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Optics Express

Optics Express

  • Editor: C. Martijin de Sterke
  • Vol. 15, Iss. 9 — Apr. 30, 2007
  • pp: 5809–5814
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Faraday rotation in femtosecond laser micromachined waveguides

Tina Shih, Rafael R. Gattass, Cleber R. Mendonca, and Eric Mazur  »View Author Affiliations


Optics Express, Vol. 15, Issue 9, pp. 5809-5814 (2007)
http://dx.doi.org/10.1364/OE.15.005809


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Abstract

We demonstrate magneto-optic switching in femtosecond-laser micromachined waveguides written inside bulk terbium-doped Faraday glass. By measuring the polarization phase shift of the light as a function of the applied magnetic field, we find that there is a slight reduction in the effective Verdet constant of the waveguide compared to that of bulk Faraday glass. Electron Paramagnetic Resonance (EPR) measurements confirm that the micromachining leaves the concentration of the terbium ions that are responsible for the Faraday effect virtually unchanged.

© 2007 Optical Society of America

1. Introduction

Femtosecond laser micromachining of transparent materials has many potential applications in integrated optics [1–11

1. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996). [CrossRef] [PubMed]

]. Many devices such as waveguides [1–5

1. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996). [CrossRef] [PubMed]

], splitters [10

10. A. M. Streltsov and N. F. Borrelli, “Fabrication and analysis of a directional coupler written in glass by nanojoule femtosecond laser pulses,” Opt. Lett. 26, 42–43 (2001). [CrossRef]

], Mach-Zehnder interferometers [8

8. K. Minoshima, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, “Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing,” Opt. Express 10, 645–652 (2002). [PubMed]

], resonators [7

7. A. M. Kowalevicz, V. Sharma, E. P. Ippen, J. G. Fujimoto, and K. Minoshima, “Three-dimensional photonic devices fabricated in glass by use of a femtosecond laser oscillator,” Opt. Lett. 30, 1060–1062 (2005). [CrossRef] [PubMed]

] and amplifiers [6

6. G. Della Valle, R. Osellame, N. Chiodo, S. Taccheo, G. Cerullo, P. Laporta, A. Killi, U. Morgner, M. Lederer, and D. Kopf, “C-band waveguide amplifier produced by femtosecond laser writing,” Opt. Express 13, 5976–5982 (2005). [CrossRef] [PubMed]

, 9

9. Y. Sikorski, A. A. Said, P. Bado, Maynard R., C. Florea, and K. A. Winick, “Optical waveguide amplifier in Nd-doped glass written with near-IR femtosecond laser pulses,” Electron. Lett. 36, 226–227 (2000). [CrossRef]

, 11

11. S. Taccheo, G. Della Valle, R. Osellame, G. Cerullo, N. Chiodo, P. Laporta, O. Svelto, A. Killi, U. Morgner, M. Lederer, and D. Kopf , “Er : Yb-doped waveguide laser fabricated by femtosecond laser pulses,” Opt. Lett. 29, 2626–2628 (2004). [CrossRef] [PubMed]

] have been fabricated using this technique. In this paper, we combine oscillator-only micromachining and an externally switchable substrate to fabricate integrated active waveguides. Oscillator-only micromachining of waveguides does not require an amplifier and the pairing of this technique with a material whose properties can be externally controlled enable the fabrication of waveguides that can serve as active optical logic devices for integrated circuits.

One externally controllable material property that can be exploited to make switchable active devices is the magneto-optic effect, also known as Faraday effect [12

12. M. Born and E. Wolf, “Principles of Optics” (1980).

]. The Faraday effect is a rotation of the light-polarization induced by a magnetic field applied to the material. The linear constant of proportionality between the angle of rotation and the applied magnetic field is called the Verdet constant, and is given by V = θ/BL, where θ is the relative angle of polarization rotation, B is the magnitude of the applied magnetic field parallel to the direction of light propagation, and L is the material length over which the magneto-optic interaction takes place. The higher the Verdet constant, the larger the polarization rotation in response to an applied magnetic field, and the more suitable the material is for optical switching. Faraday rotation is widely used in optical isolators, preventing feedback in optical circuits.

