- Email: [email protected]
mixer to determine spectral attenuation of graded index fibers
OPTICS COMMUNICATIONS
Volume 40, number 2
A COMBINED MODE-FILTER/MIXER
15 December 1981
TO DETERMINE SPECTRAL ATTENUATION
OF GRADED INDEX FIBERS
T. Le HIEP and R.Th. KERSTEN Institut fiir Hochfrequenztechnik, Technische DI 000 Berlin IO, Fed. Rep. Germany
Universitiit Berlin,
Received 11 September 198 1
The measurement of spectral dependent attenuation of graded index fibers using the cutback method assumes that an equilibrium mode distribution exists even after a short length of the fiber to be measured. We have reviewed and analyzed the losses caused by bends of multimode fibers. Using the results an easy to handle S-shaped mode-filter/mixer is investigated by far-field pattern and attenuation measurements. It is proved that the mode-filter/mixer is superior to the so called 70% excitation and is usable for estimating mode coupling and intrinsic fiber loss.
1. Introduction
Measurements of attenuation of multimode gradedindex fibers are difficult to perform because of the great influence of launching conditions [I]. Several solutions have been proposed to approximate equilibrium mode distribution (EMD) [2]. The application of a simple dummy fiber seems to be unsatisfying because in fibers with low mode conversion the so-called “steady state” mode distribution occurs after ten and more kilometers only [3]. To avoid this disadvantage one can use a special dummy fiber, which is composed of proper combinations of graded and step index fibers [4]. However it is still unknown, how far the connection “dummy fiber/test fiber” influences the field distribution and by that destroys the steady state mode distribution. Another proposal is the 70% mode-volume excitation, also called matched beam method (MBE), favored by some standardization groups [S-7]. This method assumes, that core diameter and numerical aperture of the fiber to be tested are known in advance. This procedure is therefore only advantageous, when standardized fibers are measured, i.e. in production. To avoid the excitation of leaky modes and to excite lossy higher-order modes by a certain amount only, the light source is coupled into the fiber front end using a spotsize and a numerical aperture of 70% of those of the fiber. 0 030-4018/81/0000-OOOO/$
02.75 0 1981 North-Holland
Ceckeler [8] used the phase-space diagram, well known from physics, to describe the mode propagation and distribution in light waveguides. He showed that, by exciting a graded index fiber with parabolic profile by the matched beam method, one can theoretically avoid to excite leaky modes; this is true only for fibers with a parabolic profile. The disadvantage of the method is the relative complicated adjustment of the input light beam: For a fiber-NA of 0.2, which corresponds to an acceptance angle of about 11 degrees, a light cone distorted by 1 degree only can excite higher, order modes too much as well as some leaky modes. A mode-filter composed of an aluminum-mandrel with 10 mm in diameter is used at BelI Laboratories to attenuate the higher-order modes and to decouple leaky modes. The fiber is wrapped five times around the mandrel. However, measurements for comparison showed, that there were deviations between the measured results [9], which may be due to the uncontrolled fiber tension at the mandrel as well as the fact that curvature occurs in one direction only. We have investigated an S-shaped combined modefilter/mixer [ 10,111, which can be handled easily, even in a fully automatic measuring setup. A steady mode state distribution is already attained after a short piece of fiber length (ca. 2 m). With our mode-filter/mixer we have obtained very good reproducible results by controlling the fiber tension. 111
Volume
40, number
2
OPTICS COMMUNICATIONS
In the next section we will describe briefly the properties of this mode-filter/mixer. Subsequent to it we will discuss the results of the attenuation measurements using this device.
