Abstract

In 1832 Hamilton predicted conical refraction, concluding that if a beam propagates along an optic axis of a biaxial crystal, a hollow cone of light will emerge. Nearly two centuries on, cascade conical refraction involving multiple crystals has not been investigated. We empirically investigate a unique two-crystal configuration, and use this to demonstrate an ultra-efficient conical refraction Nd:KGd(WO4)2 laser providing multi-watt output with excellent beam quality independent of resonator design with a slope efficiency close to the theoretical maximum, offering a new route for power and brightness-scaling in solid-state bulk lasers.

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  1. W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. R. Irish Acad. 17, 1–144 (1833).
  2. H. Lloyd, “On the phenomenon presented by light in its passage along the axis of biaxial crystals,” Trans. R. Irish Acad. 17, 145–158 (1833).
  3. M. V. Berry, M. R. Jeffrey, and J. L. Lunney, “Conical diffraction: observations and theory,” Proc. R Soc. A 462(2070), 1629–1642 (2006).
    [CrossRef]
  4. M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A 6, 289–300 (2004).
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    [CrossRef]
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    [CrossRef]
  8. R. Potter, “An examination of the phaenomena of conical refraction in biaxial crystals,” Philos. Mag. 18, 343–353 (1841).
  9. W. Haidinger, “Die konische Refraction am Diopsid, nebst Bemerkungen ber einige Erscheinungen der konischen Refraction an Arragonit,” Ann. Phys. Chem. 172(11), 469–487 (1855).
    [CrossRef]
  10. S. Melmore, “Conical refraction,” Nature 150(3804), 382–383 (1942).
    [CrossRef]
  11. D. L. Portigal and E. Burstein, “Effect of optical activity or Faraday rotation on internal conical refraction,” J. Opt. Soc. Am. 62(7), 859–864 (1972).
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  12. A. Belafhal, “Theoretical intensity distribution of internal conical refraction,” Opt. Commun. 178(4-6), 257–265 (2000).
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  13. A. M. Belskii and A. P. Khapalyuk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt Spectrosc (USSR) 44, 436–439 (1978).
  14. A. M. Belsky and M. A. Stepanov, “Internal conical refraction of coherent light beams,” Opt. Commun. 167(1-6), 1–5 (1999).
    [CrossRef]
  15. A. M. Belsky and M. A. Stepanov, “Internal conical refraction of light beams in biaxial gyrotropic crystals,” Opt. Commun. 204(1-6), 1–6 (2002).
    [CrossRef]
  16. M. V. Berry and M. R. Jeffrey, “Chiral conical diffraction,” J. Opt. A 8, 363–372 (2006).
  17. M. V. Berry and M. R. Jeffrey, “Conical diffraction complexified: dichroism and the transition to double refraction,” J. Opt. A 8, 1043–1051 (2006).
  18. M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
    [CrossRef]
  19. M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A 7, 685–690 (2005).
  20. N. Bloembergen and H. Shih, “Conical refraction in nonlinear optics,” Opt. Commun. 1(2), 70–72 (1969).
    [CrossRef]
  21. J. P. F`eve, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refraction in ktp,” Opt. Commun. 105, 243–252 (1994).
    [CrossRef]
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  23. O. N. Naida, “Tangential conical refraction in a three-dimensional inhomogeneous weakly anisotropic medium,” Sov. Phys. JETP 50, 239–245 (1979).
  24. B. S. Perkal’skis and Y. P. Mikhailichenko, “Demonstration of conical refraction,” Izv Vyss Uch Zav Fiz 8, 103–105 (1979).
  25. J. Hellström, H. Henricsson, V. Pasiskevicius, U. Bünting, and D. Haussmann, “Polarization-tunable Yb:KGW laser based on internal conical refraction,” Opt. Lett. 32(19), 2783–2785 (2007).
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  31. J. G. O’Hara, “The prediction and discovery of conical refraction by William Rowan Hamilton and Humphrey Lloyd (1832-1833),” Proc. R. Ir. Acad. [B] 82A, 231–257 (1982).

