Abstract

We report on the experimental characterisation of the temperature dependence of the optical rotatory power of crystalline right-handed $\alpha$-quartz at 1030 nm wavelength. The temperature range covered in this study is between 77 K and 325 K. For the measurement we propagated light through a 13.11 mm thick quartz plate collinearly with the optic axis. The plate is anti-reflection coated and rotates the polarisation plane of 1030 nm light by 89.3 deg at room temperature, corresponding to a specific rotatory power of 6.8 deg/mm. When placed between parallel polarisers, the transmission through the system was 0.03% at room temperature and increased to 1% at 77 K, showing a measurable change in rotatory power. At 77 K, the angle of rotation imparted by the quartz plate is 85 deg, corresponding to a specific rotatory power of 6.5 deg/mm. To the best of our knowledge, this is the first time that the temperature dependence of optical activity of $\alpha$-quartz is reported for cryogenic temperatures in the infrared. We expect that the measurement results provided in this paper will assist in the design and characterisation of optical systems operating under cryogenic conditions.

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References

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  1. M. Frede, R. Wilhelm, M. Brendel, C. Fallnich, F. Seifert, B. Willke, and K. Danzmann, “High power fundamental mode Nd: YAG laser with efficient birefringence compensation,” Opt. Express 12(15), 3581–3589 (2004).
    [Crossref]
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    [Crossref]
  3. S. Chandrasekhar, “The temperature variation of the rotatory power of quartz from 30$^\circ$∘ to 410$^\circ$∘ C,” Proc. - Indian Acad. Sci., Sect. A 39(6), 290–295 (1954).
    [Crossref]
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    [Crossref]
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    [Crossref]
  6. P. Gomez and C. Hernandez, “High-accuracy universal polarimeter measurement of optical activity and birefringence of $\alpha$α-quartz in the presence of multiple reflections,” J. Opt. Soc. Am. B 15(3), 1147–1154 (1998).
    [Crossref]
  7. P. Gomez and C. Hernandez, “Optical anisotropy of quartz in the presence of temperature-dependent multiple reflections using a high-accuracy universal polarimeter,” J. Phys. D: Appl. Phys. 33(22), 2985–2994 (2000).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  18. G. A. Lager, J. D. Jorgensen, and F. J. Rotella, “Crystal structure and thermal expansion of $\alpha$α-quartz SiO$_{2}$2 at low temperature,” J. Appl. Phys. 53(10), 6751–6756 (1982).
    [Crossref]

2014 (1)

2011 (1)

2009 (1)

Y. Wang, K. Inoue, H. Kan, T. Ogawa, and S. Wada, “Birefringence compensation of two tandem-set Nd:YAG rods with different thermally induced features,” J. Opt. A: Pure Appl. Opt. 11(12), 125501 (2009).
[Crossref]

2007 (1)

A. V. Voitovich, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Wide aperture Faraday isolator for kilowatt average radiation powers,” Quantum Electron. 37(5), 471–474 (2007).
[Crossref]

2004 (1)

2000 (2)

P. Gomez and C. Hernandez, “Optical anisotropy of quartz in the presence of temperature-dependent multiple reflections using a high-accuracy universal polarimeter,” J. Phys. D: Appl. Phys. 33(22), 2985–2994 (2000).
[Crossref]

W. F. Krupke, “Ytterbium solid-state lasers-the first decade,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1287–1296 (2000).
[Crossref]

1998 (1)

1986 (1)

J. P. Bachheimer, “Optical rotatory power and depolarisation of light in the $\alpha$α-, incommensurate and $\beta$β-phases of quartz (20 to 600 degrees C),” J. Phys. C: Solid State Phys. 19(27), 5509–5517 (1986).
[Crossref]

1982 (1)

G. A. Lager, J. D. Jorgensen, and F. J. Rotella, “Crystal structure and thermal expansion of $\alpha$α-quartz SiO$_{2}$2 at low temperature,” J. Appl. Phys. 53(10), 6751–6756 (1982).
[Crossref]

1980 (1)

Y. Le Page, L. D. Calvert, and E. J. Gabe, “Parameter variation in low-quartz between 94 ans 298 K,” J. Phys. Chem. Solids 41(7), 721–725 (1980).
[Crossref]

1968 (1)

