Abstract

A method for generating vector beams with higher-order states of polarization based on a setup with a one phase-only liquid crystal spatial light modulator is proposed. The polarization properties and double-slit interference of the higher-order vector beams were investigated in detail. The cross section intensity distributions were flower-like for higher-order vector beams when passing through a linear polarizer. Misplacements appeared in the double-slit interference fringes, which divided each fringe into several discrete parts, i.e., 2P1 for P2, and 3 for P=1, where P is the polarization order number. When associated with optical petal orientations analysis of the beam spots behind a linear polarizer, the double-slit interference can be used to detect and analyze higher-order vector beams.

© 2013 Optical Society of America

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2013

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

L. Yang, X. Xie, S. Wang, and J. Zhou, “Minimized spot of annular radially polarized focusing beam,” Opt. Lett. 38, 1331–1333 (2013).
[CrossRef]

2012

S. Tripathi and K. C. Toussaint, “Versatile generation of optical vector fields and vector beams using a non-interferometric approach,” Opt. Express 20, 10788–10795 (2012).
[CrossRef]

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, “Higher order Pancharatnam-Berry phase and the angular momentum of light,” Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

O. J. Allegre, W. Perrie, S. P. Edwardson, G. Dearden, and K. G. Watkins, “Laser microprocessing of steel with radially and azimuthally polarized femtosecond vortex pulses,” J. Opt. 14, 085601 (2012).
[CrossRef]

2011

2010

2009

2008

2007

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Efficient extracavity generation of radially and azimuthally polarized beams,” Opt. Lett. 32, 1468–1470 (2007).
[CrossRef]

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[CrossRef]

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[CrossRef]

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A. 86, 329–334 (2007).
[CrossRef]

W.-C. Kim and N.-C. Park, “Investigation of near-field imaging characteristics of radial polarization for application to optical data storage,” Opt. Rev. 14, 236–242 (2007).
[CrossRef]

2006

2005

2004

2003

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

2002

C. Varin and M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74, S83–S88 (2002).
[CrossRef]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27, 285–287 (2002).
[CrossRef]

2000

1997

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

1990

Aeschimann, L.

Aït-Ameur, K.

Alfano, R. R.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, “Higher order Pancharatnam-Berry phase and the angular momentum of light,” Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

H. I. Sztul and R. R. Alfano, “Double-slit interference with Laguerre–Gaussian beams,” Opt. Lett. 31, 999–1001 (2006).
[CrossRef]

Allegre, O. J.

O. J. Allegre, W. Perrie, S. P. Edwardson, G. Dearden, and K. G. Watkins, “Laser microprocessing of steel with radially and azimuthally polarized femtosecond vortex pulses,” J. Opt. 14, 085601 (2012).
[CrossRef]

Bashkansky, M.

Beversluis, M. R.

Biener, G.

Bisson, J. F.

Bomzon, Z.

Brown, T. G.

Buhl, L. L.

Chen, S.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Cottrell, D. M.

Davis, J. A.

Dearden, G.

O. J. Allegre, W. Perrie, S. P. Edwardson, G. Dearden, and K. G. Watkins, “Laser microprocessing of steel with radially and azimuthally polarized femtosecond vortex pulses,” J. Opt. 14, 085601 (2012).
[CrossRef]

Denis, R. D. S.

Descrovi, E.

Doerr, C. R.

Donegan, J. F.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Edwardson, S. P.

O. J. Allegre, W. Perrie, S. P. Edwardson, G. Dearden, and K. G. Watkins, “Laser microprocessing of steel with radially and azimuthally polarized femtosecond vortex pulses,” J. Opt. 14, 085601 (2012).
[CrossRef]

Evans, S.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, “Higher order Pancharatnam-Berry phase and the angular momentum of light,” Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

Fatemi, F. K.

Feurer, T.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A. 86, 329–334 (2007).
[CrossRef]

Ford, D. H.

Hasman, E.

