Abstract

The output polarization states of corner cubes (for both uncoated and metal-coated surfaces) with an input beam of arbitrary polarization state and of arbitrary tilt angle to the cube have been analyzed by using the three-dimensional polarization ray-tracing matrix method. The diattenuation and retardance of the corner-cube retroreflector (CCR) for all six different ray paths are calculated, and the relationships to the tilt angle and the tilt orientation angle are shown. When the tilt angle is large, hollow metal-coated CCR is more appropriate than solid metal-coated CCR for the case that the polarization states of output beam should be controlled.

© 2013 Optical Society of America

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References

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  1. S. E. Segre and V. Zanza, “Mueller calculus of polarization change in the cube-corner retroreflector,” J. Opt. Soc. Am. A 20,1804–1811 (2003).
    [CrossRef]
  2. B. C. Park, T. B. Eom, and M. S. Chung, “Polarization properties of cube-corner retroreflectors and their effects on signal strength and nonlinearity in heterodyne interferometers,” Appl. Opt. 35, 4372–4380 (1996).
    [CrossRef]
  3. R. Kalibjian, “Stokes polarization vector and Mueller matrix for a corner-cube reflector,” Opt. Commun. 240, 39–68 (2004).
    [CrossRef]
  4. M. S. Scholl, “Ray trace through a corner-cube retroreflector with complex reflection coefficients,” J. Opt. Soc. Am. A 12, 1589–1592 (1995).
    [CrossRef]
  5. X. Huaifang, “Polarization characteristics of glass corner cube reflector,” Chinese J. Lasers 13, 233–236 (1986).
  6. C. C. Shih, “Depolarization effect in a resonator with corner cube reflectors,” J. Opt. Soc. Am. A 13, 1378–1384 (1996).
    [CrossRef]
  7. E. R. Peck, “Polarization properties of corner reflectors and cavities,” J. Opt. Soc. Am. A 52, 253–257 (1962).
    [CrossRef]
  8. J. Liu and R. M. A. Azzam, “Polarization properties of corner-cube retroreflectors: theory and experiment,” Appl. Opt. 36, 1553–1559 (1997).
    [CrossRef]
  9. R. Kalibjian, “Output polarization states of a corner-cube reflector irradiated at non-normal incidence,” Opt. Laser Technol. 39, 1485–1495 (2007).
    [CrossRef]
  10. K. Crabtree and R. Chipman, “Polarization conversion cube corner retroreflector,” Appl. Opt. 49, 5882–5890 (2010).
    [CrossRef]
  11. G. Yun, K. Crabtree, and R. A. Chipman, “Three-dimensional polarization ray-tracing calculus I: definition and diattenuation,” Appl. Opt. 50, 2855–2865 (2011).
    [CrossRef]
  12. G. Yun, S. C. McClain, and R. A. Chipman, “Three-dimensional polarization ray-tracing calculus II: retardance,” Appl. Opt. 50, 2866–2874 (2011).
    [CrossRef]
  13. R. A. Chipman, “Mechanics of polarization ray tracing,” Opt. Eng. 34, 1636–1645 (1995).
    [CrossRef]
  14. E. Waluschka, “Polarization ray trace,” Opt. Eng. 28, 280286 (1989).
    [CrossRef]
  15. R. Barakat, “Conditions for the physical realizability of polarization matrices characterizing passive systems,” J. Mod. Opt. 34, 1535–1544 (1987).
    [CrossRef]
  16. P. Lancaster and M. Tismenetsky, The Theory of Matrices (Academic, 1985), pp. 1534–1546.

