Abstract

We present optical vector network analysis (OVNA) of an isotopically purified Er1663+:LiYF47 crystal. The OVNA method is based on generation and detection of a modulated optical sideband by using a radio-frequency vector network analyzer. This technique is widely used in the field of microwave photonics for the characterization of optical responses of optical devices such as filters and high-Q resonators. However, dense solid-state atomic ensembles induce a large phase shift on one of the optical sidebands that results in the appearance of extra features on the measured transmission response. We present a simple theoretical model that accurately describes the observed spectra and helps to reconstruct the absorption profile of a solid-state atomic ensemble as well as corresponding change of the refractive index in the vicinity of atomic resonances.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, Laser Photon. Rev. 7, 506 (2013).
    [Crossref]
  2. J. Dong, L. Liu, D. Gao, Y. Yu, A. Zheng, T. Yang, and X. Zhang, IEEE Photon. J. 5, 5500307 (2013).
    [Crossref]
  3. W. Jun, L. Wang, C. Yang, M. Li, N. H. Zhu, J. Guo, L. Xiong, and W. Li, Opt. Lett. 42, 4426 (2017).
    [Crossref]
  4. J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
    [Crossref]
  5. M. Ranĉić, M. P. Hedges, R. L. Ahlefeldt, and M. S. Sellars, Nat. Phys. 14, 50 (2017).
    [Crossref]
  6. A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 104, 193601 (2010).
    [Crossref]
  7. A. A. Abdumalikov, O. V. Astafiev, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 107, 043604 (2011).
    [Crossref]
  8. N. I. Agladze, M. N. Popova, G. N. Zhizhin, V. J. Egorov, and M. A. Petrova, Phys. Rev. Lett. 66, 477 (1991).
    [Crossref]
  9. R. M. Macfarlane, A. Cassanho, and R. S. Meltzer, Phys. Rev. Lett. 69, 542 (1992).
    [Crossref]
  10. R. M. Macfarlane, R. S. Meltzer, and B. Z. Malkin, Phys. Rev. B 58, 5692 (1998).
    [Crossref]
  11. K. I. Gerasimov, M. M. Minnegaliev, B. Z. Malkin, E. I. Baibekov, and S. A. Moiseev, Phys. Rev. B 94, 054429 (2016).
    [Crossref]
  12. A. Loyassa, R. Hernandez, and D. Benito, Fiber Integr. Opt. 23, 171 (2004).
    [Crossref]
  13. S. Pan and M. Xue, J. Lightwave Technol. 35, 836 (2017).
    [Crossref]
  14. W. Li, W. H. Sun, W. T. Wang, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 26, 866 (2014).
    [Crossref]
  15. T. Qing, S. Li, M. Xue, W. Li, N. Zhu, and S. Pan, Opt. Express 25, 4665 (2017).
    [Crossref]
  16. Z. Tang, S. Pan, and J. Yao, Opt. Express 20, 6555 (2012).
    [Crossref]
  17. T. Böttger, G. J. Pryde, C. W. Thiel, and R. L. Cone, J. Lumin. 127, 83 (2007).
    [Crossref]
  18. N. Kukharchyk, D. Sholokhov, O. Morozov, S. L. Korableva, A. Kalachev, and P. Bushev, New J. Phys. (2018), doi: 10.1088/1367-2630/aaa7e4.
    [Crossref]
  19. G. Grynberg, A. Aspect, and C. Fabre, Introduction into Quantum Optics (Cambridge University, 2010).
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    [Crossref]
  22. M. Xue, Y. Zhao, X. Gu, and S. Pan, J. Opt. Soc. Am. B 30, 928 (2013).
    [Crossref]
  23. R. M. Camacho, M. V. Pack, and J. C. Howell, Phys. Rev. A 73, 063812 (2006).
    [Crossref]
  24. A. Kalachev and O. Kocharovskaya, Phys. Rev. A 83, 053849 (2011).
    [Crossref]
  25. J. Clark, K. Heshami, and C. Simon, Phys. Rev. A 86, 013833 (2012).
    [Crossref]
  26. R. N. Shakhmuratov, Phys. Rev. A 95, 033805 (2017).
    [Crossref]

2017 (5)

2016 (1)

K. I. Gerasimov, M. M. Minnegaliev, B. Z. Malkin, E. I. Baibekov, and S. A. Moiseev, Phys. Rev. B 94, 054429 (2016).
[Crossref]

2014 (1)

W. Li, W. H. Sun, W. T. Wang, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 26, 866 (2014).
[Crossref]

2013 (3)

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, Laser Photon. Rev. 7, 506 (2013).
[Crossref]

