Abstract

Alpha particles accelerated towards a flat Al sample accumulate and precipitate in the form of dense He bubbles. Under fast-electron bombardment, these bubbles have been observed to generate He excimer molecules which decay by emitting vacuum-ultraviolet (VUV) fluorescent radiation. The calculation of the VUV dielectric function and reflectance shows that a thin planar film made of such He–Al composite and driven out of equilibrium can generate amplifying reflection. This phenomenon occurs at specific isolated frequencies and incidence angles when the excimer concentration in the pressurized fluid of the bubbles becomes sufficient. By use of analytical and numerical multiple-scattering simulations, the expected gain of this VUV amplifying mirror is studied, and the possible improvement brought about by shaping the film into a periodic array of adequately adjusted microresonators is demonstrated.

© 2003 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2000 (1)

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, R. P. H. Chang, and “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

1999 (2)

1997 (2)

P. Grossel and J. Vigoureux, “Calculation of wavefunctionsand of energy levels: Applications to multiple quantum wells and continuous potentials,” Phys. Rev. A 55, 796–799 (1997).
[CrossRef]

R. Soufli and E. Gullikson, “Reflectance measurements on clean surfaces for the determination of optical constants of materials in the EUV/soft X-ray region,” Appl. Opt. 36, 5499–5507 (1997).
[CrossRef] [PubMed]

1994 (2)

C.-G. Wahlström, “High-order harmonic generation using high-power lasers,” Phys. Scr. 49, 201–208 (1994).
[CrossRef]

P. Grossel, J. Vigoureux, and F. Baida, “Non-local approach to scattering in a one-dimensional problem,” Phys. Rev. A 50, 3627–3637 (1994).
[CrossRef] [PubMed]

1992 (1)

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

1984 (1)

A. Lucas, “Helium in metals,” Physica 127B, 225–239 (1984).
[CrossRef]

1983 (5)

S. Donnelly, A. Lucas, P. Lambin, and J. Vigneron, “A possible mechanism for electron bombardment-induced loop punching in helium-implanted materials,” Phys. Status Solidi A 79, 543–548 (1983).
[CrossRef]

S. E. Donnelly, A. Lucas, and J. Rife, “Vacuum ultraviolet fluorescence of helium bubbles in aluminum and tin,” Appl. Phys. Lett. 43, 35–37 (1983).
[CrossRef]

A. Lucas, S. Donnelly, J. Vigneron, and J. Rife, “Vacuum ultraviolet spectroscopy of high-pressure helium microbubbles in metals,” Surf. Sc. 126, 66–79 (1983).
[CrossRef]

A. Lucas, J. Vigneron, P. Lambin, S. Donnelly, and J. Rife, “The density of helium bubbles in implanted materials: theoretical interpretation of VUV absorption and EELS spectroscopy,” Radiat. Eff. 78, 349–363 (1983).
[CrossRef]

A. Lucas, J. Vigneron, S. Donnelly, and J. Rife, “Theoretical interpretation of the vacuum ultraviolet reflectance of liquid helium and of the absorption spectra of helium microbubbles in aluminum,” Phys. Rev. B 28, 2485–2496 (1983).
[CrossRef]

1981 (2)

J. Rife, S. E. Donnelly, A. Lucas, J. Gilles, and J. Ritsko, “Optical absorption and electron-energy-loss spectra of helium microbubbles in aluminum,” Phys. Rev. Lett. 46, 1220–1223 (1981).
[CrossRef]

S. E. Donnelly, J. Rife, J. Gilles, and A. Lucas, “The use of ion accelerators and synchrotron radiation to study the interaction of helium with metals,” IEEE Trans. Nucl. Sci. NS28, 1820–1824 (1981).
[CrossRef]

1980 (1)

S. E. Donnelly, J. Rife, J. Gilles, and A. Lucas, “Optical measurements of the density of helium in small bubbles in aluminum films,” J. Nucl. Mater. 93, 767–772 (1980).
[CrossRef]

1904 (1)

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385–420 (1904).
[CrossRef]

Baida, F.

P. Grossel, J. Vigoureux, and F. Baida, “Non-local approach to scattering in a one-dimensional problem,” Phys. Rev. A 50, 3627–3637 (1994).
[CrossRef] [PubMed]

Cao, H.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, R. P. H. Chang, and “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

Chang, R. P. H.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, R. P. H. Chang, and “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

Chang, S.-H.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, R. P. H. Chang, and “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

Donnelly, S.

