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power of the Raman effect could be reduced to around one
tenth of that for the standard single-mode fibre.10 Based on
calculations, the minimum beam spot size is in the wavelength
region of X = 1-5AC.6 The minimum beam spot sizes for fibres
A and B are estimated to be 112 /im and 1-28 /im. In addition, high coupling efficiency between these fibres and LDs or
SLDs is expected, according to the high-NA value shown in
Table 1.
Conclusion: This experiment has clarified the possibility to
fabricate high-An, small-core single-mode fibres with a low
transmission loss. It was also found that these fibres have
excellent features including bending, optical power intensity
and dispersion. The results obtained suggest that these highAn, small-core single-mode fibres can be applied to nonlinear
optical experiments. Detailed experimental results on nonlinear effects and coupling efficiencies will be reported elsewhere.
S. SUDO
22nd May 1986
T. HOSAKA
H. ITOH
K. OKAMOTO
NTT Electrical Communications Laboratories
Tokai, Ibaraki-ken 319-11, Japan
References
1 CROFT, T. D., and RITTER, J. E.: 'LOW loss dispersion-shifted single-
mode fibre manufactured by the OVD process'. OFC'85, Tech.
dig., 1985, Paper WD2, pp. 94-95
2 YAMAGUCHI, R., NISHIDA, K., ABIRU, T., MIYAMOTO, M., a n d FUKUDA,
o.: 'Effect of an additional ring profile on transmission characteristics of 1-55-jon dispersion shifted fibres'. OFC/IGWO'86, Tech.
dig., 1986, Paper WF3, pp. 96-97
3 KAWACHI, M., TOMARU, s., EDAHIRO, T., and SUDO, s.: 'Fabrication
method of single-mode optical fibre preforms'. US patent 4,345,
928, filed 19 Sept. 1980
normal to the crystal surface arising from the mixing of two
counterpropagating surface-acoustic waves (transverse-vertical
convolver, TVC). On the other hand, Monks et al.1 reported a
new type of convolver using the detection of the bilinear electric polarisation parallel to the crystal surface and perpendicular to the power flow direction of SAWs (transverse-horizontal
convolver, THC). In comparison with TVCs, the THC has the
advantages that its output electrode structure reduces the
possibility of unwanted 'fold-over' convolution from fabrication defects and increases design flexibility. However, a THC
on LiNbO3 has some problems in that its efficiency is less
than that of the highly efficient Y-Z LiNbO3 TVC and that
for the THC there is not such a precise theory as that reported
by Ganguly et al.2 for a TVC. In this letter we propose the
definition of the figure of merit (M-value) and a practically
effective equivalent circuit which have been obtained by the
results of precise analysis for the model of a THC. Next, this
letter presents the results of calculations about the M-value
for a THC with arbitrary crystal orientation and propagation
direction on LiNbO3, and shows the existence of a crystal cut
and the direction of propagation with large M-value and large
electromechanical coupling coefficient K2 of SAWs in
LiNbO3. Also, we report experimental results.
Figure of merit and equivalent circuit for THC: The definition
of the M-value for a TVC2 is not useful for designing a THC3
because it depends on the design parameter of a THC. So, the
M-value for a THC should be given by the quantity which
shows the electrical nonlinearity of the crystal substrate only
and is independent of its design parameter such as frequency
and configurations of crystal substrate and electrode to
compare some THCs with several crystal cuts and directions
of propagation. From this standpoint, we have performed
analysis about the model of a THC shown in Fig. \b by
2<JU
4 SH1BATA, N., KAWACHI, M., SUDO, S., a n d EDAHIRO, T.: 'Low-lOSS
high-numerical-aperture for optical fibre fabricated by VAD
method', Electron. Lett., 1979,15, pp. 680-681
5 BERKEY, G. E.: 'Fabrication of 0-4-N.A. fibres by the outside
process'. OFC/IGWO'86, Tech. dig., 1986, Paper TUG3, pp. 36-37
6 HOSAKA, T., SUDO, s., OKAMOTO, K., and HORIGUCHI, M.: 'Investiga-
tion of single mode fibres with zero dispersion in 1-5 nm wavelength region'. Paper of technical group, TGOQE 85-137, 1985 (in
Japanese)
7 OKAMOTO,
K., TAKADA,
K., KAWACHI,
M., a n d NODA,
J.: ' A l l -
PANDA-fibre gyroscope with long-form stability', Electron. Lett.,
1984, 20, pp.429-430
8 SHIBATA,
N., TSUBOKAWA,
M., OHASHI,
M., a n d
KITAYAMA,
K.:
'Birefringence properties of a coiled single-mode fibre and its use
in a tuned optical amplifier'. CLEO'85, Tech. dig., 1985, Paper
THP4, pp. 226-228
9 TAI, K., and TOMITA, A. : '50 x optical fibre pulse compression at
1-319 //m', Appl. Phys. Lett., 1986, 48, pp. 309-311
10 STOLEN, R. H.: 'Fibre Raman laser', Fibre & Integrated Opt., 1980,
3, pp. 21-51
11 MATSUMURA, H., and SUGANUMA, T.: 'Normalisation single-mode
fibres having an arbitrary index profile', Appl. Opt., 1980, 19, pp.