J. Dong, L. Liu, D. Gao, Y. Yu, A. Zheng, T. Yang, and X. Zhang, IEEE Photon. J. 5, 5500307 (2013).
[Crossref]

M. Xue, Y. Zhao, X. Gu, and S. Pan, J. Opt. Soc. Am. B 30, 928 (2013).
[Crossref]

2012 (2)

J. Clark, K. Heshami, and C. Simon, Phys. Rev. A 86, 013833 (2012).
[Crossref]

Z. Tang, S. Pan, and J. Yao, Opt. Express 20, 6555 (2012).
[Crossref]

2011 (3)

A. A. Abdumalikov, O. V. Astafiev, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 107, 043604 (2011).
[Crossref]

C. W. Thiel, T. Böttger, and R. L. Cone, J. Lumin. 131, 353 (2011).
[Crossref]

A. Kalachev and O. Kocharovskaya, Phys. Rev. A 83, 053849 (2011).
[Crossref]

2010 (1)

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 104, 193601 (2010).
[Crossref]

2007 (2)

J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
[Crossref]

T. Böttger, G. J. Pryde, C. W. Thiel, and R. L. Cone, J. Lumin. 127, 83 (2007).
[Crossref]

2006 (1)

R. M. Camacho, M. V. Pack, and J. C. Howell, Phys. Rev. A 73, 063812 (2006).
[Crossref]

2004 (1)

A. Loyassa, R. Hernandez, and D. Benito, Fiber Integr. Opt. 23, 171 (2004).
[Crossref]

1998 (1)

R. M. Macfarlane, R. S. Meltzer, and B. Z. Malkin, Phys. Rev. B 58, 5692 (1998).
[Crossref]

1992 (1)

R. M. Macfarlane, A. Cassanho, and R. S. Meltzer, Phys. Rev. Lett. 69, 542 (1992).
[Crossref]

1991 (1)

N. I. Agladze, M. N. Popova, G. N. Zhizhin, V. J. Egorov, and M. A. Petrova, Phys. Rev. Lett. 66, 477 (1991).
[Crossref]

Abdumalikov, A. A.

A. A. Abdumalikov, O. V. Astafiev, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 107, 043604 (2011).
[Crossref]

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 104, 193601 (2010).
[Crossref]

Agladze, N. I.

N. I. Agladze, M. N. Popova, G. N. Zhizhin, V. J. Egorov, and M. A. Petrova, Phys. Rev. Lett. 66, 477 (1991).
[Crossref]

Ahlefeldt, R. L.

M. Ranĉić, M. P. Hedges, R. L. Ahlefeldt, and M. S. Sellars, Nat. Phys. 14, 50 (2017).
[Crossref]

Aspect, A.

G. Grynberg, A. Aspect, and C. Fabre, Introduction into Quantum Optics (Cambridge University, 2010).

Astafiev, O.

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 104, 193601 (2010).
[Crossref]

Astafiev, O. V.

A. A. Abdumalikov, O. V. Astafiev, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 107, 043604 (2011).
[Crossref]

Baibekov, E. I.

K. I. Gerasimov, M. M. Minnegaliev, B. Z. Malkin, E. I. Baibekov, and S. A. Moiseev, Phys. Rev. B 94, 054429 (2016).
[Crossref]

Benito, D.

A. Loyassa, R. Hernandez, and D. Benito, Fiber Integr. Opt. 23, 171 (2004).
[Crossref]

Böttger, T.

C. W. Thiel, T. Böttger, and R. L. Cone, J. Lumin. 131, 353 (2011).
[Crossref]

T. Böttger, G. J. Pryde, C. W. Thiel, and R. L. Cone, J. Lumin. 127, 83 (2007).
[Crossref]

Bushev, P.

N. Kukharchyk, D. Sholokhov, O. Morozov, S. L. Korableva, A. Kalachev, and P. Bushev, New J. Phys. (2018), doi: 10.1088/1367-2630/aaa7e4.
[Crossref]

Camacho, R. M.

R. M. Camacho, M. V. Pack, and J. C. Howell, Phys. Rev. A 73, 063812 (2006).
[Crossref]

Capmany, J.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, Laser Photon. Rev. 7, 506 (2013).
[Crossref]

J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
[Crossref]

Cassanho, A.

R. M. Macfarlane, A. Cassanho, and R. S. Meltzer, Phys. Rev. Lett. 69, 542 (1992).
[Crossref]

Clark, J.

J. Clark, K. Heshami, and C. Simon, Phys. Rev. A 86, 013833 (2012).
[Crossref]

Cone, R. L.

