Abstract

This study proposes a three-lens configuration for generating a stable donutlike vortex laser beam with controlled Ince–Gaussian mode (IGM) operation in the model of laser-diode (LD)-pumped solid-state lasers. Simply controlling the lateral off-axis position of the pump beam's focus on the laser crystal can generate a desired donutlike vortex beam from the proposed simple and easily made three-lens configuration, a proposed astigmatic mode converter assembled into one body with a concave–convex laser cavity.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  25. G. A. Turnball, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, "The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phase plate," Opt. Commun. 127, 183-188 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  32. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123-132 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  46. See the specification of lens on the website of Newport corporation, http://www.newport.com/ and SIGMA-KOKI corporation, http://www.sigma-koki.com/english/index.html.
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  48. See the Hermite polynomial http://mathworld.wolfram.com/HermitePolynomial.html and see Laguerre polynomial http://mathworld.wolfram.com/LaguerrePolynomial.html.

2007 (1)

K. Otsuka, K. Nemoto, K. Kamikariya, and S.-C. Chu, "Linearly-polarized, single-frequency oscillations of laser-diode-pumped microchip ceramic Nd:YAG lasers with forced Ince-Gaussian mode operations," Jpn. J. Appl. Phys. , Part 1 46, 5865-5867 (2007).
[CrossRef]

2006 (5)

2004 (4)

2002 (1)

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, "Creation of Laguerre-Gaussian laser modes using diffractive optics," Phys. Rev. A 66, 043801 (2002).
[CrossRef]

2001 (3)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

X. Xu, K. Kim, W. Jhe, and N. Kwon, "Efficient optical guiding of trapped cold atoms by a hollow laser beam," Phy. Rev. A 63, 063401 (2001).
[CrossRef]

M. Endo, S. Yamaguchi, T. Uchiyama, and T. Fujioka, "Numerical simulation of the W-axicon type optical resonator for coaxial slab CO2 lasers," J. Phys. D 34, 68-77 (2001).
[CrossRef]

2000 (2)

Y. Ishii and T. Yanagida, "Single molecule detection in life sciences," Single Mol. 1, 5-16 (2000).
[CrossRef]

N. Friedman, L. Khaykovich, R. Ozeri, and N. Davidson, "Compression of cold atoms to very high densities in a rotating-beam blue-detuned optical trap," Phys. Rev. A 61, 031403 (2000).
[CrossRef]

1999 (3)

1998 (3)

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, "High-order Laguerre-Gaussian laser modes for studies of cold atoms," Opt. Commun. 156, 300-306 (1998).
[CrossRef]

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, "Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum," Phys. Rev. Lett. 80, 013601 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, "Rotational frequency shift of a light beam," Phys. Rev. Lett. 81, 4828-4830 (1998).
[CrossRef]

1996 (1)

G. A. Turnball, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, "The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phase plate," Opt. Commun. 127, 183-188 (1996).
[CrossRef]

1994 (2)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phase plate," Opt. Commun. 112, 321-327 (1994).
[CrossRef]

M. Harris, C. A. Hill, P. R. Tapster, and J. M. Vaughan, "Laser modes with helical wave fronts," Phys. Rev. A 49, 3119-3122 (1994).
[CrossRef] [PubMed]

1993 (3)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature 365, 721-727 (1993).
[CrossRef] [PubMed]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123-132 (1993).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123-132 (1993).
[CrossRef]

1992 (4)

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, "Generation of optical phase singularities by computer-generated holograms," Opt. Lett. 17, 221-223 (1992).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, and H. Masuhara, "Optical trapping of a metal particle and a water droplet by a scanning laser beam," Appl. Phys. Lett. 60, 807-809 (1992).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

1990 (1)

1987 (1)

A. Ashkin, J. M. Dziedzic, and T. Yamane, "Optical trapping and manipulation of single cells using infrared laser beams," Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

1986 (1)

1983 (1)

1974 (1)

A. Ashkin and J. M. Dziedzic, "Stability of optical levitation by radiation pressure," Appl. Phys. Lett. 24, 586-588 (1974).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (3)