2. The mode-filter/mixer 2.1. Principle and construction of the device As mentioned above one can use a mandrel wrap mode-filter to excite the EMD in a fiber. Light, which is guided in a glass-fiber, suffers from radiation loss at the fiber curvatures. Gloge [ 121 analyzed this curvature loss by using the results of Miller and Marcatili [13]. The extinction coefficient for a mode with propagation constant /I, which is not far from cut-off, can be calculated by (y =
2
r2K9exp[-2i 7(r)&], 7
0)
a
where -y2(r) = p2R2/(r + R)2 - nzk2, rn = R/3/n,k - R and k is the free-space propagation constant, R bending radius, n, refractive index of the cladding, and a core radius. For graded-index fibers Gloge has made an approach to determine the extinction coefficient og by
15 December
width narrows as it shifts. But the higher-order modes are less influenced by a bent fiber axis. Instead of narrowing, their field intensity at the core-cladding boundary opposite to the center of curvature increases and therefore contributes the most significant part of the radiation loss. Based on the geometric optics approach, Winkler et al. [ 151 made detailed calculations of the bending losses in multimode fibers. We will summarize all the above mentioned results shortly. The loss caused by the fiber curvatures is composed of two main parts: - The transition loss; it is due to mode conversion as modes of a straight fiber transform to those in a curved one. - The pure bending loss; it occurs because with increasing distance from the center of curvature the local phase velocity equals the velocity of light, guidance ceases and energy radiates away. To use both of the effects, we have constructed a device, that is a combination of a mode-filter and a modemixer. The principles of our mode-filter/mixer is shown in fig. 1. It is composed of two aluminum bars with revolving mandrels in ball-bearings. After placing the input end of the test fiber between the two mandrel rows one can drive the gliding bar downwards so that the fiber is S-shaped around the mandrel wraps. The weight is used to control the fiber tension. We have made far-field pattern (FFP) measurements on near
‘Ye = 2n(r)k(Oz - 88,) / X exp[-in(r)kR(f?z
- 00, - 2a/R)1312,
112
,flber
(2)
where 0 c is the critical angle, 0 propagation angle, and n(r) local core index. This expression gives the dependence of the curvature loss from the propagation angle. For angles close to 8,, the loss in the waveguide is very high and therefore high-order modes not far from cut-off are attenuated strongly. Marcuse [ 141 studied the field deformation in optical fibers caused by curvature; he stated that the lowest-order HE, l-mode is particularly affected by a curved fiber axis. It shifts away from the axis in the direction opposite to the center of curvature, and its
1981
vakuum chuck
controlled strength
vakuum chuck
Fig. 1. Mode-filter/mixer
assembly.
-
Volume 40, number 2
OPTICS COMMUNICATIONS
15 December 1981
FL3 small
surface
ref.
Ge-PIN
biascirCult
lock-in-
amplifier
Fig. 2. Experimental setup.
end (NE, 2-5 m) and far end (FE, corresponding to the whole fiber length, 1-3 km) to investigate the steady-state mode distribution. With mandrels of different diameters (4 mm to 16 mm in steps of 1 mm) we could vary the effective loss as well as its influence to the FFP. The number (8-20) of mandrels determines how many times the process mode-filter/mixer is repeated. 2.2. Discussion of the results Three standard, low loss graded-index fibers (see table 1) with different mode coupling coefficients are used for comparison within all measurements. The fully automated setup is shown in fig. 2. Both numerical aperture and spot size of the launched beam can Table 1 List of measured fibers ____ length in m Fiber
#l #2 #3
NAloo% A=lpm
NE
FE
5 2 5
1235 1353 2490
0.217 0.19 0.173
be controlled precisely, so that the 70% excitation could be adjusted correctly. However, fibers are overfilled (NA 0.28, spot diameter 60 r.lm) at the front end if the mode-filter/mixer is used. All FFP-measurements have been performed with chopped (-600 Hz) light at a wavelength h = 1 pm. We used a Ge-PIN-detector, cooled down to -25°C to reduce the dark current; the detector can be moved by stepmotors in both x- and y-direction, transversal to the fiber axis; step-size was 1 pm, accuracy about 0.1 pm [l 11. Use of lock-in signal detection increases the sensitivity and resolution by using large time constants. As demonstrated by fig. 3, FFPs on both NE and FE of a graded index fiber can be measured very accurately. Some of the results are shown in fig. 4. The differences of NA (given by 50% widths of FFP at FE and NE) normalized to NA
core/cladding diameter in pm
491124 51/121 561135
attenuation in dB/km h=ll.rm
X+m
2.0 2.0 1.1
1.6 0.4 0.08
113
Volume
40, number
OPTICS COMMUNICATIONS
2
15 December high
low -
modes
_
.
