Abstract

With 3D steady-state fluid simulations, we show that a negative lens can be created from a rotating gas (vortex) in a compact structure. The gas flow is well described by a compressible Bernoulli principle assuming an adiabatic, ideal gas. The gas lens’ focal length can be varied by adjusting the mass flow rate. The dominant aberration is spherical. Transient simulations show a 60 μs time scale for switching of the focal length. The gas vortex lens allows operation of high-power lasers above the damage thresholds of conventional optics and, additionally, its self-healing design allows operation near gas breakdown thresholds without risk to the optical element.

© 2019 Optical Society of America

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References

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  10. A. Beck, “Gas mixture lens measurements,” Bell Syst. Tech. J. 43, 1821–1825 (1964).
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    [Crossref]
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    [Crossref]

2018 (2)

D. Kaganovich, L. Johnson, D. Gordon, A. Mamonau, and B. Hafizi, “Lensing properties of rotational gas flow,” Appl. Opt. 57, 9392–9396 (2018).
[Crossref]

D. Gordon, A. Stamm, B. Hafizi, L. Johnson, D. Kaganovich, R. Hubbard, A. Richardson, and D. Zhigunov, “Ideal form of optical plasma lenses,” Phys. Plasmas 25, 063101 (2018).
[Crossref]

2015 (2)

P. Sprangle, B. Hafizi, A. Ting, and R. Fischer, “High-power lasers for directed-energy applications,” Appl. Opt. 54, F201–F209 (2015).
[Crossref]

M. Mortazavi, J. Urzay, and A. Mani, “Computational hydrodynamics and optical performance of inductively-coupled plasma adaptive lenses,” Phys. Plasmas 22, 062110 (2015).
[Crossref]

2014 (1)

D. Kaganovich, D. Gordon, M. Helle, and A. Ting, “Shaping gas jet plasma density profile by laser generated shock waves,” J. Appl. Phys. 116, 013304 (2014).
[Crossref]

2013 (1)

B. W. Neiswander, E. Matlis, and T. C. Corke, “Geometric optimization of a cylindrical plasma adaptive optics lens,” AIAA J. 51, 657–664 (2013).
[Crossref]

2012 (1)

B. W. Neiswander, E. Matlis, and T. C. Corke, “Plasma lens for optical path difference control,” AIAA J. 50, 123–130 (2012).
[Crossref]

2009 (1)

2008 (1)

C. Mafusire, A. Forbes, G. Snedden, and M. Michaelis, “The spinning pipe gas lens revisited,” South African J. Sci. 104, 260–264 (2008).

2007 (1)

Y. Aboelkassem and G. H. Vatistas, “New model for compressible vortices,” J. Fluids Eng. 129, 1073–1079 (2007).
[Crossref]

2005 (2)

B. Vilenchits, A. Zhdanovskii, and V. Popov, “Influence of a vortex gas flow on an axial laser beam,” J. Appl. Spectrosc. 72, 59–63 (2005).
[Crossref]

W. Liu, J.-F. Gravel, F. Théberge, A. Becker, and S. Chin, “Background reservoir: its crucial role for long-distance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80, 857–860 (2005).
[Crossref]

2003 (1)

H. Bercegol, P. R. Bouchut, L. Lamaignère, B. Le Garrec, and G. Razé, “The impact of laser damage on the lifetime of optical components in fusion lasers,” Proc. SPIE 5273, 312–325 (2003).
[Crossref]

1999 (1)

S. Chakravarthy, “A unified-grid finite volume formulation for computational fluid dynamics,” Int. J. Numer. Methods Fluids 31, 309–323 (1999).
[Crossref]

1998 (1)

U. Goldberg, O. Peroomian, and S. Chakravarthy, “A wall-distance-free k-ε model with enhanced near-wall treatment,” J. Fluids Eng. 120, 457–462 (1998).
[Crossref]

1997 (1)

B. Vilenchits, A. Zhdanovskii, N. Lemesh, and L. Senchuk, “The effect of the scale factor on the focusing properties of a vortex gas flow,” J. Appl. Spectrosc. 64, 399–402 (1997).
[Crossref]

1995 (1)

B. Vilenchits, A. Zhdanovskii, and D. Umreiko, “Focusing properties of a vortex gas flow,” J. Appl. Spectrosc. 62, 153–155 (1995).
[Crossref]

1991 (2)

G. H. Vatistas, V. Kozel, and W. Mih, “A simpler model for concentrated vortices,” Exp. Fluids 11, 73–76 (1991).
[Crossref]

M. Michaelis, C. Dempers, M. Kosch, A. Prause, M. Notcutt, P. Cunningham, and J. Waltham, “A gas-lens telescope,” Nature 353, 547–548 (1991).
[Crossref]

1990 (1)

P. Mikheev, V. Nikolaev, S. Shalaginov, and A. Shepelenko, “Investigation of the defocusing properties of a vortical gas flow,” J. Eng. Phys. 59, 1375–1379 (1990).
[Crossref]

