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Title: Direct-drive measurements of laser-imprint-induced shock velocity nonuniformities [First direct-drive measurements of laser-imprint-induced shock velocity nonuniformities]

Abstract

Perturbations in the velocity profile of a laser-ablation-driven shock wave seeded by speckle in the spatial beam intensity (i.e., laser imprint) have been measured. Direct measurements of these velocity perturbations were recorded using a two-dimensional high-resolution velocimeter probing plastic material shocked by a 100-ps picket laser pulse from the OMEGA laser system. The measured results for experiments with one, two, and five overlapping beams incident on the target clearly demonstrate a reduction in long-wavelength (>25–μm) perturbations with an increasing number of overlapping laser beams, consistent with theoretical expectations. Furthermore, these experimental measurements are crucial to validate radiation-hydrodynamics simulations of laser imprint for laser direct drive inertial confinement fusion research since they highlight the significant (factor of 3) underestimation of the level of seeded perturbation when the microphysics processes for initial plasma formation, such as multiphoton ionization are neglected.

Authors:
 [1];  [1];  [1];  [1];  [1];  [2];  [2];  [3];  [1];  [1];  [1]
  1. Univ. of Rochester, Rochester, NY (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  3. Univ. Bordeaux-CNRS-CEA, Talence (France)
Publication Date:
Research Org.:
Univ. of Rochester, Rochester, NY (United States). Lab for Laser Energetics; Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
Contributing Org.:
Laboratory for Laser Energetics, University of Rochester
OSTI Identifier:
1542619
Alternate Identifier(s):
OSTI ID: 1546318; OSTI ID: 1756732
Report Number(s):
2018-284, 1507; LLNL-JRNL-811809
Journal ID: ISSN 2470-0045; PLEEE8; 2018-284, 1507, 2467
Grant/Contract Number:  
NA0003856; AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 99; Journal Issue: 6; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Direct drive; high-energy-density plasmas; inertial confinement fusion; plasma production & heating by laster beams, laser-foil, laser-cluster; laser inertial confinement; optical interferometry

Citation Formats

Peebles, J. L., Hu, S. X., Theobald, W., Goncharov, V. N., Whiting, N., Celliers, P. M., Ali, S. J., Duchateau, G., Campbell, E. M., Boehly, T. R., and Regan, S. P. Direct-drive measurements of laser-imprint-induced shock velocity nonuniformities [First direct-drive measurements of laser-imprint-induced shock velocity nonuniformities]. United States: N. p., 2019. Web. doi:10.1103/PhysRevE.99.063208.
Peebles, J. L., Hu, S. X., Theobald, W., Goncharov, V. N., Whiting, N., Celliers, P. M., Ali, S. J., Duchateau, G., Campbell, E. M., Boehly, T. R., & Regan, S. P. Direct-drive measurements of laser-imprint-induced shock velocity nonuniformities [First direct-drive measurements of laser-imprint-induced shock velocity nonuniformities]. United States. doi:https://doi.org/10.1103/PhysRevE.99.063208
Peebles, J. L., Hu, S. X., Theobald, W., Goncharov, V. N., Whiting, N., Celliers, P. M., Ali, S. J., Duchateau, G., Campbell, E. M., Boehly, T. R., and Regan, S. P. Mon . "Direct-drive measurements of laser-imprint-induced shock velocity nonuniformities [First direct-drive measurements of laser-imprint-induced shock velocity nonuniformities]". United States. doi:https://doi.org/10.1103/PhysRevE.99.063208. https://www.osti.gov/servlets/purl/1542619.
@article{osti_1542619,
title = {Direct-drive measurements of laser-imprint-induced shock velocity nonuniformities [First direct-drive measurements of laser-imprint-induced shock velocity nonuniformities]},
author = {Peebles, J. L. and Hu, S. X. and Theobald, W. and Goncharov, V. N. and Whiting, N. and Celliers, P. M. and Ali, S. J. and Duchateau, G. and Campbell, E. M. and Boehly, T. R. and Regan, S. P.},
abstractNote = {Perturbations in the velocity profile of a laser-ablation-driven shock wave seeded by speckle in the spatial beam intensity (i.e., laser imprint) have been measured. Direct measurements of these velocity perturbations were recorded using a two-dimensional high-resolution velocimeter probing plastic material shocked by a 100-ps picket laser pulse from the OMEGA laser system. The measured results for experiments with one, two, and five overlapping beams incident on the target clearly demonstrate a reduction in long-wavelength (>25–μm) perturbations with an increasing number of overlapping laser beams, consistent with theoretical expectations. Furthermore, these experimental measurements are crucial to validate radiation-hydrodynamics simulations of laser imprint for laser direct drive inertial confinement fusion research since they highlight the significant (factor of 3) underestimation of the level of seeded perturbation when the microphysics processes for initial plasma formation, such as multiphoton ionization are neglected.},
doi = {10.1103/PhysRevE.99.063208},
journal = {Physical Review E},
number = 6,
volume = 99,
place = {United States},
year = {2019},
month = {6}
}

