Tailoring the shapes of dispersion spectra to control bandwidthsin single-mode fibers
Leonard G. Cohen, Wanda L. Mammel, and Stan Lumish
Crawford Hill Laboratory, Bell Laboratories, Holmdel, New Jersey 07733
Received November 23,1981
A numerical parametric study is used to gain insight into how the shapes of dispersion and bandwidth spectra areinfluenced by dimensions and index differences of light-guide structures with two claddings. Computer-simulatedfibers are demonstrated to have bandwidths greater than 25 GHz-km across the entire 1.3-1.55-ptm wavelength re-gion.
The use of unconventional refractive-index-profilegeometries may become a viable way of shaping wave-guide dispersion to cancel material dispersion over amuch broader wavelength range than in step-indexsingle-mode fibers. Recent publications have proposedusing double-clad light guides1 and reported experi-mental results from fibers with less than 1 psec/km-nmdispersion within the 1.32-1.43-gm spectral region.2
The purpose of this Letter is to provide an intuitivequalitative guide and a detailed quantitative guide forchoosing geometrical and index parameters for newdouble-clad light guides that should have minimalchromatic dispersion within an ultrawide-wavelengthwindow that completely covers the 1.3-1.55-jum spectralregion. Results were obtained from a numerical anal-ysis 3 that includes interdependent material- andwaveguide-dispersion effects for realistic silica fibersco-doped with germania in the core and fluorine in thecladding.4 They highlight the sensitive way in whichlight-guide-parameter variations affect dispersion ascharacterized by pulse-broadening (psec/km-nm)spectra and bandwidth (GHz-km) spectra.5
The ideal light guide consists of three sections witha common axis, as shown in Fig. 1.6 The central coresection has the largest refractive index, n, (1 + A). Theintermediate inner-cladding section has the lowestindex, n, (1 - HA), and the second-outermost claddingsection has the index ne. The radius of the core andinner cladding is normalized to unity, and the thicknessof the inner cladding is 1 - R1. The ideal double-cladstructure can be approximated by depositing ger-mania-doped silica in the core, fluorine-doped silica inthe first cladding, and pure silica in the second clad-ding,2 or alternatively by depositing a pure-silica coreand fluorine-doped silica in the two claddings.
Figure 2 qualitatively compares group-index (orgroup-delay) spectra in double-clad and, conventionalsingle-clad light guides. The upper solid curve illus-trates spectra for the core material, and the lower solidcurve illustrates spectra for the second cladding mate-rial. At short wavelengths, the LP(01)-mode groupindex is asymptotic to but larger than the group indexof the core material because the group velocity of thelight-guide mode is slower than the group velocity of a
plane wave in the core material. For single-clad fibers,the dashed curve shows the transition to the long-wavelength region where the group-index of the modebecomes asymptotic to the group index of the claddingmaterial. For double-clad fibers, the dotted-dashedcurve shows the transition between the core and theinner cladding, whose index is lower than the group-index of a second cladding. However, the LP(01) modebecomes cut off at the wavelength at which its groupindex goes below that of the second cladding.
Chromatic-dispersion spectra are proportional to theslope of group-delay spectra in Fig. 2. The single-cladfiber-delay spectrum has one minimum, and conse-quently its corresponding dispersion spectrum has onezero crossing. By comparison, the double-clad fiber-delay spectrum has two extrema, and consequently itsdispersion spectrum has two zero crossings, Furtherresults will show how the locations of zero-dispersionwavelengths can be controlled through the proper choiceof fiber parameters relating to the width of the innercladding through R1 and to the depth of the inner-cladding index through H. Decreasing the width of thefirst cladding decreases the effect of its low index andmakes the lowest-order mode cut off at a longer wave-length, thereby reducing the curvature of dispersionspectra at long wavelengths. Increasing H translatesdispersion spectra upward because the index changebetween the core and the inner cladding becomes larger.In order to make waveguide effects cancel materialdispersion near 1.3- and 1.55-gm wavelengths, optimalparameters R1 = 0.7 and H = 2 were found for struc-tures with relatively narrow and deep inner-claddingindex depressions.
Fig. 2. Qualitative group-index (or group-delay) spectra forsingle- and double-clad fibers. Solid curves illustrategroup-index spectra for the core and cladding materials.
