Abstract

Laguerre–Gauss vortex beams carrying different topological charges are generated from Hermite–Gauss laser beams emitted by a gas laser, and their phase properties are explored by studying their interference with a plane wave. Interference of two Laguerre–Gauss vortex beams carrying equal but opposite topological charge is also studied by using a modified Mach–Zehnder interferometer. Experimentally recorded intensity profiles are in good agreement with the theoretically expected profiles.

© 2008 Optical Society of America

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References

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2006

2005

K. T. Kapale and J. P. Dowling, “Vortex phase qubit: generating arbitrary counter-rotating superposition in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95, 173601 (2005).
[CrossRef] [PubMed]

2004

R. P. Singh and S. Roychowdhury, “Non-conservation of topological charge: experiment with optical vortices,” J. Mod. Opt. 51, 177-181 (2004).

M. A. Bandres, J. C. Gutirrez-Vega, and S. Chavez-Cerda, “Parabolic nondiffracting optical wavefields,” Opt. Lett. 29, 44-46 (2004).
[CrossRef] [PubMed]

M. A. Bandres and J. C. Gutierrez-Vega, “Ince-Gaussian beams,” Opt. Lett. 29, 144-146 (2004).
[CrossRef] [PubMed]

S. Roychowdhury, V. K. Jaiswal, and R. P. Singh, “Implementing controlled NOT gate with optical vortex,” Opt. Commun. 236, 419-424 (2004).
[CrossRef]

2003

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810 (2003).
[CrossRef] [PubMed]

2002

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169-175 (2002).
[CrossRef]

2001

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

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912-914 (2001).
[CrossRef] [PubMed]

G. A. Swartzlander, “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26, 497-499 (2001).
[CrossRef]

1996

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64, 77-82 (1996).
[CrossRef]

1995

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217-223 (1995).
[CrossRef]

1994

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]

1993

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

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951-S962 (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]

1991

E. Abramochkin and V. Volostnikov, “Beam transformation and nontransformed beams,” Opt. Commun. 83, 123-127 (1991).
[CrossRef]

1990

1966

Am. J. Phys.

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64, 77-82 (1996).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

R. P. Singh and S. Roychowdhury, “Non-conservation of topological charge: experiment with optical vortices,” J. Mod. Opt. 51, 177-181 (2004).

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217-223 (1995).
[CrossRef]

J. Opt. Soc. Am. B

Nature

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810 (2003).
[CrossRef] [PubMed]

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

Opt. Commun.

S. Roychowdhury, V. K. Jaiswal, and R. P. Singh, “Implementing controlled NOT gate with optical vortex,” Opt. Commun. 236, 419-424 (2004).
[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]

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]

E. Abramochkin and V. Volostnikov, “Beam transformation and nontransformed beams,” Opt. Commun. 83, 123-127 (1991).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951-S962 (1992).
[CrossRef]

Phys. Rev. A

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.

K. T. Kapale and J. P. Dowling, “Vortex phase qubit: generating arbitrary counter-rotating superposition in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95, 173601 (2005).
[CrossRef] [PubMed]

Science

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912-914 (2001).
[CrossRef] [PubMed]

Other

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1999) Vol. 39, pp. 291-372.
[CrossRef]

A. E. Siegman, Lasers (University Science Books, 1986), Chap. 16.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1988), Chap. 14.

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Figures (3)

Fig. 1
Fig. 1

Outline of the experimental setup. BS’s are beam splitters, L 1 and L 2 are the collimating lens pair, and C 1 and C 2 are the cylindrical lens pair for HG m n and LG m n mode conversions. The beam expander setup (shown in gray) is used only to observe LG mode interference with a plane wave.

Fig. 2
Fig. 2

Experimentally recorded intensity in a plane transverse to the direction of propagation. Columns 1 and 2, respectively, are the HG m n and LG m n mode patterns. Column 3 is the intensity pattern when the LG m n mode of column 2 interferes with a plane wave, and column 4 is the resulting pattern when LG modes of equal and opposite topological charge interfere. The first four rows correspond to zero radial index LG modes, whereas the bottom two rows correspond to nonzero radial index modes.

Fig. 3
Fig. 3

Theoretically expected intensity patterns in a plane transverse to the direction of propagation corresponding to Fig. 2. As in Fig. 2, the first four rows correspond to zero radial index LG modes, whereas the bottom two rows correspond to nonzero radial index modes.

Equations (15)

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E ( r , t ) = e ̂ ψ ( r ) e i ( k z ω t ) ,
2 ψ ( r ) + 2 i k ψ ( r ) z = 0 ,
2 = { 2 x 2 + 2 y 2 in Cartesian coordinates 1 ρ ρ ρ ρ + 1 ρ 2 2 φ 2 in cylindrical coordinates .
ψ m n ( r ) = 2 π m ! n ! 2 m + n 1 w e ( x 2 + y 2 ) w 2 e i k ( x 2 + y 2 ) 2 R e i ( m + n + 1 ) θ × H m ( 2 x w ) H n ( 2 y w ) .
w ( z ) = w 0 1 + ( z z R ) 2 ,
z R = 1 2 k w 0 2 = π w 0 2 λ ,
R ( z ) = z + z R 2 z = z ( 1 + z R 2 z 2 ) ,
θ ( z ) = tan 1 ( z z R ) .
ψ m n ( r ) = 2 π m ! n ! min ( m , n ) ! w ( 1 ) min ( m , n ) e ρ 2 w 2 e i ( m + n + 1 ) θ e i k ρ 2 2 R × ( 2 ρ w e i φ ) m n L min ( m , n ) m n ( 2 ρ 2 w 2 ) ,
LG m n ( r ) = s = 0 N e i s π 2 b ( m , n , s ) HG N s , s ( r ) , N = n + m ,
b ( m , n , s ) = ( ( N s ) ! s ! 2 N n ! m ! ) 1 2 × 1 s ! d s d t s [ ( 1 t ) m ( 1 + t ) n ] t = 0 .
HG m n ( ( x + y ) 2 , ( x y ) 2 , z ) = s = 0 N b ( m , n , s ) HG N s , s ( x , y , z ) , N = n + m ,
I = I 1 + I 2 + 2 I 1 I 2 cos ϕ ,
I m n = I p + I LG ( 2 ρ 2 w 2 ) e 2 ρ 2 w 2 L p ( 2 ρ 2 w 2 ) 2 + 2 I p I LG e ρ 2 w 2 L p ( 2 ρ 2 w 2 ) cos [ φ + k ρ 2 2 R + ( N + 1 ) θ 0 ] .
I m n = 4 I LG e 2 ρ 2 w 2 ( 2 ρ 2 w 2 ) L p ( 2 ρ 2 w 2 ) 2 cos 2 φ .

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