Abstract

The Laboratory for Laser Energetics plans to install KDP wedges on each beam line of the OMEGA laser system in order to improve the on-target laser uniformity by decreasing the instantaneous speckle through spatial averaging of the two resultant orthogonally polarized beams. The proposed wedge-production method, diamond turning, produces small residual scratch marks, causing each beam to acquire a pseudorandom phase perturbation. In addition, the orthogonally polarized beams interfere such that their combined polarization state continuously cycles through all elliptical states along any transverse plane. Since the nonlinear refractive index depends on the polarization state, intense beams accumulate a periodic phase perturbation that is greater for linear polarization. Propagation of both types of phase perturbation yields an intensity modulation that tends to be larger in the neighborhood of linear polarization, through a combination of diffraction and self- and cross-phase modulation. However, one- and two-dimensional calculations using a symmetrized split-step Fourier method demonstrate that diamond-turned KDP wedges are not a significant source of intensity modulation under OMEGA laser conditions. Installation of diamond-turned rather than polished wedges will reduce costs without adversely affecting the system performance.

© 2002 Optical Society of America

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References

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  1. Y. Kato, Institute of Laser Engineering, Osaka University, Suita, Osaka, Japan (personal communication, 1984).
  2. Laboratory for Laser Energetics, “Phase conversion using distributed polarization rotation,” Laboratory for Laser Energetics LLE Review 45, 1–12, NTIS document DOE/DP40200–149 (National Technical Information Service, Springfield, Va., 1990).
  3. S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam unifor-mity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
    [CrossRef]
  4. D. A. Roberts, “Dispersion equations for nonlinear optical crystals: KDP, AgGaSe2, and AgGaS2,” Appl. Opt. 35, 4677–4688 (1996).
    [CrossRef] [PubMed]
  5. R. L. Sutherland, Handbook of Nonlinear Optics, Opt. Eng. 52 (Marcel Dekker, New York, 1996), pp. 297–301.
  6. A. B. Carlson, Communication Systems: An Introduction to Signals and Noise in Electrical Communication, McGraw-Hill Electrical and Electronic Engineering Series (McGraw-Hill, New York, 1968), pp. 153–154.
  7. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed., Optics and Photonics Series (Academic, San Diego, 1995), pp. 50–54.
  8. Ts. Gantsog and R. Tanas, “Phase properties of elliptically polarized light propagating in a Kerr medium,” J. Mod. Opt. 38, 1537–1558 (1991).
    [CrossRef]
  9. K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics, Springer Series on Wave Phenomena (Springer-Verlag, Berlin, 1994), Vol. 16, pp. 124–131.
  10. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 48–54.
  11. R. W. Hellwarth, D. M. Pennington, and M. A. Henesian, “Indices governing optical self-focusing and self-induced changes in the state of polarization in N2, O2, H2, and Ar gases,” Phys. Rev. A 41, 2766–2777 (1990).
    [CrossRef] [PubMed]

1996 (1)

1991 (1)

Ts. Gantsog and R. Tanas, “Phase properties of elliptically polarized light propagating in a Kerr medium,” J. Mod. Opt. 38, 1537–1558 (1991).
[CrossRef]

1990 (1)

R. W. Hellwarth, D. M. Pennington, and M. A. Henesian, “Indices governing optical self-focusing and self-induced changes in the state of polarization in N2, O2, H2, and Ar gases,” Phys. Rev. A 41, 2766–2777 (1990).
[CrossRef] [PubMed]

1989 (1)

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam unifor-mity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Craxton, R. S.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam unifor-mity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Gantsog, Ts.

Ts. Gantsog and R. Tanas, “Phase properties of elliptically polarized light propagating in a Kerr medium,” J. Mod. Opt. 38, 1537–1558 (1991).
[CrossRef]

Hellwarth, R. W.

R. W. Hellwarth, D. M. Pennington, and M. A. Henesian, “Indices governing optical self-focusing and self-induced changes in the state of polarization in N2, O2, H2, and Ar gases,” Phys. Rev. A 41, 2766–2777 (1990).
[CrossRef] [PubMed]

Henesian, M. A.