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Cited by: 3 works
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Works referenced in this record:

Multiphoton Ionization in Dielectrics: Comparison of Circular and Linear Polarization
journal, December 2006


Two-dimensional imaging velocity interferometry: Data analysis techniques
journal, April 2012

  • Erskine, David J.; Smith, R. F.; Bolme, C. A.
  • Review of Scientific Instruments, Vol. 83, Issue 4
  • DOI: 10.1063/1.4704840

Distributed phase plates for super-Gaussian focal-plane irradiance profiles
journal, January 1995

  • Lin, Y.; Lawrence, G. N.; Kessler, T. J.
  • Optics Letters, Vol. 20, Issue 7
  • DOI: 10.1364/OL.20.000764

Use of induced spatial incoherence for uniform illumination of laser fusion targets
journal, June 1983


Initial performance results of the OMEGA laser system
journal, January 1997


Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods
journal, January 1994

  • Ghiglia, Dennis C.; Romero, Louis A.
  • Journal of the Optical Society of America A, Vol. 11, Issue 1
  • DOI: 10.1364/JOSAA.11.000107

Reduction of laser imprinting using polarization smoothing on a solid-state fusion laser
journal, April 1999

  • Boehly, T. R.; Smalyuk, V. A.; Meyerhofer, D. D.
  • Journal of Applied Physics, Vol. 85, Issue 7
  • DOI: 10.1063/1.369702

Time-dependent ionization models designed for intense and short laser pulse propagation in dielectric materials
journal, May 2012


Velocity sensing interferometer (VISAR) modification
journal, January 1979

  • Hemsing, Willard F.
  • Review of Scientific Instruments, Vol. 50, Issue 1
  • DOI: 10.1063/1.1135672

Two-dimensional simulations of the neutron yield in cryogenic deuterium-tritium implosions on OMEGA
journal, October 2010

  • Hu, S. X.; Goncharov, V. N.; Radha, P. B.
  • Physics of Plasmas, Vol. 17, Issue 10
  • DOI: 10.1063/1.3491467

Multiphoton ionization of atoms
journal, October 1991


Reduction of time-averaged irradiation speckle nonuniformity in laser-driven plasmas due to target ablation
journal, September 1997

  • Epstein, R.
  • Journal of Applied Physics, Vol. 82, Issue 5
  • DOI: 10.1063/1.366021

Direct-drive hydrodynamic instability experiments on the GEKKO XII laser
journal, November 1997

  • Azechi, H.; Nakai, M.; Shigemori, K.
  • Physics of Plasmas, Vol. 4, Issue 11
  • DOI: 10.1063/1.872528

Comparison between measured and calculated nonuniformities of Nike laser beams smoothed by induced spatial incoherence
journal, February 1998


Fourier-Space Nonlinear Rayleigh-Taylor Growth Measurements of 3D Laser-Imprinted Modulations in Planar Targets
journal, November 2005


Effects of thin high-Z layers on the hydrodynamics of laser-accelerated plastic targets
journal, May 2002

  • Obenschain, S. P.; Colombant, D. G.; Karasik, M.
  • Physics of Plasmas, Vol. 9, Issue 5
  • DOI: 10.1063/1.1464541

Understanding the effects of laser imprint on plastic-target implosions on OMEGA
journal, October 2016