We demonstrate that oscillator-only femtosecond-laser micromachining can be used to fabricate waveguides inside terbium-doped Faraday glass. The resultant waveguides are magneto-optically active, and can be used for photonic applications. The measured effective Verdet constant of the waveguide is 3600° ± 500° T−1m−1 (0.22 ± 0.03 min/Oe∙cm), comparable to that of the original material, which is 4300° ± 200° T−1m−1 (0.26 ± 0.01 min/Oe∙cm). We further investigated the compositional modification induced by femtosecond-laser micromachining by Electron Paramagnetic Resonance (EPR) spectra of the Faraday glass before and after irradiation. We observe a slight increase in the concentration of Tb+4 ions, which is not significant enough to affect the waveguide’s Faraday behavior.

2. Experimental

In Faraday glass, one class of magneto-optically active materials, rare-earth ions are responsible for the material’s magnetic susceptibility. The commercial Faraday glass used in this experiment was purchased from Shanghai Institute of Optics and Fine Mechanics. The glass, known as TG20, is doped with Tb3+ ions and has a composition of Tb2O3-SiO2-Al2O3-B2O3, with a homogenous Tb3+ ion concentration of 7.9 × 1018 ions/mm3.

The Faraday glass is micromachined using 60-fs, 800-nm, 10-nJ laser pulses from an extended cavity oscillator at a 25-MHz repetition rate. The pulses are focused through a 1.4-NA microscope objective (with a nearly spherical spot size of about 1 μm in diameter) into the bulk of a 50 mm × 5 mm × 1 mm Faraday glass sample that is translated at a speed of 10 mm/s with respect to the laser beam. The waveguides are each written in one pass along the entire 50-mm length of the sample, and are spaced by 200 μm to prevent crosstalk between waveguides, as seen in Fig. 1. The top left inset of Fig. 1 shows a cross-sectional view of the micromachined waveguides, which have an average diameter of 8 μm. After micromachining the ends of the sample are polished to allow light to be coupled into the waveguides. We found multimode behavior at 632 nm, as shown in the top right inset of Fig. 1, and single mode behavior at 1550 nm.

Fig. 1. Optical microscope image of micromachined waveguides inside the Faraday glass. Left Inset: Cross-sectional view of waveguide. Right Inset: Observed multimode behavior at 632 nm.
Fig. 2. Experimental setup for measuring Faraday rotation. A 632.8-nm laser beam is sent through a linear polarizer, coupled into and out of the sample using 10× microscope objectives, and finally analyzed by a rotating linear polarizer mounted on a motorized wheel.

We determined the magneto-optic response of the waveguides using the polarization rotation setup shown in Fig. 2. The micromachined Faraday sample is placed in a electromagnetic coil, which is mounted on a three-axis stage to facilitate alignment. HeNe laser light at 632.8 nm is coupled into and out of the waveguide using two 10× microscope objectives and an iris blocks any scattered light at the exit of the second objective lens. To determine the polarization rotation we use a rotating analyzer in front of the detector and a lock-in amplifier. The resulting signal is a sinusoidal function of the analyzer angle and any induced Faraday rotation inside the waveguide results in a phase shift of the detected sinusoidal signal.

As the field is not uniform across the length of the sample, the standard expression for the Faraday rotation has to be modified to account for the varying magnetic field profile, B(x), along the length of the sample. Because the Faraday effect is a linear response of the material to the applied magnetic field, we can write

V=θ0LB(x)dx.
(1)

To determine the Verdet constant of the material, we plot the phase shift of the signal as a function of the integrated magnetic field profile; the slope of the data then gives the Verdet constant.