1954 (1)

S. Chandrasekhar, “The temperature variation of the rotatory power of quartz from 30$^\circ$∘ to 410$^\circ$∘ C,” Proc. - Indian Acad. Sci., Sect. A 39(6), 290–295 (1954).
[Crossref]

1952 (1)

S. Chandrasekhar, “The optical rotatory power of quartz and its variation with temperature,” Proc. - Indian Acad. Sci., Sect. A 35(3), 103–113 (1952).
[Crossref]

1910 (1)

F. A. Molby, “The Rotatory Power of Quartz, Cinnobar, and Nicotine at Low Temperatures,” Phys. Rev. (Series I) 31(3), 291–310 (1910).
[Crossref]

Bachheimer, J. P.

J. P. Bachheimer, “Optical rotatory power and depolarisation of light in the $\alpha$α-, incommensurate and $\beta$β-phases of quartz (20 to 600 degrees C),” J. Phys. C: Solid State Phys. 19(27), 5509–5517 (1986).
[Crossref]

Banerjee, S.

Brendel, M.

Calvert, L. D.

Y. Le Page, L. D. Calvert, and E. J. Gabe, “Parameter variation in low-quartz between 94 ans 298 K,” J. Phys. Chem. Solids 41(7), 721–725 (1980).
[Crossref]

Chandrasekhar, S.

S. Chandrasekhar, “The temperature variation of the rotatory power of quartz from 30$^\circ$∘ to 410$^\circ$∘ C,” Proc. - Indian Acad. Sci., Sect. A 39(6), 290–295 (1954).
[Crossref]

S. Chandrasekhar, “The optical rotatory power of quartz and its variation with temperature,” Proc. - Indian Acad. Sci., Sect. A 35(3), 103–113 (1952).
[Crossref]

Collier, J. C.

Corruccini, R. J.

R. J. Corruccini and J. J. Gniewek, “Thermal expansion of technical solids at low temperatures - A compilation from the literature,” N. B. S. Circ. No. 29, U.S. Government Printing Office, Washington (1961).

Danzmann, K.

Davis, T. A.

Ertel, K.

Fallnich, C.

Frede, M.

Gabe, E. J.

Y. Le Page, L. D. Calvert, and E. J. Gabe, “Parameter variation in low-quartz between 94 ans 298 K,” J. Phys. Chem. Solids 41(7), 721–725 (1980).
[Crossref]

Gniewek, J. J.

R. J. Corruccini and J. J. Gniewek, “Thermal expansion of technical solids at low temperatures - A compilation from the literature,” N. B. S. Circ. No. 29, U.S. Government Printing Office, Washington (1961).

Gomez, P.

P. Gomez and C. Hernandez, “Optical anisotropy of quartz in the presence of temperature-dependent multiple reflections using a high-accuracy universal polarimeter,” J. Phys. D: Appl. Phys. 33(22), 2985–2994 (2000).
[Crossref]

P. Gomez and C. Hernandez, “High-accuracy universal polarimeter measurement of optical activity and birefringence of $\alpha$α-quartz in the presence of multiple reflections,” J. Opt. Soc. Am. B 15(3), 1147–1154 (1998).
[Crossref]

Hein, J.

Hellwing, M.

Hernandez, C.

P. Gomez and C. Hernandez, “Optical anisotropy of quartz in the presence of temperature-dependent multiple reflections using a high-accuracy universal polarimeter,” J. Phys. D: Appl. Phys. 33(22), 2985–2994 (2000).
[Crossref]

P. Gomez and C. Hernandez, “High-accuracy universal polarimeter measurement of optical activity and birefringence of $\alpha$α-quartz in the presence of multiple reflections,” J. Opt. Soc. Am. B 15(3), 1147–1154 (1998).
[Crossref]

Hernandez-Gomez, C.

Hornung, M.

Inoue, K.

Y. Wang, K. Inoue, H. Kan, T. Ogawa, and S. Wada, “Birefringence compensation of two tandem-set Nd:YAG rods with different thermally induced features,” J. Opt. A: Pure Appl. Opt. 11(12), 125501 (2009).
[Crossref]

Jorgensen, J. D.

