Abstract

A low-loss deflection prism for a laser beam is proposed, and its various characteristics such as beam quality, transmittance, deflection angle, and polarization state are presented. The prism having a trapezoidal form is made from BK7 glass and is designed for a He–Ne laser beam. When a p-polarized beam is incident on the slant surface of the prism at the Brewster angle, the totally reflected and transmitted beam is deflected by 90°, and the measured transmittance is nearly 98%. The theoretical transmittances of the proposed prism are compared with those of a Pellin–Broca prism.

© 2005 Optical Society of America

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References

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  1. F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-HillKogakusha, Tokyo, 1976), Chap. 2.
  2. E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, 1987), Chap. 5.
  3. W. J. Smith, Modern Optical Engineering—The Design of Optical Systems, 2nd ed. (McGraw-Hill, New York, 1990), Chap. 4.
  4. W. L. Wolfe, “Nondispersive prisms,” in Handbook of Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 4.
  5. G. J. Zissis, “Dispersive prisms and gratings,” in Handbook of Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 5.
  6. T. Kasuya, T. Suzuki, K. Shimoda, “A prism anamorphic system for Gaussian beam expander,” Appl. Phys. 17, 131–136 (1978).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. W. A. Challener, “Achromatic 90° polarization rotating prisms,” Eng. Lab. Notes in Opt. Photon. News7, 11 [Appl. Opt. 35, 6845–6846 (1996)].
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    [CrossRef] [PubMed]
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  18. H. Moosmüller, “Brewster’s angle Porro prism: a different use for a Pellin–Broca prism,” Eng. Lab. Notes in Opt. Photon. News9, 5 [Appl. Opt. 37, 8140–8142 (1998)].
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    [CrossRef] [PubMed]
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    [CrossRef]

1996 (2)

1995 (1)

1993 (1)

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

1991 (1)

1989 (4)

1987 (1)

1984 (1)

J. R. M. Barr, “Achromatic prism beam expanders,” Opt. Commun. 51, 41–46 (1984).
[CrossRef]

1978 (1)

T. Kasuya, T. Suzuki, K. Shimoda, “A prism anamorphic system for Gaussian beam expander,” Appl. Phys. 17, 131–136 (1978).
[CrossRef]

Barr, J. R. M.

J. R. M. Barr, “Achromatic prism beam expanders,” Opt. Commun. 51, 41–46 (1984).
[CrossRef]

Bewsher, A.

Boland, W.

Challener, W. A.

W. A. Challener, “Achromatic 90° polarization rotating prisms,” Eng. Lab. Notes in Opt. Photon. News7, 11 [Appl. Opt. 35, 6845–6846 (1996)].

Dobrowolski, J. A.

J. A. Dobrowolski, “Optical properties of films and coatings,” in Handbook of Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 42.

Fantone, S. D.

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, 1987), Chap. 5.

Hello, P.

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-HillKogakusha, Tokyo, 1976), Chap. 2.

Kasuya, T.

T. Kasuya, T. Suzuki, K. Shimoda, “A prism anamorphic system for Gaussian beam expander,” Appl. Phys. 17, 131–136 (1978).
[CrossRef]

Lohmann, A. W.

Man, C. N.

Moosmüller, H.

H. Moosmüller, “Brewster’s angle Porro prism: a different use for a Pellin–Broca prism,” Eng. Lab. Notes in Opt. Photon. News9, 5 [Appl. Opt. 37, 8140–8142 (1998)].

Nemoto, S.

Powell, I.

Sauer, F.

Shimoda, K.

T. Kasuya, T. Suzuki, K. Shimoda, “A prism anamorphic system for Gaussian beam expander,” Appl. Phys. 17, 131–136 (1978).
[CrossRef]

Siegman, A. E.

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

Sinzinger, S.

Smith, W. J.

W. J. Smith, Modern Optical Engineering—The Design of Optical Systems, 2nd ed. (McGraw-Hill, New York, 1990), Chap. 4.

Stetson, K. A.

Stork, W.

Suzuki, T.

T. Kasuya, T. Suzuki, K. Shimoda, “A prism anamorphic system for Gaussian beam expander,” Appl. Phys. 17, 131–136 (1978).
[CrossRef]

Townsend, S. W.

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-HillKogakusha, Tokyo, 1976), Chap. 2.

Wolfe, W. L.

W. L. Wolfe, “Nondispersive prisms,” in Handbook of Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 4.

Zissis, G. J.

G. J. Zissis, “Dispersive prisms and gratings,” in Handbook of Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 5.

Appl. Opt. (9)

Appl. Phys. (1)

T. Kasuya, T. Suzuki, K. Shimoda, “A prism anamorphic system for Gaussian beam expander,” Appl. Phys. 17, 131–136 (1978).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

Opt. Commun. (1)

J. R. M. Barr, “Achromatic prism beam expanders,” Opt. Commun. 51, 41–46 (1984).
[CrossRef]

Other (8)

J. A. Dobrowolski, “Optical properties of films and coatings,” in Handbook of Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 42.

