## Diffraction–attenuation resistant beams: their higher-order versions and finite-aperture generations

Applied Optics, Vol. 49, Issue 30, pp. 5861-5869 (2010)

http://dx.doi.org/10.1364/AO.49.005861

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### Abstract

Recently, a method for obtaining diffraction–attenuation resistant beams in absorbing media has been developed in terms of suitable superposition of ideal zero-order Bessel beams. In this work, we show that such beams keep their resistance to diffraction and absorption even when generated by finite apertures. Moreover, we shall extend the original method to allow a higher control over the transverse intensity profile of the beams. Although the method is developed for scalar fields, it can be applied to paraxial vector wave fields, as well. These new beams have many potential applications, such as in free-space optics, medical apparatus, remote sensing, and optical tweezers.

© 2010 Optical Society of America

**OCIS Codes**

(140.3300) Lasers and laser optics : Laser beam shaping

(260.1960) Physical optics : Diffraction theory

(350.7420) Other areas of optics : Waves

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: July 16, 2010

Manuscript Accepted: August 19, 2010

Published: October 18, 2010

**Citation**

Michel Zamboni-Rached, Leonardo A. Ambrósio, and Hugo E. Hernández-Figueroa, "Diffraction–attenuation resistant beams: their higher-order versions and finite-aperture generations," Appl. Opt. **49**, 5861-5869 (2010)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-49-30-5861

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### References

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- When generated by a finite aperture of radius R≫2.4/kρR situated on the plane z=0, the solution in Eq. becomes a valid approximation only in the spatial region 0<z<R/tanθ≡Z and to ρ<(1−z/Z)R.
- In this paper we use cylindrical coordinates (ρ,ϕ,z).
- Fortunately, these conditions are satisfied for a great number of situations.
- The same that was given in .
- In an absorbing medium like this, at a distance of 25 cm, these beams would have their initial field intensity attenuated 148 times.
- According to Eq. , the maximum value allowed for N is 158 and we choose to use N=20 just for simplicity. Of course, by using higher values of N we get better results.
- The analytic calculation of these coefficients is quite simple in this case and their values are not listed here; we just use them in Eq. .
- In this case, we can consider both ϵb(ω) and σ(ω) real quantities.
- J. D. Jackson, Classical Electrodynamics (Wiley, 1998).
- Notice that, according to Section , the absorption coefficient of a Bessel beam is αθ=αcosθ=2kIcosθ. When θ→0, the Bessel beam tends to a plane wave and αθ→α.
- The idea developed in this section generalizes that exposed in Section 5 of , which was addressed to nonabsorbing media.
- The same is valid for a truncated higher-order Bessel beam.
- Notice that kρRm=N is the smallest value of all kρRm, therefore, if R≫2.4/kρRm=N→R≫2.4/kρRm for all m.
- Here, θm is the axicon angle of the mth Bessel beam in Eq. .
- That is, the shortest diffractionless distance is larger than the distance L.
- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

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