Abstract

This article introduces a method to provide a continuous one-way sweep of the axis modes in a Fabry-Pérot (FP) cavity without sweeping the cavity mirror. The concept is based on the geometrical phase for circularly polarized light. When a geometric phase shifter (GPS) composed of fixed and rotating phase plates is arranged within an FP cavity, the frequencies of the axis modes are controlled by the angle of the phase plate. Two types of GPS configuration are proposed and experimentally demonstrated, providing two tunable ranges of the axis modes per revolution (these being two or four times as wide as the free spectral range). Neighboring axis modes are connected by continuous rotation.

© 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. S. M. Lindsay, M. W. Anderson, and J. R. Sandercock, “Construction and alignment of a high performance multipass vernier tandem Fabry-Pérot interferometer,” Rev. Sci. Instrum. 52, 1478–1486 (1981).
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    [Crossref]
  4. C. Honda, M. Maeda, K. Muraoka, and M. Akazaki, “Rapid-frequency-scan laser for instantaneous line-profile measurements in fluorescence spectroscopy,” Rev. Sci. Instrum. 58, 759–764 (1987).
    [Crossref]
  5. R. Wallenstein and T. W. Hänsch, “Linear pressure tuning of a multielement dye laser spectrometer,” Appl. Opt. 13, 1625–1628 (1974).
    [Crossref] [PubMed]
  6. B. J. van Wees, L. P. Kouwenhoven, C. J. P. M. Harmans, J. G. Williamson, C. E. Timmering, M. E. I. Broekaart, C. T. Foxon, and J. J. Harris, “Observation of zero-dimensional states in a one-dimensional electron interferometer,” Phys. Rev. Lett. 62, 2523–2526 (1989).
    [Crossref] [PubMed]
  7. Y. Zhang, D. T. McClure, E. M. Levenson-Falk, C. M. Marcus, L. N. Pfeiffer, and K. W. West, “Distinct signatures for coulomb blockade and Aharonov-Bohm interference in electronic Fabry-Pérot interferometers,” Phys. Rev. B 79, 241304 (2009).
    [Crossref]
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2017 (1)

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
[Crossref] [PubMed]

2016 (1)

S. Ohno, “Projection of phase singularities in moiré fringe onto a light field,” Appl. Phys. Lett. 108, 251104 (2016).
[Crossref]

2012 (1)

L. Huang, X. Chen, H. Muhlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (1)

Y.-L. Yang, Z.-H. Ding, K. Wang, L. Wu, and L. Wu, “Full-field optical coherence tomography by achromatic phase shifting with a rotating half-wave plat,” J. Opt. 12, 035301 (2010).
[Crossref]

2009 (1)

Y. Zhang, D. T. McClure, E. M. Levenson-Falk, C. M. Marcus, L. N. Pfeiffer, and K. W. West, “Distinct signatures for coulomb blockade and Aharonov-Bohm interference in electronic Fabry-Pérot interferometers,” Phys. Rev. B 79, 241304 (2009).
[Crossref]

2002 (3)

2000 (2)

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

S. Matsuura, P. Chen, G. A. Blake, J. C. Pearson, and H. M. Pickett, “A tunable cavity-locked diode laser source for terahertz photomixing,” IEEE Trans. Microw. Theory Tech. 48, 380–387 (2000).
[Crossref]

1989 (1)

B. J. van Wees, L. P. Kouwenhoven, C. J. P. M. Harmans, J. G. Williamson, C. E. Timmering, M. E. I. Broekaart, C. T. Foxon, and J. J. Harris, “Observation of zero-dimensional states in a one-dimensional electron interferometer,” Phys. Rev. Lett. 62, 2523–2526 (1989).
[Crossref] [PubMed]

1987 (1)

C. Honda, M. Maeda, K. Muraoka, and M. Akazaki, “Rapid-frequency-scan laser for instantaneous line-profile measurements in fluorescence spectroscopy,” Rev. Sci. Instrum. 58, 759–764 (1987).
[Crossref]

1981 (1)

S. M. Lindsay, M. W. Anderson, and J. R. Sandercock, “Construction and alignment of a high performance multipass vernier tandem Fabry-Pérot interferometer,” Rev. Sci. Instrum. 52, 1478–1486 (1981).
[Crossref]

1974 (1)

Akazaki, M.