H. Moosmüller, “Brewster’s angle Porro prism: a different use for a Pellin–Broca prism,” Eng. Lab. Notes in Opt. Photon. News9, 5 [Appl. Opt. 37, 8140–8142 (1998)].

F. A. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-HillKogakusha, Tokyo, 1976), Chap. 2.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, 1987), Chap. 5.

W. J. Smith, Modern Optical Engineering—The Design of Optical Systems, 2nd ed. (McGraw-Hill, New York, 1990), Chap. 4.

W. L. Wolfe, “Nondispersive prisms,” in Handbook of Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 4.

G. J. Zissis, “Dispersive prisms and gratings,” in Handbook of Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 5.

W. A. Challener, “Achromatic 90° polarization rotating prisms,” Eng. Lab. Notes in Opt. Photon. News7, 11 [Appl. Opt. 35, 6845–6846 (1996)].

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Figures (15)

Fig. 1
Fig. 1

Various angles pertaining to the low-loss deflection prism, and a trajectory of a beam incident from the lower left.

Fig. 2
Fig. 2

Variations of prism angles α and β with refractive index n.

Fig. 3
Fig. 3

Variations of angles θ1, θ2, and θB with refractive index n.

Fig. 4
Fig. 4

Values of angles and sizes of the prism.

Fig. 5
Fig. 5

Low-loss deflection prism.

Fig. 6
Fig. 6

Transmittances Tpp, Tps, and Tss as functions of incidence angle θ. Tps was calculated for φ = 45°.

Fig. 7
Fig. 7

Coordinate systems describing the incident and the transmitted beams.

Fig. 8
Fig. 8

Measured and calculated transmittances Tpp, Tps, and Tss as functions of incidence angle θ. Tps was measured and calculated for the azimuthal angle φ = 45°.

Fig. 9
Fig. 9

Measured and calculated transmittances as functions of azimuthal angle φ.

Fig. 10
Fig. 10

Trajectories of various reflected and transmitted (a) p-and (b) s-polarized beams arising from the internal reflections.

Fig. 11
Fig. 11

Measured and calculated deflection angles φd as functions of the incident angle θ.

Fig. 12
Fig. 12

Measured and calculated transmittances for a blue laser beam. Tps was measured and calculated for the azimuthal angle 45°.

Fig. 13
Fig. 13

Polarization state of the transmitted beam.

Fig. 14
Fig. 14

Beam trajectory in a Pellin–Broca prism.

Fig. 15
Fig. 15

Transmittances of a Pellin–Broca prism as functions of incidence angle θ.

Tables (4)

Tables Icon

Table 1 Comparison of Beam Parameters of the Incident Beam with Those of the Transmitted Beam

Tables Icon

Table 2 Reflectance and Transmittance of Waves Arising from an Incident p Wave (1)

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Table 3 Reflectance and Transmittance of Waves Arising from an Incident s Wave (1)

Tables Icon

Table 4 Polarization State of the Transmitted Beam

Equations (54)

