Non-reciprocal phase shift induced by an effective magnetic flux for light

Journal name:
Nature Photonics
Volume:
8,
Pages:
701–705
Year published:
DOI:
doi:10.1038/nphoton.2014.177
Received
Accepted
Published online

Photons are neutral particles that do not interact directly with a magnetic field. However, recent theoretical work1, 2 has shown that an effective magnetic field for photons can exist if the phase of light changes with its direction of propagation. This direction-dependent phase indicates the presence of an effective magnetic field, as shown experimentally for electrons in the Aharonov–Bohm experiment. Here, we replicate this experiment using photons. To create this effective magnetic field we construct an on-chip silicon-based Ramsey-type interferometer3, 4, 5, 6, 7. This interferometer has been traditionally used to probe the phase of atomic states and here we apply it to probe the phase of photonic states. We experimentally observe an effective magnetic flux between 0 and 2π corresponding to a non-reciprocal 2π phase shift with an interferometer length of 8.35 mm and an interference-fringe extinction ratio of 2.4 dB. This non-reciprocal phase is comparable to those of common monolithically integrated magneto-optical materials.

At a glance

Figures

  1. Effective magnetic field for light using a Ramsey-type interferometer.
    Figure 1: Effective magnetic field for light using a Ramsey-type interferometer.

    a, Atomic Ramsey interferometer. b, Photonic Ramsey interferometer. c, Photonic Ramsey interferometer where the two modulators have different phases φL and φR.

  2. Ramsey-type interferometer design and fabrication.
    Figure 2: Ramsey-type interferometer design and fabrication.

    a,b, Simulated mode profiles for both the even mode (a) and the odd mode (b), which coexist in a silicon coupled waveguide structure. c, Cross-sectional view of the coupled waveguides. A set of pn and np diodes is doped to modulate the refractive index. d, Top view of carrier density (N) distribution in the coupled waveguide along the x-axis (slab omitted). The width of the depletion region (grey) changes over time as a sinusoidal signal is applied to the diodes. The applied sinusoidal voltage V is shown in red. e, A photonic Ramsey interferometer implemented as a silicon coupled-waveguide structure. Bottom: microscope image and simulated light transmission of a pair of multimode interference devices located at the outer ends of the interferometer.

  3. Effective magnetic field experiment.
    Figure 3: Effective magnetic field experiment.

    a, Examples of measured (circles, normalized to the maximum curve fitted value) and theoretically fitted (solid lines) optical transmission for light travelling from left to right (L → R, blue) and right to left (R → L, red) for devices with different Lf, as a function of the phase difference between the two signals applied to the modulators (Δφ = φL − φR). Wavelength = 1,570 nm; applied radiofrequency power = 24 dBm. Error bars represent one standard deviation from the measurement mean resulting from optical alignment fluctuations. b, Measured (circles) and theoretical (solid) difference Δφ when the transmission is maximum for L → R (ΔφL→R) and R → L (ΔφR→L) versus Lf. The grey region indicates the error of the theoretical curve when a 5% process variation is introduced. c, Measured and theoretically fitted optical transmission for light travelling from left to right (blue) and right to left (red) for Lf = 350 µm with increased population in the odd mode Podd (shown as percentages) achieved by increasing the applied radiofrequency power.

  4. Wavelength dependence of the interference effect for the photonic Ramsey-type interferometer.
    Figure 4: Wavelength dependence of the interference effect for the photonic Ramsey-type interferometer.

    a, Measured (grey circles, normalized to the maximum curve fitted value) and theoretically fitted (solid lines) optical transmission of light travelling from left to right (L → R) and from right to left (R → L) versus Δφ for different laser wavelengths (1,560, 1,565, 1,570 and 1,575 nm) with Lf = 350 µm. b, Theoretical (dashed lines) and measured (circles) phase of the fringes for L → R and R → L versus wavelength.

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Affiliations

  1. School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA

    • Lawrence D. Tzuang,
    • Paulo Nussenzveig &
    • Michal Lipson
  2. Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA

    • Kejie Fang &
    • Shanhui Fan
  3. Thomas J. Watson, Sr, Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA

    • Kejie Fang
  4. Instituto de Física, Universidade de São Paulo, PO Box 66318, 05315-970 São Paulo, Brazil

    • Paulo Nussenzveig
  5. Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, New York 14853, USA

    • Michal Lipson

Contributions

L.D.T. performed the experiment. L.D.T. and K.F. designed the experiment and analysed the data. P.N., S.F. and M.L. supervised the project. L.D.T and M.L. prepared the manuscript. K.F., P.N. and S.F. edited the manuscript.

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The authors declare no competing financial interests.

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