R. W. Hellwarth, D. M. Pennington, and M. A. Henesian, “Indices governing optical self-focusing and self-induced changes in the state of polarization in N2, O2, H2, and Ar gases,” Phys. Rev. A 41, 2766–2777 (1990).
[CrossRef] [PubMed]

Kessler, T.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam unifor-mity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Letzring, S.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam unifor-mity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Pennington, D. M.

R. W. Hellwarth, D. M. Pennington, and M. A. Henesian, “Indices governing optical self-focusing and self-induced changes in the state of polarization in N2, O2, H2, and Ar gases,” Phys. Rev. A 41, 2766–2777 (1990).
[CrossRef] [PubMed]

Roberts, D. A.

Short, R. W.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam unifor-mity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Skupsky, S.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam unifor-mity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Soures, J. M.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam unifor-mity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Tanas, R.

Ts. Gantsog and R. Tanas, “Phase properties of elliptically polarized light propagating in a Kerr medium,” J. Mod. Opt. 38, 1537–1558 (1991).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (1)

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam unifor-mity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

J. Mod. Opt. (1)

Ts. Gantsog and R. Tanas, “Phase properties of elliptically polarized light propagating in a Kerr medium,” J. Mod. Opt. 38, 1537–1558 (1991).
[CrossRef]

Phys. Rev. A (1)

R. W. Hellwarth, D. M. Pennington, and M. A. Henesian, “Indices governing optical self-focusing and self-induced changes in the state of polarization in N2, O2, H2, and Ar gases,” Phys. Rev. A 41, 2766–2777 (1990).
[CrossRef] [PubMed]

Other (7)

K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics, Springer Series on Wave Phenomena (Springer-Verlag, Berlin, 1994), Vol. 16, pp. 124–131.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 48–54.

Y. Kato, Institute of Laser Engineering, Osaka University, Suita, Osaka, Japan (personal communication, 1984).

Laboratory for Laser Energetics, “Phase conversion using distributed polarization rotation,” Laboratory for Laser Energetics LLE Review 45, 1–12, NTIS document DOE/DP40200–149 (National Technical Information Service, Springfield, Va., 1990).

R. L. Sutherland, Handbook of Nonlinear Optics, Opt. Eng. 52 (Marcel Dekker, New York, 1996), pp. 297–301.

A. B. Carlson, Communication Systems: An Introduction to Signals and Noise in Electrical Communication, McGraw-Hill Electrical and Electronic Engineering Series (McGraw-Hill, New York, 1968), pp. 153–154.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed., Optics and Photonics Series (Academic, San Diego, 1995), pp. 50–54.

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Figures (6)

Fig. 1
Fig. 1

Birefringent KDP wedge achieves polarization smoothing and a theoretical 1/2 reduction in nonuniformity. The KDP crystal is cut to make a 59° angle between the crystal’s optic axis and the propagation axis. This angle yields linear refractive indices of 1.532498 and 1.498641 for the slow and fast waves, respectively, in the UV. The KDP wedge is milled from a thick slab of KDP and is specified to have a nominal thickness of 1 cm at its thinnest edge. The current requirements for OMEGA set the wedge angle to 4.5 arc min.

Fig. 2
Fig. 2

Bandpass-filtered pseudorandom noise source where the passband is set to 2π/(4 mm)ky2π/(2 mm) and the peak-to-valley scratch depth is 40 nm.

Fig. 3
Fig. 3

Two propagation steps of the symmetrized split-step Fourier method covering a distance of 2Δz.

Fig. 4
Fig. 4

Nonlinear propagation through 12 m of air past an optically smooth KDP wedge with an incident intensity level of 10.3 GW/cm2. A contrast of 1.31 is observed. Squares and circles indicate positions of linear and circular polarization, respectively. Note that only a small section of the entire transverse profile is plotted.