1988 (2)

B. E. Launder, “On the computation of convective heat transfer in complex turbulent flows,” J. Heat Transfer 110, 1112–1128 (1988).
[Crossref]

M. Notcutt, M. Michaelis, P. Cunningham, and J. Waltham, “Spinning pipe gas lens,” Opt. Laser Technol. 20, 243–250 (1988).
[Crossref]

1986 (1)

M. Michaelis, M. Notcutt, and P. Cunningham, “Drilling by gas lens focused laser,” Opt. Commun. 59, 369–374 (1986).
[Crossref]

1966 (1)

1964 (5)

D. Marcuse and S. Miller, “Analysis of a tubular gas lens,” Bell Syst. Tech. J. 43, 1759–1782 (1964).
[Crossref]

A. Beck, “Thermal gas lens measurements,” Bell Syst. Tech. J. 43, 1818–1820 (1964).
[Crossref]

D. Berreman, “A lens or light guide using convectively distorted thermal gradients in gases,” Bell Syst. Tech. J. 43, 1469–1475 (1964).
[Crossref]

A. Beck, “Gas mixture lens measurements,” Bell Syst. Tech. J. 43, 1821–1825 (1964).
[Crossref]

D. Berreman, “A gas lens using unlike, counter-flowing gases,” Bell Syst. Tech. J. 43, 1476–1479 (1964).
[Crossref]

Aboelkassem, Y.

Y. Aboelkassem and G. H. Vatistas, “New model for compressible vortices,” J. Fluids Eng. 129, 1073–1079 (2007).
[Crossref]

Applegate, R. A.

L. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, OSA Technical Digest (Optical Society of America, 2000), paper SuC1.

Beck, A.

A. Beck, “Thermal gas lens measurements,” Bell Syst. Tech. J. 43, 1818–1820 (1964).
[Crossref]

A. Beck, “Gas mixture lens measurements,” Bell Syst. Tech. J. 43, 1821–1825 (1964).
[Crossref]

Becker, A.

W. Liu, J.-F. Gravel, F. Théberge, A. Becker, and S. Chin, “Background reservoir: its crucial role for long-distance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80, 857–860 (2005).
[Crossref]

Bercegol, H.

H. Bercegol, P. R. Bouchut, L. Lamaignère, B. Le Garrec, and G. Razé, “The impact of laser damage on the lifetime of optical components in fusion lasers,” Proc. SPIE 5273, 312–325 (2003).
[Crossref]

Berreman, D.

D. Berreman, “A gas lens using unlike, counter-flowing gases,” Bell Syst. Tech. J. 43, 1476–1479 (1964).
[Crossref]

D. Berreman, “A lens or light guide using convectively distorted thermal gradients in gases,” Bell Syst. Tech. J. 43, 1469–1475 (1964).
[Crossref]

Bin Yusof, M. H.

H. Katanoda and M. H. Bin Yusof, “Energy separation mechanism in uni-flow vortex tube using compressible vortex flow,” in International Conference on Fluid Mechanics, Heat Transfer and Thermodynamics (2014), Vol. 2014, pp. 1252–1255.

Bouchut, P. R.

H. Bercegol, P. R. Bouchut, L. Lamaignère, B. Le Garrec, and G. Razé, “The impact of laser damage on the lifetime of optical components in fusion lasers,” Proc. SPIE 5273, 312–325 (2003).
[Crossref]

Chakravarthy, S.

S. Chakravarthy, “A unified-grid finite volume formulation for computational fluid dynamics,” Int. J. Numer. Methods Fluids 31, 309–323 (1999).
[Crossref]

U. Goldberg, O. Peroomian, and S. Chakravarthy, “A wall-distance-free k-ε model with enhanced near-wall treatment,” J. Fluids Eng. 120, 457–462 (1998).
[Crossref]

Chin, S.

W. Liu, J.-F. Gravel, F. Théberge, A. Becker, and S. Chin, “Background reservoir: its crucial role for long-distance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80, 857–860 (2005).
[Crossref]

Condon, E. U.

E. U. Condon and H. Odishaw, Handbook of Physics (McGraw-Hill, 1958).

Corke, T. C.

B. W. Neiswander, E. Matlis, and T. C. Corke, “Geometric optimization of a cylindrical plasma adaptive optics lens,” AIAA J. 51, 657–664 (2013).
[Crossref]

B. W. Neiswander, E. Matlis, and T. C. Corke, “Plasma lens for optical path difference control,” AIAA J. 50, 123–130 (2012).
[Crossref]

Cunningham, P.