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φ d = θ + γ , θ = α + γ , β = δ + ψ , β = ( α + π ) / 2.
n sin δ = sin θ .
θ 1 < θ < θ 2 ,
θ 1 sin - 1 [ n sin ( α / 2 ) ] , θ 2 sin - 1 [ n cos ( α / 2 - ψ c ) ] .
θ 2 sin - 1 [ sin ( α / 2 ) + ( n 2 - 1 ) 1 / 2 cos ( α / 2 ) ] .
sin ( α / 2 ) = ( sin θ B - cos θ B ) / 2 1 / 2 , cos ( α / 2 ) = ( sin θ B + cos θ B ) / 2 1 / 2 ,
sin ( α / 2 ) = ( n - 1 ) / [ 2 ( n 2 + 1 ) ] 1 / 2 cos ( α / 2 ) = ( n + 1 ) / [ 2 ( n 2 + 1 ) ] 1 / 2 .
α = 2 tan - 1 n - π / 2 = 2 tan - 1 [ ( n - 1 ) / ( n + 1 ) ] .
θ 1 = sin - 1 [ f 1 ( n ) ] ,             θ 2 = sin - 1 [ f 2 ( n ) ] ,
f 1 ( n ) n ( n - 1 ) / [ 2 ( n 2 + 1 ) ] 1 / 2 ,
f 2 ( n ) [ ( n - 1 ) + ( n + 1 ) ( n 2 - 1 ) 1 / 2 ] / [ 2 ( n 2 + 1 ) ] 1 / 2 .
T p = 1 - R p ,             R p = [ tan ( δ - θ ) / tan ( δ + θ ) ] 2 ,
T s = 1 - R s ,             R s = [ sin ( δ - θ ) / sin ( δ + θ ) ] 2 .
T p p = T p 2 = ( 1 - R p ) 2 ,             T s s = T s 2 = ( 1 - R s ) 2 .
T p s = T p p cos 2 φ + T s s sin 2 φ .
R p = 0 ,             R s = [ ( n 2 - 1 ) / ( n 2 + 1 ) ] 2 ,
T p p = 1 ,             T s s = [ 2 n / ( n 2 + 1 ) ] 4 ,
w x ( z ) = w 0 x { 1 + [ ( z - z 0 x ) / z R x ] 2 } 1 / 2 ,
z R x = π w 0 x 2 / M x 2 λ ,             θ x = 2 M x 2 λ / π w 0 x ,
E p = t p 1 t p 2 r p E cos φ ,             E s = t s 1 t s 2 r s E sin φ ,
t p 1 = 2 cos θ / ( n cos θ + cos δ ) ,
t s 1 = 2 cos θ / ( cos θ + n cos δ ) ,
t p 2 = 2 n cos δ / ( n cos θ + cos δ ) ,
t s 2 = 2 n cos δ / ( cos θ + n cos δ ) ,
r p = exp ( j δ p ) ,             r s = exp ( j δ s ) ,
δ p = 2 tan - [ n ( n 2 sin 2 ψ - 1 ) 1 / 2 / cos ψ ] ,
δ s = 2 tan - 1 [ ( n 2 sin 2 ψ - 1 ) 1 / 2 / n cos ψ ] ,
E p = τ p E cos φ exp ( j δ p ) ,             E s = τ s E sin φ exp ( j δ s ) ,
τ p t p 1 t p 2 = 4 n cos θ cos δ / ( n cos θ + cos δ ) 2 ,
τ s t s 1 t s 2 = 4 n cos θ cos δ / ( cos θ + n cos δ ) 2 .
E p ( t ) = A p cos ( ω t + δ p ) ,             E s ( t ) = A s cos ( ω t + δ s ) ,
A p τ p E cos φ ,             A s τ s E sin φ .
( x / a ) 2 + ( y / b ) 2 - 2 ( x y / a b ) cos Δ = sin 2 Δ ,
ρ 2 = ( tan 2 α 0 + r 2 - 2 r tan α 0 cos Δ ) / ( 1 + r 2 tan 2 α 0 + 2 r tan α 0 cos Δ ) ,
r 2 = [ ( 1 + ρ 2 ) sin 2 α 0 tan 2 α 0 - 2 ( sin 2 α 0 - ρ 2 cos 2 α 0 ) ] / [ ( 1 + ρ 2 ) sin 2 α 0 tan 2 α 0 + 2 ( cos 2 α 0 - ρ 2 sin 2 α 0 ) ] .
sin θ = n sin δ ,             sin θ = n sin δ ,
δ = α - ψ ,             δ = α + ψ - π / 2.
α B = sin - 1 [ ( 1 / n ) sin θ B ] + π / 4 = sin - 1 p + π / 4 ,
δ = α B - ψ ,             δ = α B + ψ - π / 2.
sin θ = n sin ( α B + ψ - π / 2 ) = - n cos ( α B + ψ ) ,
sin θ = - [ cos ( 2 α B ) ( n 2 - sin 2 θ ) 1 / 2 + sin ( 2 α B ) sin θ ] ,
cos ( 2 α B ) = - sin ( 2 sin - 1 p ) , sin ( 2 α B ) = cos ( 2 sin - 1 p ) .
sin θ = sin ( 2 sin - 1 p ) ( n 2 - sin 2 θ ) 1 / 2 - cos ( 2 sin - 1 p ) sin θ ,
θ = sin - 1 [ u ( n 2 - sin 2 θ ) 1 / 2 - v sin θ ] ,
u sin ( 2 sin - 1 p ) ,             v cos ( 2 sin - 1 p ) .
θ < sin - 1 [ n sin ( α B - sin - 1 q ) ] ,
θ < θ c sin - 1 [ n sin ( sin - 1 p - sin - 1 q + π / 4 ) ] .
T p p = ( 1 - R 1 p ) R 2 p ( 1 - R 3 p ) , T s s = ( 1 - R 1 s ) R 2 s ( 1 - R 3 s ) ,
R 1 p = [ tan ( θ - δ ) / tan ( θ + δ ) ] 2 ,
R 2 p = [ tan ( ψ - γ / tan ( ψ + γ ) ] 2 ,
R 3 p = [ tan ( θ - δ ) / tan ( θ + δ ) ] 2 ,
R 1 s = [ sin ( θ - δ ) / tan ( θ + δ ) ] 2 ,
R 2 s = [ sin ( ψ - γ ) / sin ( ψ + γ ) ] 2 ,
R 3 s = [ sin ( θ - δ ) / sin ( θ + δ ) ] 2 ,

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