0.8
0632
E16
-16
-_ . 2% 22%O.23%-&
(b) I |Dl I
%-.A
drawn to illustrate chromatic dispersion in a compara-ble single-clad fiber with A = 0.22%. The wide-spec-trum advantage for low dispersion in double-clad fibersis clearly evident from comparisons between the dot-ted-dashed curve and the curves outlined by a solid line.Another advantage of double-clad light guides is thatthey confine a mode to a smaller diameter than doconventional structures with similar waveguide pa-rameters. Solid curves in Fig. 3(b) illustrate the powerconfined in the core and inner cladding of double-cladlight guides. More than 80% of the LP(01)-mode poweris confined for wavelengths extending into the 1.6-gtmregion. The curve outlined by the dotted-dashed lineshows that less power would be confined within a con-ventional fiber with one cladding.
Figure 4 shows bandwidth spectra corresponding tochromatic-dispersion spectra in Fig. 3. These curveswere calculated by using a transfer function that in-cludes second-order dispersion effects that depend onthe value of dispersion as well as on its slope with re-spect to wavelength.5 The illustrated bandwidthspectra apply for laser sources with 4-nm linewidths.
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7WAVELENGTH Wm)
Fig. 3. (a) Dispersion spectra calculated for double-clad fi-bers with 2a = 13 Am and A = 0.21%, 0.22%, 0.23%. Opencircles illustrate material dispersion. Dashed and solid curvesillustrate waveguide-dispersion and total-dispersion charac-teristics, respectively, of double-clad fibers. The dotted-dashed curve applies to single-clad fibers. (b) The total powerconfined within the core and first cladding of double-clad fi-bers (solid curves) or within the core of single-clad fibers(dotted-dashed curve) plotted versus wavelength.
persion and bandwidth spectra for potential fibers co-doped with germania in the core and fluorine in thecladding. The curve outlined by open circles showsmaterial-dispersion spectra. The curves outlined bydashed lines show waveguide-dispersion spectra forlight-guide structures with 2a = 13 gm outer-claddingdiameters and three different core-to-outer-claddingindex differences A = 0.21%, 0.22%, 0.23%. Curvesoutlined by solid lines illustrate the total, chromaticdispersion obtained by summing points on the mate-rial-dispersion curve with points on the appropriatewaveguide-dispersion curve. Two of the chromatic-dispersion curves (for A = 0.22%, 0.23%) have one zerocrossing in the 1.3-gm wavelength region and a secondcrossing near 1.55 gim. Note that waveguide dispersionis reduced and becomes more negative if A is reduced.The effect is to displace chromatic-dispersion spectradownward and move the two zero-dispersion wave-lengths closer together. The two correspondingbandwidth peaks coalesce into a single broad peak if thechromatic-dispersion curve becomes tangent to thezero-dispersion axis. Even lower values of A wouldmove the chromatic-dispersion curve completely belowthe zero axis. In order to give some perspective on howthese results compare with properties of conventionalfibers, the curve outlined by a dotted-dashed line is
E
I
-10'
I 10F
1- 2 I~z - km < <I25 GH. -k.0.2 % /I1 I I 1.-i3 ^ -A-0 23t 1.4 1.5 1.6 1.?.. \
I 11 1,2 1.3 1.4 1.5 1.6 17
WAVELENGTH (pm)
Fig. 4. Bandwidth spectra, corresponding to curves in Fig.3(a), calculated for sources with eA = 4-nm linewidths. Thehorizontal dashed line is the 25-GHz-km boundary.
0.4
01
10 12 14 16 18
Fig. 5. Parametric curves for double-clad fibers. Pointslying between the upper and lower curves indicate the rangeof a and A parameters for bandwidth spectra that remainhigher than 25 GHz-km within the entire 1.3-1.55-gm wave-length region. The cross-hatched marks indicate ±02-gmtolerances on 2a and ±0.01% tolerances on A. Solid curvesapply for fibers with germania-silicate cores; dashed curvesapply for curves with pure-silica cores and fluorine-dopedcladdings.
April 1982 / Vol. 7, No. 4 / OPTICS LETTERS 185
32
16E
~-16 -
I ~~~~~I 0 3 0 3 H 2
-4811 153 15 17 1.9
WAVELENGTH (gm)
Fig. 6. Illustrates how changes in the light-guide parameterH influence. the shapes of waveguide-dispersion spectra(dashed curves). Minimum chromatic dispersion (solidspectral curves) occurs near X = 1.4, 1.9 bm for case 1 with H= 1; near X = 1.3,1.55 Amfor case 2 with H = 2; and near X =1.2, 1.4 gm for case 3 with H > 2.
