Source: MDPI

Numerical Representation of Ultrashort Pulses

Introduction

In the field of optics, numerical simulations of pulse propagation require a method to represent pulses numerically. The representation differs based on the pulse duration – longer pulses can be represented by optical power versus time, while ultrashort pulses with picosecond or femtosecond durations require a time-dependent complex amplitude due to the significant effect of optical phase on power evolution.

Slowly Varying Amplitudes

Optical signals in analytical or numerical calculations often use slowly varying amplitudes combined with a factor for fast oscillations, due to the bandwidth of optical signals being smaller than the average frequency. This method reduces memory and computation requirements.

Pulses in Fourier Space

Fourier transforms are commonly used in calculations and simulations, with chromatic dispersion described in the frequency domain. The process involves transforming the pulse into a frequency trace, applying necessary factors, and then converting back to the time domain if needed.

Choosing Numerical Grid Parameters

Determining numerical grid parameters involves setting the width of the time trace and the number of points, which also affects the frequency domain grid. Guidelines include ensuring the trace is long enough to contain the pulse energy and adjusting the number of points based on pulse characteristics.

Numerical Accuracy

Checking numerical accuracy during simulations is essential, and adjustments may be needed based on specific criteria. Increasing numerical resolution can improve accuracy, especially for complex simulations like supercontinuum generation.

Wrapping Effects

Wrapping effects occur when pulse energy reaches the edges of the time or frequency trace, leading to artifacts. Mitigation strategies include using larger traces or applying artificial attenuation at the edges to prevent undesirable effects.

Conclusion

Numerical representation of ultrashort pulses is crucial for accurate simulations in optics. By understanding the principles of representing pulses numerically and choosing appropriate grid parameters, researchers can conduct effective simulations and analyses in various optical systems.

Source: Physics Stack Exchange
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