Abstract

This Comment shows that the parameter called the degree of paraxiality of a monochromatic beam [Opt. Lett. 33, 1360 (2008) ] was derived using misleading criteria and that the results in that Letter might lack physical meaning.

© 2008 Optical Society of America

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References

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  1. O. El Gawhary and S. Severini, Opt. Lett. 33, 1360 (2008).
    [CrossRef]
  2. P. Vaveliuk, G. F. Zebende, M. A. Moret, and B. Ruiz, J. Opt. Soc. Am. A 24, 3297 (2007).
    [CrossRef]
  3. P. Vaveliuk, B. Ruiz, and A. Lencina, Opt. Lett. 32, 927 (2007).
    [CrossRef] [PubMed]
  4. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  5. A. E. Siegman, Lasers (University Science, 1986).

2008 (1)

2007 (2)

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Figures (1)

Fig. 1
Fig. 1

PE (dashed curve) and DP (solid curve). For example, at k w 0 = 25 , PE 0.87 such that the beam begins to be approximately paraxial, while DP 0.69 still indicates a nonparaxial beam. The inset is Fig.1 in [1] with DP correctly calculated.

Equations (5)

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+ Im { f * z f } d x d y + f 1 f 1 * k d x d y = + Im { A * z A } d p d q + A 1 A 1 * k d p d q ,
( i ) A = A ( 0 ) ( p , q ) exp [ i k z 1 ( 2 π k ) 2 ( p 2 + q 2 ) ] ,
Im { A * z A } d p d q = A ( 0 ) 2 1 ( 2 π k ) 2 ( p 2 + q 2 ) d p d q .
p 2 + q 2 k 2 4 π 2 Im { A * z A } d p d q + A 1 A 1 * k d p d q
p 2 + q 2 k 2 4 π 2 A ( 0 ) 2 ( ) d p d q A ( 0 ) 2 d p d q ,

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