A. Lucas, S. Donnelly, J. Vigneron, and J. Rife, “Vacuum ultraviolet spectroscopy of high-pressure helium microbubbles in metals,” Surf. Sc. 126, 66–79 (1983).
[CrossRef]

A. Lucas, J. Vigneron, P. Lambin, S. Donnelly, and J. Rife, “The density of helium bubbles in implanted materials: theoretical interpretation of VUV absorption and EELS spectroscopy,” Radiat. Eff. 78, 349–363 (1983).
[CrossRef]

A. Lucas, J. Vigneron, S. Donnelly, and J. Rife, “Theoretical interpretation of the vacuum ultraviolet reflectance of liquid helium and of the absorption spectra of helium microbubbles in aluminum,” Phys. Rev. B 28, 2485–2496 (1983).
[CrossRef]

S. Donnelly, A. Lucas, P. Lambin, and J. Vigneron, “A possible mechanism for electron bombardment-induced loop punching in helium-implanted materials,” Phys. Status Solidi A 79, 543–548 (1983).
[CrossRef]

Donnelly, S. E.

S. E. Donnelly, A. Lucas, and J. Rife, “Vacuum ultraviolet fluorescence of helium bubbles in aluminum and tin,” Appl. Phys. Lett. 43, 35–37 (1983).
[CrossRef]

S. E. Donnelly, J. Rife, J. Gilles, and A. Lucas, “The use of ion accelerators and synchrotron radiation to study the interaction of helium with metals,” IEEE Trans. Nucl. Sci. NS28, 1820–1824 (1981).
[CrossRef]

J. Rife, S. E. Donnelly, A. Lucas, J. Gilles, and J. Ritsko, “Optical absorption and electron-energy-loss spectra of helium microbubbles in aluminum,” Phys. Rev. Lett. 46, 1220–1223 (1981).
[CrossRef]

S. E. Donnelly, J. Rife, J. Gilles, and A. Lucas, “Optical measurements of the density of helium in small bubbles in aluminum films,” J. Nucl. Mater. 93, 767–772 (1980).
[CrossRef]

Gilles, J.

J. Rife, S. E. Donnelly, A. Lucas, J. Gilles, and J. Ritsko, “Optical absorption and electron-energy-loss spectra of helium microbubbles in aluminum,” Phys. Rev. Lett. 46, 1220–1223 (1981).
[CrossRef]

S. E. Donnelly, J. Rife, J. Gilles, and A. Lucas, “The use of ion accelerators and synchrotron radiation to study the interaction of helium with metals,” IEEE Trans. Nucl. Sci. NS28, 1820–1824 (1981).
[CrossRef]

S. E. Donnelly, J. Rife, J. Gilles, and A. Lucas, “Optical measurements of the density of helium in small bubbles in aluminum films,” J. Nucl. Mater. 93, 767–772 (1980).
[CrossRef]

Grossel, P.

P. Grossel and J. Vigoureux, “Calculation of wavefunctionsand of energy levels: Applications to multiple quantum wells and continuous potentials,” Phys. Rev. A 55, 796–799 (1997).
[CrossRef]

P. Grossel, J. Vigoureux, and F. Baida, “Non-local approach to scattering in a one-dimensional problem,” Phys. Rev. A 50, 3627–3637 (1994).
[CrossRef] [PubMed]

Gullikson, E.

Ho, S. T.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, R. P. H. Chang, and “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

Lambin, P.

S. Donnelly, A. Lucas, P. Lambin, and J. Vigneron, “A possible mechanism for electron bombardment-induced loop punching in helium-implanted materials,” Phys. Status Solidi A 79, 543–548 (1983).
[CrossRef]

A. Lucas, J. Vigneron, P. Lambin, S. Donnelly, and J. Rife, “The density of helium bubbles in implanted materials: theoretical interpretation of VUV absorption and EELS spectroscopy,” Radiat. Eff. 78, 349–363 (1983).
[CrossRef]

Liu, X.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, R. P. H. Chang, and “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

Lucas, A.

