Abstract

We have demonstrated volumetric Bragg gratings (VBGs) for mid-IR spectral range based on LiF color center (LiF:CC) crystals. γ-irradiated LiF:CC crystals feature strong absorption bands in the visible and near-IR spectral range, where selective color center photo-bleaching allows for the LiF refractive index modification. The absence of active absorption in LiF:CC crystals at wavelengths longer than 1.3 μm results in a VBG that is stable under mid-IR irradiation. Our calculations predict a ~60% diffraction efficiency over 1-6 μm spectral range, which could be realized in a ~1 cm long VBG. To verify this, we fabricated periodic structures in LiF:CC crystals using an amplified femtosecond Ti:sapphire laser. Diffraction at 1.56 μm is demonstration of a phase grating in LiF and is a proof of the feasibility of LiF:CC crystals for mid-IR VBG applications.

© 2012 OSA

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    [CrossRef]
  3. S. B. Mirov, V. V. Fedorov, D. V. Martyshkin, I. S. Moskalev, M. S. Mirov, and V. P. Gapontsev, “Progress in mid-IR Cr2+ and Fe2+ doped II-VI materials and lasers,” Opt. Mater. Express1(5), 898–910 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011

2010

S. Mirov, V. Fedorov, I. S. Moskalev, D. Martyshkin, and C. Kim, “Progress in Cr2+ and Fe2+ doped mid-IR laser materials,” Laser Photon. Rev.4(1), 21–41 (2010).
[CrossRef]

2009

2007

2006

A. Rocchetti, G. Assanto, R. M. Montereali, E. Nichelatti, and F. Somma, “Color-center waveguides in low-energy electron-bombarded lithium fluoride,” Appl. Phys. Lett.88(26), 261111 (2006).
[CrossRef]

2004

K. Kawamura, D. Takamizu, T. Kurobori, T. Kamiya, M. Hirano, and H. Hosono, “Nano-fabrication of optical devices in transparent dielectrics: volume gratings in SiO and DFB color center laser in LiF,” Nucl. Instrum. Methods Phys. Res. B218, 332–336 (2004).
[CrossRef]

D. V. Martyshkin, J. G. Parker, V. V. Fedorov, and S. B. Mirov, “Tunable distributed feedback color center laser using stabilized F2+** color centers in LiF crystal,” Appl. Phys. Lett.84(16), 3022–3024 (2004).
[CrossRef]

2002

R. Montereali and M. Piccinini, “Optical gain of F2 color centres in LiF confining structures realised by electron-beam lithography,” Opt. Commun.209(1-3), 201–208 (2002).
[CrossRef]

2001

M. Montecchi, R. M. Montereali, and E. Nichelatti, “Refractive index modification from color centres in dielectric confining structures,” Opt. Mater.17(1–2), 347–350 (2001).
[CrossRef]

2000

R. Montereali, S. Bigotta, M. Piccinini, M. Giammatteo, P. Picozzi, and S. Santucci, “Broad-band active channels induced by electron beam lithography in LiF films for waveguiding devices,” Nucl. Instrum. Methods Phys. Res. B166-167, 764–770 (2000).
[CrossRef]

1999

M. Montecchi, E. Nichelatti, A. Mancini, and R. M. Montereali, “Optical characterization of low-energy electron-beam-colored LiF crystals by spectral transmittance measurements,” J. Appl. Phys.86(7), 3745–3750 (1999).
[CrossRef]

1995

T. Kurobori, H. Hibino, Y. Q. Chen, and K. Inabe, “Distributed-feedback color center lasers using F2 centers in KCl,” Jpn. J. Appl. Phys.34(Part 2, No. 7B), L894–L896 (1995).
[CrossRef]

S. B. Mirov and T. T. Basiev, “Progress in color center lasers,” IEEE J. Sel. Top. Quantum Electron.1(1), 22–30 (1995).
[CrossRef]

1994

S. B. Mirov and T. T. Basiev, “Progress and trends in color center lasers,” Proc. SPIE2138, 248–262 (1994).
[CrossRef]

1988

T. T. Basiev, S. B. Mirov, and V. V. Osiko, “Room-temperature color center lasers,” IEEE J. Quantum Electron.24(6), 1052–1069 (1988).
[CrossRef]

1984

K. Peiponen and J. Riissanen, “On the linear and non-linear refractive index of F colour centres as a function of temperature,” J. Phys. Chem.17(31), 5617–5620 (1984).