cl
0 MBE modefi(ter
4turns
l
- 0,05
t
fiber
1981
,
10mm diameter
3
IGg. 5. PI:P-deviation
Fig. 3. FFPs on near end (NE) and far end (FE). of the undisturbed fiber, are plotted against the diameter of the mode-filter/mixer mandrels. According to Kaiser [2] the 99% width of FFP should be taken into account to provide that highest-order modes are not excited too much. Comparing FFPs of NE and FE (fig. 5) we prove that highest-order modes are not overfilled, but even sometimes underfilled at NE. The
o modefILter L turns q modefilter 0 turns x modefllter 6turns A modefilter 1, turns + modefIlter 8 turns
Fig. 4. FFPs versus mandrel
114
diameter
of modefilter/-mixer.
reason for that is assumed to be the high index primary coating of the fibers. Therefore the 50% width of FFP gives evidence in this special case likewise. Eg. 4 demonstrates also that 8 S-ahaped bounds, 8 mm to 10 mm in diameters are very well suited to excite the EMD. Deviations between FFPs of NE and FE are much smaller compared to MBE (see also fig. 5). The measurements allow us to distinguish between fibers of strong or low mode coupling. It has been proved experimentally that the mandrel surface is of small importance. The use of teflon or aluminum caused no difference. A fiber tension of about 40 p seemed to be suitable. The results have been verified by attenuation measurements. Normally differences using either high accurate MBE or the mode-filter/mixer combination were much smaller than the resolution of the measurement setup (
at our disposal
Volume 40, number 2
OPTICS COMMUNICATIONS
15 December 198 1
I..---.-.-.-I -------F --/ ._... S.&T3 l- _.-
10.0 6.8
-1 ___
4.0
-..
.-
I
/
-~
--I
---~---
E < m2.0 a
c
.d
I”
.B
.9
1.E
i
1.1
J I.3
1.2
wavelength
in
1.4
1.5
1.6
1.7
pm
Fig. 6. Attenuation results for various launching conditions.
fiber is overfilled by high NA and large spot size (#S). A mode-filter/mixer of 8 turns and 10 mm in diameter causes a wavelength independent loss of 2.0 dB at NE and 1.8 dB at FE with respect to intensity without mode-filter/mixer for special type of fiber. The attenuation difference between NE and FE is almost equal to the intrinsic loss (X + 00) of the whole fiber (0.184 dB), which can be attributed to microbending and mode conversion loss along the fiber. These results are also in very good agreement with calculations by Winkler et al. [ 151 for a bent graded index fiber. For 8 turns of fiber on a 10 mm diameter mandrel, corresponding to 125 mm effective length of the bend, a pure loss of about 1.5 dB is calculated. The rest is due to transition loss which, of course, depends on the level of mode conversion in the fiber.
3. Conclusion To improve accuracy in fiber attenuation measurement, to decrease the influence of launching conditions, and for easy handling we have developed and constructed a mode-filter/mixer by which the so called mode equilibrium distribution of a fiber can be
excited easily. The mode-filter/mixer consists of an assembly of 8 aluminum mandrels of 8 mm to 10 mm in diameter. The fiber is wounded S-shaped around the mandrels; a fiber tension of ca. 40 p is suitable for exciting the EMD in standard low-loss graded-index fibers. The mode-filter/mixer is suited for use in automated measuring setups and is superior to MBE, especially for fibers with strong mode coupling. Fundamental investigations of the mode-filter/mixer using three different types of fibers have been performed by attenuation measurements. The mode-filter/mixer assembly can be used to estimate mode coupling and intrinsic fiber loss. We would like to thank Prof. Dr. D. Krause, Schott& Gen., for fruitful discussions as well as for supplying the fibers. This work is supported by Bundesministerium fur Forschung und Technologie. The authors alone are responsible for the contents.
