Single mode light-guiding fibre, and method for its production.

0001The invention relates to a single-mode optical fiber with a refractive index profile n (r), where n is the refractive index of the fiber material at a distance r from the axis of the fiber, the refractive index profile by doping a matrix material, of which the fiber is predominantly composed, with at least one doping material is set to form a number of layers with different refractive index. The invention also relates to a method for its production.

0002From DE-OS 32 32 194 a monomode fiber with a refractive index profile is known, which is designed such that the fiber particularly fulfills three conditions with regard to chromatic dispersion: these are zeros at two preselected wavelengths and a predetermined maximum value. The refractive index profile is made up of three layers and shows a W-shaped course. It is not optimized with regard to the amount of doping material.

0003The object of the invention is to provide a single-mode optical fiber which manages with as little doping material as possible for given properties. The object of the invention is also to provide a method for producing such an optical fiber.

0004This object is solved by the characterizing features of claim 1 and claim 16. Advantageous embodiments are the subject of the dependent claims.

0005The monomode optical fiber according to the invention is characterized in that the refractive index profile n (r) at least for predetermined values ​​of the chromatic dispersion and / or the field diameter and_/or the damping and / or the upper mode cutoff is set as the desired properties, the number m of layers of thickness A r is significantly greater than the number of desired properties and each layer contains just enough dopant material that the associated refractive indices at least approximately while maintaining the desired properties the condition<maths id="math0001" num=""><img file="EP0341427A2_D0001.tif" /></maths>meet, where n_O mean the refractive index of the matrix material and r = i ° A r.

0006The fulfillment of the condition according to the invention means a minimization of the amount of the doping material and thus a corresponding reduction in the manufacturing effort, since with usual concentrations of doping material the resulting difference in refractive index from the undoped material is essentially proportional to the concentration of the doping material. In the case of conventional doping materials, this also applies at least approximately when there are several different doping materials, in particular a doping material which increases the refractive index and lowers the refractive index. Under these circumstances, the fulfillment of the condition according to the invention corresponds particularly well to a minimization of the amount of the doping material if the effects of the refractive index changing effects of the two doping materials are essentially the same. This is particularly the case with the frequently used doping materials fluorine (for lowering the refractive index) and germanium (for increasing the refractive index). The proportionality factor between the change in refractive index and the number of particles introduced per mole of matrix material is almost the same for fluorine and germanium.

0007In modern manufacturing processes, the fiber is built up by changing the refractive index in layers. The requirements according to the invention can also be met with a larger number of desired properties without unnecessarily large jumps in refractive index and without an excessive deviation from the refractive index of the matrix material in that the number of layers is large compared to the number of desired properties. This is possible, for example, in the known plasma production processes, in which the number of possible layers and thus the number of degrees of freedom available for the design of the fiber according to the invention is approximately 1,000 (PCVD process) or even 1,000,000 (PICVD- Procedure) has risen. On the other hand, in order not to complicate the calculation of the required refractive index profile too much, the number of layers included in the calculation will not be too large. In general, it is sufficient if more than 100 layers are selected during the production, preferably about 300 to 500 layers.

0008The following properties in particular come into consideration as desired properties of the optical fiber:<ul id="ul0001" list-style="none"><li>a) The chromatic dispersion has zeros around the light wavelengths 1,300 and 1,550 nm (these are preferred operating wavelengths because there are absorption minima with conventional CVD glass materials) and in the middle a maximum of 3 ps / (nm'km). This means a flattened course of the dispersion, as it corresponds to international recommendations.</li><li>b) The damping of the LP adopted as the first upper mode₁₁-Modes at 1,250 nm is at least 1 dB / m. This is useful in order to be able to operate the fiber effectively monomodally from this wavelength.</li><li>c) The attenuation of the basic mode at 1,600 nm is at most 10-⁶ dB / km. This leaves enough room for damping increases due to fiber curvature.</li><li>d) The field diameter at 1,300 nm is as large as possible and is, for example, 6.8 μm. This makes splicing easier.</li><li>e) The refractive index should not fall below a predetermined minimum value.</li></ul>

0009The fiber according to the invention is a multilayer fiber which has a characteristic sequence of almost triangular increases and decreases in the refractive index level with intermediate flat zones along the radius, known coarse structures, namely a first, highly pronounced minimum refractive index following a core having a relatively high refractive index following pronounced first maximum refractive index, find a weak second minimum and a run-out area (EP-OS 0 224 282). According to the invention, there is a second maximum at the outer edge of the core, which makes it possible to increase the chromatic dispersion at approximately 1,300 nm, which has an undesirably high negative value in known fibers, preferably to zero. Furthermore, there are several turning points between the first maximum and the second minimum. This allows the refractive index to drop economically from the first maximum to the second minimum. This applies in particular if there is a step at the level of undoped matrix material, preferably SiO, between the first maximum and the second minimum_e.g., is present.

