Abstract

A new type of diffractive optical instrument, the curved hologram, for which the spatial phase function and the hologram shape can be controlled independently, is investigated for finite distance concentration of diffuse (quasi-monochromatic) light. We show how a simple analytic design for given light source and target geometries yields spatially uniform concentrations of diffuse light at the thermodynamic limit of brightness conservation. Such diffractive elements may provide a useful alternative to reflective cavities for efficient and uniform side-pumping of solid-state lasers.

© 2004 Optical Society of America

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References

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  1. W. T. Welford, R. Winston, “The ellipsoid paradox in thermodynamics,” J. Stat. Phys. 28(3), 603–606 (1982).
    [CrossRef]
  2. W. Koechner, Solid-State Laser Engineering (Springer-Verlag, Berlin, 1999).
  3. N. Bokor, N. Davidson, “Light collimation, imaging and concentration at the thermodynamic limit,” J. Opt. Soc. Am. A 19, 2483–2489 (2002).
    [CrossRef]
  4. I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentration,” in Progress in Optics, Vol. XXVIII, E. Wolf, ed. (North-Holland, Amsterdam, 1989), pp. 161–226.
  5. H. R. Ries, R. Winston, “Tailored edge-ray reflectors for illumination,” J. Opt. Soc. Am. A 11, 1260–1264 (1994).
    [CrossRef]
  6. V. Rovenski, Geometry of Curves and Surfaces with Maple (Birkhäuser, Boston, Mass., 2000).
  7. S. B. Schuldt, R. L. Aagard, “An analysis of radiation transfer by means of elliptical cylinder reflectors,” Appl. Opt. 2, 509–513 (1963).
    [CrossRef]
  8. V. Evtuhov, J. K. Neeland, “Multiple pass effects in high efficiency laser pumping cavities,” Appl. Opt. 6, 438–441 (1968).
  9. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993), pp. 168–169.
  10. W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
    [CrossRef]
  11. W. T. Welford, “Practical design of an aplanatic hologram lens of focal length 50 mm and numerical aperture 0.5,” Opt. Commun. 15, 46–49 (1975).
    [CrossRef]
  12. N. Bokor, N. Davidson, “Aberration-free imaging with an aplanatic curved diffractive element,” Appl. Opt. 40, 5825–5829 (2001).
    [CrossRef]
  13. N. Bokor, R. Shechter, A. A. Friesem, N. Davidson, “Concentration of diffuse light at the thermodynamic limit with an aplanatic curved diffractive element,” Opt. Commun. 191, 141–148 (2001).
    [CrossRef]

2002 (1)

N. Bokor, N. Davidson, “Light collimation, imaging and concentration at the thermodynamic limit,” J. Opt. Soc. Am. A 19, 2483–2489 (2002).
[CrossRef]

2001 (2)

N. Bokor, R. Shechter, A. A. Friesem, N. Davidson, “Concentration of diffuse light at the thermodynamic limit with an aplanatic curved diffractive element,” Opt. Commun. 191, 141–148 (2001).
[CrossRef]

N. Bokor, N. Davidson, “Aberration-free imaging with an aplanatic curved diffractive element,” Appl. Opt. 40, 5825–5829 (2001).
[CrossRef]

1994 (1)

1982 (1)

W. T. Welford, R. Winston, “The ellipsoid paradox in thermodynamics,” J. Stat. Phys. 28(3), 603–606 (1982).
[CrossRef]

1975 (1)

W. T. Welford, “Practical design of an aplanatic hologram lens of focal length 50 mm and numerical aperture 0.5,” Opt. Commun. 15, 46–49 (1975).
[CrossRef]

1973 (1)

W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
[CrossRef]

1968 (1)

V. Evtuhov, J. K. Neeland, “Multiple pass effects in high efficiency laser pumping cavities,” Appl. Opt. 6, 438–441 (1968).

1963 (1)

Aagard, R. L.

Bassett, I. M.

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentration,” in Progress in Optics, Vol. XXVIII, E. Wolf, ed. (North-Holland, Amsterdam, 1989), pp. 161–226.