A. Ashkin and J. M. Dziedzic, "Stability of optical levitation by radiation pressure," Appl. Phys. Lett. 24, 586-588 (1974).
[CrossRef]

K. Sasaki, M. Koshioka, H. Misawa, N. Kitamura, and H. Masuhara, "Optical trapping of a metal particle and a water droplet by a scanning laser beam," Appl. Phys. Lett. 60, 807-809 (1992).
[CrossRef]

P. H. Jones, E. Stride, and N. Saffari, "Trapping and manipulation of microscopic bubbles with a scanning optical tweezer," Appl. Phys. Lett. 89, 081113 (2006).
[CrossRef]

IEEE J. Quantum Electron. (1)

S.-D. Pan, J.-L. He, Y.-E. Hou, Y.-X. Fan, H.-T. Wang, Y.-G. Wang, and X.-Y. Ma, "Diode-end-pumped passively CW mode-locked Nd:YLF laser by the LT-In0.25Ga0.75As absorber," IEEE J. Quantum Electron. 42, 1097-1100 (2006).
[CrossRef]

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

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

J. Phys. D (1)

M. Endo, S. Yamaguchi, T. Uchiyama, and T. Fujioka, "Numerical simulation of the W-axicon type optical resonator for coaxial slab CO2 lasers," J. Phys. D 34, 68-77 (2001).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Otsuka, K. Nemoto, K. Kamikariya, and S.-C. Chu, "Linearly-polarized, single-frequency oscillations of laser-diode-pumped microchip ceramic Nd:YAG lasers with forced Ince-Gaussian mode operations," Jpn. J. Appl. Phys. , Part 1 46, 5865-5867 (2007).
[CrossRef]

Nature (3)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature 365, 721-727 (1993).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, and T. Yamane, "Optical trapping and manipulation of single cells using infrared laser beams," Nature 330, 769-771 (1987).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Opt. Commun. (6)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123-132 (1993).
[CrossRef]

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, "High-order Laguerre-Gaussian laser modes for studies of cold atoms," Opt. Commun. 156, 300-306 (1998).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phase plate," Opt. Commun. 112, 321-327 (1994).
[CrossRef]

G. A. Turnball, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, "The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phase plate," Opt. Commun. 127, 183-188 (1996).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123-132 (1993).
[CrossRef]

J. Courtial and M. J. Padgett, "Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes," Opt. Commun. 159, 13-18 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (6)

Phy. Rev. A (1)

X. Xu, K. Kim, W. Jhe, and N. Kwon, "Efficient optical guiding of trapped cold atoms by a hollow laser beam," Phy. Rev. A 63, 063401 (2001).
[CrossRef]

Phys. Rev. A (5)

M. Harris, C. A. Hill, P. R. Tapster, and J. M. Vaughan, "Laser modes with helical wave fronts," Phys. Rev. A 49, 3119-3122 (1994).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, "Creation of Laguerre-Gaussian laser modes using diffractive optics," Phys. Rev. A 66, 043801 (2002).
[CrossRef]

N. Friedman, L. Khaykovich, R. Ozeri, and N. Davidson, "Compression of cold atoms to very high densities in a rotating-beam blue-detuned optical trap," Phys. Rev. A 61, 031403 (2000).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, "Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum," Phys. Rev. Lett. 80, 013601 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, "Rotational frequency shift of a light beam," Phys. Rev. Lett. 81, 4828-4830 (1998).
[CrossRef]

Single Mol. (1)

Y. Ishii and T. Yanagida, "Single molecule detection in life sciences," Single Mol. 1, 5-16 (2000).
[CrossRef]

Other (11)

K. J. Kuhn, Laser Engineering (Prentice Hall, 1998), pp. 86.

M. Manusuripur, Classical Optics and Its Applications (Cambridge U. Press, 2002).

S. M. Iftiquar, H. Ito, and M. Ohtsu, "Tunable donut light beam for a near-field optical funnel of atoms," in Technical Digest of the CLEO/PR01 (IEEE, 2001), pp. 34-35.

