Gaussian Optics

Analysis of Terahertz waves comes in three main forms, physical optics, geometrical optics, and Gaussian optics. Physical optics has the highest accuracy but it is time consuming when it is applied in the design of large radio telescopes. Also, it is only capable of computing radiation characteristics. Geometrical optics, on the other hand, reduces computational time significantly. But it does not give accurate results when designing telescopes which are to operate at Terahertz frequencies. Gaussian optics is a good trade-off between these two methods and it is a popular approach used in the design of large radio telescopes — particularly those which operate near/in the Terahertz band. Since it accounts for the effects of diffraction, this method produces reasonably accurate results. This chapter describes Gaussian optics, with emphasis given on its application in the design of radio telescopes.

Spatiotemporal coupling of attosecond pulses

The shortest light pulses produced to date are of the order of a few tens of attoseconds, with central frequencies in the extreme UV range and bandwidths exceeding tens of electronvolts. They are often produced as a train of pulses separated by half the driving laser period, leading in the frequency domain to a spectrum of high, odd-order harmonics. As light pulses become shorter and more spectrally wide, the widely used approximation consisting of writing the optical waveform as a product of temporal and spatial amplitudes does not apply anymore. Here, we investigate the interplay of temporal and spatial properties of attosecond pulses. We show that the divergence and focus position of the generated harmonics often strongly depend on their frequency, leading to strong chromatic aberrations of the broadband attosecond pulses. Our argument uses a simple analytical model based on Gaussian optics, numerical propagation calculations, and experimental harmonic divergence measurements. This effect needs to be considered for future applications requiring high-quality focusing while retaining the broadband/ultrashort characteristics of the radiation.