0010It is also expedient if a third maximum is provided in the run-out area in which the refractive index is preferably at the level of undoped matrix material. This increases the probability of tunneling for the LP₁₁-Photons from the core into the material located further out and thus favorably influencing the upper fashion cutoff, ie an increase in upper mode damping. This third maximum is so far out that it no longer disturbs the basic mode with regard to damping and dispersion.

0011Refractive index profiles for the fibers according to the invention can be determined mathematically with little effort. A particularly simple possibility of such a mathematical determination is to be explained in more detail below.

0012For a given set of 1 desired properties, for example with regard to dispersion, damping, field diameter and upper mode cutoff, the condition according to the invention is formulated mathematically: one searches for a minimum of the function<maths id="math0002" num=""><img file="EP0341427A2_D0002.tif" /></maths>the 1 desired properties as constraints the permissible range in Rm, the space of the refractive indices n (r_;) - n_O, define, ie you can work with a quasi-continuous profile, for example a few hundred equidistant layers. Mathematically, this sum represents an approximation of the following integral:<maths id="math0003" num=""><img file="EP0341427A2_D0003.tif" /></maths>where R₂ means the radius of the fiber.

0013The following are typical properties for a fiber with a diameter of 2 as an example_.R₂ = 125 µm diameter assumed:<ul id="ul0002" list-style="none"><li>For chromatic dispersion, zeros should be between 1,300 and 1,550 nm; in between there should be a maximum of 3 ps / (nm^*km). The damping of the LP adopted as the first upper mode₁₁-Modes at 1,250 nm should be 1 dB / m in order to be able to operate the fiber effectively from this wavelength in single-mode mode. For the basic fashion (LP_oi) an attenuation of 10-⁶ dB / km are present; this leaves enough scope for damping increases due to fiber curvature. The desired field diameter should be 6.8 µm at 1,300 nm.</li></ul>

0014The associated fiber is calculated with the refractive index profile according to the invention in two steps. First, based on a slightly rounded step index profile, a Newton-type method is used to find an element of the permissible range, ie a refractive index profile which, with the exception of the minimization condition, gives the desired properties. Then you get to the minimum with the method of the projected gradient.

0015The sum norm given in formula (1) above is convex above the R^m. Therefore, a local minimum under "benign" constraints is also a global minimum (convex optimization). The existence of convex optimization is shown by the fact that, if one bases the start profiles on a different structure, the minimum mentioned remains unaffected.

0016The Newton-type method is explained below.

0017Since one can expect a solution in the area of ​​weakly guiding fibers, the scalar wave equation and linearly polarized modes are used in the following.

0018As already mentioned, one starts from a simple step index profile for core and cladding; the jacket may be made of pure quartz glass (Si0₂) consist. This refractive index profile, like others, is determined by the vector formed from the refractive indices of the individual layers<o ostyle="rightarrow">n</o> described. According to the Newton method, the 1 (generally nonlinear) constraints are linearized locally<maths id="math0004" num=""><img file="EP0341427A2_D0004.tif" /></maths>

0019If one evaluates the constraints at point n, the residual vector with components b is obtained_j = c_j (<o ostyle="rightarrow">n1</o>) - C_yo (4) _Cjo: Setpoint of the desired property.

0020A matrix M is also introduced, which contains the gradients of the constraints in its rows, and the requirements for the vector are thus formulated<maths id="math0005" num=""><img file="EP0341427A2_D0005.tif" /></maths>At the same time, it is required that Δ <o ostyle="rightarrow">n</o> regarding the L₂-Standard should be minimal. Therefore applies with<o ostyle="rightarrow">α</o> as the vector containing the Lagrangian multipliers:<maths id="math0006" num=""><img file="EP0341427A2_D0006.tif" /></maths>Multiply this equation by M and insert it <o ostyle="rightarrow">α</o> = (MM^T)^-1 2<o ostyle="rightarrow">b</o> (7) what is calculated using this householder method. This gives Δ<o ostyle="rightarrow">n</o> = - M^T(MM^T)^-1 b (₈)

0021In general, the permissible range is reached after a few iteration steps of this type.

