Abstract

Based on the Fermat's principle, the universal theory of refraction and reflection of extraordinary rays (e-rays) in the uniaxial crystal is formulated. Using this theory, a new unit structure prism is designed, and its properties are studied. Based on the theoretical results, such a prism is achieved experimentally by using the Iceland crystal. In both theoretical and experimental studies, this new prism shows excellent polarization splitting performances such as big and adjustable splitting angle, comparing to the conventional Rochon prism. For the sample prism with the optical axis angle of 45°, the splitting angle reaches 19.8°in the normal incidence, and the maximum splitting angle reaches 28.44° while the incidence angle is −4°.

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References

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  1. S. Gräf, G. Staupendahl, C. Seiser, B.-J. Meyer, and F. A. Müller, “Generation of a dynamic polarized laser beam for applications in laser welding,” J. Appl. Phys.107(4), 043102 (2010).
    [CrossRef]
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    [CrossRef]
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  5. W. Wang, F. Q. Wu, and F. F. Su, “Symmetric polarization beamsplitting prism based on three-element Wollaston prism,” Opt. Technol.30, 182–186 (2004).
  6. Z. Liu, Z. F. Lin, and S. T. Chui, “Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium,” Phys. Rev. B69(11), 115402 (2004).
    [CrossRef]
  7. Q. Cheng and T. C. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73(11), 113104 (2006).
    [CrossRef]
  8. J. Sun, L. Liu, G. Dong, and J. Zhou, “Efficient polarization beam splitter based on an indefinite medium,” J. Electromagn. Waves Appl.26(11-12), 1423–1431 (2012).
    [CrossRef]
  9. K. Sinchuk, R. Dudley, J. D. Graham, M. Clare, M. Woldeyohannes, J. O. Schenk, R. P. Ingel, W. Yang, and M. A. Fiddy, “Tunable negative group index in metamaterial structures with large form birefringence,” Opt. Express18(2), 463–472 (2010).
    [CrossRef] [PubMed]

2012 (1)

J. Sun, L. Liu, G. Dong, and J. Zhou, “Efficient polarization beam splitter based on an indefinite medium,” J. Electromagn. Waves Appl.26(11-12), 1423–1431 (2012).
[CrossRef]

2010 (3)

2006 (1)

Q. Cheng and T. C. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73(11), 113104 (2006).
[CrossRef]

2004 (3)

H. J. Cornelissen, H. P. M. Huck, D. J. Broer, S. J. Picken, C. W. M. Bastiaansen, E. Erdhuisen, and N. Maaskant, “38.3: Polarized light LCD backlight based on liquid crystalline polymer film: A new manufacturing process,” S/D Symposium Dig. Tech. Pap.35(1), 1178–1181 (2004).
[CrossRef]

W. Wang, F. Q. Wu, and F. F. Su, “Symmetric polarization beamsplitting prism based on three-element Wollaston prism,” Opt. Technol.30, 182–186 (2004).

Z. Liu, Z. F. Lin, and S. T. Chui, “Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium,” Phys. Rev. B69(11), 115402 (2004).
[CrossRef]

Bastiaansen, C. W. M.

H. J. Cornelissen, H. P. M. Huck, D. J. Broer, S. J. Picken, C. W. M. Bastiaansen, E. Erdhuisen, and N. Maaskant, “38.3: Polarized light LCD backlight based on liquid crystalline polymer film: A new manufacturing process,” S/D Symposium Dig. Tech. Pap.35(1), 1178–1181 (2004).
[CrossRef]

Broer, D. J.

H. J. Cornelissen, H. P. M. Huck, D. J. Broer, S. J. Picken, C. W. M. Bastiaansen, E. Erdhuisen, and N. Maaskant, “38.3: Polarized light LCD backlight based on liquid crystalline polymer film: A new manufacturing process,” S/D Symposium Dig. Tech. Pap.35(1), 1178–1181 (2004).
[CrossRef]

Cheng, Q.

