Abstract

We investigate the use of the Porro prism and its application as a beam rotator. The Porro prism can reverse a light beam, and the reversed beam is rotated when the Porro prism rotates. As a result of the two total internal reflections in the Porro prism, the field polarization is changed. We present a schematic setup to realize beam rotation without polarization change and power variation. The setup includes a rotatable Porro prism accompanied by a polarized beam splitter, a quarter-wave plate, and a phase compensator. This beam rotator is useful in the measurement of the orbital angular momentum of a helical beam.

© 2009 Optical Society of America

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2008

E. Gutierrez-Herrera and M. Strojnik, “Interferometric tolerance determination for a Dove prism using exact ray trace,” Opt. Commun. 281, 897-905 (2008).
[CrossRef]

2006

R. Zambrini and S. M. Barnett, “Quasi-intrinsic angular momentum and the measurement of its spectrum,” Phys. Rev. Lett. 96, 113901 (2006).
[CrossRef] [PubMed]

2004

J. Leach, J. Courtial, K. Skeldon, and S. M. Barnett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

I. Moreno, G. Paez, and M. Strojnik, “Reversal and rotationally shearing interferometer,” Opt. Commun. 233, 245-252 (2004).
[CrossRef]

I. Moreno, “Jones matrix for image-rotation prisms,” Appl. Opt. 43, 3373-3381 (2004).
[CrossRef] [PubMed]

2003

2002

P. Ferraro, S. De Nicola, A. Finizio, and G. Pierattini, “Reflective grating interferometer: A folded reversal and shearing wave-front interferometer,” Appl. Opt. 41, 342-347 (2002).
[CrossRef] [PubMed]

G. Paez, I. Moreno, and M. Strojnik, “Polarization transforming properties of Dove prisms,” Proc. SPIE 4818, 57-61 (2002).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 025790 (2002).
[CrossRef]

1999

1997

1996

1995

1962

Azzam, R. M. A.

Barnett, S. M.

R. Zambrini and S. M. Barnett, “Quasi-intrinsic angular momentum and the measurement of its spectrum,” Phys. Rev. Lett. 96, 113901 (2006).
[CrossRef] [PubMed]

J. Leach, J. Courtial, K. Skeldon, and S. M. Barnett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 025790 (2002).
[CrossRef]

Courtial, J.

J. Leach, J. Courtial, K. Skeldon, and S. M. Barnett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 025790 (2002).
[CrossRef]

De Nicola, S.

Ferraro, P.

Finizio, A.

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 025790 (2002).
[CrossRef]

Gutierrez-Herrera, E.

E. Gutierrez-Herrera and M. Strojnik, “Interferometric tolerance determination for a Dove prism using exact ray trace,” Opt. Commun. 281, 897-905 (2008).
[CrossRef]

Hodgson, N.

N. Hodgson and H. Weber, Optical Resonators (Springer Verlag, 1997), p. 488.

Leach, J.

J. Leach, J. Courtial, K. Skeldon, and S. M. Barnett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 025790 (2002).
[CrossRef]

Liu, J.

Moreno, I.

I. Moreno, “Jones matrix for image-rotation prisms,” Appl. Opt. 43, 3373-3381 (2004).
[CrossRef] [PubMed]

I. Moreno, G. Paez, and M. Strojnik, “Reversal and rotationally shearing interferometer,” Opt. Commun. 233, 245-252 (2004).
[CrossRef]

I. Moreno, G. Paez, and M. Strojnik, “Dove prism with increased throughput for implementation in a rotational-shearing interferometer,” Appl. Opt. 42, 4514-4521 (2003).
[CrossRef] [PubMed]

G. Paez, I. Moreno, and M. Strojnik, “Polarization transforming properties of Dove prisms,” Proc. SPIE 4818, 57-61 (2002).
[CrossRef]

Padgett, M. J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 025790 (2002).
[CrossRef]

Paez, G.

Peck, E. R.

Pierattini, G.

Scholl, M. S.

Skeldon, K.

J. Leach, J. Courtial, K. Skeldon, and S. M. Barnett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

Strojnik, M.

E. Gutierrez-Herrera and M. Strojnik, “Interferometric tolerance determination for a Dove prism using exact ray trace,” Opt. Commun. 281, 897-905 (2008).
[CrossRef]

I. Moreno, G. Paez, and M. Strojnik, “Reversal and rotationally shearing interferometer,” Opt. Commun. 233, 245-252 (2004).
[CrossRef]

I. Moreno, G. Paez, and M. Strojnik, “Dove prism with increased throughput for implementation in a rotational-shearing interferometer,” Appl. Opt. 42, 4514-4521 (2003).
[CrossRef] [PubMed]

G. Paez, I. Moreno, and M. Strojnik, “Polarization transforming properties of Dove prisms,” Proc. SPIE 4818, 57-61 (2002).
[CrossRef]

Weber, H.