2009

C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12891 .
[CrossRef] [PubMed]

2007

J. Hellström, H. Henricsson, V. Pasiskevicius, U. Bünting, and D. Haussmann, “Polarization-tunable Yb:KGW laser based on internal conical refraction,” Opt. Lett. 32(19), 2783–2785 (2007).
[CrossRef] [PubMed]

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[CrossRef]

M. R. Jeffrey, “The spun cusp complexified: complex ray focusing in chiral conical diffraction,” J. Opt. A 9, 634–641 (2007).

2006

M. V. Berry, M. R. Jeffrey, and J. L. Lunney, “Conical diffraction: observations and theory,” Proc. R Soc. A 462(2070), 1629–1642 (2006).
[CrossRef]

M. V. Berry and M. R. Jeffrey, “Chiral conical diffraction,” J. Opt. A 8, 363–372 (2006).

M. V. Berry and M. R. Jeffrey, “Conical diffraction complexified: dichroism and the transition to double refraction,” J. Opt. A 8, 1043–1051 (2006).

2005

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A 7, 685–690 (2005).

2004

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A 6, 289–300 (2004).

2002

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of light beams in biaxial gyrotropic crystals,” Opt. Commun. 204(1-6), 1–6 (2002).
[CrossRef]

2000

A. Belafhal, “Theoretical intensity distribution of internal conical refraction,” Opt. Commun. 178(4-6), 257–265 (2000).
[CrossRef]

1999

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of coherent light beams,” Opt. Commun. 167(1-6), 1–5 (1999).
[CrossRef]

1994

J. P. F`eve, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refraction in ktp,” Opt. Commun. 105, 243–252 (1994).
[CrossRef]

1982

J. G. O’Hara, “The prediction and discovery of conical refraction by William Rowan Hamilton and Humphrey Lloyd (1832-1833),” Proc. R. Ir. Acad. [B] 82A, 231–257 (1982).

1979

O. N. Naida, “Tangential conical refraction in a three-dimensional inhomogeneous weakly anisotropic medium,” Sov. Phys. JETP 50, 239–245 (1979).

B. S. Perkal’skis and Y. P. Mikhailichenko, “Demonstration of conical refraction,” Izv Vyss Uch Zav Fiz 8, 103–105 (1979).

1978

A. M. Belskii and A. P. Khapalyuk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt Spectrosc (USSR) 44, 436–439 (1978).

1972

D. L. Portigal and E. Burstein, “Effect of optical activity or Faraday rotation on internal conical refraction,” J. Opt. Soc. Am. 62(7), 859–864 (1972).
[CrossRef]

1969

N. Bloembergen and H. Shih, “Conical refraction in nonlinear optics,” Opt. Commun. 1(2), 70–72 (1969).
[CrossRef]

1942

S. Melmore, “Conical refraction,” Nature 150(3804), 382–383 (1942).
[CrossRef]

C. V. Raman and T. M. K. Nedungadi, “Optical images formed by conical refraction,” Nature 149(3785), 552–553 (1942).
[CrossRef]

1941

C. V. Raman, V. S. Rajagopalan, and T. M. K. Nedungadi, “Conical refraction in naphthalene crystals,” Proc. Indian Ins. Sci. A 14, 221–227 (1941).

1855

W. Haidinger, “Die konische Refraction am Diopsid, nebst Bemerkungen ber einige Erscheinungen der konischen Refraction an Arragonit,” Ann. Phys. Chem. 172(11), 469–487 (1855).
[CrossRef]

1841

R. Potter, “An examination of the phaenomena of conical refraction in biaxial crystals,” Philos. Mag. 18, 343–353 (1841).

1839

J. C. Poggendorff, “Ueber die konische Refraction,” Pogg. Ann. 124(11), 461–462 (1839).
[CrossRef]

1833

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. R. Irish Acad. 17, 1–144 (1833).

H. Lloyd, “On the phenomenon presented by light in its passage along the axis of biaxial crystals,” Trans. R. Irish Acad. 17, 145–158 (1833).

Belafhal, A.

A. Belafhal, “Theoretical intensity distribution of internal conical refraction,” Opt. Commun. 178(4-6), 257–265 (2000).
[CrossRef]

Belskii, A. M.

A. M. Belskii and A. P. Khapalyuk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt Spectrosc (USSR) 44, 436–439 (1978).

Belsky, A. M.

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of light beams in biaxial gyrotropic crystals,” Opt. Commun. 204(1-6), 1–6 (2002).
[CrossRef]

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of coherent light beams,” Opt. Commun. 167(1-6), 1–5 (1999).
[CrossRef]

Berry, M. V.