2011

2010

2007

R. Kalibjian, “Output polarization states of a corner-cube reflector irradiated at non-normal incidence,” Opt. Laser Technol. 39, 1485–1495 (2007).
[CrossRef]

2004

R. Kalibjian, “Stokes polarization vector and Mueller matrix for a corner-cube reflector,” Opt. Commun. 240, 39–68 (2004).
[CrossRef]

2003

1997

1996

1995

1989

E. Waluschka, “Polarization ray trace,” Opt. Eng. 28, 280286 (1989).
[CrossRef]

1987

R. Barakat, “Conditions for the physical realizability of polarization matrices characterizing passive systems,” J. Mod. Opt. 34, 1535–1544 (1987).
[CrossRef]

1986

X. Huaifang, “Polarization characteristics of glass corner cube reflector,” Chinese J. Lasers 13, 233–236 (1986).

1962

E. R. Peck, “Polarization properties of corner reflectors and cavities,” J. Opt. Soc. Am. A 52, 253–257 (1962).
[CrossRef]

Azzam, R. M. A.

Barakat, R.

R. Barakat, “Conditions for the physical realizability of polarization matrices characterizing passive systems,” J. Mod. Opt. 34, 1535–1544 (1987).
[CrossRef]

Chipman, R.

Chipman, R. A.

Chung, M. S.

Crabtree, K.

Eom, T. B.

Huaifang, X.

X. Huaifang, “Polarization characteristics of glass corner cube reflector,” Chinese J. Lasers 13, 233–236 (1986).

Kalibjian, R.

R. Kalibjian, “Output polarization states of a corner-cube reflector irradiated at non-normal incidence,” Opt. Laser Technol. 39, 1485–1495 (2007).
[CrossRef]

R. Kalibjian, “Stokes polarization vector and Mueller matrix for a corner-cube reflector,” Opt. Commun. 240, 39–68 (2004).
[CrossRef]

Lancaster, P.

P. Lancaster and M. Tismenetsky, The Theory of Matrices (Academic, 1985), pp. 1534–1546.

Liu, J.

McClain, S. C.

Park, B. C.

Peck, E. R.

E. R. Peck, “Polarization properties of corner reflectors and cavities,” J. Opt. Soc. Am. A 52, 253–257 (1962).
[CrossRef]

Scholl, M. S.

Segre, S. E.

Shih, C. C.

Tismenetsky, M.

P. Lancaster and M. Tismenetsky, The Theory of Matrices (Academic, 1985), pp. 1534–1546.

Waluschka, E.

E. Waluschka, “Polarization ray trace,” Opt. Eng. 28, 280286 (1989).
[CrossRef]

Yun, G.

Zanza, V.

Appl. Opt.

Chinese J. Lasers

X. Huaifang, “Polarization characteristics of glass corner cube reflector,” Chinese J. Lasers 13, 233–236 (1986).

J. Mod. Opt.

R. Barakat, “Conditions for the physical realizability of polarization matrices characterizing passive systems,” J. Mod. Opt. 34, 1535–1544 (1987).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

R. Kalibjian, “Stokes polarization vector and Mueller matrix for a corner-cube reflector,” Opt. Commun. 240, 39–68 (2004).
[CrossRef]

Opt. Eng.

R. A. Chipman, “Mechanics of polarization ray tracing,” Opt. Eng. 34, 1636–1645 (1995).
[CrossRef]

E. Waluschka, “Polarization ray trace,” Opt. Eng. 28, 280286 (1989).
[CrossRef]

Opt. Laser Technol.

R. Kalibjian, “Output polarization states of a corner-cube reflector irradiated at non-normal incidence,” Opt. Laser Technol. 39, 1485–1495 (2007).
[CrossRef]

Other

P. Lancaster and M. Tismenetsky, The Theory of Matrices (Academic, 1985), pp. 1534–1546.

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Figures (17)

Fig. 1.
Fig. 1.

Corner-cube geometry.

Fig. 2.
Fig. 2.

Beam returned from a CCR appears to be divided into six segments.

Fig. 3.
Fig. 3.

(a) Local coordinate system has changed in spatial ray tracing and (b) rotation of the local coordinate system.

Fig. 4.
Fig. 4.

Diattenuation of an N-BK7 solid CCR at the tilt angle σ=10°.

Fig. 5.
Fig. 5.

Retardance of an N-BK7 solid CCR at the tilt angle σ=10°.

Fig. 6.
Fig. 6.

Diattenuation of an N-BK7 solid CCR at the orientation angle θ=80°.

Fig. 7.
Fig. 7.