3151-3158
THEORETICAL AND EXPERIMENTAL STUDY
OF TRANSVERSE-HORIZONTAL
CONVOLVER
Indexing terms: Ultrasonics, Convolvers
The letter presents the results of theoretical and experimental
studies for the transverse-horizontal convolver (THC) fabricated on LiNbO 3 . First, the definition of the figure of merit
for the THC is proposed and, secondly, the existence of the
crystal orientation and the direction of propagation with
high efficiency and large electromechanical coupling coefficient for an LiNbO. SAW THC is shown.
Introduction: Most SAW convolver designs have been based
on the detection of the bilinear electric polarisation field
ELECTRONICS LETTERS 31st July 1986
Vol.22
No. 16
Fig. 1
a Commonly used THC
b Model of THC used for analysis
solving the nonlinear piezoelectric equation of motion subject
to appropriate boundary conditions, as Ganguly et al.2 have
done for a TVC. Thus we have obtained the following results
that the M-value for the THC can be defined by:
M =
(C/W)
(1)
where Q'™ is the root mean square of the short-circuit charge
stored in the output electrodes, P x and P2 are the powers in
the two incident SAWs, / is the beam width of the SAW and b
is the integration length determined by the output electrode.
From this definition and the analysis of output admittance, we
have also obtained an equivalent circuit for the model of the
THC, as shown in Fig. 2a, where / s and C are the short-circuit
current and the static capacitance of the output electrode,
respectively, expressed as
Is =
=
(2)
(es33-(es32)2/e\2)j
(3)
and G is the output conductance which shows the loss arising
from the bulk wave generation. However, G is very small in
comparison with 2coC. Thus we can finally obtain the equivalent circuit for the model of the THC as shown in Fig. 2b.
Although we usually use a THC with the output electrode
835
configuration shown in Fig. la, we can assume the fact that,
even in this electrode configuration, the flux of horizontal
bilinear electric displacement, which is almost within one
,
Fig. 2 Equivalent circuit for THC
wavelength of SAW of the surface, almost ends in the output
electrode at the short-circuit condition. So the abovementioned definition offigureof merit is valid for not only the
model of a THC but also the commonly used THC, and the
equivalent circuit for the commonly used THC can be
obtained by changing the value of the output capacitance of
the model of a THC to the measured value of that of the
commonly used THC. Using all nonlinear constants of
LiNbO3 which had been determined in our laboratoryf we
have calculated M-values for THCs about all independent
crystal cuts and the propagation directions. It is necessary for
a THC to have not only a large M-value but also a large K*
of the SAW. Therefore, we have concluded that the propagation directions near the direction of + 5° from the + Z-axis to
the — 7-axis on the X-cut plane are optimum for an LiNbO3
steering angle of the SAW is 407°. The wavelength at centre
frequency and width of input beams were k = 33-75 /an, corresponding to about 100 MHz, and / = 2 mm, respectively,
and the integration length was b = 8 mm. Thus, we have
obtained experimental results M = 3-3 ± 0-3 x 10"14(C/W)
as plotted in Fig. 3.
Discussion: In the preceding Section we showed the existence
of the crystal cut and the direction of propagation with large
M-value for a THC and large Kj on LiNbO3. Because the
definition offigureof merit for a THC differs from that for a
TVC,2 to compare this (90°, 90°, 95°) THC with the highly
efficient Y-Z TVC as regards efficiency, we have calculated the
internal bilinear conversion factor Finr4 about these two types
of elastic convolver as a function of frequency as shown in
Fig. 4. From this Figure we can find the fact that, at high
frequency, the (90°, 90°, 95°) THC and Y-Z TVC of LiNbO3
have almost the same efficiency.