C. Honda, M. Maeda, K. Muraoka, and M. Akazaki, “Rapid-frequency-scan laser for instantaneous line-profile measurements in fluorescence spectroscopy,” Rev. Sci. Instrum. 58, 759–764 (1987).
[Crossref]

Anderson, M. W.

S. M. Lindsay, M. W. Anderson, and J. R. Sandercock, “Construction and alignment of a high performance multipass vernier tandem Fabry-Pérot interferometer,” Rev. Sci. Instrum. 52, 1478–1486 (1981).
[Crossref]

Bai, B.

L. Huang, X. Chen, H. Muhlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Biener, G.

Blake, G. A.

S. Matsuura, P. Chen, G. A. Blake, J. C. Pearson, and H. M. Pickett, “A tunable cavity-locked diode laser source for terahertz photomixing,” IEEE Trans. Microw. Theory Tech. 48, 380–387 (2000).
[Crossref]

Bomzon, Z.

Broekaart, M. E. I.

B. J. van Wees, L. P. Kouwenhoven, C. J. P. M. Harmans, J. G. Williamson, C. E. Timmering, M. E. I. Broekaart, C. T. Foxon, and J. J. Harris, “Observation of zero-dimensional states in a one-dimensional electron interferometer,” Phys. Rev. Lett. 62, 2523–2526 (1989).
[Crossref] [PubMed]

Chen, P.

S. Matsuura, P. Chen, G. A. Blake, J. C. Pearson, and H. M. Pickett, “A tunable cavity-locked diode laser source for terahertz photomixing,” IEEE Trans. Microw. Theory Tech. 48, 380–387 (2000).
[Crossref]

Chen, X.

L. Huang, X. Chen, H. Muhlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Cundiff, S. T.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

Diddams, S. A.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

Ding, Z.-H.

Y.-L. Yang, Z.-H. Ding, K. Wang, L. Wu, and L. Wu, “Full-field optical coherence tomography by achromatic phase shifting with a rotating half-wave plat,” J. Opt. 12, 035301 (2010).
[Crossref]

Fischer, M.

W. Haensel, T. Steinmetz, M. Fischer, M. Lezius, and R. Holzwarth, “Method for operating a laser device, resonator arrangement and use of a phase shifter,” EP patentEP3120428B1 (March16, 2017).

Fowles, G. R.

G. R. Fowles, Introduction to Modern Optics, 2nd ed. (Dover Books on Physics, 1989).

Foxon, C. T.

B. J. van Wees, L. P. Kouwenhoven, C. J. P. M. Harmans, J. G. Williamson, C. E. Timmering, M. E. I. Broekaart, C. T. Foxon, and J. J. Harris, “Observation of zero-dimensional states in a one-dimensional electron interferometer,” Phys. Rev. Lett. 62, 2523–2526 (1989).
[Crossref] [PubMed]

Gutiérrez-Vega, J. C.

Haensel, W.

R. Holzwarth and W. Haensel, “Optical resonator arrangement and a method for adusting a round-triptime in a resonator,” US patent9705279 (December22, 2017).

W. Haensel, T. Steinmetz, M. Fischer, M. Lezius, and R. Holzwarth, “Method for operating a laser device, resonator arrangement and use of a phase shifter,” EP patentEP3120428B1 (March16, 2017).

Hall, J. L.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

Hänsch, T. W.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref] [PubMed]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

R. Wallenstein and T. W. Hänsch, “Linear pressure tuning of a multielement dye laser spectrometer,” Appl. Opt. 13, 1625–1628 (1974).
[Crossref] [PubMed]

Harmans, C. J. P. M.

B. J. van Wees, L. P. Kouwenhoven, C. J. P. M. Harmans, J. G. Williamson, C. E. Timmering, M. E. I. Broekaart, C. T. Foxon, and J. J. Harris, “Observation of zero-dimensional states in a one-dimensional electron interferometer,” Phys. Rev. Lett. 62, 2523–2526 (1989).
[Crossref] [PubMed]

Harris, J. J.

B. J. van Wees, L. P. Kouwenhoven, C. J. P. M. Harmans, J. G. Williamson, C. E. Timmering, M. E. I. Broekaart, C. T. Foxon, and J. J. Harris, “Observation of zero-dimensional states in a one-dimensional electron interferometer,” Phys. Rev. Lett. 62, 2523–2526 (1989).
[Crossref] [PubMed]

Hasman, E.

