Improvements of RP Fiber Calculator: Design Helper, Four Dopants and Much More

The most important new feature addresses a typical situation in fiber design. You have a refractive index profile of some type, e.g. a step-index profile or a graded-index profile with a trench, and you want to reach a certain value of some mode property, such as a cut-off wavelength of 1260 nm for the LP₁₁ mode. Which core radius do you need for that?

So far, you would have to change the core radius by hand until you get close enough to the target. The new design helper (PRO version) does that work for you:

• You define the design goal: the cut-off wavelength of some mode, the number of guided modes, or the mode radius, effective mode area, effective index, power fraction in the core, far-field half angle or group velocity dispersion of a mode at the operation wavelength.
• You choose the parameter to vary: the core radius, the numerical aperture (for which all index differences of the core are scaled together, so that the shape of the profile is retained), the refractive index of one core segment, a doping concentration – either in one segment or scaled in the whole core –, or a parameter of an expression which defines the profile (see below).
• You set the parameter range in which solutions are to be searched.

The software then calculates the goal quantity at a number of points within the parameter range, shows the result as a design curve, and precisely determines all solutions.

Why a design curve, and not just a number? Because there is often more than one solution, or none at all. For example, the mode radius of the fundamental mode, considered as a function of the core radius, has a minimum: For small cores, the mode extends far into the cladding; for large cores, it gets large anyway. Therefore, most values of the mode radius are reached for two different core radii. The design helper lists all solutions, and the curve shows you the whole situation at a glance. If there is no solution in the chosen range, it tells you in which direction the range should be extended.

For the number of guided modes, a design goal of a different kind, the design helper delivers the parameter intervals in which the fiber has that number of modes – for example, the range of core radii for single-mode operation at a given wavelength.

With one click, you can then apply a solution to the fiber design. Before that, the design remains untouched, so that you can freely explore different design goals.

As a simple test, consider a step-index fiber with an NA of 0.12, for which we want a cut-off wavelength of 1260 nm. The design helper finds a core radius of 4.02 µm, exactly as expected from the well-known condition ($V = 2.405$) for the single-mode cut-off. Of course, the tool is far more useful for profiles where no such simple formula exists.

The PRO version of RP Fiber Calculator has long been able to calculate the refractive index profile from a doping profile, including the material dispersion. So far, however, a profile could contain only one dopant: germania (GeO₂) or, with the material selection, fluorine. Fiber designs often combine several dopants – for example, GeO₂ in the core and fluorine for lowering the refractive index in a depressed cladding or a trench; P₂O₅ and B₂O₃ are also used. Now, the doping profile can contain all four of them at the same time.

You can define the doping profiles by filling out a table or by selecting one dopant and clicking into a diagram to set the values. Alternatively, you can use expressions to define profiles.

In the PRO version, the refractive index profile – or the profile of a doping concentration – can also be defined by a mathematical expression, e.g. for a graded-index profile or with your own Sellmeier equations for the wavelength dependence. Such expressions can now refer to parameters, which you define in the editing window below the expression:

a = 3.2 um
w = 1.5 um
dn = 5e-3

An expression like 1.45 + (if r < a then dn else if r < a + w then -dn else 0) then describes a core with a surrounding trench, where the core radius a, the trench width w and the index difference dn are named parameters, which are easy to adjust. More importantly, the design helper can vary each of them – for example the trench width for a desired cut-off wavelength. All expressions of a fiber share the parameters, so that a radius used in both the GeO₂ and the fluorine profile is defined only once.

When you enter an expression, the software checks it – including whether it gives a constant refractive index in the cladding, as required for the mode calculation, and whether the values are plausible. And you of course you will see the plotted profiles as a firm sanity check.

The table of mode properties has been extended with a footer lines, which shows further properties of the mode selected in the table: its beam quality factor M², obtained from the second moments of near field and far field, its far-field half angle, and (if chromatic dispersion has been calculated) its group delay relative to the fundamental mode, which is relevant e.g. for mode division multiplexing.

Also, the index profile diagram can now show the effective refractive indices of all guided modes as horizontal lines, labeled with the mode indices and arranged in columns according to the azimuthal index l. This shows at a glance how deeply each mode is guided, and how the mode structure changes when you modify the profile. That option is available also in the free version.

In the PRO version, the mode profiles can now be displayed not only as near fields, but also as far fields, i.e., as the angular distributions of light leaving the fiber end. A circle marks the angle corresponding to the fiber's NA; one can see, for example, that higher-order modes close to their cut-off spread significantly beyond that angle.

The PRO version can plot mode properties as functions of the wavelength. Now, you can also save the plotted data as a text table (with one column per mode) for further processing in other software. In a plot of the group velocity dispersion, the zero-dispersion wavelengths are marked, and the dispersion slope there is reported.

Some further improvements are less visible, but nevertheless important:

• Improved accuracy of the mode solver: We fixed a few problems which caused non-ideal accuracy in certain situations. In particular, steps of the refractive index – between core segments or at the core boundary – are now located and treated exactly in the numerical integration. This strongly reduces the numerical errors of effective indices, and quantities like the effective mode area and the power fraction in the core are also more accurate now. (The same improvements go into our RP Fiber Power software, which uses the same mode solver.)
• Always up to date: When you modify the index profile and then return to the table of guided modes, the modes are recalculated automatically (unless that would take too long). Also, ticking the box for including chromatic dispersion immediately triggers a new calculation, and the displayed mode profile follows the selection in the mode table – a simple click or the arrow keys suffice.
• High-resolution displays: The software now fully adapts to Windows display scaling. Particularly the help panes, the propagation diagrams and the result displays for beam launching, fiber-to-fiber coupling and reflections at fiber ends were too small before on displays with 125% or 150% scaling.

RP Fiber Calculator remains available as a free version, which you can download and use for non-commercial purposes and for evaluation. The free version supports up to five core segments for the index profile, while the PRO version offers up to 20 segments, up to 10 fibers in parallel, and all the advanced features described above, such as the design helper, doping profiles, chromatic dispersion and far-field profiles.

Customers who already have a license for RP Fiber Calculator PRO can get a free update.

With the latest improvements, RP Fiber Calculator has become a substantially more powerful tool for developing fiber designs: The design helper takes over the tedious part of adjusting parameters, while the design curves keep you informed about the bigger picture. Together with the extended doping profiles, the profile expressions with parameters and the additional mode properties, this makes the software considerably more useful for practical fiber design, applicable to a wider range of fibers.

You find the details in the documentation. And if you need even more flexibility – e.g. for automatic optimization of several parameters, or for simulating complete fiber amplifiers and fiber lasers – have a look at our RP Fiber Power software.