The horizontal solid line indicates a 25-GHz-kmbandwidth level that is a reasonable transmission ob-jective for 274 Mbit/sec systems with approximately35-km-long repeater spacings.7 Notice that the cal-culated bandwidths remain larger than 25 GHz-kmwithin the entire wavelength region spanning 1.3 to 1.55gim. Bandwidth spectra can be significantly broadened
by choosing the appropriate A that makes the twobandwidth peaks coalesce into one.
As one might expect, the potentially attractiveproperties of double-clad light guides require tighttolerances on diameter and index difference. Figure5 illustrates a quantitative way of estimating tolerancesrequired to meet 25-GHz-km bandwidth specificationswithin the 1.3-1.55-gm wavelength region. Dimen-sionless parameters, R1 = 0.7 and H = 2, are assumed.The index difference A between the core and outercladding is plotted as a function of the radius a from thecenter of the core through the first cladding. Curvesoutlined by solid and dashed lines, respectively, applyfor fibers with germania-doped and pure-silica cores.Points lying between the two curves for each case yieldsatisfactory bandwidth spectra. A lower curve indicatesparameters required to achieve a single broad-band-width peak when a fiber-dispersion spectrum is justtangent to the zero-dispersion axis. Points below alower curve apply to fibers whose chromatic-dispersionspectra never cross the zero-dispersion axis. An uppercurve indicates parameters required to achieve spec-tral-bandwidth peaks near 1.3 and 1.6 gim. Higherpoints apply to fibers whose bandwidth peaks arespaced so far apart that the longer-wavelength peakoccurs beyond 1.6 ,um.
The curves in Fig. 5 cover a broad range of parametersfrom small core diameters and large index differencesto large core diameters and small index differences.The optical choice of parameters should depend ontrade-off between loss sensitivities to axial bends (favor
small diameter) and splicing difficulties (favor largediameter). As the light-guide diameter becomes larger,tolerance requirements become slightly less stringentsince the gap separating upper and lower curves be-comes larger. For reference, the cross-hatched marksindicate +0.2 gm to tolerances on diameter and ±0.01%on index difference.
Figure 6 qualitatively summarizes how the structureof a double-clad light guide should be modified in orderto minimize chromatic dispersion within specifiedwavelength regions. The variable light-guide param-eter is H, the index depression across the first claddingdivided by the index at the center of the core. Case 1applies to a symmetric index profile with H = 1. Dis-persion spectra have zero crossings near 1.4 and 1.9 gim.The minima can be shifted to shorter wavelengths byincreasing H. In fact, we have concentrated on illus-trating case 2, for which H = 2, and the resultant zerocrossings occur within the lowest-loss windows, near 1.3and 1.55 gim, for silica fibers. Case 3, with H > 2, in-dicates that the short-wavelength zero crossing canconceivably be moved to a wavelength shorter than thematerial-dispersion zero crossing.
In summary, the parametric study described in thisLetter is intended to extend the understanding of apromising class of double-clad fibers. Numerical re-sults provide a guide for fabricating new fibers with lowenough dispersion to permit wavelength-division mul-tiplexing at high bit rates throughout the entire 1.3-1.55-gum spectral region.
References
1. K. Okamoto, T. Edahiro, A. Kawana, and T. Miya, "Dis-persion minimization in single-mode fibres over a widespectral range," Electron. Lett. 15, 729-731 (1979).
2. T. Miya, K. Okamoto, Y. Ohmori, and Y. Sasaki, "Fabri-cation of low dispersion single-mode fibers over a widespectral range," IEEE J. Quantum Electron. QE-17,858-861 (1981).
3. L. G. Cohen, W. L. Mammel, and H. M. Presby, "Correla-tion between numerical predictions and measurements ofsingle-mode fiber dispersion characteristics," Appl. Opt.19,1061-1072 (1980).
4. J. W. Fleming, "Material dispersion in lightguide glasses,"Electron. Lett. 14, 362-328 (1978); J. W. Fleming and D.L. Wood, Bell Laboratories, Murray Hill, New Jersey,"Refractive-index dispersion and related properties influorine doped silica" (personal communication).
5. L. G. Cohen, W. L. Mammel, and S. Lumish, "Dispersionand bandwidth spectra in single-mode fibers," IEEE J.Quantum Electron. QE-18, 49-53 (1982).
6. S. Kawakami and S. Nishida, "Characteristics of a doublyclad optical fiber with a low-index inner cladding," IEEEJ. Quantum Electron. QE-10, 879-887 (1974).
7. L. G. Cohen, W. L. Mammel, J. Stone, and A. D. Pearson,"Transmission studies of a long single-mode fiber-mea-surements and considerations for bandwidth optimiza-tion," Bell Syst. Tech. J. 60, 1713-1725 (1981).