1982

K.-E. Peiponen and A. Vaittinen, “Light-induced refractive index change in some F coloured alkali halide crystals,” J. Phys. Chem.15(13), L415–L418 (1982).

1975

F. Mollenauer and D. H. Olson, “Broadly tunable lasers using color centers,” J. Appl. Phys.46(7), 3109–3118 (1975).
[CrossRef]

Almaviva, S.

Assanto, G.

A. Rocchetti, G. Assanto, R. M. Montereali, E. Nichelatti, and F. Somma, “Color-center waveguides in low-energy electron-bombarded lithium fluoride,” Appl. Phys. Lett.88(26), 261111 (2006).
[CrossRef]

Basiev, T. T.

S. B. Mirov and T. T. Basiev, “Progress in color center lasers,” IEEE J. Sel. Top. Quantum Electron.1(1), 22–30 (1995).
[CrossRef]

S. B. Mirov and T. T. Basiev, “Progress and trends in color center lasers,” Proc. SPIE2138, 248–262 (1994).
[CrossRef]

T. T. Basiev, S. B. Mirov, and V. V. Osiko, “Room-temperature color center lasers,” IEEE J. Quantum Electron.24(6), 1052–1069 (1988).
[CrossRef]

Bigotta, S.

R. Montereali, S. Bigotta, M. Piccinini, M. Giammatteo, P. Picozzi, and S. Santucci, “Broad-band active channels induced by electron beam lithography in LiF films for waveguiding devices,” Nucl. Instrum. Methods Phys. Res. B166-167, 764–770 (2000).
[CrossRef]

Bonfigli, F.

Chen, G.

Chen, Y. Q.

T. Kurobori, H. Hibino, Y. Q. Chen, and K. Inabe, “Distributed-feedback color center lasers using F2 centers in KCl,” Jpn. J. Appl. Phys.34(Part 2, No. 7B), L894–L896 (1995).
[CrossRef]

Cheng, G.

Fedorov, V.

S. Mirov, V. Fedorov, I. S. Moskalev, D. Martyshkin, and C. Kim, “Progress in Cr2+ and Fe2+ doped mid-IR laser materials,” Laser Photon. Rev.4(1), 21–41 (2010).
[CrossRef]

Fedorov, V. V.

S. B. Mirov, V. V. Fedorov, D. V. Martyshkin, I. S. Moskalev, M. S. Mirov, and V. P. Gapontsev, “Progress in mid-IR Cr2+ and Fe2+ doped II-VI materials and lasers,” Opt. Mater. Express1(5), 898–910 (2011).
[CrossRef]

D. V. Martyshkin, J. G. Parker, V. V. Fedorov, and S. B. Mirov, “Tunable distributed feedback color center laser using stabilized F2+** color centers in LiF crystal,” Appl. Phys. Lett.84(16), 3022–3024 (2004).
[CrossRef]

Gapontsev, V. P.

Giammatteo, M.

R. Montereali, S. Bigotta, M. Piccinini, M. Giammatteo, P. Picozzi, and S. Santucci, “Broad-band active channels induced by electron beam lithography in LiF films for waveguiding devices,” Nucl. Instrum. Methods Phys. Res. B166-167, 764–770 (2000).
[CrossRef]

He, J.

Hibino, H.

T. Kurobori, H. Hibino, Y. Q. Chen, and K. Inabe, “Distributed-feedback color center lasers using F2 centers in KCl,” Jpn. J. Appl. Phys.34(Part 2, No. 7B), L894–L896 (1995).
[CrossRef]

Hirano, M.

K. Kawamura, D. Takamizu, T. Kurobori, T. Kamiya, M. Hirano, and H. Hosono, “Nano-fabrication of optical devices in transparent dielectrics: volume gratings in SiO and DFB color center laser in LiF,” Nucl. Instrum. Methods Phys. Res. B218, 332–336 (2004).
[CrossRef]

Hosono, H.

K. Kawamura, D. Takamizu, T. Kurobori, T. Kamiya, M. Hirano, and H. Hosono, “Nano-fabrication of optical devices in transparent dielectrics: volume gratings in SiO and DFB color center laser in LiF,” Nucl. Instrum. Methods Phys. Res. B218, 332–336 (2004).
[CrossRef]

Inabe, K.