3. Results

Figure 1 shows a close up of the femtosecond laser micromachined waveguides spaced by 200 μm under transmission optical microscopy. The micromachined waveguides look similar to those fabricated in glass using this process [5

5. C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, “Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy,” Opt. Lett. 26, 93–95 (2001). [CrossRef]

, 8

8. K. Minoshima, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, “Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing,” Opt. Express 10, 645–652 (2002). [PubMed]

, 17

17. R. Osellame, N. Chiodo, V. Maselli, A. Yin, M. Zavelani-Rossi, G. Cerullo, P. Laporta, L. Aiello, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Optical properties of waveguides written by a 26 MHz stretched cavity Ti : sapphire femtosecond oscillator,” Opt. Express 13, 612–620 (2005). [CrossRef] [PubMed]

].

Fig. 3. Oscilloscope traces of the signal transmitted through the bulk Faraday glass for values of the integrated magnetic field profile of ±0.2 T∙m. The observed phase shift gives the relative Faraday polarization rotation angle.

The dependence of the detector signal on the angle of the analyzer is shown in Fig. 3 for values of the integrated magnetic field profile of ±0.2 T∙m. The phase shift between the two traces confirms that a Faraday rotation occurs inside the waveguide.

Fig. 4. Linear dependence of the induced phase change on the integrated magnetic field profile for (a) bulk Faraday glass and (b) a waveguide written in Faraday glass.

Figure 4(a) shows the dependence of the phase shift on the integrated magnetic field profile in bulk Faraday glass. In Fig. 4(b), we show the same data for the waveguide. The Verdet constant is the slope of a least-squares fit of the data to a straight line. Averaging several sets of data for both bulk glass and waveguides, we obtain an effective Verdet constant of 3600° ± 500° T−1m−1 for the waveguides, which is a slight reduction in the Verdet constant compared to that of the bulk Faraday glass (4300° ± 200° T−1m−1) to within the experimental error.

4. Discussion

Fig. 5. Electron Paramagnetic Resonance spectrum of bulk Faraday glass. The shaded region shows the paramagnetic resonance due to the Tb4+ ions.
Fig. 6. Paramagnetic resonance due to the Tb4+ ions in the Electron Paramagnetic Resonance spectrum of Faraday glass (a) before and (b) after irradiation with femtosecond laser pulses. The curves show a Lorentzian fit to the data.

Because the terbium ions are responsible for the Faraday effect [20

20. J. Qiu, J. B. Qiu, H. Higuchi, Y. Kawamoto, and K. Hirao: “Faraday effect of GaS3/2-GeS2-LaS3/2-based glasses containing various rare-earth ions” J. Appl. Phys. 80, 5297–5300 (1996). [CrossRef]

], we examined how femtosecond micromachining affects the concentration of Tb4+ ions using EPR spectroscopy. Figure 5 shows the EPR spectrum of the bulk Faraday glass. The highlighted region shows the resonant signature of the paramagnetic Tb4+ ions at a gyromagnetic ratio value of g = 4.1; this region is shown in greater detail in Fig. 6(a). The amplitude of the resonance is a measure of the ion concentration. For comparison, an additional sample was prepared by micromachining waveguides spaced 25 μm apart across the length of a piece of Faraday glass, irradiating approximately 2% of the sample’s volume before grinding it up and obtaining an EPR spectrum [Fig. 6(b)]. Fitting both spectra in Fig. 6 with a Lorentzian curve, we find a 60% increase in the Tb4+ spectral intensity after laser micromachining, indicating that Tb4+ ions are generated during the waveguide writing process. Using a theoretical model and accounting for the percentage irradiated, [20

20. J. Qiu, J. B. Qiu, H. Higuchi, Y. Kawamoto, and K. Hirao: “Faraday effect of GaS3/2-GeS2-LaS3/2-based glasses containing various rare-earth ions” J. Appl. Phys. 80, 5297–5300 (1996). [CrossRef]

] we estimate that there are a total of 5.5 × 1019 cm−3 Tb4+ ions after femtosecond-laser irradiation [20

20. J. Qiu, J. B. Qiu, H. Higuchi, Y. Kawamoto, and K. Hirao: “Faraday effect of GaS3/2-GeS2-LaS3/2-based glasses containing various rare-earth ions” J. Appl. Phys. 80, 5297–5300 (1996). [CrossRef]

]. This resulting Tb4+ ion concentration is still negligible compared to the initial Tb3+ ion concentration of 7.9 × 1021 cm−3, confirming that the micromachining process does not affect the ions responsible for the Faraday effect.

