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ERIC Number: EJ873684
Record Type: Journal
Publication Date: 2010-Mar
Pages: 12
Abstractor: As Provided
Reference Count: 18
ISSN: ISSN-0143-0807
Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform
Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos
European Journal of Physics, v31 n2 p273-284 Mar 2010
We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam "q"-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincides with the mode Rayleigh range. Finally we analyse the resonator's stability diagram in terms of the fractional orders of each FRFT subsystem, and the round trip propagation. The presented analysis represents an interesting link between two topics (optical resonators and Fourier optics) usually covered in optics and photonics courses at university level, which can be useful to teach and connect the principles of these subjects. (Contains 6 figures.)
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Publication Type: Journal Articles; Reports - Evaluative
Education Level: Higher Education
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A