Y. CHO
K. YAMANOUCHI
Research Institute of Electrical Communication
Tohoku University
Sendai980, Japan
References
1
— M
-K
^ - ^ ^
$ A
2
,
.
. it
o
T
o
3<
3
\
X
Z
/
-2
y
\
1
A /
' \J
/
i
i
r~\ \ /
n
0
XY
30
4
V
90
150 180°
120
X Z .degree
Fig. 3 Theoretical and experimental values of figure of merit for THC
and K2 of SAW on X-cut ofLiNbO3
THC, as shown in Fig. 3. This crystal cut and propagation
direction can be identified through Euler angles of (90°, 90°,
95°). So, in this letter we call the THC with this crystal cut
and propagation direction the (90°, 90°, 95°) THC.
Experiments: To confirm the above-mentioned fact, we have
measured the M-value of the (90°, 90°, 95°) THC whose beam-
KINO, G. S., LUDVIK, S., SHAW, H. J., SHREVE, W. R., WHITE, S. J., a n d
WINSLOW, D. K.: 'Signal processing by parametric interactions in
delay-line devices', IEEE Trans., 1973, SU-20, pp. 162-173
5
LIM, T. c , KRAUT, E. A., and THOMPSON, R. B.: 'Nonlinear materials
for acoustic-surface-wave convolver', Appl. Phys. Lett., 1972, 20,
pp. 127-128
LASER COUPLING TO SINGLE-MODE FIBRE
USING GRADED-INDEX LENSES AND
COMPACT DISC 1-3 urn LASER PACKAGE
Indexing terms: Optical communications, Optical couplers
A 1-3 fim laser in a compact disc package is coupled to
single-mode fibre using two graded-index lenses in a nearly
confocal scheme. An increase in the alignment tolerance at
the lens-lens interface by a factor of six suggests the design
for a potentially very low-cost connectorised laser package.
The coupling efficiency of approx. 6% (—12 dB) is shown to
be adequate for local loop applications.
-60
-70
-80
(90°. 90°. 95°) THC
-90
YZ TVC
10
10
10 J
frequency, MHz
Fig. 4 Internal bilinear conversion factor Fint against frequency for (90°,
90\ 95°) THC and Y-Z TVC
In this calculation, we have taken the parameters as the integration
length b = 30 mm, beam width of SAW / = 2 mm, thickness of
substrate d = 0-5 mm and load resistance RL = 50 Q for both types
of convolver. The value of the figure of merit for the Y-Z TVC,
M = 1-21 x 10~ 4 Vm/W, has been used 5 and, for a (90°, 90°, 95°)
THC, we have calculated Fim about the model of the THC shown
in Fig. 16
t CHO, Y., and YAMANOUCHI, K. : submitted to J. Appl. Phys.
836
MONKS, T. J., PAIGE, E. G. s., and WOODS, R. a : 'SAW and SSBW
convolvers utilising bilinear field in various directions'. Proceedings of ultrasonics symposium, 1983, pp. 402-405
1
\
60
3
2
\
MONKS, T., PAIGE, E. G. s., and WOODS, R. c.: 'SAW convolvers using
the transverse-horizontal bilinear field', Electron. Lett., 1983, 19,
pp. 466-467
2 GANGULY, A. K., and DAVIS, K. L. : 'Nonlinear interactions in degenerate surface acoustic wave elastic convolvers', J. Appl. Phys.,
1980, 51, pp. 920-926
\
\
22nd May 1986
Introduction: In new transmission applications such as singlemode distribution in the subscriber loop, very low-cost, highspeed light sources are needed. For the loop environment,
these devices must also operate over wide temperature ranges
( —40°C to +85°C). Injection lasers are ideal for the speeds
being considered (as high as 560 Mbit/s). Present laser prices,
however, are very high due to packaging complexity and yield
when selected according to stringent requirements appropriate
for long-haul applications. Prices would be reduced significantly if simple packaging schemes could be utilised.
Many conventional packaging approaches involve direct
fibre-to-laser coupling, or coupling with a single lens element,
usually a part of the fibre end. Although high coupling efficiencies (40 to 60%) are achieved, such schemes are very sensitive to lateral displacements, making their use over wide
temperature ranges questionable. Alternative, confocal lensing
schemes have also been used,1"3 with two or more lens elements. This technique relaxes lateral alignment tolerances by
trading off lateral displacement sensitivity for increased
angular sensitivity and slightly reduced coupling efficiency. In
this letter we examine a confocal arrangement, which, in conELECTRONICS LETTERS 31st July 1986 Vol. 22
No. 16
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