M. Michaelis, C. Dempers, M. Kosch, A. Prause, M. Notcutt, P. Cunningham, and J. Waltham, “A gas-lens telescope,” Nature 353, 547–548 (1991).
[Crossref]

M. Notcutt, M. Michaelis, P. Cunningham, and J. Waltham, “Spinning pipe gas lens,” Opt. Laser Technol. 20, 243–250 (1988).
[Crossref]

M. Michaelis, M. Notcutt, and P. Cunningham, “Drilling by gas lens focused laser,” Opt. Commun. 59, 369–374 (1986).
[Crossref]

Dempers, C.

M. Michaelis, C. Dempers, M. Kosch, A. Prause, M. Notcutt, P. Cunningham, and J. Waltham, “A gas-lens telescope,” Nature 353, 547–548 (1991).
[Crossref]

Fernsler, R.

D. Gordon, P. Sprangle, S. Slinker, R. Fernsler, and M. Lampe, “SPARC-a simulation model for electrical charges,” (U.S. Naval Research Lab, 2006).

Fischer, R.

Forbes, A.

C. Mafusire, A. Forbes, G. Snedden, and M. Michaelis, “The spinning pipe gas lens revisited,” South African J. Sci. 104, 260–264 (2008).

Goldberg, U.

U. Goldberg, O. Peroomian, and S. Chakravarthy, “A wall-distance-free k-ε model with enhanced near-wall treatment,” J. Fluids Eng. 120, 457–462 (1998).
[Crossref]

Gordon, D.

D. Kaganovich, L. Johnson, D. Gordon, A. Mamonau, and B. Hafizi, “Lensing properties of rotational gas flow,” Appl. Opt. 57, 9392–9396 (2018).
[Crossref]

D. Gordon, A. Stamm, B. Hafizi, L. Johnson, D. Kaganovich, R. Hubbard, A. Richardson, and D. Zhigunov, “Ideal form of optical plasma lenses,” Phys. Plasmas 25, 063101 (2018).
[Crossref]

D. Kaganovich, D. Gordon, M. Helle, and A. Ting, “Shaping gas jet plasma density profile by laser generated shock waves,” J. Appl. Phys. 116, 013304 (2014).
[Crossref]

D. Gordon, P. Sprangle, S. Slinker, R. Fernsler, and M. Lampe, “SPARC-a simulation model for electrical charges,” (U.S. Naval Research Lab, 2006).

Gravel, J.-F.

W. Liu, J.-F. Gravel, F. Théberge, A. Becker, and S. Chin, “Background reservoir: its crucial role for long-distance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80, 857–860 (2005).
[Crossref]

Hafizi, B.

Helle, M.

D. Kaganovich, D. Gordon, M. Helle, and A. Ting, “Shaping gas jet plasma density profile by laser generated shock waves,” J. Appl. Phys. 116, 013304 (2014).
[Crossref]

Hubbard, R.

D. Gordon, A. Stamm, B. Hafizi, L. Johnson, D. Kaganovich, R. Hubbard, A. Richardson, and D. Zhigunov, “Ideal form of optical plasma lenses,” Phys. Plasmas 25, 063101 (2018).
[Crossref]

Johnson, L.

D. Gordon, A. Stamm, B. Hafizi, L. Johnson, D. Kaganovich, R. Hubbard, A. Richardson, and D. Zhigunov, “Ideal form of optical plasma lenses,” Phys. Plasmas 25, 063101 (2018).
[Crossref]

D. Kaganovich, L. Johnson, D. Gordon, A. Mamonau, and B. Hafizi, “Lensing properties of rotational gas flow,” Appl. Opt. 57, 9392–9396 (2018).
[Crossref]

Kaganovich, D.

D. Kaganovich, L. Johnson, D. Gordon, A. Mamonau, and B. Hafizi, “Lensing properties of rotational gas flow,” Appl. Opt. 57, 9392–9396 (2018).
[Crossref]

D. Gordon, A. Stamm, B. Hafizi, L. Johnson, D. Kaganovich, R. Hubbard, A. Richardson, and D. Zhigunov, “Ideal form of optical plasma lenses,” Phys. Plasmas 25, 063101 (2018).
[Crossref]

D. Kaganovich, D. Gordon, M. Helle, and A. Ting, “Shaping gas jet plasma density profile by laser generated shock waves,” J. Appl. Phys. 116, 013304 (2014).
[Crossref]

Katanoda, H.

H. Katanoda and M. H. Bin Yusof, “Energy separation mechanism in uni-flow vortex tube using compressible vortex flow,” in International Conference on Fluid Mechanics, Heat Transfer and Thermodynamics (2014), Vol. 2014, pp. 1252–1255.

Khanna, B. N.

Kosch, M.

M. Michaelis, C. Dempers, M. Kosch, A. Prause, M. Notcutt, P. Cunningham, and J. Waltham, “A gas-lens telescope,” Nature 353, 547–548 (1991).
[Crossref]

Kozel, V.

G. H. Vatistas, V. Kozel, and W. Mih, “A simpler model for concentrated vortices,” Exp. Fluids 11, 73–76 (1991).
[Crossref]

Lamaignère, L.

H. Bercegol, P. R. Bouchut, L. Lamaignère, B. Le Garrec, and G. Razé, “The impact of laser damage on the lifetime of optical components in fusion lasers,” Proc. SPIE 5273, 312–325 (2003).
[Crossref]

Lampe, M.

D. Gordon, P. Sprangle, S. Slinker, R. Fernsler, and M. Lampe, “SPARC-a simulation model for electrical charges,” (U.S. Naval Research Lab, 2006).

Landau, L.

L. Landau and E. Lifshitz, Fluid Mechanics, Vol. 6 of Course of Theoretical Physics (Pergamon, 1959).

Launder, B. E.

B. E. Launder, “On the computation of convective heat transfer in complex turbulent flows,” J. Heat Transfer 110, 1112–1128 (1988).
[Crossref]

Le Garrec, B.

H. Bercegol, P. R. Bouchut, L. Lamaignère, B. Le Garrec, and G. Razé, “The impact of laser damage on the lifetime of optical components in fusion lasers,” Proc. SPIE 5273, 312–325 (2003).
[Crossref]

Lemesh, N.

B. Vilenchits, A. Zhdanovskii, N. Lemesh, and L. Senchuk, “The effect of the scale factor on the focusing properties of a vortex gas flow,” J. Appl. Spectrosc. 64, 399–402 (1997).
[Crossref]

Lifshitz, E.

L. Landau and E. Lifshitz, Fluid Mechanics, Vol. 6 of Course of Theoretical Physics (Pergamon, 1959).

Liu, W.

W. Liu, J.-F. Gravel, F. Théberge, A. Becker, and S. Chin, “Background reservoir: its crucial role for long-distance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80, 857–860 (2005).
[Crossref]

Mafusire, C.

C. Mafusire, A. Forbes, G. Snedden, and M. Michaelis, “The spinning pipe gas lens revisited,” South African J. Sci. 104, 260–264 (2008).

Mamonau, A.

Mani, A.

M. Mortazavi, J. Urzay, and A. Mani, “Computational hydrodynamics and optical performance of inductively-coupled plasma adaptive lenses,” Phys. Plasmas 22, 062110 (2015).
[Crossref]

J. Urzay, M. Mortazavi, and A. Mani, “Optical degradation of inductively-coupled plasma lenses by conversion of electromagnetic energy into unsteady flows,” Tech. Rep. (Center for Turbulence Research, 2013).

Marcuse, D.

D. Marcuse and S. Miller, “Analysis of a tubular gas lens,” Bell Syst. Tech. J. 43, 1759–1782 (1964).
[Crossref]

Matlis, E.

B. W. Neiswander, E. Matlis, and T. C. Corke, “Geometric optimization of a cylindrical plasma adaptive optics lens,” AIAA J. 51, 657–664 (2013).
[Crossref]

B. W. Neiswander, E. Matlis, and T. C. Corke, “Plasma lens for optical path difference control,” AIAA J. 50, 123–130 (2012).
[Crossref]

McConnel, R. J.

R. J. McConnel, “Method and apparatus for refracting a laser beam,” U.S. patent4,402,574 (September6, 1983).

Michaelis, M.

C. Mafusire, A. Forbes, G. Snedden, and M. Michaelis, “The spinning pipe gas lens revisited,” South African J. Sci. 104, 260–264 (2008).

M. Michaelis, C. Dempers, M. Kosch, A. Prause, M. Notcutt, P. Cunningham, and J. Waltham, “A gas-lens telescope,” Nature 353, 547–548 (1991).
[Crossref]

M. Notcutt, M. Michaelis, P. Cunningham, and J. Waltham, “Spinning pipe gas lens,” Opt. Laser Technol. 20, 243–250 (1988).
[Crossref]

M. Michaelis, M. Notcutt, and P. Cunningham, “Drilling by gas lens focused laser,” Opt. Commun. 59, 369–374 (1986).
[Crossref]

Mih, W.

G. H. Vatistas, V. Kozel, and W. Mih, “A simpler model for concentrated vortices,” Exp. Fluids 11, 73–76 (1991).
[Crossref]

Mikheev, P.

P. Mikheev, V. Nikolaev, S. Shalaginov, and A. Shepelenko, “Investigation of the defocusing properties of a vortical gas flow,” J. Eng. Phys. 59, 1375–1379 (1990).
[Crossref]

Miller, S.

D. Marcuse and S. Miller, “Analysis of a tubular gas lens,” Bell Syst. Tech. J. 43, 1759–1782 (1964).
[Crossref]

Mortazavi, M.

M. Mortazavi, J. Urzay, and A. Mani, “Computational hydrodynamics and optical performance of inductively-coupled plasma adaptive lenses,” Phys. Plasmas 22, 062110 (2015).
[Crossref]

J. Urzay, M. Mortazavi, and A. Mani, “Optical degradation of inductively-coupled plasma lenses by conversion of electromagnetic energy into unsteady flows,” Tech. Rep. (Center for Turbulence Research, 2013).