C. W. Thiel, T. Böttger, and R. L. Cone, J. Lumin. 131, 353 (2011).
[Crossref]

T. Böttger, G. J. Pryde, C. W. Thiel, and R. L. Cone, J. Lumin. 127, 83 (2007).
[Crossref]

Demtroder, W.

W. Demtroder, Laser Spectroscopy (Springer-Verlag, 2003).

Dong, J.

J. Dong, L. Liu, D. Gao, Y. Yu, A. Zheng, T. Yang, and X. Zhang, IEEE Photon. J. 5, 5500307 (2013).
[Crossref]

Egorov, V. J.

N. I. Agladze, M. N. Popova, G. N. Zhizhin, V. J. Egorov, and M. A. Petrova, Phys. Rev. Lett. 66, 477 (1991).
[Crossref]

Fabre, C.

G. Grynberg, A. Aspect, and C. Fabre, Introduction into Quantum Optics (Cambridge University, 2010).

Gao, D.

J. Dong, L. Liu, D. Gao, Y. Yu, A. Zheng, T. Yang, and X. Zhang, IEEE Photon. J. 5, 5500307 (2013).
[Crossref]

Gerasimov, K. I.

K. I. Gerasimov, M. M. Minnegaliev, B. Z. Malkin, E. I. Baibekov, and S. A. Moiseev, Phys. Rev. B 94, 054429 (2016).
[Crossref]

Grynberg, G.

G. Grynberg, A. Aspect, and C. Fabre, Introduction into Quantum Optics (Cambridge University, 2010).

Gu, X.

Guo, J.

Hedges, M. P.

M. Ranĉić, M. P. Hedges, R. L. Ahlefeldt, and M. S. Sellars, Nat. Phys. 14, 50 (2017).
[Crossref]

Heideman, R.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, Laser Photon. Rev. 7, 506 (2013).
[Crossref]

Hernandez, R.

A. Loyassa, R. Hernandez, and D. Benito, Fiber Integr. Opt. 23, 171 (2004).
[Crossref]

Heshami, K.

J. Clark, K. Heshami, and C. Simon, Phys. Rev. A 86, 013833 (2012).
[Crossref]

Howell, J. C.

R. M. Camacho, M. V. Pack, and J. C. Howell, Phys. Rev. A 73, 063812 (2006).
[Crossref]

Jun, W.

Kalachev, A.

A. Kalachev and O. Kocharovskaya, Phys. Rev. A 83, 053849 (2011).
[Crossref]

N. Kukharchyk, D. Sholokhov, O. Morozov, S. L. Korableva, A. Kalachev, and P. Bushev, New J. Phys. (2018), doi: 10.1088/1367-2630/aaa7e4.
[Crossref]

Kocharovskaya, O.

A. Kalachev and O. Kocharovskaya, Phys. Rev. A 83, 053849 (2011).
[Crossref]

Korableva, S. L.

N. Kukharchyk, D. Sholokhov, O. Morozov, S. L. Korableva, A. Kalachev, and P. Bushev, New J. Phys. (2018), doi: 10.1088/1367-2630/aaa7e4.
[Crossref]

Kukharchyk, N.

N. Kukharchyk, D. Sholokhov, O. Morozov, S. L. Korableva, A. Kalachev, and P. Bushev, New J. Phys. (2018), doi: 10.1088/1367-2630/aaa7e4.
[Crossref]

Leinse, A.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, Laser Photon. Rev. 7, 506 (2013).
[Crossref]

Li, M.

Li, S.

Li, W.

Liu, J. G.

W. Li, W. H. Sun, W. T. Wang, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 26, 866 (2014).
[Crossref]

Liu, L.

J. Dong, L. Liu, D. Gao, Y. Yu, A. Zheng, T. Yang, and X. Zhang, IEEE Photon. J. 5, 5500307 (2013).
[Crossref]

Loyassa, A.

A. Loyassa, R. Hernandez, and D. Benito, Fiber Integr. Opt. 23, 171 (2004).
[Crossref]

Macfarlane, R. M.

R. M. Macfarlane, R. S. Meltzer, and B. Z. Malkin, Phys. Rev. B 58, 5692 (1998).
[Crossref]

R. M. Macfarlane, A. Cassanho, and R. S. Meltzer, Phys. Rev. Lett. 69, 542 (1992).
[Crossref]

Malkin, B. Z.