A. E. Siegman, Lasers (University Science Books, 1986), pp. 647.

W. J. Smith, Modern Optical Engineering (McGraw-Hill Professional, 2000), pp. 42.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 1991), pp. 92.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Co., 2004), Chap. 4.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Co., 2004), pp. 97-101.

A. E. Siegman, Lasers (University Science Books, 1986), pp. 295.

See the specification of lens on the website of Newport corporation, http://www.newport.com/ and SIGMA-KOKI corporation, http://www.sigma-koki.com/english/index.html.

See the Hermite polynomial http://mathworld.wolfram.com/HermitePolynomial.html and see Laguerre polynomial http://mathworld.wolfram.com/LaguerrePolynomial.html.

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Figures (8)

Fig. 1
Fig. 1

(Color online) Scheme of donutlike vortex laser beam generation.

Fig. 2
Fig. 2

Some analystic patterns of the Ince–Gaussian modes.

Fig. 3
Fig. 3

Resulting I G 5 , 5 e modes from different shape of gain.

Fig. 4
Fig. 4

Demonstration of the mode superposition of (a) the H I G 1 , 1 ± mode and (b) the tilted I G 1 ,1 e mode.

Fig. 5
Fig. 5

(Color online) Simulated Ince–Gaussian mode lasing pattern formation starting from a random pattern.

Fig. 6
Fig. 6

Amplitude and phase distribution of (a) the selected I G 1 ,1 e mode in concave–convex cavity (b) resulting donutlike vortex beam.

Fig. 7
Fig. 7

Resulting I G 1 ,1 e modes with different shapes of gain.

Fig. 8
Fig. 8

MP of the generated beams versus system errors.

Equations (39)