Neiswander, B. W.

B. W. Neiswander, E. Matlis, and T. C. Corke, “Geometric optimization of a cylindrical plasma adaptive optics lens,” AIAA J. 51, 657–664 (2013).
[Crossref]

B. W. Neiswander, E. Matlis, and T. C. Corke, “Plasma lens for optical path difference control,” AIAA J. 50, 123–130 (2012).
[Crossref]

Nikolaev, V.

P. Mikheev, V. Nikolaev, S. Shalaginov, and A. Shepelenko, “Investigation of the defocusing properties of a vortical gas flow,” J. Eng. Phys. 59, 1375–1379 (1990).
[Crossref]

Notcutt, M.

M. Michaelis, C. Dempers, M. Kosch, A. Prause, M. Notcutt, P. Cunningham, and J. Waltham, “A gas-lens telescope,” Nature 353, 547–548 (1991).
[Crossref]

M. Notcutt, M. Michaelis, P. Cunningham, and J. Waltham, “Spinning pipe gas lens,” Opt. Laser Technol. 20, 243–250 (1988).
[Crossref]

M. Michaelis, M. Notcutt, and P. Cunningham, “Drilling by gas lens focused laser,” Opt. Commun. 59, 369–374 (1986).
[Crossref]

Odishaw, H.

E. U. Condon and H. Odishaw, Handbook of Physics (McGraw-Hill, 1958).

Peck, E. R.

Peñano, J.

Peroomian, O.

U. Goldberg, O. Peroomian, and S. Chakravarthy, “A wall-distance-free k-ε model with enhanced near-wall treatment,” J. Fluids Eng. 120, 457–462 (1998).
[Crossref]

Popov, V.

B. Vilenchits, A. Zhdanovskii, and V. Popov, “Influence of a vortex gas flow on an axial laser beam,” J. Appl. Spectrosc. 72, 59–63 (2005).
[Crossref]

Prause, A.

M. Michaelis, C. Dempers, M. Kosch, A. Prause, M. Notcutt, P. Cunningham, and J. Waltham, “A gas-lens telescope,” Nature 353, 547–548 (1991).
[Crossref]

Razé, G.

H. Bercegol, P. R. Bouchut, L. Lamaignère, B. Le Garrec, and G. Razé, “The impact of laser damage on the lifetime of optical components in fusion lasers,” Proc. SPIE 5273, 312–325 (2003).
[Crossref]

Richardson, A.

D. Gordon, A. Stamm, B. Hafizi, L. Johnson, D. Kaganovich, R. Hubbard, A. Richardson, and D. Zhigunov, “Ideal form of optical plasma lenses,” Phys. Plasmas 25, 063101 (2018).
[Crossref]

Schwiegerling, J. T.

L. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, OSA Technical Digest (Optical Society of America, 2000), paper SuC1.

Senchuk, L.

B. Vilenchits, A. Zhdanovskii, N. Lemesh, and L. Senchuk, “The effect of the scale factor on the focusing properties of a vortex gas flow,” J. Appl. Spectrosc. 64, 399–402 (1997).
[Crossref]

Serafim, P.

Shalaginov, S.

P. Mikheev, V. Nikolaev, S. Shalaginov, and A. Shepelenko, “Investigation of the defocusing properties of a vortical gas flow,” J. Eng. Phys. 59, 1375–1379 (1990).
[Crossref]

Shepelenko, A.

P. Mikheev, V. Nikolaev, S. Shalaginov, and A. Shepelenko, “Investigation of the defocusing properties of a vortical gas flow,” J. Eng. Phys. 59, 1375–1379 (1990).
[Crossref]

Slinker, S.

D. Gordon, P. Sprangle, S. Slinker, R. Fernsler, and M. Lampe, “SPARC-a simulation model for electrical charges,” (U.S. Naval Research Lab, 2006).

Snedden, G.

C. Mafusire, A. Forbes, G. Snedden, and M. Michaelis, “The spinning pipe gas lens revisited,” South African J. Sci. 104, 260–264 (2008).

Sprangle, P.

Stamm, A.

D. Gordon, A. Stamm, B. Hafizi, L. Johnson, D. Kaganovich, R. Hubbard, A. Richardson, and D. Zhigunov, “Ideal form of optical plasma lenses,” Phys. Plasmas 25, 063101 (2018).
[Crossref]

Théberge, F.

W. Liu, J.-F. Gravel, F. Théberge, A. Becker, and S. Chin, “Background reservoir: its crucial role for long-distance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80, 857–860 (2005).
[Crossref]

Thibos, L.

L. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, OSA Technical Digest (Optical Society of America, 2000), paper SuC1.

Ting, A.

Umreiko, D.

