Various Improvements for the Simulation Software RP Fiber Power

When we simulate pulse propagation through an optical fiber, the pulse can undergo various changes due to laser gain or absorption by the laser-active dopant, chromatic dispersion and fiber nonlinearities. Now I have introduced the new function set_mod(expr$, cond$). That defines an additional modulation in the time or frequency domain, which is applied after each numerical step in the fiber. The first argument is a real or complex expression, which can depend on the position z and on either t (time) or f (frequency); the amplitude trace of the pulse in the time or frequency domain will be multiplied with the defined factor. If the second argument is not an empty string, it defines an expression which determines whether or not the modulation is applied at a certain z position. Those expressions can also depend on pulse properties, e.g. the pulse energy.

The function could be used for simulating additional spectral filtering effects. In that case, one would use a frequency-dependent multiplication factor of the amplitudes. Through the second argument (a condition), one could apply such filtering only at certain locations – for example at a point where one inserted some kind of bandpass filter into the fiber. (Previously, one would have had to simulate the propagation through a sequence of fibers and other optical elements, somewhat less conveniently.) Also, one can make that filtering dependent on the spatial position. Imagine, for example, that some extra loss is introduced by bending the fiber, where the bend radius is gradually decreasing along the fiber. (Bend losses would normally be taken into account only in numerical beam propagation, but not for ultrashort pulse propagation, where we ignore the transverse dimension.)

The new function set_add() works similarly – the difference to set_mod() is only that some amplitudes are added in the time or frequency domain. This feature could be used e.g. to add another pulse at a certain location in the fiber, or to add noise (e.g. using random numbers with Gaussian probability distribution).

There have already been functions for applying phase shifts in the time or frequency domain. In some simpler cases, however, one applies a phase shift without time or frequency dependence. For that, the new function pp_phase_shift() has been introduced, which is somewhat more convenient to use. The software will apply it in the time or frequency domain, depending on what is numerically more efficient in your situation.

In optical fibers, gain and absorption are usually not polarization-dependent. However, the software is increasingly applied to bulk laser systems, and those may contain optically anisotropic laser crystals. For such applications, the new function set_polarization() has been introduced. After defining the “optical channels” in a fiber (e.g. pump, forward and backward signal wave), one can use that function to assign polarization directions to them. The effect of that is that the transition cross sections are calculated with different functions. Normally, if we have an Yb-doped gain medium, for example, the wavelength-dependent absorption and emission cross sections would be calculated with the functions s_a_Yb(l) and s_e_Yb(l). If you define the polarization direction to be “x”, for example, those functions would be s_a_Yb_x(l) and s_e_Yb_x(l).

The same things can be done in the context of numerical beam propagation. The function bp_set_channel_p() can be used to define a beam propagation channel with polarization. Also, the function bp_set_I_p() now has a third argument for the polarization direction.

When you simulate numerical beam propagation, you can use the function bp_I(x, y, z) to obtain the calculated intensity at any location. In some cases, you want to have that integrated in x or y direction. For that purpose, the new functions bp_I_x() and bp_I_y() have been introduced. They are convenient, for example, if you want to make a color plot where the intensity distribution is shown in the x-z plane. If you would simply plot the intensity values with y = 0, you would not “see” optical powers outside that plane. If you use bp_I_y(), you effectively project all power to the x-z plane.