Phase space optics

First-order optical system design and linear canonical transformations

Our main research line comprises the generation of laser beams (either using holography or specific optical transformations) as well as their optical characterization. It implies the development of techniques and experimental setups in the field of phase space optics. For instance, the fractional Fourier transform is a well-known operation from which the reconstruction of the Wigner distribution (WD) of the beam can be obtained. Indeed, the WD provides a complete characterization of the beam.

We have developed advanced optical systems capable to perform important operations such as gyrator and the Fractional Fourier transformations. These systems are optimal because a minimum number of optical elements are required. Moreover they are programmable following user input interactively.

 

Selection of our representative works in this research line:

 

  Phase space tomography based on Fractional Fourier transformation (FRFT)

 

 
 

A. CámaraT. AlievaJ. A. Rodrigo, and M. L. Calvo, "Phase space tomography reconstruction of the Wigner distribution for optical beams separable in Cartesian coordinates," J. Opt. Soc. Am. A 26, 1301-1306 (2009). 

 

 

 
  Programmable optical setup for 2D FRFT 
 
 
J. A. RodrigoT. Alieva, and M. L. Calvo, "Programmable two-dimensional optical fractional Fourier processor," Opt. Express 17, 4976-4983 (2009).

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  Gyrator transform 
 
 

 J. A. Rodrigo, T. Alieva, and M. L. Calvo, "Gyrator transform: properties and applications," Opt. Express 15, 2190-2203 (2007).

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J. A. Rodrigo, T. Alieva, and M. L. Calvo, "Experimental implementation of the gyrator transform," J. Opt. Soc. Am. A 24, 3135-3139 (2007).

J. A. Rodrigo, T. Alieva, and M. L. Calvo, "Applications of gyrator transform for image processing," Opt. Comm. 278, 279-284 (2007). 

 
  
 Linear canonical transforms 
  

M. Bastiaans and T. Alieva, "Signal representation on the angular Poincaré sphere, based on second-order moments," J. Opt. Soc. Am. A  27, 918-927 (2010). 

T. Alieva and M. J. Bastiaans, "Properties of the linear canonical integral transformation," J. Opt. Soc. Am. A 24, 3658-3665 (2007).

T. Alieva and M. J. Bastiaans, "Orthonormal mode sets for the two-dimensional fractional Fourier transformation," Opt. Lett. 32, 1226-1228 (2007). 

M. J. Bastiaans and T. Alieva, "Classification of lossless first-order optical systems and the linear canonical transformation," J. Opt. Soc. Am. A 24, 1053-1062 (2007). 

M. J. Bastiaans and T. Alieva, "Synthesis of an arbitrary ABCD system with fixed lens positions," Opt. Lett. 31, 2414-2416 (2006).

M. J. Bastiaans and T. Alieva, "First-order optical systems with unimodular eigenvalues," J. Opt. Soc. Am. A 23, 1875-1883 (2006). 

 

 

 

 

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