Bokor, N.

N. Bokor, N. Davidson, “Light collimation, imaging and concentration at the thermodynamic limit,” J. Opt. Soc. Am. A 19, 2483–2489 (2002).
[CrossRef]

N. Bokor, R. Shechter, A. A. Friesem, N. Davidson, “Concentration of diffuse light at the thermodynamic limit with an aplanatic curved diffractive element,” Opt. Commun. 191, 141–148 (2001).
[CrossRef]

N. Bokor, N. Davidson, “Aberration-free imaging with an aplanatic curved diffractive element,” Appl. Opt. 40, 5825–5829 (2001).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993), pp. 168–169.

Davidson, N.

N. Bokor, N. Davidson, “Light collimation, imaging and concentration at the thermodynamic limit,” J. Opt. Soc. Am. A 19, 2483–2489 (2002).
[CrossRef]

N. Bokor, R. Shechter, A. A. Friesem, N. Davidson, “Concentration of diffuse light at the thermodynamic limit with an aplanatic curved diffractive element,” Opt. Commun. 191, 141–148 (2001).
[CrossRef]

N. Bokor, N. Davidson, “Aberration-free imaging with an aplanatic curved diffractive element,” Appl. Opt. 40, 5825–5829 (2001).
[CrossRef]

Evtuhov, V.

V. Evtuhov, J. K. Neeland, “Multiple pass effects in high efficiency laser pumping cavities,” Appl. Opt. 6, 438–441 (1968).

Friesem, A. A.

N. Bokor, R. Shechter, A. A. Friesem, N. Davidson, “Concentration of diffuse light at the thermodynamic limit with an aplanatic curved diffractive element,” Opt. Commun. 191, 141–148 (2001).
[CrossRef]

Koechner, W.

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, Berlin, 1999).

Neeland, J. K.

V. Evtuhov, J. K. Neeland, “Multiple pass effects in high efficiency laser pumping cavities,” Appl. Opt. 6, 438–441 (1968).

Ries, H. R.

Rovenski, V.

V. Rovenski, Geometry of Curves and Surfaces with Maple (Birkhäuser, Boston, Mass., 2000).

Schuldt, S. B.

Shechter, R.

N. Bokor, R. Shechter, A. A. Friesem, N. Davidson, “Concentration of diffuse light at the thermodynamic limit with an aplanatic curved diffractive element,” Opt. Commun. 191, 141–148 (2001).
[CrossRef]

Welford, W. T.

W. T. Welford, R. Winston, “The ellipsoid paradox in thermodynamics,” J. Stat. Phys. 28(3), 603–606 (1982).
[CrossRef]

W. T. Welford, “Practical design of an aplanatic hologram lens of focal length 50 mm and numerical aperture 0.5,” Opt. Commun. 15, 46–49 (1975).
[CrossRef]

W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
[CrossRef]

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentration,” in Progress in Optics, Vol. XXVIII, E. Wolf, ed. (North-Holland, Amsterdam, 1989), pp. 161–226.

Winston, R.

H. R. Ries, R. Winston, “Tailored edge-ray reflectors for illumination,” J. Opt. Soc. Am. A 11, 1260–1264 (1994).
[CrossRef]

W. T. Welford, R. Winston, “The ellipsoid paradox in thermodynamics,” J. Stat. Phys. 28(3), 603–606 (1982).
[CrossRef]

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentration,” in Progress in Optics, Vol. XXVIII, E. Wolf, ed. (North-Holland, Amsterdam, 1989), pp. 161–226.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993), pp. 168–169.