G. A. Lager, J. D. Jorgensen, and F. J. Rotella, “Crystal structure and thermal expansion of $\alpha$α-quartz SiO$_{2}$2 at low temperature,” J. Appl. Phys. 53(10), 6751–6756 (1982).
[Crossref]

Kaluza, M. C.

Kan, H.

Y. Wang, K. Inoue, H. Kan, T. Ogawa, and S. Wada, “Birefringence compensation of two tandem-set Nd:YAG rods with different thermally induced features,” J. Opt. A: Pure Appl. Opt. 11(12), 125501 (2009).
[Crossref]

Katin, E. V.

A. V. Voitovich, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Wide aperture Faraday isolator for kilowatt average radiation powers,” Quantum Electron. 37(5), 471–474 (2007).
[Crossref]

Keppler, S.

Kessler, A.

Khazanov, E. A.

A. V. Voitovich, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Wide aperture Faraday isolator for kilowatt average radiation powers,” Quantum Electron. 37(5), 471–474 (2007).
[Crossref]

Körner, J.

Krupke, W. F.

W. F. Krupke, “Ytterbium solid-state lasers-the first decade,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1287–1296 (2000).
[Crossref]

Lager, G. A.

G. A. Lager, J. D. Jorgensen, and F. J. Rotella, “Crystal structure and thermal expansion of $\alpha$α-quartz SiO$_{2}$2 at low temperature,” J. Appl. Phys. 53(10), 6751–6756 (1982).
[Crossref]

Le Page, Y.

Y. Le Page, L. D. Calvert, and E. J. Gabe, “Parameter variation in low-quartz between 94 ans 298 K,” J. Phys. Chem. Solids 41(7), 721–725 (1980).
[Crossref]

Liebetrau, H.

Mason, P. D.

Molby, F. A.

F. A. Molby, “The Rotatory Power of Quartz, Cinnobar, and Nicotine at Low Temperatures,” Phys. Rev. (Series I) 31(3), 291–310 (1910).
[Crossref]

Mukhin, I. B.

A. V. Voitovich, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Wide aperture Faraday isolator for kilowatt average radiation powers,” Quantum Electron. 37(5), 471–474 (2007).
[Crossref]

Ogawa, T.

Y. Wang, K. Inoue, H. Kan, T. Ogawa, and S. Wada, “Birefringence compensation of two tandem-set Nd:YAG rods with different thermally induced features,” J. Opt. A: Pure Appl. Opt. 11(12), 125501 (2009).
[Crossref]

Palashov, O. V.

A. V. Voitovich, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Wide aperture Faraday isolator for kilowatt average radiation powers,” Quantum Electron. 37(5), 471–474 (2007).
[Crossref]

Phillips, P. J.

Rotella, F. J.

G. A. Lager, J. D. Jorgensen, and F. J. Rotella, “Crystal structure and thermal expansion of $\alpha$α-quartz SiO$_{2}$2 at low temperature,” J. Appl. Phys. 53(10), 6751–6756 (1982).
[Crossref]

Schnepp, M.

Schorcht, F.

Seifert, F.

Siebold, M.

Svert, A.

Vedam, K.

Voitovich, A. V.

A. V. Voitovich, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Wide aperture Faraday isolator for kilowatt average radiation powers,” Quantum Electron. 37(5), 471–474 (2007).
[Crossref]

Wada, S.

Y. Wang, K. Inoue, H. Kan, T. Ogawa, and S. Wada, “Birefringence compensation of two tandem-set Nd:YAG rods with different thermally induced features,” J. Opt. A: Pure Appl. Opt. 11(12), 125501 (2009).
[Crossref]

Wang, Y.

Y. Wang, K. Inoue, H. Kan, T. Ogawa, and S. Wada, “Birefringence compensation of two tandem-set Nd:YAG rods with different thermally induced features,” J. Opt. A: Pure Appl. Opt. 11(12), 125501 (2009).
[Crossref]

Wilhelm, R.

Willke, B.

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 2003).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 2003).