  • Hu, S. X.; Michel, D. T.; Davis, A. K.
  • Physics of Plasmas, Vol. 23, Issue 10, 102701
  • DOI: 10.1063/1.4962993

Improved laser‐beam uniformity using the angular dispersion of frequency‐modulated light
journal, October 1989

  • Skupsky, S.; Short, R. W.; Kessler, T.
  • Journal of Applied Physics, Vol. 66, Issue 8
  • DOI: 10.1063/1.344101

Multidimensional analysis of direct-drive, plastic-shell implosions on OMEGA
journal, May 2005

  • Radha, P. B.; Collins, T. J. B.; Delettrez, J. A.
  • Physics of Plasmas, Vol. 12, Issue 5
  • DOI: 10.1063/1.1882333

Saturation of the Rayleigh-Taylor Growth of Broad-Bandwidth Laser-Imposed Nonuniformities in Planar Targets
journal, December 1998


A model for multiphoton absorption in dielectric materials induced by short laser pulses at moderate intensities
journal, May 2013

  • Mézel, Candice; Duchateau, Guillaume; Geneste, Grégory
  • Journal of Physics: Condensed Matter, Vol. 25, Issue 23
  • DOI: 10.1088/0953-8984/25/23/235501

Suppression of the Rayleigh-Taylor Instability due to Self-Radiation in a Multiablation Target
journal, May 2004


Measurement of a Dispersion Curve for Linear-Regime Rayleigh-Taylor Growth Rates in Laser-Driven Planar Targets
journal, April 1997


Mitigating Laser Imprint in Direct-Drive Inertial Confinement Fusion Implosions with High- Z Dopants
journal, May 2012


X-ray preheating of window materials in direct-drive shock-wave timing experiments
journal, December 2006

  • Theobald, W.; Miller, J. E.; Boehly, T. R.
  • Physics of Plasmas, Vol. 13, Issue 12
  • DOI: 10.1063/1.2397581

Multimode Rayleigh-Taylor Experiments on Nova
journal, July 1994


Suppression of Laser Nonuniformity Imprinting Using a Thin High- Z Coating
journal, February 2015


Measurements of laser-imprinting sensitivity to relative beam mistiming in planar plastic foils driven by multiple overlapping laser beams
journal, July 2005

  • Smalyuk, V. A.; Goncharov, V. N.; Boehly, T. R.
  • Physics of Plasmas, Vol. 12, Issue 7
  • DOI: 10.1063/1.1943900

Minimum Lp-norm two-dimensional phase unwrapping
journal, January 1996

  • Ghiglia, Dennis C.; Romero, Louis A.
  • Journal of the Optical Society of America A, Vol. 13, Issue 10
  • DOI: 10.1364/JOSAA.13.001999

X‐ray laser radiography of perturbations due to imprint of laser speckle in 0.35 μm laser irradiation of a thin Si foil
journal, March 1996

  • Kalantar, D. H.; Barbee, T. W.; DaSilva, L. B.
  • Review of Scientific Instruments, Vol. 67, Issue 3
  • DOI: 10.1063/1.1146809

Convergent Rayleigh-Taylor Experiments on the Nova Laser
journal, December 1999


Theory of induced spatial incoherence
journal, October 1987

  • Lehmberg, R. H.; Schmitt, A. J.; Bodner, S. E.
  • Journal of Applied Physics, Vol. 62, Issue 7
  • DOI: 10.1063/1.339419

Localized Dynamics during Laser-Induced Damage in Optical Materials
journal, February 2004


Measurement of the shell decompression in direct-drive inertial-confinement-fusion implosions
journal, May 2017


Rayleigh-Taylor Instability and Laser-Pellet Fusion
journal, September 1974


Experimental investigation of smoothing by spectral dispersion
journal, January 2000

  • Regan, Sean P.; Marozas, John A.; Kelly, John H.
  • Journal of the Optical Society of America B, Vol. 17, Issue 9
  • DOI: 10.1364/JOSAB.17.001483

A high-resolution two-dimensional imaging velocimeter
journal, March 2010

  • Celliers, P. M.; Erskine, D. J.; Sorce, C. M.
  • Review of Scientific Instruments, Vol. 81, Issue 3
  • DOI: 10.1063/1.3310076

