We can, however, employ an approximate solution which is much faster to compute. Concerning the wavelength interval, we are mostly dealing with a very small vicinity of a central wavelength. To save more simulation time, we can run the simulation just for this wavelength to obtain the one set of matrix elements. Let us call the matrix Sc (the *.s file will then be just one line with the headings). In most practical applications, the weighted power distribution coming from the power overlap integral in an output port varies by a negligible amount. The phase change may be crucial, on the other hand. We can then approximately derive the phase change with respect to the wavelength. We can approximately write in the vicinity of a central wavelength λc

S( k ) ≈ Sc exp { i( kc k )n0 L } ,

with kc   = 2π ⁄ λc , while =  2π ⁄ λ where λ is the actual wavelength. The values Sc are the S-data obtained after the ordinary simulation for the central wavelength. In conclusion, we may need just one wavelength simulation to describe the device optical response. The limitation of the central wavelength approximation is obvious. The accuracy is decreased with increasing propagation length as well as with the broader wavelength interval. The approximation will be also suitable for lower values of the reference refractive index.