0022For this method of the Newtonian type, calculations of physical properties from the refractive index profile are required, furthermore the calculations of the derivatives of the mathematical functions embodying these properties according to the refractive indices of the individual layers.

00231.) The chromatic dispersion is calculated by numerically differentiating the group delay, the mode field and propagation constant being determined numerically, for example according to U. Foringham, D. Krause, R. Kunstmann, "Calculations to Determine the Effective Cutoff Wavelength of Single-Mode Fibers ", JOpt.Commun.8, 4, pp.143-147, 1987, and AWSnyder, JdLove," Optical Waveguide Theory ", London. New York: Chapman and Hall, 1983 ".

0024The calculation of the gradient of the chromatic dispersion is based on the first-order perturbation correction that applies to the longitudinal propagation constant β in the case of the transition <o ostyle="rightarrow">n</o> → <o ostyle="rightarrow">n</o> + Δ <o ostyle="rightarrow">n</o> results from. In integral notation you get:<maths id="math0007" num=""><img file="EP0341427A2_D0007.tif" /></maths>E (r): field function, λ: wavelength,<maths id="math0008" num=""><img file="EP0341427A2_D0008.tif" /></maths>

0025The following applies to chromatic dispersion:<maths id="math0009" num=""><img file="EP0341427A2_D0009.tif" /></maths>With Schwarz's theorem this means:<maths id="math0010" num=""><img file="EP0341427A2_D0010.tif" /></maths>

0026The change in the refractive index profile A n (r) is assumed to be independent of the wavelength, but not the initial refractive index profile, which is recalculated for each wavelength from the concentration profile of the doping materials. This concentration profile is in turn recalculated for each step of the interation. So for the gradient:<maths id="math0011" num=""><img file="EP0341427A2_D0011.tif" /></maths>where n (r_k) with n_k has been designated.

00272.) The damping of the LP₀₁- and the LP₁₁-Modes is calculated according to the work by Fotheringham et al. There is the loss per length with<maths id="math0012" num=""><img file="EP0341427A2_D0012.tif" /></maths> given, where here the ratio of the field-amplitude square weighted with the radius at the fiber radius R calculated according to the WKB method (cf. for example H.-G.Unger, "Optical Communication Technology", Part I, Heidelberg (1984) 92)₂ to the one at the effective core radius R₁ is obtained from the numerical field calculation. With R_O the inner caustic is called. k_{r, inf} stands for the radial component of the wave number in the medium surrounding the fiber.

0028The essential spectral dependence of this damping expression is contained in the ratio of the squares of the amplitudes. When forming the gradient, R_O and R₁ and β are regarded as constant in a good approximation, so that only the derivatives of the field at point R₁ according to the individual refractive indices. In order to achieve this, the scalar wave equation is differentiated and an inhomogeneous differential equation is obtained for the derivative of the field function:<maths id="math0013" num=""><img file="EP0341427A2_D0013.tif" /></maths>

0029All occurring differential quotients are to be understood as difference quotients. The method of varying the constants is used to solve the problem, since all the derivative functions can be obtained in one step by taking advantage of computing advantages.

0030The damping calculations serve to determine the basic mode damping (see above c)) and to determine the upper mode damping (upper mode cutoff, see above b)).

00313.) For the mode field diameter where the I / e definition is used here, ie E (w_O) / E (0) = l / e. By changing the refractive index n_k goes where into where + Δ where, and it applies in the first approximation:<maths id="math0014" num=""><img file="EP0341427A2_D0014.tif" /></maths>from which one calculates:<maths id="math0015" num=""><img file="EP0341427A2_D0015.tif" /></maths>

0032In the following, the minimum search using the method of the projected gradient is now described: Since the function to be minimized is in the present form<maths id="math0016" num=""><img file="EP0341427A2_D0016.tif" /></maths>for n (r,) = n_O not partially according to n (r_;) is differentiable, you modify it as follows:<maths id="math0017" num=""><img file="EP0341427A2_D0017.tif" /></maths>n_" represents an arbitrary "small" refractive index barrier (about n_x = 0.0001). The function so defined is on the whole R^m steady and differentiable.

0033One then proceeds according to a kind of predictor-corrector method by moving along the direction of the negative projected gradient<maths id="math0018" num=""><img file="EP0341427A2_D0018.tif" /></maths>search for a minimum of the modified sum norm (for this you use the algorithm of the "golden ratio") and then take a step back into the permissible range. The procedure is terminated when the L_e.g.-Norm of the projected gradient has become much smaller than that of the non-projected gradient (ie smaller than a corresponding arbitrary limit, about 0.1).

0034The course of the method is explained below with reference to the attached figures.<ul id="ul0003" list-style="none"><li>1 shows desired values ​​(marked (sa)) of the chromatic dispersion of the fiber at different wavelengths and a corresponding desired course of the dispersion curve, which is actually achieved.</li><li>2 shows the starting profile on which the calculation is based.</li><li>FIG. 3 shows the refractive index profile that results after the first step of the calculation in the direction of the permissible refractive index range (the range of those refractive indices with which the desired properties can be achieved).</li><li>4 shows the first refractive index profile obtained after further calculation steps, which lies in the permissible refractive index range.</li><li>5 and 6 show refractive index profiles after a few (e.g. 5) or many (e.g. 15) approximation steps along the projected gradient towards the minimum.</li><li>7 shows the finally calculated refractive index profile.</li><li>8 shows a further modified refractive index profile.</li></ul>

0035The curve shown in FIG. 1 relates to the profile from FIG. 5. It should be noted that the refractive indices were varied in 1/10 µm intervals from zero radius to 35 µm radius.

0036According to 7 shows a refractive index profile similar to that of a multilayer fiber. Along the radius, the profile has a characteristic sequence of almost triangular increases and decreases in the refractive index level with flat zones in between, with known coarse structures, namely a relatively high first refractive index minimum 2 following the core 1, and a pronounced first following thereafter Find refractive index maximum 4, a weak second minimum 5 and an outlet area 6 (EP-OS 0 224 282).

0037Compared to known refractive index profiles, e.g. according to EP-OS 0 224 282 already mentioned, there are significant changes:<ul id="ul0004" list-style="none"><li>For simple fibers, ie those with a single step in the refractive index profile, the only zero point of the chromatic dispersion can still be below 1,300 nm. In known TC (triple-clad) and QC (quadruple-clad) structures, the course of the chromatic dispersion in the long-wave range is bent downward by additional refractive index stages, so that two zeros of the chromatic dispersion are obtained, the first zero compared to simple fiber is shifted to a value above 1,300 nm. If you want to have the first zero at 1,300 nm, the chromatic dispersion at 1,300 nm must be raised to zero. This is achieved in the fiber according to the invention, in that a second maximum 7 of the refractive index is provided on the outer edge of the core 1, which is connected to the first minimum 2 by the steeply descending descent flank 3. At its core, the refractive index increases towards the second maximum 7 in a concave curve.</li></ul>

0038Furthermore, the gradual decrease in the refractive index in FIG. 4 from the first refractive index maximum 4 to the second refractive index minimum 5 can be made more economical if it is carried out in a step-wise manner and keeps a step at the level of the matrix material. There are therefore several turning points, for example 8, 9, 10, provided there.

0039As FIG. 7 shows, the first refractive index minimum 2 is relatively low. This can cause technical difficulties. It is therefore usually advisable to introduce a minimum value of the refractive index, which should not be undercut, into the calculation process as the desired property. This can be taken into account in the calculation by introducing lower refractive index barriers in the manner of "penalty" functions into the standard mentioned above. The result of the calculation is a natural refractive index profile which has a third refractive index maximum 11 in the outlet area 6. Such a refractive index profile is shown in FIG. 8. The third maximum 11 causes an increase in the tunneling probability for the LP11 photons from the core zone into the material surrounding the fiber and thus a favorable influence on the upper mode cutoff, ie an increase in the upper mode attenuation.

0040This enables field diameters that require such wide core structures that the effective upper mode cutoff would normally be shifted upwards beyond 1,300 nm. The third maximum 11 is so far out that it no longer interferes with the basic mode (ie its damping and dispersion). The third maximum had also occurred early in the calculation process without establishing a low refractive index value, as can be seen from FIG. 4. But it had disappeared again on the way along the projected gradient.

0041The present invention was made as part of a doctoral thesis at the Johannes Gutenberg University Mainz, Department of Physics.