Holzwarth, R.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref] [PubMed]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

W. Haensel, T. Steinmetz, M. Fischer, M. Lezius, and R. Holzwarth, “Method for operating a laser device, resonator arrangement and use of a phase shifter,” EP patentEP3120428B1 (March16, 2017).

R. Holzwarth and W. Haensel, “Optical resonator arrangement and a method for adusting a round-triptime in a resonator,” US patent9705279 (December22, 2017).

Honda, C.

C. Honda, M. Maeda, K. Muraoka, and M. Akazaki, “Rapid-frequency-scan laser for instantaneous line-profile measurements in fluorescence spectroscopy,” Rev. Sci. Instrum. 58, 759–764 (1987).
[Crossref]

Huang, L.

L. Huang, X. Chen, H. Muhlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Jin, G.

L. Huang, X. Chen, H. Muhlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Jones, D. J.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

Keller, U.

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
[Crossref] [PubMed]

Kleiner, V.

Kouwenhoven, L. P.

B. J. van Wees, L. P. Kouwenhoven, C. J. P. M. Harmans, J. G. Williamson, C. E. Timmering, M. E. I. Broekaart, C. T. Foxon, and J. J. Harris, “Observation of zero-dimensional states in a one-dimensional electron interferometer,” Phys. Rev. Lett. 62, 2523–2526 (1989).
[Crossref] [PubMed]

Levenson-Falk, E. M.

Y. Zhang, D. T. McClure, E. M. Levenson-Falk, C. M. Marcus, L. N. Pfeiffer, and K. W. West, “Distinct signatures for coulomb blockade and Aharonov-Bohm interference in electronic Fabry-Pérot interferometers,” Phys. Rev. B 79, 241304 (2009).
[Crossref]

Lezius, M.

W. Haensel, T. Steinmetz, M. Fischer, M. Lezius, and R. Holzwarth, “Method for operating a laser device, resonator arrangement and use of a phase shifter,” EP patentEP3120428B1 (March16, 2017).

Li, G.

L. Huang, X. Chen, H. Muhlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Lindsay, S. M.

S. M. Lindsay, M. W. Anderson, and J. R. Sandercock, “Construction and alignment of a high performance multipass vernier tandem Fabry-Pérot interferometer,” Rev. Sci. Instrum. 52, 1478–1486 (1981).
[Crossref]

Link, S. M.

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
[Crossref] [PubMed]

Maas, D. J. H. C.

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
[Crossref] [PubMed]

Maeda, M.

C. Honda, M. Maeda, K. Muraoka, and M. Akazaki, “Rapid-frequency-scan laser for instantaneous line-profile measurements in fluorescence spectroscopy,” Rev. Sci. Instrum. 58, 759–764 (1987).
[Crossref]

Marcus, C. M.

Y. Zhang, D. T. McClure, E. M. Levenson-Falk, C. M. Marcus, L. N. Pfeiffer, and K. W. West, “Distinct signatures for coulomb blockade and Aharonov-Bohm interference in electronic Fabry-Pérot interferometers,” Phys. Rev. B 79, 241304 (2009).
[Crossref]

Matsuura, S.

S. Matsuura, P. Chen, G. A. Blake, J. C. Pearson, and H. M. Pickett, “A tunable cavity-locked diode laser source for terahertz photomixing,” IEEE Trans. Microw. Theory Tech. 48, 380–387 (2000).
[Crossref]

McClure, D. T.

Y. Zhang, D. T. McClure, E. M. Levenson-Falk, C. M. Marcus, L. N. Pfeiffer, and K. W. West, “Distinct signatures for coulomb blockade and Aharonov-Bohm interference in electronic Fabry-Pérot interferometers,” Phys. Rev. B 79, 241304 (2009).
[Crossref]

Muhlenbernd, H.

L. Huang, X. Chen, H. Muhlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Muraoka, K.

C. Honda, M. Maeda, K. Muraoka, and M. Akazaki, “Rapid-frequency-scan laser for instantaneous line-profile measurements in fluorescence spectroscopy,” Rev. Sci. Instrum. 58, 759–764 (1987).
[Crossref]

Niv, A.

Ohno, S.

S. Ohno, “Projection of phase singularities in moiré fringe onto a light field,” Appl. Phys. Lett. 108, 251104 (2016).
[Crossref]

Pearson, J. C.

S. Matsuura, P. Chen, G. A. Blake, J. C. Pearson, and H. M. Pickett, “A tunable cavity-locked diode laser source for terahertz photomixing,” IEEE Trans. Microw. Theory Tech. 48, 380–387 (2000).
[Crossref]

Pfeiffer, L. N.