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[CrossRef]

M. V. Berry and M. R. Jeffrey, “Chiral conical diffraction,” J. Opt. A 8, 363–372 (2006).

M. V. Berry and M. R. Jeffrey, “Conical diffraction complexified: dichroism and the transition to double refraction,” J. Opt. A 8, 1043–1051 (2006).

M. V. Berry, M. R. Jeffrey, and J. L. Lunney, “Conical diffraction: observations and theory,” Proc. R Soc. A 462(2070), 1629–1642 (2006).
[CrossRef]

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A 7, 685–690 (2005).

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A 6, 289–300 (2004).

Bloembergen, N.

N. Bloembergen and H. Shih, “Conical refraction in nonlinear optics,” Opt. Commun. 1(2), 70–72 (1969).
[CrossRef]

Boulanger, B.

J. P. F`eve, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refraction in ktp,” Opt. Commun. 105, 243–252 (1994).
[CrossRef]

Bünting, U.

J. Hellström, H. Henricsson, V. Pasiskevicius, U. Bünting, and D. Haussmann, “Polarization-tunable Yb:KGW laser based on internal conical refraction,” Opt. Lett. 32(19), 2783–2785 (2007).
[CrossRef] [PubMed]

Burstein, E.

D. L. Portigal and E. Burstein, “Effect of optical activity or Faraday rotation on internal conical refraction,” J. Opt. Soc. Am. 62(7), 859–864 (1972).
[CrossRef]

Donegan, J. F.

C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12891 .
[CrossRef] [PubMed]

Feve, J. P.

J. P. F`eve, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refraction in ktp,” Opt. Commun. 105, 243–252 (1994).
[CrossRef]

Haidinger, W.

W. Haidinger, “Die konische Refraction am Diopsid, nebst Bemerkungen ber einige Erscheinungen der konischen Refraction an Arragonit,” Ann. Phys. Chem. 172(11), 469–487 (1855).
[CrossRef]

Hamilton, W. R.

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. R. Irish Acad. 17, 1–144 (1833).

Haussmann, D.

J. Hellström, H. Henricsson, V. Pasiskevicius, U. Bünting, and D. Haussmann, “Polarization-tunable Yb:KGW laser based on internal conical refraction,” Opt. Lett. 32(19), 2783–2785 (2007).
[CrossRef] [PubMed]

Hellström, J.

J. Hellström, H. Henricsson, V. Pasiskevicius, U. Bünting, and D. Haussmann, “Polarization-tunable Yb:KGW laser based on internal conical refraction,” Opt. Lett. 32(19), 2783–2785 (2007).
[CrossRef] [PubMed]

Henricsson, H.

J. Hellström, H. Henricsson, V. Pasiskevicius, U. Bünting, and D. Haussmann, “Polarization-tunable Yb:KGW laser based on internal conical refraction,” Opt. Lett. 32(19), 2783–2785 (2007).
[CrossRef] [PubMed]

Jeffrey, M. R.

M. R. Jeffrey, “The spun cusp complexified: complex ray focusing in chiral conical diffraction,” J. Opt. A 9, 634–641 (2007).

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[CrossRef]

M. V. Berry and M. R. Jeffrey, “Conical diffraction complexified: dichroism and the transition to double refraction,” J. Opt. A 8, 1043–1051 (2006).

M. V. Berry and M. R. Jeffrey, “Chiral conical diffraction,” J. Opt. A 8, 363–372 (2006).

M. V. Berry, M. R. Jeffrey, and J. L. Lunney, “Conical diffraction: observations and theory,” Proc. R Soc. A 462(2070), 1629–1642 (2006).
[CrossRef]

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A 7, 685–690 (2005).

Khapalyuk, A. P.

A. M. Belskii and A. P. Khapalyuk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt Spectrosc (USSR) 44, 436–439 (1978).

Lloyd, H.

H. Lloyd, “On the phenomenon presented by light in its passage along the axis of biaxial crystals,” Trans. R. Irish Acad. 17, 145–158 (1833).

Lunney, J. G.

C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12891 .
[CrossRef] [PubMed]

Lunney, J. L.