Q. Cheng and T. C. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73(11), 113104 (2006).
[CrossRef]

Chui, S. T.

Z. Liu, Z. F. Lin, and S. T. Chui, “Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium,” Phys. Rev. B69(11), 115402 (2004).
[CrossRef]

Clare, M.

Cornelissen, H. J.

H. J. Cornelissen, H. P. M. Huck, D. J. Broer, S. J. Picken, C. W. M. Bastiaansen, E. Erdhuisen, and N. Maaskant, “38.3: Polarized light LCD backlight based on liquid crystalline polymer film: A new manufacturing process,” S/D Symposium Dig. Tech. Pap.35(1), 1178–1181 (2004).
[CrossRef]

Cui, T. C.

Q. Cheng and T. C. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73(11), 113104 (2006).
[CrossRef]

Dong, G.

J. Sun, L. Liu, G. Dong, and J. Zhou, “Efficient polarization beam splitter based on an indefinite medium,” J. Electromagn. Waves Appl.26(11-12), 1423–1431 (2012).
[CrossRef]

Dudley, R.

Erdhuisen, E.

H. J. Cornelissen, H. P. M. Huck, D. J. Broer, S. J. Picken, C. W. M. Bastiaansen, E. Erdhuisen, and N. Maaskant, “38.3: Polarized light LCD backlight based on liquid crystalline polymer film: A new manufacturing process,” S/D Symposium Dig. Tech. Pap.35(1), 1178–1181 (2004).
[CrossRef]

Fatome, J.

Fiddy, M. A.

Gräf, S.

S. Gräf, G. Staupendahl, C. Seiser, B.-J. Meyer, and F. A. Müller, “Generation of a dynamic polarized laser beam for applications in laser welding,” J. Appl. Phys.107(4), 043102 (2010).
[CrossRef]

Graham, J. D.

Huck, H. P. M.

H. J. Cornelissen, H. P. M. Huck, D. J. Broer, S. J. Picken, C. W. M. Bastiaansen, E. Erdhuisen, and N. Maaskant, “38.3: Polarized light LCD backlight based on liquid crystalline polymer film: A new manufacturing process,” S/D Symposium Dig. Tech. Pap.35(1), 1178–1181 (2004).
[CrossRef]

Ingel, R. P.

Lin, Z. F.

Z. Liu, Z. F. Lin, and S. T. Chui, “Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium,” Phys. Rev. B69(11), 115402 (2004).
[CrossRef]

Liu, L.

J. Sun, L. Liu, G. Dong, and J. Zhou, “Efficient polarization beam splitter based on an indefinite medium,” J. Electromagn. Waves Appl.26(11-12), 1423–1431 (2012).
[CrossRef]

Liu, Z.

Z. Liu, Z. F. Lin, and S. T. Chui, “Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium,” Phys. Rev. B69(11), 115402 (2004).
[CrossRef]

Maaskant, N.

H. J. Cornelissen, H. P. M. Huck, D. J. Broer, S. J. Picken, C. W. M. Bastiaansen, E. Erdhuisen, and N. Maaskant, “38.3: Polarized light LCD backlight based on liquid crystalline polymer film: A new manufacturing process,” S/D Symposium Dig. Tech. Pap.35(1), 1178–1181 (2004).
[CrossRef]

Meyer, B.-J.

S. Gräf, G. Staupendahl, C. Seiser, B.-J. Meyer, and F. A. Müller, “Generation of a dynamic polarized laser beam for applications in laser welding,” J. Appl. Phys.107(4), 043102 (2010).
[CrossRef]

Millot, G.

Morin, P.

Müller, F. A.

S. Gräf, G. Staupendahl, C. Seiser, B.-J. Meyer, and F. A. Müller, “Generation of a dynamic polarized laser beam for applications in laser welding,” J. Appl. Phys.107(4), 043102 (2010).
[CrossRef]

Picken, S. J.