T. Kurobori, H. Hibino, Y. Q. Chen, and K. Inabe, “Distributed-feedback color center lasers using F2 centers in KCl,” Jpn. J. Appl. Phys.34(Part 2, No. 7B), L894–L896 (1995).
[CrossRef]

Kalinowski, H. J.

Kaminskii, A. A.

A. A. Kaminskii, “Laser crystals and ceramics: recent advances,” Laser Photon. Rev.1(2), 93–177 (2007).
[CrossRef]

Kamiya, T.

K. Kawamura, D. Takamizu, T. Kurobori, T. Kamiya, M. Hirano, and H. Hosono, “Nano-fabrication of optical devices in transparent dielectrics: volume gratings in SiO and DFB color center laser in LiF,” Nucl. Instrum. Methods Phys. Res. B218, 332–336 (2004).
[CrossRef]

Kawamura, K.

K. Kawamura, D. Takamizu, T. Kurobori, T. Kamiya, M. Hirano, and H. Hosono, “Nano-fabrication of optical devices in transparent dielectrics: volume gratings in SiO and DFB color center laser in LiF,” Nucl. Instrum. Methods Phys. Res. B218, 332–336 (2004).
[CrossRef]

Kim, C.

S. Mirov, V. Fedorov, I. S. Moskalev, D. Martyshkin, and C. Kim, “Progress in Cr2+ and Fe2+ doped mid-IR laser materials,” Laser Photon. Rev.4(1), 21–41 (2010).
[CrossRef]

Kurobori, T.

K. Kawamura, D. Takamizu, T. Kurobori, T. Kamiya, M. Hirano, and H. Hosono, “Nano-fabrication of optical devices in transparent dielectrics: volume gratings in SiO and DFB color center laser in LiF,” Nucl. Instrum. Methods Phys. Res. B218, 332–336 (2004).
[CrossRef]

T. Kurobori, H. Hibino, Y. Q. Chen, and K. Inabe, “Distributed-feedback color center lasers using F2 centers in KCl,” Jpn. J. Appl. Phys.34(Part 2, No. 7B), L894–L896 (1995).
[CrossRef]

Mancini, A.

M. Montecchi, E. Nichelatti, A. Mancini, and R. M. Montereali, “Optical characterization of low-energy electron-beam-colored LiF crystals by spectral transmittance measurements,” J. Appl. Phys.86(7), 3745–3750 (1999).
[CrossRef]

Martyshkin, D.

S. Mirov, V. Fedorov, I. S. Moskalev, D. Martyshkin, and C. Kim, “Progress in Cr2+ and Fe2+ doped mid-IR laser materials,” Laser Photon. Rev.4(1), 21–41 (2010).
[CrossRef]

Martyshkin, D. V.

S. B. Mirov, V. V. Fedorov, D. V. Martyshkin, I. S. Moskalev, M. S. Mirov, and V. P. Gapontsev, “Progress in mid-IR Cr2+ and Fe2+ doped II-VI materials and lasers,” Opt. Mater. Express1(5), 898–910 (2011).
[CrossRef]

D. V. Martyshkin, J. G. Parker, V. V. Fedorov, and S. B. Mirov, “Tunable distributed feedback color center laser using stabilized F2+** color centers in LiF crystal,” Appl. Phys. Lett.84(16), 3022–3024 (2004).
[CrossRef]

Mirov, M. S.

Mirov, S.

S. Mirov, V. Fedorov, I. S. Moskalev, D. Martyshkin, and C. Kim, “Progress in Cr2+ and Fe2+ doped mid-IR laser materials,” Laser Photon. Rev.4(1), 21–41 (2010).
[CrossRef]

Mirov, S. B.

S. B. Mirov, V. V. Fedorov, D. V. Martyshkin, I. S. Moskalev, M. S. Mirov, and V. P. Gapontsev, “Progress in mid-IR Cr2+ and Fe2+ doped II-VI materials and lasers,” Opt. Mater. Express1(5), 898–910 (2011).
[CrossRef]

D. V. Martyshkin, J. G. Parker, V. V. Fedorov, and S. B. Mirov, “Tunable distributed feedback color center laser using stabilized F2+** color centers in LiF crystal,” Appl. Phys. Lett.84(16), 3022–3024 (2004).
[CrossRef]

S. B. Mirov and T. T. Basiev, “Progress in color center lasers,” IEEE J. Sel. Top. Quantum Electron.1(1), 22–30 (1995).
[CrossRef]

S. B. Mirov and T. T. Basiev, “Progress and trends in color center lasers,” Proc. SPIE2138, 248–262 (1994).
[CrossRef]

T. T. Basiev, S. B. Mirov, and V. V. Osiko, “Room-temperature color center lasers,” IEEE J. Quantum Electron.24(6), 1052–1069 (1988).
[CrossRef]

Mollenauer, F.