B. Vilenchits, A. Zhdanovskii, and D. Umreiko, “Focusing properties of a vortex gas flow,” J. Appl. Spectrosc. 62, 153–155 (1995).
[Crossref]

Urzay, J.

M. Mortazavi, J. Urzay, and A. Mani, “Computational hydrodynamics and optical performance of inductively-coupled plasma adaptive lenses,” Phys. Plasmas 22, 062110 (2015).
[Crossref]

J. Urzay, M. Mortazavi, and A. Mani, “Optical degradation of inductively-coupled plasma lenses by conversion of electromagnetic energy into unsteady flows,” Tech. Rep. (Center for Turbulence Research, 2013).

Vatistas, G. H.

Y. Aboelkassem and G. H. Vatistas, “New model for compressible vortices,” J. Fluids Eng. 129, 1073–1079 (2007).
[Crossref]

G. H. Vatistas, V. Kozel, and W. Mih, “A simpler model for concentrated vortices,” Exp. Fluids 11, 73–76 (1991).
[Crossref]

Vilenchits, B.

B. Vilenchits, A. Zhdanovskii, and V. Popov, “Influence of a vortex gas flow on an axial laser beam,” J. Appl. Spectrosc. 72, 59–63 (2005).
[Crossref]

B. Vilenchits, A. Zhdanovskii, N. Lemesh, and L. Senchuk, “The effect of the scale factor on the focusing properties of a vortex gas flow,” J. Appl. Spectrosc. 64, 399–402 (1997).
[Crossref]

B. Vilenchits, A. Zhdanovskii, and D. Umreiko, “Focusing properties of a vortex gas flow,” J. Appl. Spectrosc. 62, 153–155 (1995).
[Crossref]

Waltham, J.

M. Michaelis, C. Dempers, M. Kosch, A. Prause, M. Notcutt, P. Cunningham, and J. Waltham, “A gas-lens telescope,” Nature 353, 547–548 (1991).
[Crossref]

M. Notcutt, M. Michaelis, P. Cunningham, and J. Waltham, “Spinning pipe gas lens,” Opt. Laser Technol. 20, 243–250 (1988).
[Crossref]

Webb, R.

L. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, OSA Technical Digest (Optical Society of America, 2000), paper SuC1.

Zhdanovskii, A.

B. Vilenchits, A. Zhdanovskii, and V. Popov, “Influence of a vortex gas flow on an axial laser beam,” J. Appl. Spectrosc. 72, 59–63 (2005).
[Crossref]

B. Vilenchits, A. Zhdanovskii, N. Lemesh, and L. Senchuk, “The effect of the scale factor on the focusing properties of a vortex gas flow,” J. Appl. Spectrosc. 64, 399–402 (1997).
[Crossref]

B. Vilenchits, A. Zhdanovskii, and D. Umreiko, “Focusing properties of a vortex gas flow,” J. Appl. Spectrosc. 62, 153–155 (1995).
[Crossref]

Zhigunov, D.

D. Gordon, A. Stamm, B. Hafizi, L. Johnson, D. Kaganovich, R. Hubbard, A. Richardson, and D. Zhigunov, “Ideal form of optical plasma lenses,” Phys. Plasmas 25, 063101 (2018).
[Crossref]

AIAA J. (2)

B. W. Neiswander, E. Matlis, and T. C. Corke, “Plasma lens for optical path difference control,” AIAA J. 50, 123–130 (2012).
[Crossref]

B. W. Neiswander, E. Matlis, and T. C. Corke, “Geometric optimization of a cylindrical plasma adaptive optics lens,” AIAA J. 51, 657–664 (2013).
[Crossref]

Appl. Opt. (2)

Appl. Phys. B (1)

W. Liu, J.-F. Gravel, F. Théberge, A. Becker, and S. Chin, “Background reservoir: its crucial role for long-distance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80, 857–860 (2005).
[Crossref]

Bell Syst. Tech. J. (5)

D. Marcuse and S. Miller, “Analysis of a tubular gas lens,” Bell Syst. Tech. J. 43, 1759–1782 (1964).
[Crossref]

A. Beck, “Thermal gas lens measurements,” Bell Syst. Tech. J. 43, 1818–1820 (1964).
[Crossref]

D. Berreman, “A lens or light guide using convectively distorted thermal gradients in gases,” Bell Syst. Tech. J. 43, 1469–1475 (1964).
[Crossref]

A. Beck, “Gas mixture lens measurements,” Bell Syst. Tech. J. 43, 1821–1825 (1964).
[Crossref]

D. Berreman, “A gas lens using unlike, counter-flowing gases,” Bell Syst. Tech. J. 43, 1476–1479 (1964).
[Crossref]

Exp. Fluids (1)

G. H. Vatistas, V. Kozel, and W. Mih, “A simpler model for concentrated vortices,” Exp. Fluids 11, 73–76 (1991).
[Crossref]

Int. J. Numer. Methods Fluids (1)