Fig. 5
Fig. 5

Nonlinear propagation through 12 m of air past a pseudorandomly scratched KDP wedge with 40-nm peak-to-valley scratch depth and a passband of 2π/(4 mm)ky2π/(2 mm) (a) at 1.3 GW/cm2 and (b) at 10.3 GW/cm2. The resulting contrast is 1.32 in (a) and 2.63 in (b). Squares and circles indicate positions of linear and circular polarization, respectively. Note that only a small section of the entire transverse profile is plotted.

Fig. 6
Fig. 6

Three lineouts from a 2-D simulation (taken at the center and near the edges of the beam) of nonlinear beam propagation with a 1.3-GW/cm2 intensity, through 12 m of air, past a pseudorandomly scratched KDP wedge with 40-nm peak-to-valley scratch depth and a passband of 2π/(4 mm)kx, ky2π/(2 mm). An overall contrast of 1.35 is observed. Note that only a small section of the entire transverse profile is plotted.

Tables (2)

Tables Icon

Table 1 Resultant Contrast for Linear Propagation Through 12 m of Air Past a Scratched KDP Wedge at an Incident Intensity Level of 1.3 GW/cm2 for Different Scratch Depths and Filter Types

Tables Icon

Table 2 Resultant Contrast for Nonlinear Propagation Through 12 m of Air Past a Scratched KDP Wedge at an Incident Intensity Level of 1.3 GW/cm2 for Different Scratch Depths and Filter Types

Equations (33)

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λpol=λ0sin(θ)=351 nmsin(44 µrad)=8 mm,
Φmill=k0(nKDP-1)S(y),
S(y)=F-1F [N(y)]rectky-ky0kymax-kymin,
rect(x)=1|x|120|x|>12
E(y, z, t)=12{pˆE(y, z)exp[-i(ω0t-k0n0z)]+c.c.},
E(y, z, t)=12{[pˆRHERH(y, z)+pˆLHELH(y, z)]exp[-i(ω0t-k0n0z)]+c.c.},
ERH(y, z)=12[Ex(y, z)-Ey(y, z)],
ELH(y, z)=12[Ex(y, z)+Ey(y, z)],
pˆRH12(xˆ+iyˆ), pˆLH12(xˆ-iyˆ).
n=n0+Δn.
ERH(y, z)z=i2kT2ERH(y, z)+ik0ΔnRHERH(y, z),
ELH(y, z)z=i2kT2ELH(y, z)+ik0ΔnLHELH(y, z),
ΔnRH=34n0[χxyxy(3)|ERH(y, z)|2+(χxyxy(3)+χxxyy(3))|ELH(y, z)|2],
ΔnLH=34n0[χxyxy(3)|ELH(y, z)|2+(χxyxy(3)+χxxyy(3))|ERH(y, z)|2],
E(y, z)z=(Dˆ+Eˆ)E(y, z),
Dˆi2kT2,
Nˆik0Δn,
E(y, z+Δz)=exp[Δz(Dˆ+Nˆ)]E(y, z).
|ERH(y, z)|2z=0,|ELH(y, z)|2z=0.
Δnlin=38n0[χxxyy(3)+2χxyxy(3)]|Elin|2.
Δncir=34n0χxyxy(3)|Ecir|2.
Δnlin>Δncir.
2E(y, z)+k02n02E(y, z)=0,
E(y, z+Δz)=12π -E˜(ky, z)×exp[i(Δzk02n02-ky2+kyy)]dky,
E˜(ky, z)=-E(y, z)exp(-ikyy)dy.
E(y, z)z=NˆE(y, z),
E(y, z+Δz)=E(y, z)exp(ik0ΔnΔz),
E(y, z+Δz)exp(ΔzDˆ)exp(ΔzNˆ)E(y, z).
E(y, z+Δz)expΔz2Dˆexp(ΔzNˆ)expΔz2DˆE(y, z).
E(y)=12{tanh[100(y+0.14)]-tanh[100(y-0.14)]},
Contrast=max{I(y)}mean{I(y)},
χxyxy(3)(-ω, -ω, ω, ω)=28.16×10-19 esu,
χxxyy(3)(-ω, -ω, ω ω)=172.4×10-19 esu.

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