Article | Published:

Realizing effective magnetic field for photons by controlling the phase of dynamic modulation

Nature Photonics volume 6, pages 782787 (2012) | Download Citation

Subjects

Abstract

The goal to achieve arbitrary control of photon flow has motivated much of the recent research on photonic crystals and metamaterials. As a new mechanism for controlling photon flow, we introduce a scheme that generates an effective magnetic field for photons. We consider a resonator lattice in which the coupling constants between the resonators are harmonically modulated in time. With appropriate choice of the spatial distribution of the modulation phases, an effective magnetic field for photons can be created, leading to a Lorentz force for photons and the emergence of topologically protected one-way photon edge states that are robust against disorders—without the use of magneto-optical effects.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    , & New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980).

  2. 2.

    , & Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982).

  3. 3.

    Quantized Hall conductivity in two dimensions. Phys. Rev. B 23, 5632–5633 (1981).

  4. 4.

    Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential. Phys. Rev. B 25, 2185–2190 (1982).

  5. 5.

    , , & Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982).

  6. 6.

    Chern number and edge states in the integer quantum Hall effect. Phys. Rev. Lett. 71, 3697–3700 (1993).

  7. 7.

    Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett. 58, 2059–2062 (1987).

  8. 8.

    Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58, 2486–2489 (1987).

  9. 9.

    , & Photonic crystals: putting a new twist on light. Nature 386, 143–149 (1997).

  10. 10.

    Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000).

  11. 11.

    , & Metamaterials and negative refractive index. Science 305, 788–792 (2004).

  12. 12.

    Optical negative-index metamaterials. Nature Photon. 1, 41–48 (2007).

  13. 13.

    , & Hall effect of light. Phys. Rev. Lett. 93, 083901 (2004).

  14. 14.

    & Analogs of quantum-Hall-effect edge states in photonic crystals. Phys. Rev. A 78, 033834 (2008).

  15. 15.

    & Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008).

  16. 16.

    , , & Reflection-free one-way edge modes in a gyromagnetic photonic crystal. Phys. Rev. Lett. 100, 013905 (2008).

  17. 17.

    , , & Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).

  18. 18.

    , , & One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal. Phys. Rev. Lett. 100, 023902 (2008).

  19. 19.

    , , & Robust optical delay lines with topological protection. Nature Phys. 7, 907–912 (2011).

  20. 20.

    & Artificial gauge field for photons in coupled cavity arrays. Phys. Rev. A 84, 043804 (2011).

  21. 21.

    Graphene and the quantum spin Hall effect. Int. J. Mod. Phys. B 21, 1155–1164 (2007).

  22. 22.

    et al. Observation of backscattering-immune chiral electromagnetic modes without time reversal breaking. Phys. Rev. Lett. 107, 023901 (2011).

  23. 23.

    , & Photonic Aharonov–Bohm effect based on dynamic modulation. Phys. Rev. Lett. 108, 153901 (2012).

  24. 24.

    , , & Interband transitions in photonic crystals. Phys. Rev. B 59, 1551–1554 (1999).

  25. 25.

    , , , & Inducing photonic transitions between discrete modes in a silicon optical microcavity. Phys. Rev. Lett. 100, 033904 (2008).

  26. 26.

    & Complete optical isolation created by indirect interband photonic transitions. Nature Photon. 3, 91–94 (2009).

  27. 27.

    The effect of a magnetic field on electrons in a periodic potential. Phys. Rev. 84, 814–817 (1951).

  28. 28.

    Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields. Phys. Rev. B 14, 2239–2249 (1976).

  29. 29.

    Solution of the Schrödinger equation with a Hamiltonian periodic in time. Phys. Rev. 138, B979–B987 (1965).

  30. 30.

    Steady states and quasi energies of a quantum-mechanical system in an oscillating field. Phys. Rev. A 7, 2203–2213 (1973).

  31. 31.

    , , & Micrometre-scale silicon electro-optic modulator. Nature 435, 325–327 (2005).

  32. 32.

    et al. Strong quantum-confined Stark effect in germanium quantum-well structures on silicon. Nature 437, 1334–1336 (2005).

  33. 33.

    , & Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency. Phys. Rev. B 54, 7837–7842 (1996).

  34. 34.

    et al. High-Q nanocavity with a 2-ns photon lifetime. Opt. Express 15, 17206–17213 (2007).

  35. 35.

    , & Large-scale arrays of ultrahigh-Q coupled nanocavities. Nature Photon. 2, 741–747 (2008).

  36. 36.

    , , & Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap. Phys. Rev. B 64, 075313 (2001).

  37. 37.

    & Manipulation of photons at the surface of three-dimensional photonic crystals. Nature 460, 367–370 (2009).

  38. 38.

    , , & Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip. Phys. Rev. Lett. 109, 033901 (2012).

  39. 39.

    in Microwave Engineering Ch. 12, 618 (Wiley, 2005).

  40. 40.

    , , & Time-reversal-symmetry breaking in circuit-QED-based photon lattices. Phys. Rev. A 82, 043811 (2010).

  41. 41.

    , , & Low-disorder microwave cavity lattices for quantum simulation with photons. Phys. Rev. A 86, 023837 (2012).

  42. 42.

    , & On-chip quantum simulation with superconducting circuits. Nature Phys. 8, 292–299 (2012).

  43. 43.

    & Optomechanically induced non-reciprocity in microring resonators. Opt. Express 20, 7672–7684 (2012).

Download references

Acknowledgements

This work was supported in part by the US Air Force Office of Scientific Research (grant no. FA9550-09-1-0704) and the US National Science Foundation (grant no. ECCS-1201914).

Author information

Affiliations

  1. Department of Physics, Stanford University, Stanford, California 94305, USA

    • Kejie Fang
  2. Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA

    • Zongfu Yu
    •  & Shanhui Fan

Authors

  1. Search for Kejie Fang in:

  2. Search for Zongfu Yu in:

  3. Search for Shanhui Fan in:

Contributions

K.F. conceived the mechanism for achieving an effective magnetic field and performed the calculations. All authors contributed to the design of the study, discussion of the results and writing of the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Shanhui Fan.

Supplementary information

PDF files

  1. 1.

    Supplementary information

    Supplementary information

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nphoton.2012.236

Further reading

Newsletter Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing