Abstract

In application of ultra-short laser pulses the pulse parameters have to be controlled accurately. Hence the manipulation of the propagation behavior of ultra-short pulses requires for specially designed optics. We have developed a tool for the simulation of ultra-short laser pulse propagation through complex real optical systems based on a combination of ray-tracing and wave optical propagation methods. For the practical implementation of the approach two commercially available software packages have been linked together, which are ZEMAX and Virtual Optics Lab. The focussing properties of different lenses will be analyzed and the results are demonstrated.

©2005 Optical Society of America

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References

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  1. S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51(16–18), 2533–2542 (2004).
    [Crossref]
  2. S. Szatmári and G. Kühnle, “Pulse front and pulse duration distortion in refractive optics, and its compensation,” Opt. Commun. 69, 60–65 (1988).
    [Crossref]
  3. Z. Bor, “Distortion of femtosecond laser pulses in lenses,” Opt. Lett. 14, 119–121 (1989).
    [Crossref] [PubMed]
  4. T. E. Sharp and P. J. Wisoff, “Analysis of lens and zone plate combinations for achromatic focusing of ultrashort laser pulses,” Appl. Opt. 31, 2765–2769 (1992).
    [Crossref] [PubMed]
  5. Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992).
    [Crossref]
  6. M. Kempe, U. Stamm, and B. Wilhelmi, “Spatial and temporal transformation of femtosecond laser pulses by lenses with annular aperture,” Opt. Commun. 89, 119–125 (1992).
    [Crossref]
  7. M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
    [Crossref] [PubMed]
  8. E. Ibragimov, “Focusing of ultrashort laser pulses by the combination of diffractive and refractive elements,” Appl. Opt. 34, 7280–7285 (1995).
    [Crossref] [PubMed]
  9. G. O. Mattei and M. A. Gil, “Spherical aberration in spatial and temporal transforming lenses of femtosecond laser pulses,” Appl. Opt. 38, 1058–1064 (1999).
    [Crossref]
  10. Z. L. Horváth and Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63(026601), 1–11 (2001).
  11. R. Piestun and D. A. B. Miller, “Spatiotemporal control of ultrashort optical pulses by refractive-diffractive-dispersive structured optical elements,” Opt. Lett. 26, 1373–1375 (2001).
    [Crossref]
  12. R. Ashman and M. Gu, “Effect of ultrashort pulsed illumination on foci caused by a Fresnel zone plate,” Appl. Opt. 42, 1852–1855 (2003).
    [Crossref] [PubMed]
  13. J. J. Stamnes, Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves (Bristol [u.a.] : Hilger, 1986).
  14. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (New York [u.a.] : McGraw-Hill, 1996).
  15. Y. M. Engelberg and S. Ruschin, “Fast method for physical optics propagation of high-numerical-aperture beams,” J. Opt. Soc. Am. A 21, 2135–2145 (2004).
    [Crossref]
  16. U. Fuchs and U. D. Zeitner, “Method for fast calculation of ultra-short pulses in focal regions,” (2005). To be published.
  17. “ZEMAX Optical Design Program,” ZEMAX Development Corporation, USA.
  18. “Virtual Optics Lab 4.1,” LightTrans GmbH, Germany.
  19. R. M. Herman and T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991).
    [Crossref]
  20. C. L. Arnold, A. Heisterkamp, W. Ertmer, and H. Lubatschowski, “Streak formation as a side effect of optical breakdown during processing the bulk of transparent Kerr media with ultra-short laser pulses,” Appl. Phys. B 80, 247–253 (2005).
    [Crossref]
  21. H. Sonajalg and P. Saari, “Suppression of temporal spread of ultrashort pulses in dispersive media by Bessel beam generators,” Opt. Lett. 21, 1162–1164 (1996).
    [Crossref] [PubMed]

2005 (1)

C. L. Arnold, A. Heisterkamp, W. Ertmer, and H. Lubatschowski, “Streak formation as a side effect of optical breakdown during processing the bulk of transparent Kerr media with ultra-short laser pulses,” Appl. Phys. B 80, 247–253 (2005).
[Crossref]

2004 (2)

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51(16–18), 2533–2542 (2004).
[Crossref]

Y. M. Engelberg and S. Ruschin, “Fast method for physical optics propagation of high-numerical-aperture beams,” J. Opt. Soc. Am. A 21, 2135–2145 (2004).
[Crossref]

2003 (1)

2001 (2)

R. Piestun and D. A. B. Miller, “Spatiotemporal control of ultrashort optical pulses by refractive-diffractive-dispersive structured optical elements,” Opt. Lett. 26, 1373–1375 (2001).
[Crossref]

Z. L. Horváth and Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63(026601), 1–11 (2001).

1999 (1)

1996 (1)

1995 (1)

1993 (1)

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[Crossref] [PubMed]

1992 (3)

Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992).
[Crossref]

M. Kempe, U. Stamm, and B. Wilhelmi, “Spatial and temporal transformation of femtosecond laser pulses by lenses with annular aperture,” Opt. Commun. 89, 119–125 (1992).
[Crossref]

T. E. Sharp and P. J. Wisoff, “Analysis of lens and zone plate combinations for achromatic focusing of ultrashort laser pulses,” Appl. Opt. 31, 2765–2769 (1992).
[Crossref] [PubMed]

1991 (1)

1989 (1)

1988 (1)

S. Szatmári and G. Kühnle, “Pulse front and pulse duration distortion in refractive optics, and its compensation,” Opt. Commun. 69, 60–65 (1988).
[Crossref]

Arnold, C. L.

