Proceedings of Topical Meeting on Optoinformatics (pdf-format, 1.21 ...

SAINT-PETERSBURG, October 17 – 20, 2005 53
The designations in Fig. 1 are as follows: h(x) is the function <strong>of</strong> the DOE relief
depth, x is the transverse coordinate (for simplicity, a 1D case is shown).
F r, ϕ = A r,
ϕ exp iΦ
r,
ϕ is transformed as
In the general case, the field ( ) ( ) ( ( ))
⎛ iΦ′
( ) ( )
( r,
ϕ )
( ) ⎟ ⎞
F накл
r,
ϕ = A′
r,
ϕ exp⎜
, where A′ ( r,ϕ ), ( r,ϕ )
⎝ cos α ⎠
distorted functions A ( r,ϕ ), Ф ( r,ϕ )
Ф′ are the astigmatically
. Thus, with increasing angle <strong>of</strong> the DOE tilt, α, the
DOE singularity order is changed. Note that generally speaking, the singularity order
ceases to be integral in this case. Hence, while possessing the properties <strong>of</strong> an astigmatic
laser beam, the light field generated with the tilted DOE, will simultaneously show
peculiar properties, which are more pronounced for greater DOE tilt.
In Ref. [7] the generation <strong>of</strong> optical vortices in illumination <strong>of</strong> a spiral phase plate
with a plane or Gaussian beam was discussed. In the present paper, experimental studies <strong>of</strong>
the generation <strong>of</strong> singular beams in oblique illumination <strong>of</strong> similar spiral phase plates are
conducted. Figure 2b-e illustrates some results <strong>of</strong> the experiments in oblique illumination
<strong>of</strong> the third-order phase plate (Fig. 2a) with a converging laser beam.
a b c d e
Fig. 2. Experimental results with oblique illumination <strong>of</strong> the third-order phase plate (a) under
different angles from 5 grad to 35 grad (b-e)
The work is financially supported by the CRDF (grant REC-SA-014-02), the
presidential grant <strong>of</strong> Russian Federation NS-1007.2003.1 and the grant <strong>of</strong> the Russian
Foundation for Basic Research 05-01-96505.
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