References [l] P. Kaiser, Trans. of IECE of Japan E61 (1978) 225. [ 21 P. Kaiser, Techn. Digest Symposium on Optical fiber measurements, Boulder 1980, p. 11.
115
Volume
40, number
2
OPTICS COMMUNICATIONS
[3] G.T. Holmes, Techn. Digest, 6th ECOC, York 1980, p. 144. [4] CCITT, Reproducible measurements of baseband frequency responses of (X-fibers by excitation with a SI fiber, 46 E/WG 1 (Japan) Oct. 1979. [S] M.P. Smid, Techn. Digest Symposium on Optical fiber measurements, Boulder 1980, p. 121. [6] F. Bigi and G. Bonaventura, ibid., p. 129. [7] R.E. Love, ibid., p. 135. [8] S. Geckeler, Siemens Forsch. u. Entwickl.-Ber. 10 (1981) 162. [9] A.H. Cherin and W.B. Gardner, Laser Focus 16 (1980) 60.
116
[lo]
[ 1 l]
[12] [13] [14] [ 151
15 December
198 1
T. Okoshi, J.C. Chang and S. Saito, Record of Technical Group, IECE Japan, Opt. Quant. Electron 79 (1979) 73. R.Th. Kersten and T. LeHiep: Techn. Digest Symposium on Measurements in optical communications, Berlin 1980, p. 66. D. Gloge, Appl. Optics 11 (1973) 2506. E.A.J. Marcatili and S.E. Miller, Bell Syst. Techn. J. 48 (1969) 2161. D. Marcuse, J. Opt. Sot. Am. 66 (1976) 311. C. Winkler, J.D. Love and A.K. Ghatak, Opt. Quant. Electr. 11 (1979) 173.
Volume 40, number 2
A COMBINED MODE-FILTER/MIXER
15 December 1981
TO DETERMINE SPECTRAL ATTENUATION
OF GRADED INDEX FIBERS
T. Le HIEP and R.Th. KERSTEN Institut fiir Hochfrequenztechnik, Technische DI 000 Berlin IO, Fed. Rep. Germany
Universitiit Berlin,
Received 11 September 198 1
The measurement of spectral dependent attenuation of graded index fibers using the cutback method assumes that an equilibrium mode distribution exists even after a short length of the fiber to be measured. We have reviewed and analyzed the losses caused by bends of multimode fibers. Using the results an easy to handle S-shaped mode-filter/mixer is investigated by far-field pattern and attenuation measurements. It is proved that the mode-filter/mixer is superior to the so called 70% excitation and is usable for estimating mode coupling and intrinsic fiber loss.