Herzig, H. P.

Hierle, R.

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

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Jackel, S.

Jia, H.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Jin, G.

Kim, W.-C.

W.-C. Kim and N.-C. Park, “Investigation of near-field imaging characteristics of radial polarization for application to optical data storage,” Opt. Rev. 14, 236–242 (2007).
[CrossRef]

Kimura, W. D.

Kleiner, V.

Kozawa, Y.

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Lai, W. J.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Li, J.

Li, X.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Liao, J.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Lim, B. C.

Liu, J.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Liu, X.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Lu, M.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Lumer, Y.

Lunney, J. G.

Machavariani, G.

McNamara, D. E.

Meier, M.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A. 86, 329–334 (2007).
[CrossRef]

Meir, A.

Milione, G.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, “Higher order Pancharatnam-Berry phase and the angular momentum of light,” Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Moshe, I.

Nakagawa, W.

Nie, Y.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Nolan, D. A.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, “Higher order Pancharatnam-Berry phase and the angular momentum of light,” Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Novotny, L.

Park, D.

Park, N.-C.

W.-C. Kim and N.-C. Park, “Investigation of near-field imaging characteristics of radial polarization for application to optical data storage,” Opt. Rev. 14, 236–242 (2007).
[CrossRef]

Passilly, N.

Perrie, W.

O. J. Allegre, W. Perrie, S. P. Edwardson, G. Dearden, and K. G. Watkins, “Laser microprocessing of steel with radially and azimuthally polarized femtosecond vortex pulses,” J. Opt. 14, 085601 (2012).
[CrossRef]

Phelan, C. F.

Phua, P. B.

Piché, M.

C. Varin and M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74, S83–S88 (2002).
[CrossRef]

Qi, J.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Roch, J.

Romano, V.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A. 86, 329–334 (2007).
[CrossRef]

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Sato, S.

Senatsky, Y.

Sheppard, C. J. R.

E. Y. S. Yew and C. J. R. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275, 453–457 (2007).
[CrossRef]

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Sonehara, T.

Staufer, U.

Stranick, S. J.

Sun, W.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Sztul, H. I.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

H. I. Sztul and R. R. Alfano, “Double-slit interference with Laguerre–Gaussian beams,” Opt. Lett. 31, 999–1001 (2006).
[CrossRef]

Tan, J.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Tan, Q.

Teo, H. H.

Tiaw, K. S.

Tidwell, S. C.

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[CrossRef]

Toussaint, K. C.

Treussart, F.

Tripathi, S.

Ueda, K.

Vaccaro, L.

Varin, C.

C. Varin and M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74, S83–S88 (2002).
[CrossRef]

Wang, S.

Wang, X.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Watkins, K. G.

O. J. Allegre, W. Perrie, S. P. Edwardson, G. Dearden, and K. G. Watkins, “Laser microprocessing of steel with radially and azimuthally polarized femtosecond vortex pulses,” J. Opt. 14, 085601 (2012).
[CrossRef]

Xie, X.

Yang, J.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Yang, L.

Yew, E. Y. S.

E. Y. S. Yew and C. J. R. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275, 453–457 (2007).
[CrossRef]

Yonezawa, K.

K. Yonezawa, Y. Kozawa, and S. Sato, “Compact laser with radial polarization using birefringent laser medium,” Jpn. J. Appl. Phys. 46, 5160–5163 (2007).
[CrossRef]

K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31, 2151–2153 (2006).
[CrossRef]

Youngworth, K. S.

Zhan, Q.

Zhang, J.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Zhou, J.

Zhou, Z.

Adv. Opt. Photon.

Appl. Opt.

Appl. Phys. A.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A. 86, 329–334 (2007).
[CrossRef]

Appl. Phys. B

C. Varin and M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74, S83–S88 (2002).
[CrossRef]

Chin. Opt. Lett.