5. Conclusion

In summary, we demonstrate that it is possible to fabricate waveguides in Faraday materials using femtosecond micromachining. The fabricated waveguides exhibit no significant reduction in Verdet constant and the micromachined waveguides can be used as magneto-optic switches. We confirmed that the femtosecond-laser micromachining does not convert a significant fraction of the active Tb3+ ions into Tb4+ ions. These findings pave the way for light-by-light magneto-optic switching and integrated optical isolators.

Acknowledgments

The authors would like to acknowledge B. Tull and I. Maxwell for their help editing the manuscript. R. Gattass provided the idea for this experiments and assisted T. Shih in carrying out the experiments. C.R. Mendonca helped with the acquisition and analysis of the experimental data. T. Shih acknowledges financial support from an NSF Graduate Research Fellowship and C. R. Mendonca acknowledges financial support from the Fundação de Amparo a Pesquisa do Estado de São Paulo. The research described in this paper was supported by the NSF under contracts DMI-0334984 and ARO-W911NF-05-1-0471.

References and links

1.

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996). [CrossRef] [PubMed]

2.

C. Florea and K. A. Winick, “Fabrication and characterization of photonic devices directly written in glass using femtosecond laser pulses,” J. Lightwave Technol. 21, 246–253 (2003). [CrossRef]

3.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A-Mater. 77, 109–111 (2003). [CrossRef]

4.

R. Osellame, S. Taccheo, M. Marangoni, R. Ramponi, P. Laporta, D. Polli, S. De Silvestri, and G. Cerullo,“Femtosecond writing of active optical waveguides with astigmatically shaped beams,” J. Opt. Soc. Am. B 20, 1559–1567 (2003). [CrossRef]

5.

C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, “Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy,” Opt. Lett. 26, 93–95 (2001). [CrossRef]

6.

G. Della Valle, R. Osellame, N. Chiodo, S. Taccheo, G. Cerullo, P. Laporta, A. Killi, U. Morgner, M. Lederer, and D. Kopf, “C-band waveguide amplifier produced by femtosecond laser writing,” Opt. Express 13, 5976–5982 (2005). [CrossRef] [PubMed]

7.

A. M. Kowalevicz, V. Sharma, E. P. Ippen, J. G. Fujimoto, and K. Minoshima, “Three-dimensional photonic devices fabricated in glass by use of a femtosecond laser oscillator,” Opt. Lett. 30, 1060–1062 (2005). [CrossRef] [PubMed]

8.

K. Minoshima, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, “Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing,” Opt. Express 10, 645–652 (2002). [PubMed]

9.

Y. Sikorski, A. A. Said, P. Bado, Maynard R., C. Florea, and K. A. Winick, “Optical waveguide amplifier in Nd-doped glass written with near-IR femtosecond laser pulses,” Electron. Lett. 36, 226–227 (2000). [CrossRef]

10.

A. M. Streltsov and N. F. Borrelli, “Fabrication and analysis of a directional coupler written in glass by nanojoule femtosecond laser pulses,” Opt. Lett. 26, 42–43 (2001). [CrossRef]

11.

S. Taccheo, G. Della Valle, R. Osellame, G. Cerullo, N. Chiodo, P. Laporta, O. Svelto, A. Killi, U. Morgner, M. Lederer, and D. Kopf , “Er : Yb-doped waveguide laser fabricated by femtosecond laser pulses,” Opt. Lett. 29, 2626–2628 (2004). [CrossRef] [PubMed]

12.