1. Introduction
Measurements of attenuation of multimode gradedindex fibers are difficult to perform because of the great influence of launching conditions [I]. Several solutions have been proposed to approximate equilibrium mode distribution (EMD) [2]. The application of a simple dummy fiber seems to be unsatisfying because in fibers with low mode conversion the so-called “steady state” mode distribution occurs after ten and more kilometers only [3]. To avoid this disadvantage one can use a special dummy fiber, which is composed of proper combinations of graded and step index fibers [4]. However it is still unknown, how far the connection “dummy fiber/test fiber” influences the field distribution and by that destroys the steady state mode distribution. Another proposal is the 70% mode-volume excitation, also called matched beam method (MBE), favored by some standardization groups [S-7]. This method assumes, that core diameter and numerical aperture of the fiber to be tested are known in advance. This procedure is therefore only advantageous, when standardized fibers are measured, i.e. in production. To avoid the excitation of leaky modes and to excite lossy higher-order modes by a certain amount only, the light source is coupled into the fiber front end using a spotsize and a numerical aperture of 70% of those of the fiber. 0 030-4018/81/0000-OOOO/$
02.75 0 1981 North-Holland
Ceckeler [8] used the phase-space diagram, well known from physics, to describe the mode propagation and distribution in light waveguides. He showed that, by exciting a graded index fiber with parabolic profile by the matched beam method, one can theoretically avoid to excite leaky modes; this is true only for fibers with a parabolic profile. The disadvantage of the method is the relative complicated adjustment of the input light beam: For a fiber-NA of 0.2, which corresponds to an acceptance angle of about 11 degrees, a light cone distorted by 1 degree only can excite higher, order modes too much as well as some leaky modes. A mode-filter composed of an aluminum-mandrel with 10 mm in diameter is used at BelI Laboratories to attenuate the higher-order modes and to decouple leaky modes. The fiber is wrapped five times around the mandrel. However, measurements for comparison showed, that there were deviations between the measured results [9], which may be due to the uncontrolled fiber tension at the mandrel as well as the fact that curvature occurs in one direction only. We have investigated an S-shaped combined modefilter/mixer [ 10,111, which can be handled easily, even in a fully automatic measuring setup. A steady mode state distribution is already attained after a short piece of fiber length (ca. 2 m). With our mode-filter/mixer we have obtained very good reproducible results by controlling the fiber tension. 111
Volume
40, number
2
OPTICS COMMUNICATIONS
In the next section we will describe briefly the properties of this mode-filter/mixer. Subsequent to it we will discuss the results of the attenuation measurements using this device.
2. The mode-filter/mixer 2.1. Principle and construction of the device As mentioned above one can use a mandrel wrap mode-filter to excite the EMD in a fiber. Light, which is guided in a glass-fiber, suffers from radiation loss at the fiber curvatures. Gloge [ 121 analyzed this curvature loss by using the results of Miller and Marcatili [13]. The extinction coefficient for a mode with propagation constant /I, which is not far from cut-off, can be calculated by (y =
2
r2K9exp[-2i 7(r)&], 7
0)
a
where -y2(r) = p2R2/(r + R)2 - nzk2, rn = R/3/n,k - R and k is the free-space propagation constant, R bending radius, n, refractive index of the cladding, and a core radius. For graded-index fibers Gloge has made an approach to determine the extinction coefficient og by
15 December
width narrows as it shifts. But the higher-order modes are less influenced by a bent fiber axis. Instead of narrowing, their field intensity at the core-cladding boundary opposite to the center of curvature increases and therefore contributes the most significant part of the radiation loss. Based on the geometric optics approach, Winkler et al. [ 151 made detailed calculations of the bending losses in multimode fibers. We will summarize all the above mentioned results shortly. The loss caused by the fiber curvatures is composed of two main parts: - The transition loss; it is due to mode conversion as modes of a straight fiber transform to those in a curved one. - The pure bending loss; it occurs because with increasing distance from the center of curvature the local phase velocity equals the velocity of light, guidance ceases and energy radiates away. To use both of the effects, we have constructed a device, that is a combination of a mode-filter and a modemixer. The principles of our mode-filter/mixer is shown in fig. 1. It is composed of two aluminum bars with revolving mandrels in ball-bearings. After placing the input end of the test fiber between the two mandrel rows one can drive the gliding bar downwards so that the fiber is S-shaped around the mandrel wraps. The weight is used to control the fiber tension. We have made far-field pattern (FFP) measurements on near
‘Ye = 2n(r)k(Oz - 88,) / X exp[-in(r)kR(f?z
- 00, - 2a/R)1312,
112
,flber
(2)
where 0 c is the critical angle, 0 propagation angle, and n(r) local core index. This expression gives the dependence of the curvature loss from the propagation angle. For angles close to 8,, the loss in the waveguide is very high and therefore high-order modes not far from cut-off are attenuated strongly. Marcuse [ 141 studied the field deformation in optical fibers caused by curvature; he stated that the lowest-order HE, l-mode is particularly affected by a curved fiber axis. It shifts away from the axis in the direction opposite to the center of curvature, and its
1981
vakuum chuck
controlled strength
vakuum chuck
Fig. 1. Mode-filter/mixer
assembly.
