirror 12 is maximal at the pumping wavelength and minimal at 
the laser wavelength .lambda. and at the wavelength .lambda./2. The 
transmittance of the outlet mirror is minimal at the pumping wavelength 
and at the laser wavelength .lambda. and it matches the wavelength 
.lambda./2 for the utilization under consideration. 
If a laser emission wavelength is selected, than a rare earth ion is 
selected (cf. Table I). This fixes a pumping wavelength compatible with a 
silica-based fiber doped with the selected rare earth ion. Given the 
emission wavelength of the laser, the parameters of the germanium doped 
silica ring corresponding to the core of the invention suitable for 
obtaining frequency doubling of the laser emission can then be defined. It 
is then possible to determine the LP.sub.01 profile and consequently to 
determine the most effective distribution of the rare earth ion in the 
fiber. 
By way of example, a fiber of the invention doped with neodymium could be 
used. In this case, a pumping wavelength of 0.82 .mu.m (0.8 
.mu.m.ltoreq..lambda.p.ltoreq.0.830 .mu.m) could be used. This wavelength 
may be delivered by a pumping source constituted by an array of power 
laser diodes. 
Depending on the exact composition of the vitreous matrix of the optical 
fiber under consideration, the emission wavelength of the neodymium laser 
lies in the range 1.06 .mu.m to 1.09 .mu.m. When using a fiber of the 
invention which is highly doped with germanium, the laser emission 
wavelength is close to 1.09 .mu.m. 
By causing this laser to operate under locked mode conditions and under 
triggered mode conditions, the highest peak pulse power may be around 
several kilowatts within the optical fiber. At this power level, the 
conversion efficiency may be about 50%. The resulting wavelength is about 
0.545 .mu.m. 
Naturally the invention is not limited to the embodiments described above.