A. Lucas, “Helium in metals,” Physica 127B, 225–239 (1984).
[CrossRef]

A. Lucas, J. Vigneron, P. Lambin, S. Donnelly, and J. Rife, “The density of helium bubbles in implanted materials: theoretical interpretation of VUV absorption and EELS spectroscopy,” Radiat. Eff. 78, 349–363 (1983).
[CrossRef]

A. Lucas, S. Donnelly, J. Vigneron, and J. Rife, “Vacuum ultraviolet spectroscopy of high-pressure helium microbubbles in metals,” Surf. Sc. 126, 66–79 (1983).
[CrossRef]

S. Donnelly, A. Lucas, P. Lambin, and J. Vigneron, “A possible mechanism for electron bombardment-induced loop punching in helium-implanted materials,” Phys. Status Solidi A 79, 543–548 (1983).
[CrossRef]

A. Lucas, J. Vigneron, S. Donnelly, and J. Rife, “Theoretical interpretation of the vacuum ultraviolet reflectance of liquid helium and of the absorption spectra of helium microbubbles in aluminum,” Phys. Rev. B 28, 2485–2496 (1983).
[CrossRef]

S. E. Donnelly, A. Lucas, and J. Rife, “Vacuum ultraviolet fluorescence of helium bubbles in aluminum and tin,” Appl. Phys. Lett. 43, 35–37 (1983).
[CrossRef]

S. E. Donnelly, J. Rife, J. Gilles, and A. Lucas, “The use of ion accelerators and synchrotron radiation to study the interaction of helium with metals,” IEEE Trans. Nucl. Sci. NS28, 1820–1824 (1981).
[CrossRef]

J. Rife, S. E. Donnelly, A. Lucas, J. Gilles, and J. Ritsko, “Optical absorption and electron-energy-loss spectra of helium microbubbles in aluminum,” Phys. Rev. Lett. 46, 1220–1223 (1981).
[CrossRef]

S. E. Donnelly, J. Rife, J. Gilles, and A. Lucas, “Optical measurements of the density of helium in small bubbles in aluminum films,” J. Nucl. Mater. 93, 767–772 (1980).
[CrossRef]

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385–420 (1904).
[CrossRef]

Ohtaka, K.

Rife, J.

A. Lucas, S. Donnelly, J. Vigneron, and J. Rife, “Vacuum ultraviolet spectroscopy of high-pressure helium microbubbles in metals,” Surf. Sc. 126, 66–79 (1983).
[CrossRef]

A. Lucas, J. Vigneron, P. Lambin, S. Donnelly, and J. Rife, “The density of helium bubbles in implanted materials: theoretical interpretation of VUV absorption and EELS spectroscopy,” Radiat. Eff. 78, 349–363 (1983).
[CrossRef]

A. Lucas, J. Vigneron, S. Donnelly, and J. Rife, “Theoretical interpretation of the vacuum ultraviolet reflectance of liquid helium and of the absorption spectra of helium microbubbles in aluminum,” Phys. Rev. B 28, 2485–2496 (1983).
[CrossRef]

S. E. Donnelly, A. Lucas, and J. Rife, “Vacuum ultraviolet fluorescence of helium bubbles in aluminum and tin,” Appl. Phys. Lett. 43, 35–37 (1983).
[CrossRef]

S. E. Donnelly, J. Rife, J. Gilles, and A. Lucas, “The use of ion accelerators and synchrotron radiation to study the interaction of helium with metals,” IEEE Trans. Nucl. Sci. NS28, 1820–1824 (1981).
[CrossRef]

J. Rife, S. E. Donnelly, A. Lucas, J. Gilles, and J. Ritsko, “Optical absorption and electron-energy-loss spectra of helium microbubbles in aluminum,” Phys. Rev. Lett. 46, 1220–1223 (1981).
[CrossRef]

S. E. Donnelly, J. Rife, J. Gilles, and A. Lucas, “Optical measurements of the density of helium in small bubbles in aluminum films,” J. Nucl. Mater. 93, 767–772 (1980).
[CrossRef]

Ritsko, J.

J. Rife, S. E. Donnelly, A. Lucas, J. Gilles, and J. Ritsko, “Optical absorption and electron-energy-loss spectra of helium microbubbles in aluminum,” Phys. Rev. Lett. 46, 1220–1223 (1981).
[CrossRef]

Rocca, J. J.

J. J. Rocca, “Table-top soft x-ray lasers,” Rev. Sci. Instrum. 70, 3799–3827 (1999).
[CrossRef]

Seelig, E. W.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, R. P. H. Chang, and “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

Soufli, R.

Vigneron, J.