-
Volume 40, number 2
OPTICS COMMUNICATIONS
15 December 1981
FL3 small
surface
ref.
Ge-PIN
biascirCult
lock-in-
amplifier
Fig. 2. Experimental setup.
end (NE, 2-5 m) and far end (FE, corresponding to the whole fiber length, 1-3 km) to investigate the steady-state mode distribution. With mandrels of different diameters (4 mm to 16 mm in steps of 1 mm) we could vary the effective loss as well as its influence to the FFP. The number (8-20) of mandrels determines how many times the process mode-filter/mixer is repeated. 2.2. Discussion of the results Three standard, low loss graded-index fibers (see table 1) with different mode coupling coefficients are used for comparison within all measurements. The fully automated setup is shown in fig. 2. Both numerical aperture and spot size of the launched beam can Table 1 List of measured fibers ____ length in m Fiber
#l #2 #3
NAloo% A=lpm
NE
FE
5 2 5
1235 1353 2490
0.217 0.19 0.173
be controlled precisely, so that the 70% excitation could be adjusted correctly. However, fibers are overfilled (NA 0.28, spot diameter 60 r.lm) at the front end if the mode-filter/mixer is used. All FFP-measurements have been performed with chopped (-600 Hz) light at a wavelength h = 1 pm. We used a Ge-PIN-detector, cooled down to -25°C to reduce the dark current; the detector can be moved by stepmotors in both x- and y-direction, transversal to the fiber axis; step-size was 1 pm, accuracy about 0.1 pm [l 11. Use of lock-in signal detection increases the sensitivity and resolution by using large time constants. As demonstrated by fig. 3, FFPs on both NE and FE of a graded index fiber can be measured very accurately. Some of the results are shown in fig. 4. The differences of NA (given by 50% widths of FFP at FE and NE) normalized to NA
core/cladding diameter in pm
491124 51/121 561135
attenuation in dB/km h=ll.rm
X+m
2.0 2.0 1.1
1.6 0.4 0.08
113
Volume
40, number
OPTICS COMMUNICATIONS
2
15 December high
low -
modes
_
.
cl
0 MBE modefi(ter
4turns
l
- 0,05
t
fiber
1981
,
10mm diameter
3
IGg. 5. PI:P-deviation
Fig. 3. FFPs on near end (NE) and far end (FE). of the undisturbed fiber, are plotted against the diameter of the mode-filter/mixer mandrels. According to Kaiser [2] the 99% width of FFP should be taken into account to provide that highest-order modes are not excited too much. Comparing FFPs of NE and FE (fig. 5) we prove that highest-order modes are not overfilled, but even sometimes underfilled at NE. The
o modefILter L turns q modefilter 0 turns x modefllter 6turns A modefilter 1, turns + modefIlter 8 turns
Fig. 4. FFPs versus mandrel
114
diameter
of modefilter/-mixer.
reason for that is assumed to be the high index primary coating of the fibers. Therefore the 50% width of FFP gives evidence in this special case likewise. Eg. 4 demonstrates also that 8 S-ahaped bounds, 8 mm to 10 mm in diameters are very well suited to excite the EMD. Deviations between FFPs of NE and FE are much smaller compared to MBE (see also fig. 5). The measurements allow us to distinguish between fibers of strong or low mode coupling. It has been proved experimentally that the mandrel surface is of small importance. The use of teflon or aluminum caused no difference. A fiber tension of about 40 p seemed to be suitable. The results have been verified by attenuation measurements. Normally differences using either high accurate MBE or the mode-filter/mixer combination were much smaller than the resolution of the measurement setup (
at our disposal
Volume 40, number 2
OPTICS COMMUNICATIONS
15 December 198 1
I..---.-.-.-I -------F --/ ._... S.&T3 l- _.-
10.0 6.8
-1 ___
4.0
-..