Random Phasing of High-Power Lasers for Uniform Target Acceleration and Plasma-Instability Suppression
journal, September 1984


Studies of Plastic-Ablator Compressibility for Direct-Drive Inertial Confinement Fusion on Omega
journal, May 2008


Performance of 1-THz-bandwidth, two-dimensional smoothing by spectral dispersion and polarization smoothing of high-power, solid-state laser beams
journal, January 2005

  • Regan, Sean P.; Marozas, John A.; Craxton, R. Stephen
  • Journal of the Optical Society of America B, Vol. 22, Issue 5
  • DOI: 10.1364/JOSAB.22.000998

Simulations of laser imprint reduction using underdense foams and its consequences on the hydrodynamic instability growth
journal, August 2013


Mitigating laser-imprint effects in direct-drive inertial confinement fusion implosions with an above-critical-density foam layer
journal, August 2018

  • Hu, S. X.; Theobald, W.; Radha, P. B.
  • Physics of Plasmas, Vol. 25, Issue 8
  • DOI: 10.1063/1.5044609

Direct-drive inertial confinement fusion: A review
journal, November 2015

  • Craxton, R. S.; Anderson, K. S.; Boehly, T. R.
  • Physics of Plasmas, Vol. 22, Issue 11
  • DOI: 10.1063/1.4934714

Comprehensive Diagnosis of Growth Rates of the Ablative Rayleigh-Taylor Instability
journal, January 2007


Extreme ultraviolet probing of laser imprint in a thin foil using an x-ray laser backlighter
journal, January 1997

  • Kalantar, D. H.; Da Silva, L. B.; Glendinning, S. G.
  • Review of Scientific Instruments, Vol. 68, Issue 1
  • DOI: 10.1063/1.1147747

Enhanced Direct-Drive Implosions with Thin High- Z Ablation Layers
journal, February 2008


Measurements of direct drive laser imprint in thin foils by radiography using an x-ray laser backlighter
journal, May 1997

  • Kalantar, D. H.; Key, M. H.; Da Silva, L. B.
  • Physics of Plasmas, Vol. 4, Issue 5
  • DOI: 10.1063/1.872340

Laser Smoothing and Imprint Reduction with a Foam Layer in the Multikilojoule Regime
journal, May 2009


Numerical refocusing of 2d-VISAR data
journal, May 2014


    Works referencing / citing this record:

    Laser Smoothing and Imprint Reduction with a Foam Layer in the Multikilojoule Regime
    journal, May 2009


    Modeling the solid-to-plasma transition for laser imprinting in direct-drive inertial confinement fusion
    journal, September 2019


    Effects of thin high-Z layers on the hydrodynamics of laser-accelerated plastic targets
    journal, May 2002

    • Obenschain, S. P.; Colombant, D. G.; Karasik, M.
    • Physics of Plasmas, Vol. 9, Issue 5
    • DOI: 10.1063/1.1464541

    Mitigating Laser Imprint in Direct-Drive Inertial Confinement Fusion Implosions with High- Z Dopants
    journal, May 2012


    Extreme ultraviolet probing of laser imprint in a thin foil using an x-ray laser backlighter
    journal, January 1997

    • Kalantar, D. H.; Da Silva, L. B.; Glendinning, S. G.
    • Review of Scientific Instruments, Vol. 68, Issue 1
    • DOI: 10.1063/1.1147747

    Convergent Rayleigh-Taylor Experiments on the Nova Laser
    journal, December 1999


    Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods
    journal, January 1994

    • Ghiglia, Dennis C.; Romero, Louis A.
    • Journal of the Optical Society of America A, Vol. 11, Issue 1
    • DOI: 10.1364/josaa.11.000107

    Saturation of the Rayleigh-Taylor Growth of Broad-Bandwidth Laser-Imposed Nonuniformities in Planar Targets
    journal, December 1998


    Measurement of the shell decompression in direct-drive inertial-confinement-fusion implosions
    journal, May 2017


    Measurements of laser-imprinting sensitivity to relative beam mistiming in planar plastic foils driven by multiple overlapping laser beams
    journal, July 2005