K. I. Gerasimov, M. M. Minnegaliev, B. Z. Malkin, E. I. Baibekov, and S. A. Moiseev, Phys. Rev. B 94, 054429 (2016).
[Crossref]

R. M. Macfarlane, R. S. Meltzer, and B. Z. Malkin, Phys. Rev. B 58, 5692 (1998).
[Crossref]

Marpaung, D.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, Laser Photon. Rev. 7, 506 (2013).
[Crossref]

Meltzer, R. S.

R. M. Macfarlane, R. S. Meltzer, and B. Z. Malkin, Phys. Rev. B 58, 5692 (1998).
[Crossref]

R. M. Macfarlane, A. Cassanho, and R. S. Meltzer, Phys. Rev. Lett. 69, 542 (1992).
[Crossref]

Minnegaliev, M. M.

K. I. Gerasimov, M. M. Minnegaliev, B. Z. Malkin, E. I. Baibekov, and S. A. Moiseev, Phys. Rev. B 94, 054429 (2016).
[Crossref]

Moiseev, S. A.

K. I. Gerasimov, M. M. Minnegaliev, B. Z. Malkin, E. I. Baibekov, and S. A. Moiseev, Phys. Rev. B 94, 054429 (2016).
[Crossref]

Morozov, O.

N. Kukharchyk, D. Sholokhov, O. Morozov, S. L. Korableva, A. Kalachev, and P. Bushev, New J. Phys. (2018), doi: 10.1088/1367-2630/aaa7e4.
[Crossref]

Nakamura, Y.

A. A. Abdumalikov, O. V. Astafiev, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 107, 043604 (2011).
[Crossref]

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 104, 193601 (2010).
[Crossref]

Novak, D.

J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
[Crossref]

Pack, M. V.

R. M. Camacho, M. V. Pack, and J. C. Howell, Phys. Rev. A 73, 063812 (2006).
[Crossref]

Pan, S.

Pashkin, Y. A.

A. A. Abdumalikov, O. V. Astafiev, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 107, 043604 (2011).
[Crossref]

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 104, 193601 (2010).
[Crossref]

Petrova, M. A.

N. I. Agladze, M. N. Popova, G. N. Zhizhin, V. J. Egorov, and M. A. Petrova, Phys. Rev. Lett. 66, 477 (1991).
[Crossref]

Popova, M. N.

N. I. Agladze, M. N. Popova, G. N. Zhizhin, V. J. Egorov, and M. A. Petrova, Phys. Rev. Lett. 66, 477 (1991).
[Crossref]

Pryde, G. J.

T. Böttger, G. J. Pryde, C. W. Thiel, and R. L. Cone, J. Lumin. 127, 83 (2007).
[Crossref]

Qing, T.

Rancic, M.

M. Ranĉić, M. P. Hedges, R. L. Ahlefeldt, and M. S. Sellars, Nat. Phys. 14, 50 (2017).
[Crossref]

Roeloffzen, C.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, Laser Photon. Rev. 7, 506 (2013).
[Crossref]

Sales, S.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, Laser Photon. Rev. 7, 506 (2013).
[Crossref]

Sellars, M. S.

M. Ranĉić, M. P. Hedges, R. L. Ahlefeldt, and M. S. Sellars, Nat. Phys. 14, 50 (2017).
[Crossref]

Shakhmuratov, R. N.

R. N. Shakhmuratov, Phys. Rev. A 95, 033805 (2017).
[Crossref]

Sholokhov, D.

N. Kukharchyk, D. Sholokhov, O. Morozov, S. L. Korableva, A. Kalachev, and P. Bushev, New J. Phys. (2018), doi: 10.1088/1367-2630/aaa7e4.
[Crossref]

Simon, C.

J. Clark, K. Heshami, and C. Simon, Phys. Rev. A 86, 013833 (2012).
[Crossref]

Sun, W. H.

W. Li, W. H. Sun, W. T. Wang, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 26, 866 (2014).
[Crossref]

Tang, Z.

Thiel, C. W.

C. W. Thiel, T. Böttger, and R. L. Cone, J. Lumin. 131, 353 (2011).
[Crossref]

T. Böttger, G. J. Pryde, C. W. Thiel, and R. L. Cone, J. Lumin. 127, 83 (2007).
[Crossref]

Tsai, J. S.

A. A. Abdumalikov, O. V. Astafiev, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 107, 043604 (2011).
[Crossref]

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 104, 193601 (2010).
[Crossref]

Wang, L.

Wang, L. X.

W. Li, W. H. Sun, W. T. Wang, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 26, 866 (2014).
[Crossref]

Wang, W. T.

W. Li, W. H. Sun, W. T. Wang, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 26, 866 (2014).
[Crossref]

Xiong, L.

Xue, M.

Yang, C.

Yang, T.