F. Mollenauer and D. H. Olson, “Broadly tunable lasers using color centers,” J. Appl. Phys.46(7), 3109–3118 (1975).
[CrossRef]

Montecchi, M.

M. Montecchi, R. M. Montereali, and E. Nichelatti, “Refractive index modification from color centres in dielectric confining structures,” Opt. Mater.17(1–2), 347–350 (2001).
[CrossRef]

M. Montecchi, E. Nichelatti, A. Mancini, and R. M. Montereali, “Optical characterization of low-energy electron-beam-colored LiF crystals by spectral transmittance measurements,” J. Appl. Phys.86(7), 3745–3750 (1999).
[CrossRef]

Montereali, R.

R. Montereali and M. Piccinini, “Optical gain of F2 color centres in LiF confining structures realised by electron-beam lithography,” Opt. Commun.209(1-3), 201–208 (2002).
[CrossRef]

R. Montereali, S. Bigotta, M. Piccinini, M. Giammatteo, P. Picozzi, and S. Santucci, “Broad-band active channels induced by electron beam lithography in LiF films for waveguiding devices,” Nucl. Instrum. Methods Phys. Res. B166-167, 764–770 (2000).
[CrossRef]

Montereali, R. M.

F. Bonfigli, M. A. Vincenti, S. Almaviva, R. M. Montereali, E. Nichelatti, R. N. Nogueira, and H. J. Kalinowski, “Photo-induced gratings in thin color center layers on lithium fluoride,” Appl. Opt.48(31), G38–G43 (2009).
[CrossRef] [PubMed]

A. Rocchetti, G. Assanto, R. M. Montereali, E. Nichelatti, and F. Somma, “Color-center waveguides in low-energy electron-bombarded lithium fluoride,” Appl. Phys. Lett.88(26), 261111 (2006).
[CrossRef]

M. Montecchi, R. M. Montereali, and E. Nichelatti, “Refractive index modification from color centres in dielectric confining structures,” Opt. Mater.17(1–2), 347–350 (2001).
[CrossRef]

M. Montecchi, E. Nichelatti, A. Mancini, and R. M. Montereali, “Optical characterization of low-energy electron-beam-colored LiF crystals by spectral transmittance measurements,” J. Appl. Phys.86(7), 3745–3750 (1999).
[CrossRef]

Moskalev, I. S.

S. B. Mirov, V. V. Fedorov, D. V. Martyshkin, I. S. Moskalev, M. S. Mirov, and V. P. Gapontsev, “Progress in mid-IR Cr2+ and Fe2+ doped II-VI materials and lasers,” Opt. Mater. Express1(5), 898–910 (2011).
[CrossRef]

S. Mirov, V. Fedorov, I. S. Moskalev, D. Martyshkin, and C. Kim, “Progress in Cr2+ and Fe2+ doped mid-IR laser materials,” Laser Photon. Rev.4(1), 21–41 (2010).
[CrossRef]

Nichelatti, E.

F. Bonfigli, M. A. Vincenti, S. Almaviva, R. M. Montereali, E. Nichelatti, R. N. Nogueira, and H. J. Kalinowski, “Photo-induced gratings in thin color center layers on lithium fluoride,” Appl. Opt.48(31), G38–G43 (2009).
[CrossRef] [PubMed]

A. Rocchetti, G. Assanto, R. M. Montereali, E. Nichelatti, and F. Somma, “Color-center waveguides in low-energy electron-bombarded lithium fluoride,” Appl. Phys. Lett.88(26), 261111 (2006).
[CrossRef]

M. Montecchi, R. M. Montereali, and E. Nichelatti, “Refractive index modification from color centres in dielectric confining structures,” Opt. Mater.17(1–2), 347–350 (2001).
[CrossRef]

M. Montecchi, E. Nichelatti, A. Mancini, and R. M. Montereali, “Optical characterization of low-energy electron-beam-colored LiF crystals by spectral transmittance measurements,” J. Appl. Phys.86(7), 3745–3750 (1999).
[CrossRef]

Nogueira, R. N.