C. L. Arnold, A. Heisterkamp, W. Ertmer, and H. Lubatschowski, “Streak formation as a side effect of optical breakdown during processing the bulk of transparent Kerr media with ultra-short laser pulses,” Appl. Phys. B 80, 247–253 (2005).
[Crossref]

Ashman, R.

Bor, Z.

Z. L. Horváth and Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63(026601), 1–11 (2001).

Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992).
[Crossref]

Z. Bor, “Distortion of femtosecond laser pulses in lenses,” Opt. Lett. 14, 119–121 (1989).
[Crossref] [PubMed]

Burghoff, J.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51(16–18), 2533–2542 (2004).
[Crossref]

Engelberg, Y. M.

Ertmer, W.

C. L. Arnold, A. Heisterkamp, W. Ertmer, and H. Lubatschowski, “Streak formation as a side effect of optical breakdown during processing the bulk of transparent Kerr media with ultra-short laser pulses,” Appl. Phys. B 80, 247–253 (2005).
[Crossref]

Fuchs, U.

U. Fuchs and U. D. Zeitner, “Method for fast calculation of ultra-short pulses in focal regions,” (2005). To be published.

Gil, M. A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (New York [u.a.] : McGraw-Hill, 1996).

Gu, M.

Heisterkamp, A.

C. L. Arnold, A. Heisterkamp, W. Ertmer, and H. Lubatschowski, “Streak formation as a side effect of optical breakdown during processing the bulk of transparent Kerr media with ultra-short laser pulses,” Appl. Phys. B 80, 247–253 (2005).
[Crossref]

Herman, R. M.

Horváth, Z. L.

Z. L. Horváth and Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63(026601), 1–11 (2001).

Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992).
[Crossref]

Ibragimov, E.

Kempe, M.

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[Crossref] [PubMed]

M. Kempe, U. Stamm, and B. Wilhelmi, “Spatial and temporal transformation of femtosecond laser pulses by lenses with annular aperture,” Opt. Commun. 89, 119–125 (1992).
[Crossref]

Kühnle, G.

S. Szatmári and G. Kühnle, “Pulse front and pulse duration distortion in refractive optics, and its compensation,” Opt. Commun. 69, 60–65 (1988).
[Crossref]

Lubatschowski, H.

C. L. Arnold, A. Heisterkamp, W. Ertmer, and H. Lubatschowski, “Streak formation as a side effect of optical breakdown during processing the bulk of transparent Kerr media with ultra-short laser pulses,” Appl. Phys. B 80, 247–253 (2005).
[Crossref]

Mattei, G. O.

Miller, D. A. B.

Nolte, S.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51(16–18), 2533–2542 (2004).
[Crossref]

Piestun, R.

Rudolph, W.

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[Crossref] [PubMed]

Ruschin, S.

Saari, P.

Sharp, T. E.

Sonajalg, H.

Stamm, U.

M. Kempe, U. Stamm, and B. Wilhelmi, “Spatial and temporal transformation of femtosecond laser pulses by lenses with annular aperture,” Opt. Commun. 89, 119–125 (1992).
[Crossref]

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves (Bristol [u.a.] : Hilger, 1986).

Szatmári, S.

S. Szatmári and G. Kühnle, “Pulse front and pulse duration distortion in refractive optics, and its compensation,” Opt. Commun. 69, 60–65 (1988).
[Crossref]

Tünnermann, A.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51(16–18), 2533–2542 (2004).
[Crossref]

Wiggins, T. A.

Wilhelmi, B.

M. Kempe, U. Stamm, and B. Wilhelmi, “Spatial and temporal transformation of femtosecond laser pulses by lenses with annular aperture,” Opt. Commun. 89, 119–125 (1992).
[Crossref]

Will, M.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51(16–18), 2533–2542 (2004).
[Crossref]

Wisoff, P. J.

Zeitner, U. D.

U. Fuchs and U. D. Zeitner, “Method for fast calculation of ultra-short pulses in focal regions,” (2005). To be published.