M. Born and E. Wolf, “Principles of Optics” (1980).

13.

H. Dotsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, P. Hertel, and A. F. Popkov, “Applications of magneto-optical waveguides in integrated optics: review,” J. Opt. Soc. Am. B 22, 240–253 (2005). [CrossRef]

14.

M. Levy, H. Hegde, F. J. Cadieu, R. Wolfe, V. J. Fratello, and R. M. J. Osgood, “Integrated optical isolators with sputter-deposited thin-film magnets,” IEEE Photonic Technol. Lett. 8, 903–905 (1996). [CrossRef]

15.

M. Levy, I. Ilic, R. Scarmozzino, R. M. J. Osgood, R. Wolfe, C. J. Gutierrez, and G. A. Prinz, “Thin-film- magnet magnetooptic waveguide isolator,” IEEE Photonic. Tech. Lett. 5, 198–200 (1993). [CrossRef]

16.

M. Kamata, M. Obara, R. R. Gattass, L. R. Cerami, and E. Mazur, “Optical vibration sensor fabricated by femtosecond laser micromachining,” Appl. Phys. Lett. 87, 051106–051101–051103 (2005). [CrossRef]

17.

R. Osellame, N. Chiodo, V. Maselli, A. Yin, M. Zavelani-Rossi, G. Cerullo, P. Laporta, L. Aiello, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Optical properties of waveguides written by a 26 MHz stretched cavity Ti : sapphire femtosecond oscillator,” Opt. Express 13, 612–620 (2005). [CrossRef] [PubMed]

18.

H. Ebendorff-Heidepriem and D. Ehrt: “Effect of Tb3+ ions on X-ray induced defect formation in phosphate containing glasses,” Opt. Mater. 18, 419–422 (2002). [CrossRef]

19.

Ebendorff-Heidepriem H. and D. Ehrt: “Electron spin resonance spectra of Eu2+ and Tb4+ ions in glasses” J. Phys-Condens. Mat. 11, 7627–7629 (1999). [CrossRef]

20.

J. Qiu, J. B. Qiu, H. Higuchi, Y. Kawamoto, and K. Hirao: “Faraday effect of GaS3/2-GeS2-LaS3/2-based glasses containing various rare-earth ions” J. Appl. Phys. 80, 5297–5300 (1996). [CrossRef]

OCIS Codes
(230.2240) Optical devices : Faraday effect
(230.7370) Optical devices : Waveguides
(320.7090) Ultrafast optics : Ultrafast lasers
(350.3390) Other areas of optics : Laser materials processing

ToC Category:
Laser Micromachining

History
Original Manuscript: March 1, 2007
Revised Manuscript: April 15, 2007
Manuscript Accepted: April 17, 2007
Published: April 27, 2007

Citation
Tina Shih, Rafael R. Gattass, Cleber R. Mendonca, and Eric Mazur, "Faraday rotation in femtosecond laser micromachined waveguides," Opt. Express 15, 5809-5814 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-9-5809