M. V. Berry, M. R. Jeffrey, and J. L. Lunney, “Conical diffraction: observations and theory,” Proc. R Soc. A 462(2070), 1629–1642 (2006).
[CrossRef]

Mansuripur, M.

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A 7, 685–690 (2005).

Marnier, G.

J. P. F`eve, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refraction in ktp,” Opt. Commun. 105, 243–252 (1994).
[CrossRef]

Melmore, S.

S. Melmore, “Conical refraction,” Nature 150(3804), 382–383 (1942).
[CrossRef]

Mikhailichenko, Y. P.

B. S. Perkal’skis and Y. P. Mikhailichenko, “Demonstration of conical refraction,” Izv Vyss Uch Zav Fiz 8, 103–105 (1979).

Naida, O. N.

O. N. Naida, “Tangential conical refraction in a three-dimensional inhomogeneous weakly anisotropic medium,” Sov. Phys. JETP 50, 239–245 (1979).

Nedungadi, T. M. K.

C. V. Raman and T. M. K. Nedungadi, “Optical images formed by conical refraction,” Nature 149(3785), 552–553 (1942).
[CrossRef]

C. V. Raman, V. S. Rajagopalan, and T. M. K. Nedungadi, “Conical refraction in naphthalene crystals,” Proc. Indian Ins. Sci. A 14, 221–227 (1941).

O’Dwyer, D. P.

C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12891 .
[CrossRef] [PubMed]

O’Hara, J. G.

J. G. O’Hara, “The prediction and discovery of conical refraction by William Rowan Hamilton and Humphrey Lloyd (1832-1833),” Proc. R. Ir. Acad. [B] 82A, 231–257 (1982).

Pasiskevicius, V.

J. Hellström, H. Henricsson, V. Pasiskevicius, U. Bünting, and D. Haussmann, “Polarization-tunable Yb:KGW laser based on internal conical refraction,” Opt. Lett. 32(19), 2783–2785 (2007).
[CrossRef] [PubMed]

Perkal’skis, B. S.

B. S. Perkal’skis and Y. P. Mikhailichenko, “Demonstration of conical refraction,” Izv Vyss Uch Zav Fiz 8, 103–105 (1979).

Phelan, C. F.

C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12891 .
[CrossRef] [PubMed]

Poggendorff, J. C.

J. C. Poggendorff, “Ueber die konische Refraction,” Pogg. Ann. 124(11), 461–462 (1839).
[CrossRef]

Portigal, D. L.

D. L. Portigal and E. Burstein, “Effect of optical activity or Faraday rotation on internal conical refraction,” J. Opt. Soc. Am. 62(7), 859–864 (1972).
[CrossRef]

Potter, R.

R. Potter, “An examination of the phaenomena of conical refraction in biaxial crystals,” Philos. Mag. 18, 343–353 (1841).

Rajagopalan, V. S.

C. V. Raman, V. S. Rajagopalan, and T. M. K. Nedungadi, “Conical refraction in naphthalene crystals,” Proc. Indian Ins. Sci. A 14, 221–227 (1941).

Rakovich, Y. P.

C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12891 .
[CrossRef] [PubMed]

Raman, C. V.

C. V. Raman and T. M. K. Nedungadi, “Optical images formed by conical refraction,” Nature 149(3785), 552–553 (1942).
[CrossRef]

C. V. Raman, V. S. Rajagopalan, and T. M. K. Nedungadi, “Conical refraction in naphthalene crystals,” Proc. Indian Ins. Sci. A 14, 221–227 (1941).

Shih, H.

N. Bloembergen and H. Shih, “Conical refraction in nonlinear optics,” Opt. Commun. 1(2), 70–72 (1969).
[CrossRef]

Stepanov, M. A.

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of light beams in biaxial gyrotropic crystals,” Opt. Commun. 204(1-6), 1–6 (2002).
[CrossRef]

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of coherent light beams,” Opt. Commun. 167(1-6), 1–5 (1999).
[CrossRef]

Ann. Phys. Chem.

W. Haidinger, “Die konische Refraction am Diopsid, nebst Bemerkungen ber einige Erscheinungen der konischen Refraction an Arragonit,” Ann. Phys. Chem. 172(11), 469–487 (1855).
[CrossRef]

Izv Vyss Uch Zav Fiz

B. S. Perkal’skis and Y. P. Mikhailichenko, “Demonstration of conical refraction,” Izv Vyss Uch Zav Fiz 8, 103–105 (1979).