H. J. Cornelissen, H. P. M. Huck, D. J. Broer, S. J. Picken, C. W. M. Bastiaansen, E. Erdhuisen, and N. Maaskant, “38.3: Polarized light LCD backlight based on liquid crystalline polymer film: A new manufacturing process,” S/D Symposium Dig. Tech. Pap.35(1), 1178–1181 (2004).
[CrossRef]

Pitois, S.

Schenk, J. O.

Seiser, C.

S. Gräf, G. Staupendahl, C. Seiser, B.-J. Meyer, and F. A. Müller, “Generation of a dynamic polarized laser beam for applications in laser welding,” J. Appl. Phys.107(4), 043102 (2010).
[CrossRef]

Sinchuk, K.

Staupendahl, G.

S. Gräf, G. Staupendahl, C. Seiser, B.-J. Meyer, and F. A. Müller, “Generation of a dynamic polarized laser beam for applications in laser welding,” J. Appl. Phys.107(4), 043102 (2010).
[CrossRef]

Su, F. F.

W. Wang, F. Q. Wu, and F. F. Su, “Symmetric polarization beamsplitting prism based on three-element Wollaston prism,” Opt. Technol.30, 182–186 (2004).

Sun, J.

J. Sun, L. Liu, G. Dong, and J. Zhou, “Efficient polarization beam splitter based on an indefinite medium,” J. Electromagn. Waves Appl.26(11-12), 1423–1431 (2012).
[CrossRef]

Wang, W.

W. Wang, F. Q. Wu, and F. F. Su, “Symmetric polarization beamsplitting prism based on three-element Wollaston prism,” Opt. Technol.30, 182–186 (2004).

Woldeyohannes, M.

Wu, F. Q.

W. Wang, F. Q. Wu, and F. F. Su, “Symmetric polarization beamsplitting prism based on three-element Wollaston prism,” Opt. Technol.30, 182–186 (2004).

Yang, W.

Zhou, J.

J. Sun, L. Liu, G. Dong, and J. Zhou, “Efficient polarization beam splitter based on an indefinite medium,” J. Electromagn. Waves Appl.26(11-12), 1423–1431 (2012).
[CrossRef]

J. Appl. Phys. (1)

S. Gräf, G. Staupendahl, C. Seiser, B.-J. Meyer, and F. A. Müller, “Generation of a dynamic polarized laser beam for applications in laser welding,” J. Appl. Phys.107(4), 043102 (2010).
[CrossRef]

J. Electromagn. Waves Appl. (1)

J. Sun, L. Liu, G. Dong, and J. Zhou, “Efficient polarization beam splitter based on an indefinite medium,” J. Electromagn. Waves Appl.26(11-12), 1423–1431 (2012).
[CrossRef]

Opt. Express (2)

Opt. Technol. (1)

W. Wang, F. Q. Wu, and F. F. Su, “Symmetric polarization beamsplitting prism based on three-element Wollaston prism,” Opt. Technol.30, 182–186 (2004).

Phys. Rev. B (2)

Z. Liu, Z. F. Lin, and S. T. Chui, “Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium,” Phys. Rev. B69(11), 115402 (2004).
[CrossRef]

Q. Cheng and T. C. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73(11), 113104 (2006).
[CrossRef]

S/D Symposium Dig. Tech. Pap. (1)

H. J. Cornelissen, H. P. M. Huck, D. J. Broer, S. J. Picken, C. W. M. Bastiaansen, E. Erdhuisen, and N. Maaskant, “38.3: Polarized light LCD backlight based on liquid crystalline polymer film: A new manufacturing process,” S/D Symposium Dig. Tech. Pap.35(1), 1178–1181 (2004).
[CrossRef]

Other (1)

J. N. Damask, Polarization Optics in Telecommunications (Springer, 2005).

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Figures (5)

Fig. 1
Fig. 1

P -polarization incident the uniaxial crystal in xoz plane.

