Abstract

We study the influence of third-order spherical aberration on the group velocity dispersion and on the propagation time delay of a plane pulse that is focused by a thin lens. Applications in refractive–diffractive propagation time delay compensation systems and in Gaussian temporal-shaped pulses are analyzed.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Z. Bor, “Distortion of femtosecond laser pulses in lenses and lens systems,” J. Mod. Opt. 35, 1907–1918 (1988).
    [CrossRef]
  2. Z. Bor, “Distortions of femtosecond laser pulses in lenses,” Opt. Lett. 14, 119–121 (1989).
    [CrossRef] [PubMed]
  3. Z. Bor, Z. Horvath, “Distortions of femtosecond pulses in lenses: wave optical description,” Opt. Commun. 94, 249–258 (1992).
    [CrossRef]
  4. M. Kempe, U. Stamm, B. Wilhelmi, W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 7, 1158–1165 (1992).
    [CrossRef]
  5. M. Kempe, W. Rudolph, “Impact of chromatic and spherical aberration on the focusing of ultrashort light pulses by lenses,” Opt. Lett. 18, 137–139 (1993).
    [CrossRef] [PubMed]
  6. M. Kempe, W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
    [CrossRef] [PubMed]
  7. T. E. Sharp, P. J. Wilsoff, “Analysis of lens zone plate combinations for achromatic focusing of ultrashort laser pulses,” Appl. Opt. 31, 2765–2769 (1992).
    [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. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), pp. 96–107.
  10. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 226–230.
  11. M. Bass, E. Van Stryland, D. Williams, W. Wolfe, Handbook of Optics (McGraw-Hill, New York, 1995).

1995 (1)

1993 (2)

1992 (3)

Z. Bor, Z. Horvath, “Distortions of femtosecond pulses in lenses: wave optical description,” Opt. Commun. 94, 249–258 (1992).
[CrossRef]

M. Kempe, U. Stamm, B. Wilhelmi, W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 7, 1158–1165 (1992).
[CrossRef]

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

1989 (1)

1988 (1)

Z. Bor, “Distortion of femtosecond laser pulses in lenses and lens systems,” J. Mod. Opt. 35, 1907–1918 (1988).
[CrossRef]

Bass, M.

M. Bass, E. Van Stryland, D. Williams, W. Wolfe, Handbook of Optics (McGraw-Hill, New York, 1995).

Bor, Z.

Z. Bor, Z. Horvath, “Distortions of femtosecond pulses in lenses: wave optical description,” Opt. Commun. 94, 249–258 (1992).
[CrossRef]

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

Z. Bor, “Distortion of femtosecond laser pulses in lenses and lens systems,” J. Mod. Opt. 35, 1907–1918 (1988).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 226–230.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), pp. 96–107.

Horvath, Z.

Z. Bor, Z. Horvath, “Distortions of femtosecond pulses in lenses: wave optical description,” Opt. Commun. 94, 249–258 (1992).
[CrossRef]

Ibragimov, E.

Kempe, M.

M. Kempe, W. Rudolph, “Impact of chromatic and spherical aberration on the focusing of ultrashort light pulses by lenses,” Opt. Lett. 18, 137–139 (1993).
[CrossRef] [PubMed]

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

M. Kempe, U. Stamm, B. Wilhelmi, W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 7, 1158–1165 (1992).
[CrossRef]

Rudolph, W.

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

M. Kempe, W. Rudolph, “Impact of chromatic and spherical aberration on the focusing of ultrashort light pulses by lenses,” Opt. Lett. 18, 137–139 (1993).
[CrossRef] [PubMed]

M. Kempe, U. Stamm, B. Wilhelmi, W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 7, 1158–1165 (1992).
[CrossRef]

Sharp, T. E.

Stamm, U.

M. Kempe, U. Stamm, B. Wilhelmi, W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 7, 1158–1165 (1992).
[CrossRef]

Van Stryland, E.

M. Bass, E. Van Stryland, D. Williams, W. Wolfe, Handbook of Optics (McGraw-Hill, New York, 1995).

Wilhelmi, B.

M. Kempe, U. Stamm, B. Wilhelmi, W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 7, 1158–1165 (1992).
[CrossRef]

Williams, D.

M. Bass, E. Van Stryland, D. Williams, W. Wolfe, Handbook of Optics (McGraw-Hill, New York, 1995).

Wilsoff, P. J.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 226–230.

Wolfe, W.

M. Bass, E. Van Stryland, D. Williams, W. Wolfe, Handbook of Optics (McGraw-Hill, New York, 1995).

Appl. Opt. (2)

J. Mod. Opt. (1)

Z. Bor, “Distortion of femtosecond laser pulses in lenses and lens systems,” J. Mod. Opt. 35, 1907–1918 (1988).
[CrossRef]

J. Opt. Soc. Am. B (1)

M. Kempe, U. Stamm, B. Wilhelmi, W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 7, 1158–1165 (1992).
[CrossRef]

Opt. Commun. (1)

Z. Bor, Z. Horvath, “Distortions of femtosecond pulses in lenses: wave optical description,” Opt. Commun. 94, 249–258 (1992).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

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

Other (3)

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), pp. 96–107.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 226–230.

M. Bass, E. Van Stryland, D. Williams, W. Wolfe, Handbook of Optics (McGraw-Hill, New York, 1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

(a) Coordinate system, (b) lens parameters.