J. Opt. A

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A 7, 685–690 (2005).

M. R. Jeffrey, “The spun cusp complexified: complex ray focusing in chiral conical diffraction,” J. Opt. A 9, 634–641 (2007).

M. V. Berry and M. R. Jeffrey, “Chiral conical diffraction,” J. Opt. A 8, 363–372 (2006).

M. V. Berry and M. R. Jeffrey, “Conical diffraction complexified: dichroism and the transition to double refraction,” J. Opt. A 8, 1043–1051 (2006).

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A 6, 289–300 (2004).

J. Opt. Soc. Am.

D. L. Portigal and E. Burstein, “Effect of optical activity or Faraday rotation on internal conical refraction,” J. Opt. Soc. Am. 62(7), 859–864 (1972).
[CrossRef]

Nature

S. Melmore, “Conical refraction,” Nature 150(3804), 382–383 (1942).
[CrossRef]

C. V. Raman and T. M. K. Nedungadi, “Optical images formed by conical refraction,” Nature 149(3785), 552–553 (1942).
[CrossRef]

Opt Spectrosc (USSR)

A. M. Belskii and A. P. Khapalyuk, “Internal conical refraction of bounded light beams in biaxial crystals,” Opt Spectrosc (USSR) 44, 436–439 (1978).

Opt. Commun.

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of coherent light beams,” Opt. Commun. 167(1-6), 1–5 (1999).
[CrossRef]

A. M. Belsky and M. A. Stepanov, “Internal conical refraction of light beams in biaxial gyrotropic crystals,” Opt. Commun. 204(1-6), 1–6 (2002).
[CrossRef]

A. Belafhal, “Theoretical intensity distribution of internal conical refraction,” Opt. Commun. 178(4-6), 257–265 (2000).
[CrossRef]

N. Bloembergen and H. Shih, “Conical refraction in nonlinear optics,” Opt. Commun. 1(2), 70–72 (1969).
[CrossRef]

J. P. F`eve, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refraction in ktp,” Opt. Commun. 105, 243–252 (1994).
[CrossRef]

Opt. Express

C. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan, and J. G. Lunney, “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal,” Opt. Express 17(15), 12891–12899 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12891 .
[CrossRef] [PubMed]

Opt. Lett.

J. Hellström, H. Henricsson, V. Pasiskevicius, U. Bünting, and D. Haussmann, “Polarization-tunable Yb:KGW laser based on internal conical refraction,” Opt. Lett. 32(19), 2783–2785 (2007).
[CrossRef] [PubMed]

Philos. Mag.

R. Potter, “An examination of the phaenomena of conical refraction in biaxial crystals,” Philos. Mag. 18, 343–353 (1841).

Pogg. Ann.

J. C. Poggendorff, “Ueber die konische Refraction,” Pogg. Ann. 124(11), 461–462 (1839).
[CrossRef]

Proc. Indian Ins. Sci. A

C. V. Raman, V. S. Rajagopalan, and T. M. K. Nedungadi, “Conical refraction in naphthalene crystals,” Proc. Indian Ins. Sci. A 14, 221–227 (1941).

Proc. R Soc. A

M. V. Berry, M. R. Jeffrey, and J. L. Lunney, “Conical diffraction: observations and theory,” Proc. R Soc. A 462(2070), 1629–1642 (2006).
[CrossRef]

Proc. R. Ir. Acad. [B]

J. G. O’Hara, “The prediction and discovery of conical refraction by William Rowan Hamilton and Humphrey Lloyd (1832-1833),” Proc. R. Ir. Acad. [B] 82A, 231–257 (1982).

Prog. Opt.

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[CrossRef]

Sov. Phys. JETP

O. N. Naida, “Tangential conical refraction in a three-dimensional inhomogeneous weakly anisotropic medium,” Sov. Phys. JETP 50, 239–245 (1979).

Trans. R. Irish Acad.

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. R. Irish Acad. 17, 1–144 (1833).

H. Lloyd, “On the phenomenon presented by light in its passage along the axis of biaxial crystals,” Trans. R. Irish Acad. 17, 145–158 (1833).