Olson, D. H.

F. Mollenauer and D. H. Olson, “Broadly tunable lasers using color centers,” J. Appl. Phys.46(7), 3109–3118 (1975).
[CrossRef]

Osiko, V. V.

T. T. Basiev, S. B. Mirov, and V. V. Osiko, “Room-temperature color center lasers,” IEEE J. Quantum Electron.24(6), 1052–1069 (1988).
[CrossRef]

Parker, J. G.

D. V. Martyshkin, J. G. Parker, V. V. Fedorov, and S. B. Mirov, “Tunable distributed feedback color center laser using stabilized F2+** color centers in LiF crystal,” Appl. Phys. Lett.84(16), 3022–3024 (2004).
[CrossRef]

Peiponen, K.

K. Peiponen and J. Riissanen, “On the linear and non-linear refractive index of F colour centres as a function of temperature,” J. Phys. Chem.17(31), 5617–5620 (1984).

Peiponen, K.-E.

K.-E. Peiponen and A. Vaittinen, “Light-induced refractive index change in some F coloured alkali halide crystals,” J. Phys. Chem.15(13), L415–L418 (1982).

Piccinini, M.

R. Montereali and M. Piccinini, “Optical gain of F2 color centres in LiF confining structures realised by electron-beam lithography,” Opt. Commun.209(1-3), 201–208 (2002).
[CrossRef]

R. Montereali, S. Bigotta, M. Piccinini, M. Giammatteo, P. Picozzi, and S. Santucci, “Broad-band active channels induced by electron beam lithography in LiF films for waveguiding devices,” Nucl. Instrum. Methods Phys. Res. B166-167, 764–770 (2000).
[CrossRef]

Picozzi, P.

R. Montereali, S. Bigotta, M. Piccinini, M. Giammatteo, P. Picozzi, and S. Santucci, “Broad-band active channels induced by electron beam lithography in LiF films for waveguiding devices,” Nucl. Instrum. Methods Phys. Res. B166-167, 764–770 (2000).
[CrossRef]

Riissanen, J.

K. Peiponen and J. Riissanen, “On the linear and non-linear refractive index of F colour centres as a function of temperature,” J. Phys. Chem.17(31), 5617–5620 (1984).

Rocchetti, A.

A. Rocchetti, G. Assanto, R. M. Montereali, E. Nichelatti, and F. Somma, “Color-center waveguides in low-energy electron-bombarded lithium fluoride,” Appl. Phys. Lett.88(26), 261111 (2006).
[CrossRef]

Santucci, S.

R. Montereali, S. Bigotta, M. Piccinini, M. Giammatteo, P. Picozzi, and S. Santucci, “Broad-band active channels induced by electron beam lithography in LiF films for waveguiding devices,” Nucl. Instrum. Methods Phys. Res. B166-167, 764–770 (2000).
[CrossRef]

Somma, F.

A. Rocchetti, G. Assanto, R. M. Montereali, E. Nichelatti, and F. Somma, “Color-center waveguides in low-energy electron-bombarded lithium fluoride,” Appl. Phys. Lett.88(26), 261111 (2006).
[CrossRef]

Takamizu, D.

K. Kawamura, D. Takamizu, T. Kurobori, T. Kamiya, M. Hirano, and H. Hosono, “Nano-fabrication of optical devices in transparent dielectrics: volume gratings in SiO and DFB color center laser in LiF,” Nucl. Instrum. Methods Phys. Res. B218, 332–336 (2004).
[CrossRef]

Vaittinen, A.

K.-E. Peiponen and A. Vaittinen, “Light-induced refractive index change in some F coloured alkali halide crystals,” J. Phys. Chem.15(13), L415–L418 (1982).

Vincenti, M. A.

Wang, Y.

Zhao, W.

Appl. Opt.

Appl. Phys. Lett.

A. Rocchetti, G. Assanto, R. M. Montereali, E. Nichelatti, and F. Somma, “Color-center waveguides in low-energy electron-bombarded lithium fluoride,” Appl. Phys. Lett.88(26), 261111 (2006).
[CrossRef]

D. V. Martyshkin, J. G. Parker, V. V. Fedorov, and S. B. Mirov, “Tunable distributed feedback color center laser using stabilized F2+** color centers in LiF crystal,” Appl. Phys. Lett.84(16), 3022–3024 (2004).
[CrossRef]

IEEE J. Quantum Electron.

