Abstract

Reconstituting the intense irradiance of short-arc discharge lamps at a remote target, at high radiative efficiency, represents a central challenge in the design of high-temperature chemical reactors, heightened by the need for high numerical aperture at both the target and the source. Separating the optical system from both the source and the reactor allows pragmatic operation, monitoring, and control. We explore near-field unfolded aplanats as feasible solutions and report measurements for a prototype that constitutes a double-ellipsoid mirror. We also propose compound unfolded aplanats that collect lamp emission over all angles (in lieu of light recycling optics) and irradiate the reactor over nearly its full circumference.

© 2008 Optical Society of America

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References

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  1. D. Nakar, A. Malul, D. Feuermann, and J. M. Gordon, “Radiometric characterization of ultra-high radiance xenon short-arc discharge lamps,” Appl. Opt. 47, 224-229 (2008).
    [CrossRef] [PubMed]
  2. A. Malul, D. Nakar, D. Feuermann, and J. M. Gordon, “Effectiveness of recycling light in ultra-bright short-arc discharge lamps,” Opt. Express 15, 14194-14201 (2007).
    [CrossRef] [PubMed]
  3. A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight,” Adv. Mater. 18, 2993-2996(2006).
    [CrossRef]
  4. A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight: erratum,” Adv. Mater. 18, 3199(2006).
    [CrossRef]
  5. J. M. Gordon, E. A. Katz, D. Feuermann, A. Albu-Yaron, M. Levy, and R. Tenne, “Singular MoS2, SiO2 and Si nanostructures and synthesis by solar ablation,” J. Mater. Chem. 18, 458-462 (2008).
    [CrossRef]
  6. R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).
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    [CrossRef]
  8. J. M. Gordon and D. Feuermann, “Optical performance at the thermodynamic limit with tailored imaging designs,” Appl. Opt. 44, 2327-2331 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2008 (3)

2007 (1)

2006 (3)

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight,” Adv. Mater. 18, 2993-2996(2006).
[CrossRef]

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight: erratum,” Adv. Mater. 18, 3199(2006).
[CrossRef]

D. Nakar, D. Feuermann, and J. M. Gordon, “Aplanatic near-field optics for efficient light transfer,” Opt. Eng. 45, 030502(2006).
[CrossRef]

2005 (1)

1981 (1)

1957 (1)

A. K. Head, “The two-mirror aplanat,” Proc. Phys. Soc. London Sect. B 70, 945-949 (1957).
[CrossRef]

Albu-Yaron, A.

J. M. Gordon, E. A. Katz, D. Feuermann, A. Albu-Yaron, M. Levy, and R. Tenne, “Singular MoS2, SiO2 and Si nanostructures and synthesis by solar ablation,” J. Mater. Chem. 18, 458-462 (2008).
[CrossRef]

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight,” Adv. Mater. 18, 2993-2996(2006).
[CrossRef]

Albu-Yaron, A. M.

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight: erratum,” Adv. Mater. 18, 3199(2006).
[CrossRef]

Arad, T.

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight,” Adv. Mater. 18, 2993-2996(2006).
[CrossRef]

Arad, T. M.

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight: erratum,” Adv. Mater. 18, 3199(2006).
[CrossRef]

Benítez, P.

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

Feuermann, D.

J. M. Gordon, E. A. Katz, D. Feuermann, A. Albu-Yaron, M. Levy, and R. Tenne, “Singular MoS2, SiO2 and Si nanostructures and synthesis by solar ablation,” J. Mater. Chem. 18, 458-462 (2008).
[CrossRef]

J. M. Gordon, D. Feuermann, and P. Young, “Unfolded aplanats for high-concentration photovoltaics,” Opt. Lett. 33, 1114-1116 (2008).
[CrossRef] [PubMed]

D. Nakar, A. Malul, D. Feuermann, and J. M. Gordon, “Radiometric characterization of ultra-high radiance xenon short-arc discharge lamps,” Appl. Opt. 47, 224-229 (2008).
[CrossRef] [PubMed]

A. Malul, D. Nakar, D. Feuermann, and J. M. Gordon, “Effectiveness of recycling light in ultra-bright short-arc discharge lamps,” Opt. Express 15, 14194-14201 (2007).
[CrossRef] [PubMed]

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight,” Adv. Mater. 18, 2993-2996(2006).
[CrossRef]

D. Nakar, D. Feuermann, and J. M. Gordon, “Aplanatic near-field optics for efficient light transfer,” Opt. Eng. 45, 030502(2006).
[CrossRef]

J. M. Gordon and D. Feuermann, “Optical performance at the thermodynamic limit with tailored imaging designs,” Appl. Opt. 44, 2327-2331 (2005).
[CrossRef] [PubMed]

Feuermann, D. M.

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight: erratum,” Adv. Mater. 18, 3199(2006).
[CrossRef]

Gordon, J. M.