S. Chakravarthy, “A unified-grid finite volume formulation for computational fluid dynamics,” Int. J. Numer. Methods Fluids 31, 309–323 (1999).
[Crossref]

J. Appl. Phys. (1)

D. Kaganovich, D. Gordon, M. Helle, and A. Ting, “Shaping gas jet plasma density profile by laser generated shock waves,” J. Appl. Phys. 116, 013304 (2014).
[Crossref]

J. Appl. Spectrosc. (3)

B. Vilenchits, A. Zhdanovskii, and D. Umreiko, “Focusing properties of a vortex gas flow,” J. Appl. Spectrosc. 62, 153–155 (1995).
[Crossref]

B. Vilenchits, A. Zhdanovskii, N. Lemesh, and L. Senchuk, “The effect of the scale factor on the focusing properties of a vortex gas flow,” J. Appl. Spectrosc. 64, 399–402 (1997).
[Crossref]

B. Vilenchits, A. Zhdanovskii, and V. Popov, “Influence of a vortex gas flow on an axial laser beam,” J. Appl. Spectrosc. 72, 59–63 (2005).
[Crossref]

J. Eng. Phys. (1)

P. Mikheev, V. Nikolaev, S. Shalaginov, and A. Shepelenko, “Investigation of the defocusing properties of a vortical gas flow,” J. Eng. Phys. 59, 1375–1379 (1990).
[Crossref]

J. Fluids Eng. (2)

U. Goldberg, O. Peroomian, and S. Chakravarthy, “A wall-distance-free k-ε model with enhanced near-wall treatment,” J. Fluids Eng. 120, 457–462 (1998).
[Crossref]

Y. Aboelkassem and G. H. Vatistas, “New model for compressible vortices,” J. Fluids Eng. 129, 1073–1079 (2007).
[Crossref]

J. Heat Transfer (1)

B. E. Launder, “On the computation of convective heat transfer in complex turbulent flows,” J. Heat Transfer 110, 1112–1128 (1988).
[Crossref]

J. Opt. Soc. Am. (1)

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

Nature (1)

M. Michaelis, C. Dempers, M. Kosch, A. Prause, M. Notcutt, P. Cunningham, and J. Waltham, “A gas-lens telescope,” Nature 353, 547–548 (1991).
[Crossref]

Opt. Commun. (1)

M. Michaelis, M. Notcutt, and P. Cunningham, “Drilling by gas lens focused laser,” Opt. Commun. 59, 369–374 (1986).
[Crossref]

Opt. Laser Technol. (1)

M. Notcutt, M. Michaelis, P. Cunningham, and J. Waltham, “Spinning pipe gas lens,” Opt. Laser Technol. 20, 243–250 (1988).
[Crossref]

Phys. Plasmas (2)

D. Gordon, A. Stamm, B. Hafizi, L. Johnson, D. Kaganovich, R. Hubbard, A. Richardson, and D. Zhigunov, “Ideal form of optical plasma lenses,” Phys. Plasmas 25, 063101 (2018).
[Crossref]

M. Mortazavi, J. Urzay, and A. Mani, “Computational hydrodynamics and optical performance of inductively-coupled plasma adaptive lenses,” Phys. Plasmas 22, 062110 (2015).
[Crossref]

Proc. SPIE (1)

H. Bercegol, P. R. Bouchut, L. Lamaignère, B. Le Garrec, and G. Razé, “The impact of laser damage on the lifetime of optical components in fusion lasers,” Proc. SPIE 5273, 312–325 (2003).
[Crossref]

South African J. Sci. (1)

C. Mafusire, A. Forbes, G. Snedden, and M. Michaelis, “The spinning pipe gas lens revisited,” South African J. Sci. 104, 260–264 (2008).

Other (8)

J. Urzay, M. Mortazavi, and A. Mani, “Optical degradation of inductively-coupled plasma lenses by conversion of electromagnetic energy into unsteady flows,” Tech. Rep. (Center for Turbulence Research, 2013).

R. J. McConnel, “Method and apparatus for refracting a laser beam,” U.S. patent4,402,574 (September6, 1983).

L. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, OSA Technical Digest (Optical Society of America, 2000), paper SuC1.

E. U. Condon and H. Odishaw, Handbook of Physics (McGraw-Hill, 1958).

L. Landau and E. Lifshitz, Fluid Mechanics, Vol. 6 of Course of Theoretical Physics (Pergamon, 1959).

H. Katanoda and M. H. Bin Yusof, “Energy separation mechanism in uni-flow vortex tube using compressible vortex flow,” in International Conference on Fluid Mechanics, Heat Transfer and Thermodynamics (2014), Vol. 2014, pp. 1252–1255.

D. Gordon, P. Sprangle, S. Slinker, R. Fernsler, and M. Lampe, “SPARC-a simulation model for electrical charges,” (U.S. Naval Research Lab, 2006).