S. Donnelly, A. Lucas, P. Lambin, and J. Vigneron, “A possible mechanism for electron bombardment-induced loop punching in helium-implanted materials,” Phys. Status Solidi A 79, 543–548 (1983).
[CrossRef]

A. Lucas, J. Vigneron, S. Donnelly, and J. Rife, “Theoretical interpretation of the vacuum ultraviolet reflectance of liquid helium and of the absorption spectra of helium microbubbles in aluminum,” Phys. Rev. B 28, 2485–2496 (1983).
[CrossRef]

A. Lucas, J. Vigneron, P. Lambin, S. Donnelly, and J. Rife, “The density of helium bubbles in implanted materials: theoretical interpretation of VUV absorption and EELS spectroscopy,” Radiat. Eff. 78, 349–363 (1983).
[CrossRef]

A. Lucas, S. Donnelly, J. Vigneron, and J. Rife, “Vacuum ultraviolet spectroscopy of high-pressure helium microbubbles in metals,” Surf. Sc. 126, 66–79 (1983).
[CrossRef]

Vigoureux, J.

P. Grossel and J. Vigoureux, “Calculation of wavefunctionsand of energy levels: Applications to multiple quantum wells and continuous potentials,” Phys. Rev. A 55, 796–799 (1997).
[CrossRef]

P. Grossel, J. Vigoureux, and F. Baida, “Non-local approach to scattering in a one-dimensional problem,” Phys. Rev. A 50, 3627–3637 (1994).
[CrossRef] [PubMed]

J. Vigoureux, “Use of Einstein addition law in studies of reflection by stratified planar structures,” J. Opt. Soc. Am. A 9, 1313–1319 (1992).
[CrossRef]

Wahlström, C.-G.

C.-G. Wahlström, “High-order harmonic generation using high-power lasers,” Phys. Scr. 49, 201–208 (1994).
[CrossRef]

Xu, J. Y.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, R. P. H. Chang, and “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Zhang, D. Z.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, R. P. H. Chang, and “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. E. Donnelly, A. Lucas, and J. Rife, “Vacuum ultraviolet fluorescence of helium bubbles in aluminum and tin,” Appl. Phys. Lett. 43, 35–37 (1983).
[CrossRef]

IEEE Trans. Nucl. Sci. (1)

S. E. Donnelly, J. Rife, J. Gilles, and A. Lucas, “The use of ion accelerators and synchrotron radiation to study the interaction of helium with metals,” IEEE Trans. Nucl. Sci. NS28, 1820–1824 (1981).
[CrossRef]

J. Lightwave Technol. (1)

J. Nucl. Mater. (1)

S. E. Donnelly, J. Rife, J. Gilles, and A. Lucas, “Optical measurements of the density of helium in small bubbles in aluminum films,” J. Nucl. Mater. 93, 767–772 (1980).
[CrossRef]

J. Opt. Soc. Am. A (1)

Philos. Trans. R. Soc. London (1)

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385–420 (1904).
[CrossRef]

Phys. Rev. A (2)

P. Grossel, J. Vigoureux, and F. Baida, “Non-local approach to scattering in a one-dimensional problem,” Phys. Rev. A 50, 3627–3637 (1994).
[CrossRef] [PubMed]

P. Grossel and J. Vigoureux, “Calculation of wavefunctionsand of energy levels: Applications to multiple quantum wells and continuous potentials,” Phys. Rev. A 55, 796–799 (1997).
[CrossRef]

Phys. Rev. B (1)

A. Lucas, J. Vigneron, S. Donnelly, and J. Rife, “Theoretical interpretation of the vacuum ultraviolet reflectance of liquid helium and of the absorption spectra of helium microbubbles in aluminum,” Phys. Rev. B 28, 2485–2496 (1983).
[CrossRef]

Phys. Rev. Lett. (4)

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, R. P. H. Chang, and “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

J. Rife, S. E. Donnelly, A. Lucas, J. Gilles, and J. Ritsko, “Optical absorption and electron-energy-loss spectra of helium microbubbles in aluminum,” Phys. Rev. Lett. 46, 1220–1223 (1981).
[CrossRef]

Phys. Scr. (1)

C.-G. Wahlström, “High-order harmonic generation using high-power lasers,” Phys. Scr. 49, 201–208 (1994).
[CrossRef]

Phys. Status Solidi A (1)

S. Donnelly, A. Lucas, P. Lambin, and J. Vigneron, “A possible mechanism for electron bombardment-induced loop punching in helium-implanted materials,” Phys. Status Solidi A 79, 543–548 (1983).
[CrossRef]