J. M. Gordon, E. A. Katz, D. Feuermann, A. Albu-Yaron, M. Levy, and R. Tenne, “Singular MoS2, SiO2 and Si nanostructures and synthesis by solar ablation,” J. Mater. Chem. 18, 458-462 (2008).
[CrossRef]

D. Nakar, A. Malul, D. Feuermann, and J. M. Gordon, “Radiometric characterization of ultra-high radiance xenon short-arc discharge lamps,” Appl. Opt. 47, 224-229 (2008).
[CrossRef] [PubMed]

J. M. Gordon, D. Feuermann, and P. Young, “Unfolded aplanats for high-concentration photovoltaics,” Opt. Lett. 33, 1114-1116 (2008).
[CrossRef] [PubMed]

A. Malul, D. Nakar, D. Feuermann, and J. M. Gordon, “Effectiveness of recycling light in ultra-bright short-arc discharge lamps,” Opt. Express 15, 14194-14201 (2007).
[CrossRef] [PubMed]

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight,” Adv. Mater. 18, 2993-2996(2006).
[CrossRef]

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight: erratum,” Adv. Mater. 18, 3199(2006).
[CrossRef]

D. Nakar, D. Feuermann, and J. M. Gordon, “Aplanatic near-field optics for efficient light transfer,” Opt. Eng. 45, 030502(2006).
[CrossRef]

J. M. Gordon and D. Feuermann, “Optical performance at the thermodynamic limit with tailored imaging designs,” Appl. Opt. 44, 2327-2331 (2005).
[CrossRef] [PubMed]

Head, A. K.

A. K. Head, “The two-mirror aplanat,” Proc. Phys. Soc. London Sect. B 70, 945-949 (1957).
[CrossRef]

Jansen, M.

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight,” Adv. Mater. 18, 2993-2996(2006).
[CrossRef]

Jansen, M. M.

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight: erratum,” Adv. Mater. 18, 3199(2006).
[CrossRef]

Katz, E. A.

J. M. Gordon, E. A. Katz, D. Feuermann, A. Albu-Yaron, M. Levy, and R. Tenne, “Singular MoS2, SiO2 and Si nanostructures and synthesis by solar ablation,” J. Mater. Chem. 18, 458-462 (2008).
[CrossRef]

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight,” Adv. Mater. 18, 2993-2996(2006).
[CrossRef]

Katz, E. M.

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight: erratum,” Adv. Mater. 18, 3199(2006).
[CrossRef]

Levy, M.

J. M. Gordon, E. A. Katz, D. Feuermann, A. Albu-Yaron, M. Levy, and R. Tenne, “Singular MoS2, SiO2 and Si nanostructures and synthesis by solar ablation,” J. Mater. Chem. 18, 458-462 (2008).
[CrossRef]

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight,” Adv. Mater. 18, 2993-2996(2006).
[CrossRef]

Levy, M. M.

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight: erratum,” Adv. Mater. 18, 3199(2006).
[CrossRef]

Malul, A.

Mertz, L.

Miñano, J. C.

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

Mühle, C.

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight,” Adv. Mater. 18, 2993-2996(2006).
[CrossRef]

Mühle, C. M.

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight: erratum,” Adv. Mater. 18, 3199(2006).
[CrossRef]

Nakar, D.

Popovitz-Biro, R.

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight,” Adv. Mater. 18, 2993-2996(2006).
[CrossRef]

Popovitz-Biro, R. M.

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight: erratum,” Adv. Mater. 18, 3199(2006).
[CrossRef]

Tenne, R.

J. M. Gordon, E. A. Katz, D. Feuermann, A. Albu-Yaron, M. Levy, and R. Tenne, “Singular MoS2, SiO2 and Si nanostructures and synthesis by solar ablation,” J. Mater. Chem. 18, 458-462 (2008).
[CrossRef]

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight,” Adv. Mater. 18, 2993-2996(2006).
[CrossRef]

Tenne, R. M.

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight: erratum,” Adv. Mater. 18, 3199(2006).
[CrossRef]

Winston, R.

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

Young, P.

Adv. Mater. (2)

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight,” Adv. Mater. 18, 2993-2996(2006).
[CrossRef]

A. Albu-Yaron, T. Arad, M. Levy, R. Popovitz-Biro, R. Tenne, J. M. Gordon, D. Feuermann, E. A. Katz, M. Jansen, and C. Mühle, “Synthesis of fullerene-like Cs2O nanoparticles by concentrated sunlight: erratum,” Adv. Mater. 18, 3199(2006).
[CrossRef]

Appl. Opt. (3)

J. Mater. Chem. (1)

J. M. Gordon, E. A. Katz, D. Feuermann, A. Albu-Yaron, M. Levy, and R. Tenne, “Singular MoS2, SiO2 and Si nanostructures and synthesis by solar ablation,” J. Mater. Chem. 18, 458-462 (2008).
[CrossRef]

Opt. Eng. (1)

D. Nakar, D. Feuermann, and J. M. Gordon, “Aplanatic near-field optics for efficient light transfer,” Opt. Eng. 45, 030502(2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. Phys. Soc. London Sect. B (1)

A. K. Head, “The two-mirror aplanat,” Proc. Phys. Soc. London Sect. B 70, 945-949 (1957).
[CrossRef]

Other (1)

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

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Figures (9)

Fig. 1
Fig. 1

Representative 150 W commercial xenon short-arc discharge lamp [1, 2]: (a) schematic., (b) normalized plasma radiance within the 2.0 mm interelectrode gap, (c) photograph prior to ignition.