    • Smalyuk, V. A.; Goncharov, V. N.; Boehly, T. R.
    • Physics of Plasmas, Vol. 12, Issue 7
    • DOI: 10.1063/1.1943900

    Theory of induced spatial incoherence
    journal, October 1987

    • Lehmberg, R. H.; Schmitt, A. J.; Bodner, S. E.
    • Journal of Applied Physics, Vol. 62, Issue 7
    • DOI: 10.1063/1.339419

    Multimode Rayleigh-Taylor Experiments on Nova
    journal, July 1994


    Localized Dynamics during Laser-Induced Damage in Optical Materials
    journal, February 2004


    Measurement of a Dispersion Curve for Linear-Regime Rayleigh-Taylor Growth Rates in Laser-Driven Planar Targets
    journal, April 1997


    Fourier-Space Nonlinear Rayleigh-Taylor Growth Measurements of 3D Laser-Imprinted Modulations in Planar Targets
    journal, November 2005


    Reduction of time-averaged irradiation speckle nonuniformity in laser-driven plasmas due to target ablation
    journal, September 1997

    • Epstein, R.
    • Journal of Applied Physics, Vol. 82, Issue 5
    • DOI: 10.1063/1.366021

    Initial performance results of the OMEGA laser system
    journal, January 1997


    Numerical refocusing of 2d-VISAR data
    journal, May 2014


    Measurements of direct drive laser imprint in thin foils by radiography using an x-ray laser backlighter
    journal, May 1997

    • Kalantar, D. H.; Key, M. H.; Da Silva, L. B.
    • Physics of Plasmas, Vol. 4, Issue 5
    • DOI: 10.1063/1.872340

    A high-resolution two-dimensional imaging velocimeter
    journal, March 2010

    • Celliers, P. M.; Erskine, D. J.; Sorce, C. M.
    • Review of Scientific Instruments, Vol. 81, Issue 3
    • DOI: 10.1063/1.3310076

    Multiphoton ionization of atoms
    journal, October 1991


    Two-dimensional imaging velocity interferometry: Data analysis techniques
    journal, April 2012

    • Erskine, David J.; Smith, R. F.; Bolme, C. A.
    • Review of Scientific Instruments, Vol. 83, Issue 4
    • DOI: 10.1063/1.4704840

    Mitigating laser-imprint effects in direct-drive inertial confinement fusion implosions with an above-critical-density foam layer
    journal, August 2018

    • Hu, S. X.; Theobald, W.; Radha, P. B.
    • Physics of Plasmas, Vol. 25, Issue 8
    • DOI: 10.1063/1.5044609

    Reduction of laser imprinting using polarization smoothing on a solid-state fusion laser
    journal, April 1999

    • Boehly, T. R.; Smalyuk, V. A.; Meyerhofer, D. D.
    • Journal of Applied Physics, Vol. 85, Issue 7
    • DOI: 10.1063/1.369702

    Simulations of laser imprint reduction using underdense foams and its consequences on the hydrodynamic instability growth
    journal, August 2013


    X‐ray laser radiography of perturbations due to imprint of laser speckle in 0.35 μm laser irradiation of a thin Si foil
    journal, March 1996

    • Kalantar, D. H.; Barbee, T. W.; DaSilva, L. B.
    • Review of Scientific Instruments, Vol. 67, Issue 3
    • DOI: 10.1063/1.1146809

    Understanding the effects of laser imprint on plastic-target implosions on OMEGA
    journal, October 2016

    • Hu, S. X.; Michel, D. T.; Davis, A. K.
    • Physics of Plasmas, Vol. 23, Issue 10, 102701
    • DOI: 10.1063/1.4962993

    Experimental investigation of smoothing by spectral dispersion
    journal, January 2000

    • Regan, Sean P.; Marozas, John A.; Kelly, John H.
    • Journal of the Optical Society of America B, Vol. 17, Issue 9
    • DOI: 10.1364/josab.17.001483

    Use of induced spatial incoherence for uniform illumination of laser fusion targets
    journal, June 1983


    Two-dimensional simulations of the neutron yield in cryogenic deuterium-tritium implosions on OMEGA
    journal, October 2010