J. Opt.

O. J. Allegre, W. Perrie, S. P. Edwardson, G. Dearden, and K. G. Watkins, “Laser microprocessing of steel with radially and azimuthally polarized femtosecond vortex pulses,” J. Opt. 14, 085601 (2012).
[CrossRef]

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

K. Yonezawa, Y. Kozawa, and S. Sato, “Compact laser with radial polarization using birefringent laser medium,” Jpn. J. Appl. Phys. 46, 5160–5163 (2007).
[CrossRef]

Opt. Commun.

E. Y. S. Yew and C. J. R. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275, 453–457 (2007).
[CrossRef]

Opt. Eng.

J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond pulse beam,” Opt. Eng. 52, 024201 (2013).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Rev.

W.-C. Kim and N.-C. Park, “Investigation of near-field imaging characteristics of radial polarization for application to optical data storage,” Opt. Rev. 14, 236–242 (2007).
[CrossRef]

Phys. Rev. Lett.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Experimental setup for the generation and double-slit interference of HV beams. Lenses 1 and 2 constitute a beam expander; HWP: half-wave plate; QWP: quarter-wave plate; HLP: horizontally linearly polarizer.

Fig. 2.
Fig. 2.

Gray phase pictures loaded to the LC-SLM to generate HRP beams.

Fig. 3.
Fig. 3.

Spot intensity distribution of generated HRP beams.

Fig. 4.
Fig. 4.

Optical field distribution of the horizontal component Ex (a) and vertical component Ey (b) for the RP beam.

Fig. 5.
Fig. 5.

Theoretical field distribution of the horizontal component Ex and vertical component Ey for the HRP beam.

Fig. 6.
Fig. 6.

Theoretical double-slit interference intensity distribution for the incident Gaussian beam.

Fig. 7.
Fig. 7.

Theoretical double-slit interference intensity distribution for the HRP beams.

Fig. 8.
Fig. 8.

Experimental double-slit interference intensity distribution of Gaussian, RP, and HRP with P=2.

Fig. 9.
Fig. 9.

Experimental double-slit interference intensity distribution of HRP beams with P=3 and 4, respectively.

Equations (16)

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J(δ)=[100eiδ]=eiδ[eiδ001].
J1=12[1ii1],J2=[100eiδ],J3=12[1ii1].
J=J3J2J1=12[1ii1]×[100eiδ]×12[1ii1]=eiδ2[cosδ2sinδ2sinδ2cosδ2].
EHV(r,θ)=E0(r)[cos(Pθ+ϕ0)·x+sin(Pθ+ϕ0)·y].
EHRP(r,θ)=E0(r)[cosPθ·x+sinPθ·y]
EHAP(r,θ)=E0(r)[sinPθ·x+cosPθ·y]
E0(r)=A0rexp(r2ω02)=A0x2+y2exp(x2+y2ω02)
Ex(x,y)=E0(r)cosPθ·x=A0x2+y2exp(x2+y2ω02)cosPθ·x
Ey(x,y)=E0(r)sinPθ·y=A0x2+y2exp(x2+y2ω02)sinPθ·y.
Ex(x,y)=E0(r)cos(Pθ+ϕ0)·x=A0x2+y2exp(x2+y2ω02)cos(Pθ+ϕ0)·x
Ey(x,y)=E0(r)sin(Pθ+ϕ0)·y=A0x2+y2exp(x2+y2ω02)sin(Pθ+ϕ0)·y.
Ex(x,y,z)=(iλz)exp(ikz)Ex(x,y)exp{ik2z[(xx)2+(yy)]2}dxdy
Ey(x,y,z)=(iλz)exp(ikz)Ey(x,y)exp{ik2z[(xx)2+(yy)]2}dxdy,
Ix(x,y,z)=Ex(x,y,z)Ex(x,y,z)*
Iy(x,y,z)=Ey(x,y,z)Ey(x,y,z)*
I(x,y,z)=Ix(x,y,z)+Iy(x,y,z).

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