T. T. Basiev, S. B. Mirov, and V. V. Osiko, “Room-temperature color center lasers,” IEEE J. Quantum Electron.24(6), 1052–1069 (1988).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

S. B. Mirov and T. T. Basiev, “Progress in color center lasers,” IEEE J. Sel. Top. Quantum Electron.1(1), 22–30 (1995).
[CrossRef]

J. Appl. Phys.

F. Mollenauer and D. H. Olson, “Broadly tunable lasers using color centers,” J. Appl. Phys.46(7), 3109–3118 (1975).
[CrossRef]

M. Montecchi, E. Nichelatti, A. Mancini, and R. M. Montereali, “Optical characterization of low-energy electron-beam-colored LiF crystals by spectral transmittance measurements,” J. Appl. Phys.86(7), 3745–3750 (1999).
[CrossRef]

J. Phys. Chem.

K.-E. Peiponen and A. Vaittinen, “Light-induced refractive index change in some F coloured alkali halide crystals,” J. Phys. Chem.15(13), L415–L418 (1982).

K. Peiponen and J. Riissanen, “On the linear and non-linear refractive index of F colour centres as a function of temperature,” J. Phys. Chem.17(31), 5617–5620 (1984).

Jpn. J. Appl. Phys.

T. Kurobori, H. Hibino, Y. Q. Chen, and K. Inabe, “Distributed-feedback color center lasers using F2 centers in KCl,” Jpn. J. Appl. Phys.34(Part 2, No. 7B), L894–L896 (1995).
[CrossRef]

Laser Photon. Rev.

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Figures (7)

Fig. 1
Fig. 1

Optical microscopy image of 83 grooves/mm (A) and 42 grooves/mm (B) diffraction gratings.

Fig. 2
Fig. 2

Photoluminescence spectra of LiF CC crystals a) before laser irradiation, b) area of the crystal adjacent to the bleached stripe, c) bleached stripe (irradiated area), and d) bleached stripe after 12 hours.

Fig. 3
Fig. 3

Photoluminescence imaging and optical microscopy image of 83 grooves/mm diffraction grating. a) as prepared, b) same as (a) zoomed in 500-600 μm region, c) 12 hours after preparation, d) same as (c) zoomed in 500-600 μm region. The photoluminescence imaging was performed using PL integral intensity in 650-700 μm spectral region, the scanning was performed using XY translation stage with 1 μm step.

Fig. 4
Fig. 4

Photoluminescence imaging and optical microscopy image of 42 grooves/mm diffraction grating. a) as prepared, b) same as (a) zoomed in 500-600 μm region, c) 12 hours after preparation, d) same as (c) zoomed in 500-600 μm region. The photoluminescence imaging was performed using PL integral intensity in 650-700 μm spectral region, the scanning was performed using XY translation stage with 1 μm step.

Fig. 5
Fig. 5

Image of the diffraction pattern of 532 and 632 nm radiations obtained with a 12 μm period grating; left- position of the zero order; b and a-first order diffraction of 532 nm and 632 laser beams, respectively.

Fig. 6
Fig. 6

Absorption spectra of the LiF CCs crystal.

Fig. 7
Fig. 7

The calculation of refractive index changes induced by color centers. The black curve shows the results of calculations taking into account all color centers in the sample and the red curve shows the results including only absorption by two major bands (F and F2 & F3+).

Tables (1)

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Table 1 Results of the Absorption Spectrum Deconvolution by Gaussian Bandsa

Equations (12)

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F 2 +ω F 2 + +e
F 3 + +e F 3
F 3 + +ωF+ F 2 +
F 3 +ω= F 3 + +e
F+ω ( F ) * + H i [ F ion ]
Δn( ω )= 1 π P + κ( ω ) ω ω d ω
κ( ω )= 1 π P + n( ω )1 ω ω d ω ,
Δn= α 0 λ 0 4π ( 2( ω ω 0 )/Δω ) 1+ ( 2( ω ω 0 )/Δω ) 2
Δn( 0 )= α 0 λ 0 4π Δω 2 ω 0 = n max Δω ω 0
η 1 = J 1 2 ( 2| k |l )= J 1 2 ( πΔn l G λ ) ( kl ) 2 = ( πΔn l G λ ) 2
η= [ tanh( πL λ ( Δn ) ) ] 2
πL λ 0 ( δn )1

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