Physica (1)

A. Lucas, “Helium in metals,” Physica 127B, 225–239 (1984).
[CrossRef]

Radiat. Eff. (1)

A. Lucas, J. Vigneron, P. Lambin, S. Donnelly, and J. Rife, “The density of helium bubbles in implanted materials: theoretical interpretation of VUV absorption and EELS spectroscopy,” Radiat. Eff. 78, 349–363 (1983).
[CrossRef]

Rev. Sci. Instrum. (1)

J. J. Rocca, “Table-top soft x-ray lasers,” Rev. Sci. Instrum. 70, 3799–3827 (1999).
[CrossRef]

Surf. Sc. (1)

A. Lucas, S. Donnelly, J. Vigneron, and J. Rife, “Vacuum ultraviolet spectroscopy of high-pressure helium microbubbles in metals,” Surf. Sc. 126, 66–79 (1983).
[CrossRef]

Other (10)

A. Yariv, Quantum Electronics (Wiley, New York, 1989).

Handbook of Optical Constants of Solids, Academic Press Handbook Series, E. D. Palik, ed. (Academic, New York, 1985).

J. M. Ziman, Principles of the Theory of Solids (Cambridge University, London, 1972).

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables, M. Abramowitz and I. Stegun, eds. (Dover, New York, 1974).

H. Hagemann, W. Gudet, and C. Kunz, “Optical properties of thin films,” DESY-Report SR74/7 (Deutsche Elektronen-Synchrotron, 2 Hamburg 52, Notkestieg 1, 1974).

I. Ternov, V. Mikhailin, and V. Khalilov, Synchrotron Radiation and Its Applications (Harwood Academic, Chur, Switzerland, 1985).

E. Weihreter, Compact Synchrotron Light Sources (Series on Synchrotron Radiation Techniques and Applications, Vol. 3) (World Scientific, Singapore, 1996).

Excimer Lasers (Topics in Applied Physics, Vol 30), C. K. Rhodes, ed. (Springer-Verlag, Berlin, 1984).

R. Waynant and M. N. Ediger, eds., Selected Papers on UV, VUV, and X-Ray Lasers (SPIE, Bellingham, Wash., 1993).

L. Schlapbach, “Hydrogen storage and electron emission of nanostructured carbon-based materials,” in Nanostructured Carbon for Advanced Applications, G. Benedek, P. Milani, V. G. Ralchenko, eds. (Plenum, New York, 2001).

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Figures (13)

Fig. 1
Fig. 1

Experimental fluorescence spectrum of He condensed into bubbles distributed in solid Al, for different conditions of implantation; from Donnelly et al.7

Fig. 2
Fig. 2

Imaginary part of the model dielectric function of He-excimer-doped Al in the frequency region pertinent to this work; fv is the volume fraction occupied by the bubbles in the Al matrix, a parameter used in the Maxwell-Garnett expression of the dielectric function and r is the fraction of He pairs in the excimer state (r=0.3 means 15% of He atoms have been pumped into the 1s2p state). The strong positive peak near 23.7 eV corresponds to the high-density fluid absorption while the two negative dips at about 15 eV and 21.2 eV are associated with the radiation emission by, respectively, the excimer or the atom in the low-density state.

Fig. 3
Fig. 3

Energy levels of the 1s1s and 1s2p states of a He atom pair as a function of the distance separating the nuclei. The ground state 1s1s is dissociative except for a weak binding force important only at very low temperatures and explained by van der Waals interaction. The 1s2p state is also dissociative at distances larger than about 2 Å but presents a stable minimum for a shorter distance, the point where excimers are formed. Under the high pressure experienced by the He fluid in a nanometer-sized bubble (atomic densities around 60 nm-3), absorption takes place at 23.7 eV. Then, in the 1s2p excited state, He atoms can either bind to an unexcited atom to form an excimer molecule (and subsequently decay emitting a 15-eV photon), or repel all neighboring atoms before decaying under low density, emitting a 21.2-eV photon.

Fig. 4
Fig. 4

Film geometry studied in Section 3. A He-Al composite layer (1 μm thick) covers an Al substrate. The layer is traversed by a flux of fast electrons which produce excimers in the He bubbles contained in the Al film. An incident plane wave with TE polarization is reflected by the surface and the interface with the substrate.