J. Dong, L. Liu, D. Gao, Y. Yu, A. Zheng, T. Yang, and X. Zhang, IEEE Photon. J. 5, 5500307 (2013).
[Crossref]

Yao, J.

Yu, Y.

J. Dong, L. Liu, D. Gao, Y. Yu, A. Zheng, T. Yang, and X. Zhang, IEEE Photon. J. 5, 5500307 (2013).
[Crossref]

Zagoskin, A. M.

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett. 104, 193601 (2010).
[Crossref]

Zhang, X.

J. Dong, L. Liu, D. Gao, Y. Yu, A. Zheng, T. Yang, and X. Zhang, IEEE Photon. J. 5, 5500307 (2013).
[Crossref]

Zhao, Y.

Zheng, A.

J. Dong, L. Liu, D. Gao, Y. Yu, A. Zheng, T. Yang, and X. Zhang, IEEE Photon. J. 5, 5500307 (2013).
[Crossref]

Zhizhin, G. N.

N. I. Agladze, M. N. Popova, G. N. Zhizhin, V. J. Egorov, and M. A. Petrova, Phys. Rev. Lett. 66, 477 (1991).
[Crossref]

Zhu, N.

Zhu, N. H.

W. Jun, L. Wang, C. Yang, M. Li, N. H. Zhu, J. Guo, L. Xiong, and W. Li, Opt. Lett. 42, 4426 (2017).
[Crossref]

W. Li, W. H. Sun, W. T. Wang, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 26, 866 (2014).
[Crossref]

Fiber Integr. Opt. (1)

A. Loyassa, R. Hernandez, and D. Benito, Fiber Integr. Opt. 23, 171 (2004).
[Crossref]

IEEE Photon. J. (1)

J. Dong, L. Liu, D. Gao, Y. Yu, A. Zheng, T. Yang, and X. Zhang, IEEE Photon. J. 5, 5500307 (2013).
[Crossref]

IEEE Photon. Technol. Lett. (1)

W. Li, W. H. Sun, W. T. Wang, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 26, 866 (2014).
[Crossref]

J. Lightwave Technol. (1)

J. Lumin. (2)

T. Böttger, G. J. Pryde, C. W. Thiel, and R. L. Cone, J. Lumin. 127, 83 (2007).
[Crossref]

C. W. Thiel, T. Böttger, and R. L. Cone, J. Lumin. 131, 353 (2011).
[Crossref]

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

Laser Photon. Rev. (1)

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, Laser Photon. Rev. 7, 506 (2013).
[Crossref]

Nat. Photonics (1)

J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
[Crossref]

Nat. Phys. (1)

M. Ranĉić, M. P. Hedges, R. L. Ahlefeldt, and M. S. Sellars, Nat. Phys. 14, 50 (2017).
[Crossref]

Opt. Express (2)

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Figures (5)

Fig. 1.
Fig. 1. Sketch of the experimental setup. MZ-IM stands for the Mach–Zehnder intensity modulator. PD is the high-speed InGaAs photodetector. RF-VNA is the radio-frequency vector network analyzer.
Fig. 2.
Fig. 2. Measured (a) microwave transmission | S 21 ( Ω ) | and (b) phase delay arg ( S 21 ( Ω ) ) through the Er:LYF crystal. The inset shows addressed optical levels of Er:YLF crystal and transitions corresponding to the absorption components 1 and 2.
Fig. 3.
Fig. 3. Recovered (a) optical depth α L and (b) the change of the refractive index Δ n in the vicinity of atomic resonances measured by using OVNA.
Fig. 4.
Fig. 4. Comparison between the optical depth measured by using the conventional transmission spectroscopy and OVNA. Solid line shows the conventional transmission spectrum and dotted line is the fit to Lorentzians. Dashed line shows the recovered optical depth measured by OVNA, shown also in Fig. 3.
Fig. 5.
Fig. 5. Solid line: the measured depth of the absorption peak at the resonance frequency of the atomic transition ω 0 + Ω = ω r as a function of the optical depth of the sample α L . Dotted line represents linear response of OVNA at α L 1 .

Equations (4)

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α ( ω ) = α 0 ( Γ 2 Γ 2 + 4 ( ω ω r ) 2 ) ,
i RF cos ( Ω t ) + A ( ω + ) cos ( Ω t + ϕ ( ω + ) ) .
| S 21 | 2 1 + A ( ω + ) 2 + 2 A ( ω + ) cos ( ϕ ( ω + ) ) ,
arg ( S 21 ) = arctan ( A ( ω + ) sin ϕ ( ω + ) 1 + A ( ω + ) cos ϕ ( ω + ) ) .

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