Page 115 - Phase Space Optics Fundamentals and Applications

96 Chapter Three

(a) (b) (c) (d) (e)

FIGURE 3.10 The amplitude (upper row) and the phase (lower row) of the
orthosymplectic modes obtained from the HG H m,n (r) by gyrator at angles
◦
◦
◦
◦
◦
(a) ϑ = 0 , (b) ϑ = 135 , (c) ϑ = 150 , (d) ϑ = 165 , and (e) ϑ = 180 .
transformation of the HG mode by gyrator is illustrated. There the
U g (ϑ)
amplitude (upper row) and phase (lower row) of H m,n (r) are dis-
played for angles (a) ϑ = 0 ,(b) ϑ = 135 ,(c) ϑ = 150 ,(d) ϑ = 165 ,
◦
◦
◦
◦
and (e) ϑ = 180 correspondingly. The experimental realization of
◦
mode conversion by the flexible gyrator setup 31 demonstrates good
agreement with numerical calculations.
While the HG and LG modes are widely used in various areas
of science and technology, including metrology, interferometry, laser
surgery, etc, the application of the other orthosymplectic modes is still
under development. It seems that as well as the HG and LG modes
they can used for microparticle manipulation. 63 We also emphasize
that systems used as mode converters serve for the orbital angular mo-
mentum management of coherent as well as partially coherent parax-
ial light.
3.7.6 Beam Characterization
Since in optics the measurements of the intensity distribution are the
only feasible ones, the phase recovering from intensity information
is one of the important problems. 64 As mentioned above, the phase-
space rotators produce the rotation of the Wigner distribution, which
completely characterizes the signal up to the constant phase factor.
Moreover, the squared modulus of the RCT of the signal, associated
with intensity distribution, corresponds to a certain projection of the
Wigner distribution. After exploration of this connection, a method
of phase-space tomography was proposed. 65,66 It permits one to re-
construct the Wigner distribution and therefore the complex field am-
plitude or the mutual intensity for the case of coherent or partially
coherent fields, respectively, from the measurements of the intensity