IEEE J. Sel. Top. Quantum Electron. (1)

W. F. Krupke, “Ytterbium solid-state lasers-the first decade,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1287–1296 (2000).
[Crossref]

J. Appl. Phys. (1)

G. A. Lager, J. D. Jorgensen, and F. J. Rotella, “Crystal structure and thermal expansion of $\alpha$α-quartz SiO$_{2}$2 at low temperature,” J. Appl. Phys. 53(10), 6751–6756 (1982).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

Y. Wang, K. Inoue, H. Kan, T. Ogawa, and S. Wada, “Birefringence compensation of two tandem-set Nd:YAG rods with different thermally induced features,” J. Opt. A: Pure Appl. Opt. 11(12), 125501 (2009).
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Phys. C: Solid State Phys. (1)

J. P. Bachheimer, “Optical rotatory power and depolarisation of light in the $\alpha$α-, incommensurate and $\beta$β-phases of quartz (20 to 600 degrees C),” J. Phys. C: Solid State Phys. 19(27), 5509–5517 (1986).
[Crossref]

J. Phys. Chem. Solids (1)

Y. Le Page, L. D. Calvert, and E. J. Gabe, “Parameter variation in low-quartz between 94 ans 298 K,” J. Phys. Chem. Solids 41(7), 721–725 (1980).
[Crossref]

J. Phys. D: Appl. Phys. (1)

P. Gomez and C. Hernandez, “Optical anisotropy of quartz in the presence of temperature-dependent multiple reflections using a high-accuracy universal polarimeter,” J. Phys. D: Appl. Phys. 33(22), 2985–2994 (2000).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. (Series I) (1)

F. A. Molby, “The Rotatory Power of Quartz, Cinnobar, and Nicotine at Low Temperatures,” Phys. Rev. (Series I) 31(3), 291–310 (1910).
[Crossref]

Proc. - Indian Acad. Sci., Sect. A (2)

S. Chandrasekhar, “The optical rotatory power of quartz and its variation with temperature,” Proc. - Indian Acad. Sci., Sect. A 35(3), 103–113 (1952).
[Crossref]

S. Chandrasekhar, “The temperature variation of the rotatory power of quartz from 30$^\circ$∘ to 410$^\circ$∘ C,” Proc. - Indian Acad. Sci., Sect. A 39(6), 290–295 (1954).
[Crossref]

Quantum Electron. (1)

A. V. Voitovich, E. V. Katin, I. B. Mukhin, O. V. Palashov, and E. A. Khazanov, “Wide aperture Faraday isolator for kilowatt average radiation powers,” Quantum Electron. 37(5), 471–474 (2007).
[Crossref]

Other (3)

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 2003).

eData: STFC Research Data Repository, http://dx.doi.org/10.5286/edata/724 .

R. J. Corruccini and J. J. Gniewek, “Thermal expansion of technical solids at low temperatures - A compilation from the literature,” N. B. S. Circ. No. 29, U.S. Government Printing Office, Washington (1961).

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Figures (7)

Fig. 1.
Fig. 1. Rotation angle imparted by the quartz plate across its aperture at room temperature and 1030 nm measured using a polarimeter.
Fig. 2.
Fig. 2. Experimental setup used to characterise the temperature dependence of the rotatory power of quartz (PD1, PD2 = photo-detectors). The insert shows the holder in which the quartz sample is mounted.
Fig. 3.
Fig. 3. Orientation of the transmission axes of the polariser and analyser and of the optic axis of the quartz plate with respect to the reference system (a). Dependence of transmission on the temperature of the quartz sample while the transmission axes of polariser and analyser are kept parallel to the y-axis (b). Data shown in this article are available at [15].
Fig. 4.
Fig. 4. Experimental data points (dots) and polynomial fitting curves (black lines) showing the temperature dependence of the transmission through the system as the axis of the analyser is rotated (a). Zoomed-in view of experimental data and fitting curves for $\phi$ values between -10 deg and 5 deg (b).
Fig. 5.
Fig. 5. Temperature dependence of the transmission at $\phi _{min}$.
Fig. 6.
Fig. 6. Temperature dependence of the rotation angle $\gamma$ imparted on the polarisation plane by the quartz plate and of the refractive index difference $\Delta n$.
Fig. 7.
Fig. 7. Temperature dependence of the length of the quartz sample calculated using the linear expansion coefficient data reported in [16].

Equations (3)

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γ ( T ) = π λ Δ n ( T ) L ( T ) ,
Δ n ( T ) = n L ( T ) n R ( T ) .
ρ ( T ) = γ ( T ) L ( T ) = π λ Δ n ( T ) .

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