    • Hu, S. X.; Goncharov, V. N.; Radha, P. B.
    • Physics of Plasmas, Vol. 17, Issue 10
    • DOI: 10.1063/1.3491467

    Direct-drive inertial confinement fusion: A review
    journal, November 2015

    • Craxton, R. S.; Anderson, K. S.; Boehly, T. R.
    • Physics of Plasmas, Vol. 22, Issue 11
    • DOI: 10.1063/1.4934714

    Comparison between measured and calculated nonuniformities of Nike laser beams smoothed by induced spatial incoherence
    journal, February 1998


    Direct-drive hydrodynamic instability experiments on the GEKKO XII laser
    journal, November 1997

    • Azechi, H.; Nakai, M.; Shigemori, K.
    • Physics of Plasmas, Vol. 4, Issue 11
    • DOI: 10.1063/1.872528

    Suppression of the Rayleigh-Taylor Instability due to Self-Radiation in a Multiablation Target
    journal, May 2004


    Distributed phase plates for super-Gaussian focal-plane irradiance profiles
    journal, January 1995

    • Lin, Y.; Lawrence, G. N.; Kessler, T. J.
    • Optics Letters, Vol. 20, Issue 7
    • DOI: 10.1364/ol.20.000764

    A model for multiphoton absorption in dielectric materials induced by short laser pulses at moderate intensities
    journal, May 2013

    • Mézel, Candice; Duchateau, Guillaume; Geneste, Grégory
    • Journal of Physics: Condensed Matter, Vol. 25, Issue 23
    • DOI: 10.1088/0953-8984/25/23/235501

    Studies of Plastic-Ablator Compressibility for Direct-Drive Inertial Confinement Fusion on Omega
    journal, May 2008


    X-ray preheating of window materials in direct-drive shock-wave timing experiments
    journal, December 2006

    • Theobald, W.; Miller, J. E.; Boehly, T. R.
    • Physics of Plasmas, Vol. 13, Issue 12
    • DOI: 10.1063/1.2397581

    Suppression of Laser Nonuniformity Imprinting Using a Thin High- Z Coating
    journal, February 2015


    Random Phasing of High-Power Lasers for Uniform Target Acceleration and Plasma-Instability Suppression
    journal, September 1984


    Minimum Lp-norm two-dimensional phase unwrapping
    journal, January 1996

    • Ghiglia, Dennis C.; Romero, Louis A.
    • Journal of the Optical Society of America A, Vol. 13, Issue 10
    • DOI: 10.1364/josaa.13.001999

    Rayleigh-Taylor Instability and Laser-Pellet Fusion
    journal, September 1974


    Comprehensive Diagnosis of Growth Rates of the Ablative Rayleigh-Taylor Instability
    journal, January 2007


    Time-dependent ionization models designed for intense and short laser pulse propagation in dielectric materials
    journal, May 2012


    Multidimensional analysis of direct-drive, plastic-shell implosions on OMEGA
    journal, May 2005

    • Radha, P. B.; Collins, T. J. B.; Delettrez, J. A.
    • Physics of Plasmas, Vol. 12, Issue 5
    • DOI: 10.1063/1.1882333

    Velocity sensing interferometer (VISAR) modification
    journal, January 1979

    • Hemsing, Willard F.
    • Review of Scientific Instruments, Vol. 50, Issue 1
    • DOI: 10.1063/1.1135672

    Multiphoton Ionization in Dielectrics: Comparison of Circular and Linear Polarization
    journal, December 2006


    Improved laser‐beam uniformity using the angular dispersion of frequency‐modulated light
    journal, October 1989

    • Skupsky, S.; Short, R. W.; Kessler, T.
    • Journal of Applied Physics, Vol. 66, Issue 8
    • DOI: 10.1063/1.344101

    Enhanced Direct-Drive Implosions with Thin High- Z Ablation Layers
    journal, February 2008


    Performance of 1-THz-bandwidth, two-dimensional smoothing by spectral dispersion and polarization smoothing of high-power, solid-state laser beams
    journal, January 2005

    • Regan, Sean P.; Marozas, John A.; Craxton, R. Stephen
    • Journal of the Optical Society of America B, Vol. 22, Issue 5
    • DOI: 10.1364/josab.22.000998