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References

  1. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, "Writing waveguides in glass with a femtosecond laser," Opt. Lett. 21, 1729-1731 (1996). [CrossRef] [PubMed]
  2. C. Florea and K. A. Winick, "Fabrication and characterization of photonic devices directly written in glass using femtosecond laser pulses," J. Lightwave Technol. 21, 246-253 (2003). [CrossRef]
  3. S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics," Appl. Phys.A-Mater. 77, 109-111 (2003). [CrossRef]
  4. R. Osellame, S. Taccheo, M. Marangoni, R. Ramponi, P. Laporta, D. Polli, S. De Silvestri, and G. Cerullo, "Femtosecond writing of active optical waveguides with astigmatically shaped beams," J. Opt. Soc. Am. B 20, 1559-1567 (2003). [CrossRef]
  5. C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, "Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy," Opt. Lett. 26, 93-95 (2001). [CrossRef]
  6. G. Della Valle, R. Osellame, N. Chiodo, S. Taccheo, G. Cerullo, P. Laporta, A. Killi, U. Morgner, M. Lederer, and D. Kopf, "C-band waveguide amplifier produced by femtosecond laser writing," Opt. Express 13, 5976-5982 (2005). [CrossRef] [PubMed]
  7. A. M. Kowalevicz, V. Sharma, E. P. Ippen, J. G. Fujimoto, and K. Minoshima, "Three-dimensional photonic devices fabricated in glass by use of a femtosecond laser oscillator," Opt. Lett. 30, 1060-1062 (2005). [CrossRef] [PubMed]
  8. K. Minoshima, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, "Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing," Opt. Express 10, 645-652 (2002). [PubMed]
  9. Y. Sikorski, A. A. Said, P. Bado, R. Maynard, C. Florea, and K. A. Winick, "Optical waveguide amplifier in Nd-doped glass written with near-IR femtosecond laser pulses," Electron. Lett. 36, 226-227 (2000). [CrossRef]
  10. A. M. Streltsov and N. F. Borrelli, "Fabrication and analysis of a directional coupler written in glass by nanojoule femtosecond laser pulses," Opt. Lett. 26, 42-43 (2001). [CrossRef]
  11. S. Taccheo, G. Della Valle, R. Osellame, G. Cerullo, N. Chiodo, P. Laporta, O. Svelto, A. Killi, U. Morgner, M. Lederer, and D. Kopf, "Er : Yb-doped waveguide laser fabricated by femtosecond laser pulses," Opt. Lett. 29, 2626-2628 (2004). [CrossRef] [PubMed]
  12. M. Born and E. Wolf, "Principles of Optics" (1980).
  13. H. Dotsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, P. Hertel, and A. F. Popkov, "Applications of magneto-optical waveguides in integrated optics: review," J. Opt. Soc. Am. B 22, 240-253 (2005). [CrossRef]
  14. M. Levy, H. Hegde, F. J. Cadieu, R. Wolfe, V. J. Fratello, and R. M. J. Osgood, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photonic Technol. Lett. 8, 903-905 (1996). [CrossRef]
  15. M. Levy, I. Ilic, R. Scarmozzino, R. M. J. Osgood, R. Wolfe, C. J. Gutierrez, and G. A. Prinz, "Thin-film-magnet magnetooptic waveguide isolator," IEEE Photonic. Tech. Lett. 5, 198-200 (1993). [CrossRef]
  16. M. Kamata, M. Obara, R. R. Gattass, L. R. Cerami, and E. Mazur, "Optical vibration sensor fabricated by femtosecond laser micromachining," Appl. Phys. Lett. 87, 051106-051101-051103 (2005). [CrossRef]
  17. R. Osellame, N. Chiodo, V. Maselli, A. Yin, M. Zavelani-Rossi, G. Cerullo, P. Laporta, L. Aiello, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, "Optical properties of waveguides written by a 26 MHz stretched cavity Ti : sapphire femtosecond oscillator," Opt. Express 13, 612-620 (2005). [CrossRef] [PubMed]
  18. H. Ebendorff-Heidepriem and D. Ehrt: "Effect of Tb3+ ions on X-ray induced defect formation in phosphate containing glasses," Opt. Mater. 18, 419-422 (2002). [CrossRef]
  19. H. Ebendorff-Heidepriem and D. Ehrt: "Electron spin resonance spectra of Eu2+ and Tb4+ ions in glasses," J. Phys-Condens.Mat. 11, 7627-7629 (1999). [CrossRef]
  20. J. Qiu, J. B. Qiu, H. Higuchi, Y. Kawamoto, and K. Hirao: "Faraday effect of GaS3/2-GeS2-LaS3/2-based glasses containing various rare-earth ions," J. Appl. Phys. 80, 5297-5300 (1996). [CrossRef]

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