.-
I
/
-~
--I
---~---
E < m2.0 a
c
.d
I”
.B
.9
1.E
i
1.1
J I.3
1.2
wavelength
in
1.4
1.5
1.6
1.7
pm
Fig. 6. Attenuation results for various launching conditions.
fiber is overfilled by high NA and large spot size (#S). A mode-filter/mixer of 8 turns and 10 mm in diameter causes a wavelength independent loss of 2.0 dB at NE and 1.8 dB at FE with respect to intensity without mode-filter/mixer for special type of fiber. The attenuation difference between NE and FE is almost equal to the intrinsic loss (X + 00) of the whole fiber (0.184 dB), which can be attributed to microbending and mode conversion loss along the fiber. These results are also in very good agreement with calculations by Winkler et al. [ 151 for a bent graded index fiber. For 8 turns of fiber on a 10 mm diameter mandrel, corresponding to 125 mm effective length of the bend, a pure loss of about 1.5 dB is calculated. The rest is due to transition loss which, of course, depends on the level of mode conversion in the fiber.
3. Conclusion To improve accuracy in fiber attenuation measurement, to decrease the influence of launching conditions, and for easy handling we have developed and constructed a mode-filter/mixer by which the so called mode equilibrium distribution of a fiber can be
excited easily. The mode-filter/mixer consists of an assembly of 8 aluminum mandrels of 8 mm to 10 mm in diameter. The fiber is wounded S-shaped around the mandrels; a fiber tension of ca. 40 p is suitable for exciting the EMD in standard low-loss graded-index fibers. The mode-filter/mixer is suited for use in automated measuring setups and is superior to MBE, especially for fibers with strong mode coupling. Fundamental investigations of the mode-filter/mixer using three different types of fibers have been performed by attenuation measurements. The mode-filter/mixer assembly can be used to estimate mode coupling and intrinsic fiber loss. We would like to thank Prof. Dr. D. Krause, Schott& Gen., for fruitful discussions as well as for supplying the fibers. This work is supported by Bundesministerium fur Forschung und Technologie. The authors alone are responsible for the contents.
References [l] P. Kaiser, Trans. of IECE of Japan E61 (1978) 225. [ 21 P. Kaiser, Techn. Digest Symposium on Optical fiber measurements, Boulder 1980, p. 11.
115
Volume
40, number
2
OPTICS COMMUNICATIONS
[3] G.T. Holmes, Techn. Digest, 6th ECOC, York 1980, p. 144. [4] CCITT, Reproducible measurements of baseband frequency responses of (X-fibers by excitation with a SI fiber, 46 E/WG 1 (Japan) Oct. 1979. [S] M.P. Smid, Techn. Digest Symposium on Optical fiber measurements, Boulder 1980, p. 121. [6] F. Bigi and G. Bonaventura, ibid., p. 129. [7] R.E. Love, ibid., p. 135. [8] S. Geckeler, Siemens Forsch. u. Entwickl.-Ber. 10 (1981) 162. [9] A.H. Cherin and W.B. Gardner, Laser Focus 16 (1980) 60.
116
[lo]
[ 1 l]
[12] [13] [14] [ 151
15 December
198 1
T. Okoshi, J.C. Chang and S. Saito, Record of Technical Group, IECE Japan, Opt. Quant. Electron 79 (1979) 73. R.Th. Kersten and T. LeHiep: Techn. Digest Symposium on Measurements in optical communications, Berlin 1980, p. 66. D. Gloge, Appl. Optics 11 (1973) 2506. E.A.J. Marcatili and S.E. Miller, Bell Syst. Techn. J. 48 (1969) 2161. D. Marcuse, J. Opt. Sot. Am. 66 (1976) 311. C. Winkler, J.D. Love and A.K. Ghatak, Opt. Quant. Electr. 11 (1979) 173.