Fig. 2
Fig. 2

Spherical aberration as a function of radius of curvature R 1 and the deformation coefficient of one surface of the lens, C. The arrow points in the direction of increasing C, which takes equidistant values from -0.74 to -0.44 for each curve.

Fig. 3
Fig. 3

Relative weight of the linear chirp and the spherical aberration GVD contributions as functions of radius of curvature R 1 and the deformation coefficient of one surface of the lens, C. The arrow points in the direction of increasing C, which takes equidistant values from -0.74 to -0.44 for each curve (adim means dimensionless).

Fig. 4
Fig. 4

Relative weight of the time delay and the spherical aberration PTD contribution as a function of radius of curvature R 1 and the deformation coefficient of one surface of the lens, C. The arrow points in the direction of increasing C, which takes equidistant values from -0.74 to -0.44 for each curve (adim means dimensionless).

Fig. 5
Fig. 5

Intensity distribution I(v, t) in the focal plane. Free from aberrations (adim means dimensionless).

Fig. 6
Fig. 6

Intensity distribution I(v, t) in the focal plane. Spherical aberration of λ0 (adim means dimensionless).

Equations (66)

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

Ux2, y2, z, ω  dx1dy1Px1, y1Aωtx1, y1×expJka2zx2-x12+y2-y12,
tx1, y1=expJkld×exp-Jkl-kax12+y1221R1-1R2,
Px1, y1=expJkaϕx1, y1   x12+y12r12,
=0 otherwise,
ϕx1, y1=-¼Bx12+y122.
B=12 β+nω28nω-12P3-nω2nω+2 2P+12nωnω+2Pnω+22nω-1 σ+2nω+12,
kl=ωc nω=k0n01+a1Δω+a2Δω2,
kl-ka=ωcnω-1=k0n0-11+b1Δω+b2Δω2,
a1=1ω0+1n0 D,  a2=1ω0n0 D+12n0 D,  Ddndωω=ω0,  Dd2ndω2ω=ω0,  ka=ωc,
ka=k01+Δωω0,  k0kaω0,  n0nω0,  biai,  changing n0by n0-1.
B=B0+B1Δω+B2Δω2.
x12+y12=r12=ar2,
x22+y22=r22,
vak0r2f0.
Pr=exp-Jk0a4B04 r4×exp-Jk0a44B1+B0/ω0r4Δω×exp-Jk0a44B2+B1/ω0r4Δω2circr.
Uv, Δω  AΔωexp-Jk0n0dΔωa1+a2Δω×exp-J v24N1+Δωω0×01rdrJ0rv1+Δωω0×exp-J k02f0ar2Δωb1-1ω0+b2Δω×exp-Jk0B04ar4×exp-Jk0¼B1+B0/ω0ar4Δω×exp-Jk0¼B2+B1/ω0ar4Δω2,
Uv, t  dΔωAΔω01 rdrJ0rv1+Δωω0×exp-Jk0B04ar4×exp-JΔω2δ-δr2-δr4×exp-JΔωt-τ+τr2+τr4,
δa2k02f0 b2,
δk0n0da2,
δ"a4k04B2+B1ω0,
τa2k02f0n0-1 D,
τk0n0da1,
τ"a4k04B1+B0ω0.
WGVDδr4δr2r=a=f0a2B2+B1/ω03/2D/ω0n0-1,
WPTDτr4τr2r=a=f0a2B1+B0/ω02D/n0-1.
Nλ0a44λ0 B0
Fr=coskω2r0r12,
Fr=12expJk0a22r01+Δω/ω0r2+exp-Jk0a22r01+Δω/ω0r2.
1r0=12Dω0f0n0-1+a24 B1r2,
1zc=-1f1±1r0-a22 B0r2.
at=exp-t/T2AΔω=exp-T2Δω2,
Uv, t  01 rdrJ0rvexp-Jk0B04ar4×1+Jδ-δr2-δr4/T21+δ-δr2-δr4/T221/2×exp-t-τ+τr2+τr42T21+δ-δr2-δr4/T22×1+Jδ-δr2-δr4/T2.
Uv, t  01 rdrJ0rvexp-Jk0B04ar4×exp-t-τT+τr2T+τr4T2.
K01R1-1R2,
K11R1+1R2,
K2C1R13-C2R23,
B0=i=16 B0i,
B01=n0-1n02K03,
B02=-18n0-13n0n0+2 K03,
B03=½n0-1K23,
B04=18n0-1n0+22n0 K0K12,
B05=-12n0+1n0-12n0 K1K02,
B06=12n0-13n0+12n0n0+2 K03.
B0=B0iUi
g101n0 D,
g2012n0Dω0,
g111n0-1 D,
g2112n0-1Dω0,
g121n0+1 D,
g2212n0+1Dω0,
g131n0+2 D,
g2312n0+2Dω0.
G11g11+2g10,
G123g11+g10-g13,
G13g11,
G14g11+g13-g10,
G15g12+2g11-g10,
G163g11+2g12-g10-g13;
G21g21+g102+2g20+2g11g10,
G22g112+g21+g20+g132-g23-g10g13+3g11g10-3g11g13,
G23g21,
G24g21+g23+g11g13+g102-g20+g11g10-g13g10,
G25g22+g112+2g12g11+g102-g20-g12g10-2g11g10,
G263g112+3g21+g122+2g22+6g11g12+g102-g20+g132-g23+g10g13-3g11+2g12g10+g13,
B1=B0iG1i,
B2=B0iG2i.

Metrics