Retardance of an N-BK7 solid CCR at the orientation angle θ=80°.

Fig. 8.
Fig. 8.

Three-dimensional plot of the diattenuation as a function of the tilt angle and the tilt orientation angle.

Fig. 9.
Fig. 9.

Three-dimensional plot of the retardance as a function of the tilt angle and the tilt orientation angle.

Fig. 10.
Fig. 10.

Diattenuation of an Al-coated hollow CCR.

Fig. 11.
Fig. 11.

Diattenuation of an Ag-coated hollow CCR.

Fig. 12.
Fig. 12.

Reflection coefficients of s-polarization and p-polarization components for Al-coated and Ag-coated surfaces.

Fig. 13.
Fig. 13.

Diattenuation of an Al-coated solid CCR.

Fig. 14.
Fig. 14.

Diattenuation of an Ag-coated solid CCR.

Fig. 15.
Fig. 15.

Retardance of an Al-coated solid CCR.

Fig. 16.
Fig. 16.

Retardance of an Ag-coated solid CCR.

Fig. 17.
Fig. 17.

Output polarization states of the CCRs are (a) for uncoated N-BK7 CCR and (b) for Al-coated N-BK7 CCR.

Tables (2)

Tables Icon

Table 1. Propagation Vectors, Local Coordinate Basis Vectors, Surface Normal Vectors, and P Matrices Associated with a Ray Path Through an Uncoated N-BK7 Solid CCR

Tables Icon

Table 2. Diattenuation and Retardance Associated with Six Different Ray Paths

Equations (24)

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{cosσ=a+b+c3cosθ=2cba21abacbc,a2+b2+c2=1,
a=13cosσ16sinσ(cosθ3sinθ),
b=13cosσ16sinσ(cosθ+3sinθ),
c=13cosσ+23sinσcosθ.
r⃗=i⃗2(i⃗·N⃗)N⃗,
t⃗=n1n2i⃗+(n1n2cosθi1(n1n2)2(1cos2θi))N⃗,
cosθi=i⃗·N⃗.
Eout=PTotal·Ein,
PTotal=q=1QPq,
Pq=(s⃗x,qp⃗x,qk⃗x,qs⃗y,qp⃗y,qk⃗y,qs⃗z,qp⃗z,qk⃗z,q)·(αs,q000αp,q0001)·(s⃗x,qs⃗y,qs⃗z,qp⃗x,qp⃗y,qp⃗z,qk⃗x,q1k⃗y,q1k⃗z,q1),
s⃗q=k⃗q1×k⃗q|k⃗q1×k⃗q|,p⃗q=k⃗q1×s⃗q,s⃗q=s⃗q,p⃗q=k⃗q×s⃗q.
PTotal=P5·P4·P3·P2·P1=(0.48670.4621i0.5288+0.3119i0.1979+0.2986i0.2364+0.5052i0.60880.1222i0.01720.4871i0.4125+0.1567i0.31660.2664i0.7614+0.0166i).
tanδ=sinδ1a22asin2φ+cos2φcosδ,
a=sinφ+acosφcosδcosφcosδasinφcos(δ+δ),
D0=1a21+a2.
δ=f(δ),
δtotal=f4,5{f3,4[f2,3(f1,2(δ1)+δ2)+δ3]+δ4}+δ5.
Eout=Oout,51·Ptotal·p⃗1=(0.6530+0.4290i0.27250.5616i0).
J=[EsEp]=a1a12+a22[1aexp(iδ)],
J=[EsEp]=[cosφsinφsinφcosφ]·[EsEp]=a1[cosφasinφexp(iδ)]a12+a22[1sinφ+acosφexp(iδ)cosφasinφexp(iδ)].
aexp(iδ)=sinφ+acosφexp(iδ)cosφasinφexp(iδ).
{sinφ+acosφcosδacosφcosδ+aasinφcos(δ+δ)=0acosφsinδacosφsinδ+aasinφsin(δ+δ)=0.
tanδ=sinδ1a22asin2φ+cos2φcosδ,
a=sinφ+acosφcosδcosφcosδasinφcos(δ+δ).

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