Other

A. Abdolvand, K. G. Wilcox, T. K. Kalkandjiev, and E. U. Rfailov, “Solid-state conical refraction laser,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Application Systemes Technologies, Technical Digest (CD) (Optical Society of America, 2009), Post-deadline paper CPDB1. http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2009-CPDB1

W. Koechner, Solid-State Laser Engineering, 5th ed. (Springer-Verlag, 1999), pp. 198–205.

O. Svelto, Principles of lasers, 4th ed. (Plenum Press, 1998), pp. 249–272.

T. K. Kalkandjiev, and M. A. Bursukova, “Conical refraction: an experimental introduction,” Proc. SPIE 6994, 69940B1–69940B10 (2008).

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Figures (5)

Fig. 1
Fig. 1

The features of single-crystal conical refraction: (a) spatial evolution of a focused beam upon its passage along the optic axis of a biaxial crystal. The dashed red lines are the imagined continuation of the beam to its focus. (b) The Lloyd plane is also a symmetry plane. Existence of two focal planes can be seen. Here, an expanded beam from a Helium Neon laser was brought to a focus by a lens (f=100 mm). The focal spot size was measured to be 18 μm in radius. A Nd:KGd(WO4)2 crystal cut for CR and of length d = 17 mm, was positioned before the focus of the incident beam so that the beam radius on the entrance facet was measured to be ~ 375 μm. Further alignment by rotating the crystal about an axis perpendicular to the plane of the optic axes results in the direct observation on a charge-coupled device (CCD) with no imaging optics of a ring pattern located at the Lloyd plane. The spatial evolution of the beam in free space was measured by recording CCD images at 2 mm intervals. The entire evolution occurred over a distance of ~ 30 mm either side of the Lloyd ring plane.

Fig. 2
Fig. 2

Conical refraction laser cavity. HR is the 75 mm radius of curvature concave high reflector through which the active medium was optically pumped along the 17 mm axis. OC is the plane output coupler with a transmission of 3% at the lasing wavelength. For all experiments the pump beam was focused on the entrance facet of the crystal. L denotes the distance between the input mirror and the entrance facet of the crystal. This distance was varied in the second set of the experiments while the pump beam focus was kept on the entrance facet of the crystal. In the third set of experiments the cavity was set to 50 mm and left unchanged whilst the pump mode diameter was varied between 235 and 1570 µm.

Fig. 3
Fig. 3

Performance of the conical refraction laser. Measured output power versus incident pump power for two laser cavities of different lengths. The pump mode diameter was set to 400 µm. Characteristics of the 50 mm cavity are shown in black and the 80 mm cavity in red. Both configurations have a slope efficiency of 74%. Inset is the 3-D profile of the laser output from the 50 mm cavity at the maximum output.

Fig. 4
Fig. 4

Performance of the conical refraction laser for various pump mode diameters on the crystal. (a) The length of the cavity was always 50 mm. Lasing action was observed with all pump mode diameters investigated. A maximum output power of 3.3 W with an incident pump power of 5 W was obtained for both the 235 and 400 µm pump mode diameters. This corresponds to a slope efficiency of ~ 74%. As the pump diameter increases beyond 400 µm the efficiency of the laser decreases in a near-linear fashion as shown in next figure. (b) Graph of measured and calculated laser slope efficiency versus pump mode diameters on the crystal. The black squares show the measured slope efficiency of the CR laser. The calculated theoretical maximum slope efficiency of the lasers if they were operating as Gaussian lasers are shown in red dots - dashed line. The blue triangles represent the calculated theoretical maximum slope efficiency where only the losses due to the quantum defect heating in the active medium and cavity losses are considered.

Fig. 5
Fig. 5

Two-crystal cascade conical refraction. Experimental setup of cascade conical refraction where the two CR crystals have identical length and are orientated with opposite orientations of the pseudovector Λ. When both crystals are in place in the cascade scheme, after the first crystal the Lloyd ring was observed but after the second crystal instead of observing a Lloyd ring, the observed beam had an identical beam profile to the initial Gaussian beam before the first crystal. This is direct evidence of transformation of an annular beam between the two CR crystals to the original Guassian beam after the second crystal (CR 2).

Equations (2)

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Δ = d ( 1 1 n ) ,
η s = η p η c η t η q ,

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