D. Gordon, “SeaRay,” 2018, https://github.com/USNavalResearchLaboratory/SeaRay . Commit: d4f58d5ed5310aadafccff958c4b927bec0da93c.

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Figures (11)

Fig. 1.
Fig. 1. Interior walls of the gas lens are shown in gray. The inlets and outlets are shown in yellow and blue, respectively. The optical axis corresponds to the z axis. Characteristic streamlines of the flow are shown in blue for fluid parcels that originate in the z > 0 half of the top inlet. The flow has mirror symmetry across the z = 0 plane and two-fold rotational symmetry around the z axis.
Fig. 2.
Fig. 2. Cross section of the gas lens in the x = + 0 plane. The regions referred to by name are labeled. Named volumes and surfaces are shown with a unique color or line style, respectively.
Fig. 3.
Fig. 3. (a) Angular velocity, (b) radial velocity, (c) axial velocity, and (d) number density of the gas at different z locations. The position z = 0 is the mid-plane of the gas lens, z = 0.5 mm is the outlet entrance, and z = 1 mm is the outlet exit. The mass flow rate is 0.65 g s 1 . Line outs were taken along the cylindrical radius r , specifically, where y = 0 . The black, dashed line is the average number density from z = 0 to 1.5 mm.
Fig. 4.
Fig. 4. Estimated area-averaged axial velocity [solid black line from Eq. (1) with ρ o = ρ atm ] and total velocity [dashed red line from Eq. (3)] at the gas lens outlet are shown as functions of the mass flow rate through the device. The density averaged axial velocity (black cross) and total velocity (red plus) from CFD++ simulations are shown for comparison. The gray line marks the speed of sound in the outlet chamber.
Fig. 5.
Fig. 5. Total mass flow rate of the inlets (black) and outlets (red). The gray band shows the region with mass flow rates between 0.5 and 1 g s 1 .
Fig. 6.
Fig. 6. Zernike spectrum of the optical phase shift induced by a gas vortex lens with mass flow rate of 1 g s 1 . The OSA single-index j is used [32]. The defocus and spherical aberration modes are j = 4 and j = 12 .
Fig. 7.
Fig. 7. Focal length of the diverging lens as a function of mass flow rate.
Fig. 8.
Fig. 8. Fractional difference in focal length between paraxial and margin rays is shown as a function of mass flow rate.
Fig. 9.
Fig. 9. Simulation domain is one quadrant of the physical domain and is the union of the gas vortex lens and an outlet chamber.
Fig. 10.
Fig. 10. Example of mesh ( 50 μm ) near the outlet on the yz-plane.
Fig. 11.
Fig. 11. Percent difference between radial density profiles between the 100 and 50 μm simulations.

Tables (1)

Tables Icon

Table 1. Functional Form of Zernike Polynomials on the Unit Circle, ρ [ 0 , 1 ] and θ [ 0 , 2 π ) , Their OSA Single-Index j , and Description

Equations (14)

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

v z , o = m ˙ ρ o A o ,
Δ h = 1 4 ( m ˙ ρ i A i ) 2 ( R i R o ) 2 + 1 2 ( m ˙ ρ o A o ) 2 1 2 ( m ˙ ρ i A i ) 2 + P o ρ o ( 1 ( ρ i ρ o ) γ 1 ) .
v tot = 2 v o , z ( ( 1 + β 2 ) 1 + β 2 ) / ( 3 β 2 ) ,
t ρ + x k ( ρ v k ) = 0 ,
t ( ρ v i ) + x k ( p δ i k + ρ v i v k σ i k ) = 0 ,
t E + x k ( v k ( E + p ) v i σ i k k i x i T ) = 0 ,
σ i k = μ ( v i x k + v k x i 2 3 δ i k v l x l ) ζ δ i k v l x l ,
μ μ 0 = ( T T 0 μ ) 3 / 2 T 0 μ + S μ T + S μ ,
k k 0 = ( T T 0 k ) 3 / 2 T 0 k + S k T + S k ,
Z n m ( ρ , θ ) = { R n | m | ( ρ ) sin ( | m | θ ) , m < 0 R n | m | ( ρ ) cos ( | m | θ ) , m 0 ,
R n m ( ρ ) = k = 0 ( n m ) / 2 ( 1 ) k ( n k ) ! k ! [ ( n + m ) / 2 k ] ! [ ( n m ) / 2 k ] ! ρ n 2 k ,
0 1 d ρ ρ 0 2 π d θ Z n m ( ρ , θ ) Z n m ( ρ , θ ) = ϵ m π 2 n + 2 δ n , n δ m , m ,
ϕ ( ρ , θ ) = n = 0 m = n , n m even n s n , m Z n m ( ρ , θ ) ,
s n , m = 2 n + 2 ϵ m π 0 1 d ρ ρ 0 2 π d ϕ ϕ ( ρ , θ ) Z n m ( ρ , ϕ ) .