Fig. 2
Fig. 2

The e-rays refraction in uniaxial crystal.

Fig. 3
Fig. 3

Beam path diagram of the unit Rochon prism.

Fig. 4
Fig. 4

Variation curve of splitting angle relationship with the change of incident light wavelength.

Fig. 5
Fig. 5

Variation curve of splitting angle relationship with the change of optical axis angle.

Tables (1)

Tables Icon

Table 1 Test results using a 633nm and 532nm laser source.

Equations (20)

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δ a b ( n e 2 sin 2 ψ R + n o 2 cos 2 ψ R ) 1 2 dl=0,
n R '= ( n e 2 sin 2 ψ R + n o 2 cos 2 ψ R ) 1 2 ,
δ[ n l A + ( n e 2 sin 2 ψ R + n o 2 cos 2 ψ R ) 1 2 l B ]=0,
δ l A =cos α i δ l Ax ,
δ l B =cos α R δ l Bx ,
δcos ψ R = 1 l B (cos α 0 δ l B cos ψ R δ l B ),
nδ l A + l B n R ' ( n o 2 n e 2 )cos ψ R δcos ψ R + n R 'δ l B =0,
ncos α i = 1 n R ' [ n e 2 cos α R +( n o 2 n e 2 )cos α 0 cos ψ R ].
cos α R =[ nsini n e f( ψ R )+(1 n o 2 n e 2 )sin γ 0 ]cos ψ R ,
cos γ R = cos ψ R cos α 0 cos α R cos γ 0 =[ n R ' 2 ( γ 0 ) n e 2 cos γ 0 nsinisin γ 0 n e cos γ 0 f( ψ R ) ]cos ψ R
1 n o 2 ( n 2 sin 2 i n e 2 cos 2 γ 0 ) f 2 ( ψ R ) 2n n e sinisin γ 0 f( ψ R )+ n R 2 ( γ 0 ) n e 2 =0.
f( ψ R )= n o n e | n n o sinisin γ 0 n e cos γ 0 ( n R( γ 0 ) 2 n 2 sin 2 i) 1 2 n 2 sin 2 i n e 2 cos 2 γ 0 |.
tan γ R = 1 n R( γ 0 ) 2 [ n n o n e sini ( n R( γ 0 ) 2 n 2 sin 2 i ) 1 2 +( n e 2 n o 2 )sin γ 0 cos γ 0 ]
sin i e =± [ n i( γ 0 ) 2 tan γ i ( n e 2 n o 2 )sin γ 0 cos γ 0 ] n i( γ 0 ) n { [ n i( γ 0 ) 2 tan γ i ( n e 2 n o 2 )sin γ 0 cos γ 0 ] 2 + n e 2 n o 2 } 1 2 ,
tan α rr =tan α ri n o 2 n e 2 n r 2 ( α 0 ) sin2 α 0 ,
tan γ R = 1 n e 2 + n o 2 [ 2 2 n e n o sini ( n e 2 + n o 2 2 sin 2 i) 1/2 +( n e 2 n o 2 ) ],
tan α rr =| cot γ R |+ 2( n e 2 n o 2 ) n e 2 + n o 2 = 1 | tan γ R | + 2( n o 2 n e 2 ) n e 2 + n o 2 ,
sin i e =± 1 2 [ ( n e 2 + n o 2 )tan γ i ( n e 2 + n o 2 ) ] ( n e 2 + n o 2 ) 1 2 { [ ( n e 2 + n o 2 )tan γ i +( n e 2 + n o 2 ) ] 2 +4 n e 2 n o 2 } 1 2 ,
tan γ i =cot α rr = 1 tan α rr = ( n e 2 + n o 2 )| tan γ R | n e 2 + n o 2 +2( n e 2 + n o 2 )| tan γ R | ,
φ= i e i,

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