Appl. Opt. (3)

J. Opt. Soc. Am. A (2)

H. R. Ries, R. Winston, “Tailored edge-ray reflectors for illumination,” J. Opt. Soc. Am. A 11, 1260–1264 (1994).
[CrossRef]

N. Bokor, N. Davidson, “Light collimation, imaging and concentration at the thermodynamic limit,” J. Opt. Soc. Am. A 19, 2483–2489 (2002).
[CrossRef]

J. Stat. Phys. (1)

W. T. Welford, R. Winston, “The ellipsoid paradox in thermodynamics,” J. Stat. Phys. 28(3), 603–606 (1982).
[CrossRef]

Opt. Commun. (3)

W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
[CrossRef]

W. T. Welford, “Practical design of an aplanatic hologram lens of focal length 50 mm and numerical aperture 0.5,” Opt. Commun. 15, 46–49 (1975).
[CrossRef]

N. Bokor, R. Shechter, A. A. Friesem, N. Davidson, “Concentration of diffuse light at the thermodynamic limit with an aplanatic curved diffractive element,” Opt. Commun. 191, 141–148 (2001).
[CrossRef]

Other (4)

V. Rovenski, Geometry of Curves and Surfaces with Maple (Birkhäuser, Boston, Mass., 2000).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993), pp. 168–169.

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, Berlin, 1999).

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentration,” in Progress in Optics, Vol. XXVIII, E. Wolf, ed. (North-Holland, Amsterdam, 1989), pp. 161–226.

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Figures (8)

Fig. 1
Fig. 1

(a) Cross section of a reflective tube (heavy solid curve) consisting of circular and elliptical sections that gives rise to a thermodynamic paradox: All rays emitted by source A seem to reach B, whereas some rays emitted by source B are reflected back on B, leading to spontaneous cooling of A and warming of B. (b) The solution to the paradox, taking into account the finite size of the two sources and the different magnifications of the two elliptical sections.

Fig. 2
Fig. 2

Design geometry of a curved holographic optical element (HOE) working in (a) reflection, (b) transmission. Source A and target B are at a distance t from each other, α is the angle between a central ray emitted by A and the line connecting A and B, β is the angle between a central ray intercepted by B and the line connecting A and B, and r is the distance between A and the given point on the HOE.

Fig. 3
Fig. 3

HOE profiles for a cylindrical source A and cylindrical targets of different sizes B, B, B, and B. The corresponding magnifications are M=1.1, 2, 3, and ∞, respectively.

Fig. 4
Fig. 4

Calculated normalized spot sizes as a function of α for a curved HOE (dotted line) and for reflective elliptical cavities having different eccentricities (solid curves), indicating that the HOE yields a uniform intensity distribution on the target, whereas the concentration profiles of the elliptical cavities are highly nonuniform.

Fig. 5
Fig. 5

Calculated efficiency as a function of (cavity size)/(source–target distance) for reflective curved HOEs (dotted line) and elliptical reflectors (solid curve). The target sizes of the two devices are equal.

Fig. 6
Fig. 6

Double lamp pumping configurations using (a) two reflective elliptical cavities and (b) two reflective curved HOEs. In this case our design leads to simple cylindrical HOE shapes. The HOEs yield smaller geometrical loss and a more uniform pump-density profile than the elliptical cavities.

Fig. 7
Fig. 7

Phase-space spot diagrams obtained from numerical ray tracing at the cylindrical target of (a) the double elliptical reflector cavity of Fig. 6(a) and (b) the double HOE cavity of Fig. 6(b). Rays coming from the left-side source and the right-side source are represented by filled circles and open circles, respectively. The double HOE device has a much more uniform phase-space than the double elliptical reflector, and achieves uniform concentration at the thermodynamic limit of brightness conservation.

Fig. 8
Fig. 8

Curved HOE profiles for a one-sided (vertical), flat Lambertian source placed at A and different Lambertian targets placed at B. The different HOE profiles correspond to the following target shapes: cylindrical target (dashed curve), double-sided (horizontal) flat target (solid curve), and one-sided (vertical) flat target with a magnification M=2 (dotted curve). The first two cases represent reflection HOEs, the third, a transmission HOE.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

S1(α)dα=S2(β)dβ.
Δ1(α)dα=Δ2(β)dβ.
r(α)=t sin β(α)sin[α-β(α)],
r(α)=t sin β(α)sin[α+β(α)].
S1(α)sin αdα=S2(β)sin βdβ,

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