Fig. 2
Fig. 2

Cross section of a near-field two-mirror folded aplanat where the light path from source O is reversed twice before reaching focus F. Solutions for high exit NA (and for shading of the primary by the secondary mirror not exceeding a few percent) require the focus to be inside the optical system, which is problematic for reactor applications.

Fig. 3
Fig. 3

Cross section of a near-field two-mirror unfolded aplanat, drawn for NA in = 0.9 , NA out = 0.66 , ρ o = 100 , l o = 11.584 , r o = 74.589 , and 3% of the rays that enter the optic traversing the waist unreflected and hence not being focused. A ray emitted at arbitrary angle θ from a point source O within NA in = sin ( θ max ) is traced to focus F at angle ϕ within the target’s NA out = sin ( ϕ max ) . The solid contours represent the actual mirrored surfaces. The dotted curves represent the unbuilt continuations calculated with Eqs (3, 4).

Fig. 4
Fig. 4

Computer ray trace results for the near-field unfolded aplanat of Fig. 5 with NA in = 0.923 , ρ o = 100 , l o = 20 , r o = 100 , and a source that subtends a maximum angular radius of 10 mrad (which corresponds to a point at the entry to the aplanat). Efficiency refers to the fraction of source rays that enter the optic that reach a target of a given area (barring material losses). The initial slopes for the two curves are 5% lower than their respective étendue limits, and the efficiency asymptotes at 0.95 rather than 1.00, due to 5% of the collected rays that cross the optic’s waist without having undergone reflection and therefore missing the target.

Fig. 5
Fig. 5

Cross section of a double-ellipsoid unfolded aplanat with NA in = NA out = 0.923 and identical (truncated) ellipsoids.

Fig. 6
Fig. 6

Computer-generated side view (with several rays traced from the lamp to the reactor) of the unfolded aplanat produced for our reactor experiments, comprising two identical (truncated) ellipsoids. The locations of the lamp source and reactor target are indicated. The lamp includes a small hemispherical mirror that recycles its emission from the hemisphere facing away from the optical system back into the radiant plasma.

Fig. 7
Fig. 7

Photograph of the assembled double-ellipsoid unfolded aplanat of Figs. 5, 6.

Fig. 8
Fig. 8

Flux map of the optical system of Figs. 5, 6, 7, measured with an Ophir Optronics 10 A thermal sensor, through a 1.03 mm diameter orifice on an x y grid with a grid spacing of 0.2 mm . The peak irradiance averaged over a central diameter of 1.03 mm is 5.1 W / mm 2 .

Fig. 9
Fig. 9

Cross section of two complementary dual-mirror unfolded aplanats that (1) capture essentially the full angular extent of lamp emission (modeled here as a Lambertian sphere) and (2) irradiate the reactor nearly over its full circumference. This design has the same internal double-ellipsoid aplanat as Figs. 5, 6, 7, plus an external aplanat that comprises two identical ellipsoidal caps with the same NA values (0.923), ρ o = 115 , l o = 50 , and r o = 115 .

Equations (6)

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

ρ + l + r = const. = ρ o + l o + r o .
m = sin ( θ ) / sin ( ϕ ) = const. NA in / NA out ,
o ρ ( θ ) = 1 + k 2 k + 1 k 2 k cos ( θ ) + ( k o ρ o ) ( 1 + m ) [ γ ( θ ) 1 + m ] α [ γ ( θ ) + 1 m ] β [ γ ( θ ) ( k + 1 ) + ( 1 k ) ( 1 + m ) ] 2 α β 4 k ρ o γ ( θ ) m α ( 1 + m ) 2 α β ,
k = ρ o + r o o , α = m k m k 1 , β = m m k , γ ( θ ) = cos ( θ ) m 2 sin 2 ( θ ) ;
o r ( ϕ ) = 1 + k 2 k + 1 k 2 k cos ( ϕ ) + ( k o r o ) ( 1 + M ) [ δ ( ϕ ) 1 + M ] α [ δ ( ϕ ) + 1 M ] β [ δ ( ϕ ) ( k + 1 ) + ( 1 k ) ( 1 + M ) ] 2 α β 4 k r o δ ( ϕ ) M α ( 1 + M ) 2 α β ,
M = 1 / m , α = M k M k 1 , β = M M k , δ ( ϕ ) = cos ( ϕ ) M 2 sin 2 ( ϕ ) ,

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