Y. Zhang, D. T. McClure, E. M. Levenson-Falk, C. M. Marcus, L. N. Pfeiffer, and K. W. West, “Distinct signatures for coulomb blockade and Aharonov-Bohm interference in electronic Fabry-Pérot interferometers,” Phys. Rev. B 79, 241304 (2009).
[Crossref]

Pickett, H. M.

S. Matsuura, P. Chen, G. A. Blake, J. C. Pearson, and H. M. Pickett, “A tunable cavity-locked diode laser source for terahertz photomixing,” IEEE Trans. Microw. Theory Tech. 48, 380–387 (2000).
[Crossref]

Ranka, J. K.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

Sandercock, J. R.

S. M. Lindsay, M. W. Anderson, and J. R. Sandercock, “Construction and alignment of a high performance multipass vernier tandem Fabry-Pérot interferometer,” Rev. Sci. Instrum. 52, 1478–1486 (1981).
[Crossref]

Steinmetz, T.

W. Haensel, T. Steinmetz, M. Fischer, M. Lezius, and R. Holzwarth, “Method for operating a laser device, resonator arrangement and use of a phase shifter,” EP patentEP3120428B1 (March16, 2017).

Tan, Q.

L. Huang, X. Chen, H. Muhlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

Timmering, C. E.

B. J. van Wees, L. P. Kouwenhoven, C. J. P. M. Harmans, J. G. Williamson, C. E. Timmering, M. E. I. Broekaart, C. T. Foxon, and J. J. Harris, “Observation of zero-dimensional states in a one-dimensional electron interferometer,” Phys. Rev. Lett. 62, 2523–2526 (1989).
[Crossref] [PubMed]

Udem, T.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref] [PubMed]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

van Wees, B. J.

B. J. van Wees, L. P. Kouwenhoven, C. J. P. M. Harmans, J. G. Williamson, C. E. Timmering, M. E. I. Broekaart, C. T. Foxon, and J. J. Harris, “Observation of zero-dimensional states in a one-dimensional electron interferometer,” Phys. Rev. Lett. 62, 2523–2526 (1989).
[Crossref] [PubMed]

Waldburger, D.

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
[Crossref] [PubMed]

Wallenstein, R.

Wang, K.

Y.-L. Yang, Z.-H. Ding, K. Wang, L. Wu, and L. Wu, “Full-field optical coherence tomography by achromatic phase shifting with a rotating half-wave plat,” J. Opt. 12, 035301 (2010).
[Crossref]

West, K. W.

Y. Zhang, D. T. McClure, E. M. Levenson-Falk, C. M. Marcus, L. N. Pfeiffer, and K. W. West, “Distinct signatures for coulomb blockade and Aharonov-Bohm interference in electronic Fabry-Pérot interferometers,” Phys. Rev. B 79, 241304 (2009).
[Crossref]

Williamson, J. G.

B. J. van Wees, L. P. Kouwenhoven, C. J. P. M. Harmans, J. G. Williamson, C. E. Timmering, M. E. I. Broekaart, C. T. Foxon, and J. J. Harris, “Observation of zero-dimensional states in a one-dimensional electron interferometer,” Phys. Rev. Lett. 62, 2523–2526 (1989).
[Crossref] [PubMed]

Windeler, R. S.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref] [PubMed]

Wu, L.

Y.-L. Yang, Z.-H. Ding, K. Wang, L. Wu, and L. Wu, “Full-field optical coherence tomography by achromatic phase shifting with a rotating half-wave plat,” J. Opt. 12, 035301 (2010).
[Crossref]

Y.-L. Yang, Z.-H. Ding, K. Wang, L. Wu, and L. Wu, “Full-field optical coherence tomography by achromatic phase shifting with a rotating half-wave plat,” J. Opt. 12, 035301 (2010).
[Crossref]

Yang, Y.-L.

Y.-L. Yang, Z.-H. Ding, K. Wang, L. Wu, and L. Wu, “Full-field optical coherence tomography by achromatic phase shifting with a rotating half-wave plat,” J. Opt. 12, 035301 (2010).
[Crossref]

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford University Press, 1997).

Ye, J.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
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L. Huang, X. Chen, H. Muhlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
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Zhang, S.