Appl. Opt. (4)

Appl. Phys. B (1)

C. L. Arnold, A. Heisterkamp, W. Ertmer, and H. Lubatschowski, “Streak formation as a side effect of optical breakdown during processing the bulk of transparent Kerr media with ultra-short laser pulses,” Appl. Phys. B 80, 247–253 (2005).
[Crossref]

J. Mod. Opt. (1)

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51(16–18), 2533–2542 (2004).
[Crossref]

J. Opt. Soc. Am. A (2)

Opt. Commun. (3)

S. Szatmári and G. Kühnle, “Pulse front and pulse duration distortion in refractive optics, and its compensation,” Opt. Commun. 69, 60–65 (1988).
[Crossref]

Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992).
[Crossref]

M. Kempe, U. Stamm, and B. Wilhelmi, “Spatial and temporal transformation of femtosecond laser pulses by lenses with annular aperture,” Opt. Commun. 89, 119–125 (1992).
[Crossref]

Opt. Lett. (3)

Phys. Rev. A (1)

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[Crossref] [PubMed]

Phys. Rev. E (1)

Z. L. Horváth and Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63(026601), 1–11 (2001).

Other (5)

J. J. Stamnes, Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves (Bristol [u.a.] : Hilger, 1986).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (New York [u.a.] : McGraw-Hill, 1996).

U. Fuchs and U. D. Zeitner, “Method for fast calculation of ultra-short pulses in focal regions,” (2005). To be published.

“ZEMAX Optical Design Program,” ZEMAX Development Corporation, USA.

“Virtual Optics Lab 4.1,” LightTrans GmbH, Germany.

Supplementary Material (5)

» Media 1: AVI (248 KB)     
» Media 2: AVI (348 KB)     
» Media 3: AVI (262 KB)     
» Media 4: AVI (2335 KB)     
» Media 5: AVI (7036 KB)     

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Figures (7)

Fig. 1.
Fig. 1. Illustration of a typical imaging system, e.g. a microscope objective (Linos 038723), containing entrance and exit pupil with their specific coordinates (px, py, zen) and (px, py, zex). The reference sphere in the exit pupil is is centered in the focus. The positions of entrance and exit pupil depend on the particular optical system. For imaging systems the focal plane (x, y, zf ) is of special interest.

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Fig. 2.
Fig. 2. Spectral phase coded in gray scale in the exit pupil of the three optics. The horizontal axis shows the variation of the phase as a function of py which is therefore the aberration for each frequency v. The vertical dependence in phase with the frequency shows the influence of material dispersion. The planoconvex lens (a) is having severe spherical aberrations, the Geltech asphere (b) is showing chromatic aberrations as well as dispersion effects and the microscope objective (c) is having strong dispersion effects. The frequency slices depicted are 8·1013Hz centered at 3.75·1014Hz (800nm).

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Fig. 3.
Fig. 3. Radial intensity distribution of the focussing of an ultrashort laser pulse (24fs) with an ideal lens. Light is propagating from left to right. The time is chosen so that 0fs refers to the pulse intensity maximum arriving at the focus. The movie shows an animation of the focussing of the ultra-short laser pulse with the same scaling as depicted above. [Media 1]

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Fig. 4.
Fig. 4. Radial intensity distribution of the focussing of an ultrashort laser pulse (24fs) with the microscope objective (a) causing an increase of the pulse duration to 116fs. The chromatic aberrations of the Geltech asphere (b) lead to the typical horseshoe shape of the pulse front. The pulse duration is increased as well depending on the thickness of the lens. The movie shows an animation of the focussing of the ultra-short laser pulse with the same scaling as depicted above. [Media 2] [Media 3]

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Fig. 5.
Fig. 5. Radial intensity distribution of an ultrashort laser pulse (24fs) focussed by the planoconvex lens. There are three intensity maximums traveling along the optical axis, explanation is given in the text. The pulses are propagating from bottom to top. The movie shows an animations of the focussing of the ultra-short laser pulse between the marginal and paraxial focal plane, which are about 2mm apart. The observation window is traveling with the main pulse (max1) and covers an area of 660µm width and 500µm length. [Media 4, Media 5]

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Fig. 6.
Fig. 6. Intensity distribution along the optical axis (Due to the numerical calculation the optical axis has got a width of 831nm.) compared to the total pulse intensity for the microscope objective with NA=0.45 and NA=0.1. The position z=0µm marks the geometrical focus for each microscope objective. For a homogeneous illuminated aperture the intensity along the optical axis is oscillating. If the illumination is gaussian shaped (0:5% of the maximum intensity at the rim) the envelop is unchanged but the oscillation disappears.

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Fig. 7.
Fig. 7. Illustration of the formation of the additional pulse as a interference pattern along the optical axis (red circle). At each point along the optical axis different parts of the pulse front interfere which is marked with an a. Therefore it is no classical wave package.

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Equations (4)

Equations on this page are rendered with MathJax. Learn more.

E ( t , x , y , z ) = ℱ − 1 [ E ( v , x , y , z ) ] = ∫ − ∞ ∞ d v A ( v , x , y , z ) · e i ϕ ( v , x , y , z ) e i 2 π v t ,
E ( v , p x , p y , z ex ) = A ( v , p x , p y , z en ) · e i ϕ ( v , p x , p y , z en ) · e i ϕ ab ( v , p x , p y , z ex )
E ( v , x , y , z f ) ∝ v . ℱ p x p y → xy [ E ( v , p x , p y , z ex ) ] .
v b = c cos α .

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