N. Hodgson and H. Weber, Optical Resonators (Springer Verlag, 1997), p. 488.

Zambrini, R.

R. Zambrini and S. M. Barnett, “Quasi-intrinsic angular momentum and the measurement of its spectrum,” Phys. Rev. Lett. 96, 113901 (2006).
[CrossRef] [PubMed]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

E. Gutierrez-Herrera and M. Strojnik, “Interferometric tolerance determination for a Dove prism using exact ray trace,” Opt. Commun. 281, 897-905 (2008).
[CrossRef]

I. Moreno, G. Paez, and M. Strojnik, “Reversal and rotationally shearing interferometer,” Opt. Commun. 233, 245-252 (2004).
[CrossRef]

Phys. Rev. Lett.

R. Zambrini and S. M. Barnett, “Quasi-intrinsic angular momentum and the measurement of its spectrum,” Phys. Rev. Lett. 96, 113901 (2006).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 025790 (2002).
[CrossRef]

J. Leach, J. Courtial, K. Skeldon, and S. M. Barnett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

Proc. SPIE

G. Paez, I. Moreno, and M. Strojnik, “Polarization transforming properties of Dove prisms,” Proc. SPIE 4818, 57-61 (2002).
[CrossRef]

Other

N. Hodgson and H. Weber, Optical Resonators (Springer Verlag, 1997), p. 488.

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Figures (6)

Fig. 1
Fig. 1

Ray trace in (a) Pechan prism, (b) Dove prism, and (c) K-shape prism. The small triangle denotes the beam reversion. When the prisms rotate, the beam may be rotated too. These prisms may be used as beam rotators.

Fig. 2
Fig. 2

The Porro prism and the coordinate systems. The Porro prism rotates around the axis. When the Porro prism is at the initial position ( θ = 0 ) , the right-angle edge is parallel to the y-axis. The Porro prism rotates the incident beam by an angle 2 θ .

Fig. 3
Fig. 3

Polarization states of the beam passing through the the Porro prism rotated by θ. The values above each panel denote the corresponding phase differences δ [ 0 , π 2 ) , where the beam is right-handed elliptically polarized. The values under each panel denote the corresponding phase differences δ [ π 2 , π ) , where the beam is left-handed elliptically polarized.

Fig. 4
Fig. 4

Relative power variations of the two electric field components with the Porro prism rotation angle θ. (a) δ = 0 , (b) δ = 1.3275 for the BK7 Porro prism, (c) δ = π 2 , (d) δ = π .

Fig. 5
Fig. 5

Setup to realize beam rotation by using the Porro prism. PBS, polarized beam splitter: 1 4 WP, quarter-wave plate; PC, phase compensator; Porro, Porro prism. The Porro prism rotates around the axis parallel to the incident beam propagation direction.

Fig. 6
Fig. 6

Relative power ( P out P in ) variation of the two electric field components of the reflected beam by the Porro prism with phase compensation before the PBS in Fig. 5. The x- and y-polarized electric field components take about 62% and 38% of the total power when the Porro prism is made of BK7 glass with δ = 1.3275 .

Equations (11)

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T porro = [ 1 0 0 exp ( i δ ) ] , tan δ 4 = 1 2 n 2 , n 2 > 2 ,
T tot = R ( θ ) T porro R ( θ ) = [ cos 2 θ exp ( i δ ) sin 2 θ sin θ cos θ ( 1 + exp ( i δ ) ) sin θ cos θ ( 1 + exp ( i δ ) ) sin 2 θ + exp ( i δ ) cos 2 θ ] ,
R ( θ ) = [ cos θ sin θ sin θ cos θ ]
E out ( δ , θ ) = E 0 ( cos 2 θ exp ( i δ ) sin 2 θ sin θ cos θ ( 1 + exp ( i δ ) ) ) .
E out ( δ = 0 ) = E 0 ( cos 2 θ , sin 2 θ ) T ,
E out ( δ = π ) = E 0 ( 1 , 0 ) T .
T res = R ( π 4 ) T WP R ( π 4 ) T tot R ( π 4 ) T WP R ( π 4 ) = 1 2 [ i exp ( i 2 θ ) ( 1 + exp ( i δ ) ) 1 exp ( i δ ) exp ( i δ ) 1 i exp ( i 2 θ ) ( 1 + exp ( i δ ) ) ] .
T WP = [ 1 0 0 i ]
E out ( δ , θ ) = 1 2 E 0 ( i exp ( i 2 θ ) ( 1 + exp ( i δ ) ) exp ( i δ ) 1 ) .
P out , x = 1 2 ( 1 + cos δ ) P in ,
P out , y = 1 2 ( 1 cos δ ) P in ,

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