Fig. 5
Fig. 5

Reflectance spectrum of an active He-Al composite film 1 μm thick pumped to an excimer molecular fraction r=0.5 as a function of the photon energy. At normal incidence, the reflectance takes a value much larger than one in a region close to 16 eV, the excimer fluorescence transition. For other incidences, a reflectance gain remains with lower reflectance coefficients.

Fig. 6
Fig. 6

Amplification map in frequency-pumping-rate coordinates for a doped Al film 1 μm thick. The dark region corresponds to values which result in an amplifying reflectance R=|R|2>1. It is enclosed by the contour R=|R|2=1. The gray shades correspond to the logarithm of the reflectance. This plot is for normal incidence and TE waves.

Fig. 7
Fig. 7

Amplification map in frequency-incidence-angle space for a doped Al film 1 μm thick. The dark region corresponds to values which result in an amplifying reflectance R=|R|2>1. The two nearly vertical contours near 16 eV correspond to the amplification threshold R=|R|2=1. This plot is for a fixed value of the pumping rate r=0.5 and TE waves.

Fig. 8
Fig. 8

Distribution of signs of the complex denominator of the reflectance of a TE wave. The color code is as follows, assuming ρ=Re(1+uv) and η=Im(1+uv): black (ρ>0, η>0); dark gray (ρ>0, η<0); light gray (ρ<0, η>0); white (ρ<0, η<0). Complex zeros of this function are seen on the diagram at isolated points where four shades meet. These are exact singularities in the reflectance spectrum. The film is 1 μm thick with an excimer molecular fraction r=0.5.

Fig. 9
Fig. 9

Reflectance spectrum of an active He-Al composite film (1 μm thick, pumping parameter r=0.5) for an incident frequency of 15.9 eV. The sharp reflectance resonances arise from the proximity of the poles shown in Fig. 7. The vertical lines give the resonances predicted by a simple standing-wave model.

Fig. 10
Fig. 10

Complete dielectric function of the He-Al composite as a function of the incident photon frequency.

Fig. 11
Fig. 11

The array of microresonators designed to improve on the amplification of the reflected light. Dimensions a and b are chosen to favor the formation of standing waves through which reflection proceeds.

Fig. 12
Fig. 12

Reflectance spectrum of crenellated film as a function of the incidence angle. The photon energy is chosen in the amplification range of the He-Al composite at 16.28 eV. One finds resonances at near grazing incidence, even above 70 degrees. This large amplification for such a large incidence was not found on a flat surface.

Fig. 13
Fig. 13

Reflectance spectrum of the crenellated film, mapped as a function of the incidence angle and the photon energy. The gray shades correspond to the logarithm of the total (not just specular) reflectance. The photon energy is chosen in the amplification range of the He-Al composite between 15.85 and 16.5 eV. One finds resonance series at low and high incidences with very high maxima at isolated points close to the edges of the amplification domain.

Equations (26)

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εeff=εm2εm+εp-2 fv(εm-εp)2εm+εp+fv(εm-εp),
fv=VolumetakenbyparticlesTotalvolume.
ε(ω)=1+N2Ze2ε0mfeωe2-ω2+iωeωγ2+N3Ze2ε0mfaωa2-ω2-iωaωγ3+N6Ze2ε0mffωf2-ω2+iωfωγ6,
ωe=15eV,
ωa=23.7eV,
ωf=21.2eV.
fi=ωi/(2/2m|D0i|2).
jfj=1.
r=N2N,
N6N2+N6=f00.15.
N2Ze2ε0m fe=N2N feωp2=rfeωp2,
N3Ze2ε0m fa=N3N faωp2=1-r1-f0faωp2,
N6Ze2ε0m ff=N6N ffωp2=r f01-f0 ffωp2.
ωp=NZe2ε0m=12.9eV.
ε(ω)=1+r feωp2ωe2-ω2+iωωeγe+1-r1-f0faωp2ωa2-ω2-iωωaγa+r f01-f0ffωp2ωf2-ω2+iωωfγf.
γa=0.1.
γf=0.1.
1ωe2-ω2+iωωeγe
1πk=1nwk(ωe+2γexk)2-ω2+i(ωe+2γexk)ωγ.
H(r, t)=[Hx(z)ex+Hy(z)ey+Hz(z)ez]×exp i(kρ-ωt),
R=u+v1+uv.
u=q-κq+κ,
v=κ-kκ+kexp(2iκL),
2πλ=n ωccos t,
L=m λ2.
cos tm=m 12nL2πcω,

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