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

I G p , m e ( r , ε ) = C [ w 0 / w ( z ) ] C p m ( i ξ , ε ) C p m ( η , ε ) exp [ r 2 / w 2 ( z ) ] × exp   i [ k z + { k r 2 / 2 R ( z ) } ( p + 1 ) ψ z ( z ) ] ,
I G p , m o ( r , ε ) = S [ w 0 / w ( z ) ] S p m ( i ξ , ε ) S p m ( η , ε ) exp [ r 2 / w 2 ( z ) ] × exp   i [ k z + { k r 2 / 2 R ( z ) } ( p + 1 ) ψ z ( z ) ] ,
L G n , l e , o ( r , ϕ , z ) = [ 4 n ! ( 1 + δ 0 , l ) π ( n + l ) ! ] 1 / 2 1 w ( z ) ( cos   l ϕ sin   l ϕ ) × [ 2 r w ( z ) ] l L n l ( 2 r 2 w ( z ) 2 ) exp ( r 2 w ( z ) 2 ) × exp   i [ k z + k r 2 2 R ( z ) ( 2 n + l + 1 ) ψ G S ( z ) ] ,
H G n x , n y ( x , y , z ) = ( 1 2 n x + n y 1 π n x ! n y ! ) 1 / 2 1 w ( z ) × H n x ( 2 x w ( z ) ) H n y ( 2 y w ( z ) ) exp [ r 2 w ( z ) 2 ] × exp   i [ k z + k r 2 2 R ( z ) ( n x + n y + 1 ) ψ G S ( z ) ] ,
I G 0 , 0 e , o = L G 0 , 0 e , o = H G 0 , 0 ,
I G 1 ,1 o = L G 0 ,1 o = H G 0 ,1 ,
I G 1 ,1 e = L G 0 ,1 e = H G 1 ,0 .
H I G p , m ± = I G p , m e ± i × I G p , m o .
( n x + 1 / 2 ) ψ x ( z ) + ( n y + 1 / 2 ) ψ y ( z ) ,
ψ x ( z ) = arctan [ ( z z o x ) / z R x ] ,
ψ y ( z ) = arctan [ ( z z o y ) / z R y ] ,
2 [ arctan ( l 0 / z R x ) arctan ( l 0 / z R y ) ] = ± π / 2 .
g i ( x , y ) = g i 0 ( x , y ) / ( 1 + I ˜ i + ( x , y ) + I ˜ i ( x , y ) I s ( x , y ) ) ,
I ˜ i + ( x , y ) = ( 1 α ) i = 0 q α i I i + ( q i ) ,
I ˜ i ( x , y ) = ( 1 α ) i = 0 q α i I i ( q i ) .
E i o u t ( x , y ) = E i i n ( x , y ) exp [ 1 2 g i ( x , y ) d ] ,
E q + 1 ( x , y ) E q ( x , y ) .
M P = | u , u p m | 2 = | u ( u p m ) * d A | 2 .
H n + 1 ( x ) = 2 × H n ( x ) 2 n H n 1 ( x ) ,
L n k ( x ) = L n k + 1 ( x ) L n 1 k + 1 ( x ) ,
C 2 n 2 k ( x , ε ) = r = 0 n A r   cos ( 2 r x ) ,
( p / 2 + 1 ) ε A 1 = a A 0 ,
( p / 2 + 2 ) ε A 2 = p ε A 0 ( 4 a ) A 1 ,
( p / 2 + r + 2 ) ε A r + 2 = [ a 4 ( r + 1 ) 2 ] A r + 1 + ( r p / 2 ) ε A r .
C 2 n + 1 2 k + 1 ( x , ε ) = r = 0 n A r   cos [ ( 2 r + 1 ) x ] ,
( p + 3 ) ε A 1 / 2 = [ a ε ( p + 1 ) / 2 1 ] A 0 ,
( p + 2 r + 3 ) ε A r + 1 / 2 = [ a ( 2 r + 1 ) 2 ] A r + ( 2 r p 1 ) ε A r 1 / 2 .
S 2 n 2 k ( x , ε ) = r = 0 n B r   sin ( 2 r x ) ,
( p / 2 + 2 ) ε B 2 = ( a 4 ) B 1 ,
( p / 2 + r + 2 ) ε B r + 2 = [ a 4 ( r + 1 ) 2 ] B r + 1 + ( r p / 2 ) ε B r .
S 2 n + 1 2 k + 1 ( x , ε ) = r = 0 n B r   sin [ ( 2 r + 1 ) x ] ,
( p + 3 ) ε B 1 / 2 = [ a + ε ( p + 1 ) / 2 1 ] B 0 ,
( p + 2 r + 3 ) ε B r + 1 / 2 = [ a ( 2 r + 1 ) 2 ] B r + ( 2 r p 1 ) ε B r 1 / 2 .
H G 0 , 0 = L G 0 , 0 e , o = 2 π 1 w ( z )   exp [ r 2 w ( z ) 2 ] × exp   i [ k z + k r 2 2 R ( z ) ψ G S ( z ) ] .
I G 0 , 0 e = I G 0 , 0 o = C w ( z )   exp [ r 2 w ( z ) 2 ] × exp   i [ k z + k r 2 2 R ( z ) ψ G S ( z ) ] ,
H G 0 , 1 = L G 0 ,1 o = 2 π 2 y w ( z ) 2   exp [ r 2 w ( z ) 2 ] × exp   i [ k z + k r 2 2 R ( z ) 2 ψ G S ( z ) ] .
I G 1 ,1 o ( r , ε ) = B 1 2 S [ w 0 / w ( z ) ] sinh ( ξ ) sin ( η ) exp [ r 2 / w 2 ( z ) ] × exp   i [ k z + { k r 2 / 2 R ( z ) } 2 ψ z ( z ) ] .
H G 0 , 1 = L G 0 , 1 o = 2 π 2 x w ( z ) 2   exp [ r 2 w ( z ) 2 ] × exp   i [ k z + k r 2 2 R ( z ) 2 ψ G S ( z ) ] .
I G 1 , 1 e ( r , ε ) = A 0 2 C [ w 0 / w ( z ) ] cosh ( ξ ) cos ( η ) exp [ r 2 / w 2 ( z ) ] × exp   i [ k z + { k r 2 / 2 R ( z ) } 2 ψ z ( z ) ] .

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