L. Huang, X. Chen, H. Muhlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
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Y. Zhang, D. T. McClure, E. M. Levenson-Falk, C. M. Marcus, L. N. Pfeiffer, and K. W. West, “Distinct signatures for coulomb blockade and Aharonov-Bohm interference in electronic Fabry-Pérot interferometers,” Phys. Rev. B 79, 241304 (2009).
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Y.-L. Yang, Z.-H. Ding, K. Wang, L. Wu, and L. Wu, “Full-field optical coherence tomography by achromatic phase shifting with a rotating half-wave plat,” J. Opt. 12, 035301 (2010).
[Crossref]

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L. Huang, X. Chen, H. Muhlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref] [PubMed]

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Y. Zhang, D. T. McClure, E. M. Levenson-Falk, C. M. Marcus, L. N. Pfeiffer, and K. W. West, “Distinct signatures for coulomb blockade and Aharonov-Bohm interference in electronic Fabry-Pérot interferometers,” Phys. Rev. B 79, 241304 (2009).
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A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford University Press, 1997).

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Figures (5)

Fig. 1
Fig. 1 Concept of a geometrical phase shifter (GPS) consisting of fixed quarter-wave plates (QWPs) and a rotating half-wave plate (HWP) in a Fabry-Pérot cavity confined by two mirrors. During multi-reflection in the cavity, a light experiences a geometric phase of 2θ with every pass through the GPS. The spectral behavior of the separated axis modes in the free spectral range (FSR) resembles that of the spiral thread on a rotating drill.
Fig. 2
Fig. 2 Type-I configuration of a geometric phase shifter (GPS) in a cavity formed by two mirrors (Ml and M2). The GPS consists of two quarter-wave plates (QWP1, QWP2) and a half-wave plate (HWP). The fast axes of QWP1 and QWP2 are oriented along the x and y axes, respectively. The HWP rotates through an angle θ from the x-axis. An incident light is linearly polarized in the direction of (x, y) = (1, 1). d is the optical-path length between the mirrors (excluding the phase retardation imposed by the phase plates)
Fig. 3
Fig. 3 Type-II configuration of a GPS in a cavity. The GPS consists of two quarter-wave plates labeled QWP1 and QWP2. The fast axis of QWP1 is oriented along the x axis, while QWP2 rotates through angle θ from the x-axis. The incident light is polarized identically to its polarization in the Type-I configuration illustrated in Fig. 2. The polarization of the transmitted light depends on the rotation angle θ, as depicted in Eq. (7)
Fig. 4
Fig. 4 Two-dimensional interferograms obtained by rotating the phase plate and scanning the piezo-actuator for (a, upper panel) type I and (b, upper panel) type II. The dashed lines depict the expected isophase lines. Typical interferograms for the phase-plate rotation are extracted on the lower panels.
Fig. 5
Fig. 5 Two-dimensional mapping of the axis modes with scanning of the cavity length and a rotation angle that depends on the phase retardation of the rotating phase plate in the type-I (a) and -II (b) configurations. Lighter-color curves indicate relatively low peak intensities of the modes.

Equations (7)

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E 0 = Q [ R 1 ( θ ) H R ( θ ) ] Q + E 0 = 1 2 ( 1 1 ) exp 2 i θ ,
E 1 = M Q + [ R 1 ( θ ) H R ( θ ) ] Q M E 0 r 2 exp 4 i θ E 0 ,
E T = ( 1 R ) e i ( k d + 2 θ ) n = 0 [ R e 2 i ( k d + 2 θ ) ] n 1 2 ( 1 1 ) = ( 1 R ) exp i ( k d + 2 θ ) 1 R exp i ( 2 k d + 4 θ ) 1 2 ( 1 1 ) ,
T = | E T | 2 = [ 1 + 4 R ( 1 R ) 2 sin 2 δ 2 ] 1 ,
E 0 = [ R 1 ( θ ) Q + R ( θ ) ] Q + E 0 = ( cos θ π 4 sin θ π 4 ) exp i θ .
E 1 = M Q + [ R 1 ( θ ) Q + R ( θ ) ] M E 0 = r 2 exp 2 i θ E 0 .
E T = ( 1 R ) e i ( k d + θ ) n = 0 [ R e 2 i ( k d + θ ) ] n ( cos θ π 4 sin θ π 4 ) = ( 1 R ) exp i ( k d + θ ) 1 R exp i ( 2 k d + 2 θ ) ( cos θ π 4 sin θ π 4 )

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