Non-reciprocity without magneto-optics: a tutorial Shanhui Fan
Ginzton Laboratory and Department of Electrical Engineering
Stanford University
Slide 2
Large-scale on-chip network Towards large-scale on-chip
information network Large-scale communication network
Slide 3
Optical isolator: a one-way street for light Single-mode signal
Any backreflection
Slide 4
Silicon Photonics Platform The main question of the tutorial
How does one achieve optical isolation on a standard optoelectronic
platform?
Slide 5
Outline of my talk The basics of reciprocity. Options for
on-chip non-reciprocity. Nonlinear optical isolator: fundamental
limitation. Dynamic modulation: effective gauge potential for
photons.
Slide 6
Outline of my talk The basics of reciprocity. Options for
on-chip non-reciprocity. Nonlinear optical isolator: fundamental
limitation. Dynamic modulation: effective gauge potential for
photons.
Slide 7
What do you need isolator for? Device Output signal Parasitic
reflection Device Isolator Output signal Parasitic reflection
Parasitic reflection is assumed to be unknown in system design.
Therefore isolator needs to be non-reciprocal device.
Slide 8
Lorentz Reciprocity Theorem H. Lorentz (1896); H. A. Haus,
Waves and Fields in Optoelectronics (1984) The theorem applies to
any electromagnetic system that is: linear, time-independent, has a
symmetric permittivity and permeability tensor, including medium
that has gain or loss. It applies independent of structural
complexity, e.g. Dielectric (Si, SiO 2, GaAs, Ge, .) Metal (Al,
Cu,) If the optical properties are entirely described by
Slide 9
Reciprocal system has a symmetric scattering matrix
Input-output is defined by the scattering matrix (S-matrix) a1a1
b1b1 Device a2a2 b2b2 a3a3 b3b3 Reciprocity theorem implies that
e.g. Reciprocity relates two pathways that are related by
time-reversal. Reciprocity therefore is closely related to
time-reversal symmetry.
Slide 10
5cm Conventional optical isolators Images from www.ofr.com Use
magneto-optical materials
Slide 11
Magneto-optical effect is non-reciprocal M e. g. YIG z
Dielectric tensor Asymmetric Non-reciprocal Hermitian Energy
conserving
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Faraday Rotation M M E k
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Faraday Rotation Has An Asymetric S-matrix M M E k Mode 1Mode
2
Slide 14
Isolator Based on Faraday Rotation Polarizer at 0 o Polarizer
at 45 o M M E k X High transmission in the forward direction.
Suppress backward propagation for every mode of reflection.
Suppress backward propagation independent of the existence of
forward signal SMF
Slide 15
Silicon Photonics Platform The main question of the tutorial
How does one achieve optical isolation on a standard optoelectronic
platform? As a matter of principle, one can not construct a
passive, linear, silicon isolator.
Slide 16
Reciprocal system has a symmetric scattering matrix
Input-output relation is defined by the scattering matrix a1a1 b1b1
Device a2a2 b2b2 a3a3 b3b3 Reciprocity theorem implies that
e.g.
Slide 17
Isolator needs to suppress reflection from every mode High
transmission, left to right Necessarily implies that one can create
a input mode profile to achieve high transmission from right to
left For reciprocal structure Therefore, one cannot construct an
isolator out of reciprocal structure. Device
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But I see asymmetry in my experiment and simulations! High
transmission, left to rightLow transmission, right to left Is this
an isolator? Silicon Unidirectionality, Optical Diode, ..
Slide 19
Nonreciprocal light propagation in an aperiodic silicon
photonic circuits? S. Fan et al, Science 335, 38 (2012) [Comment on
Feng et al, Science 333, 729, 2011] Near perfect transmission, left
to right Near perfect reflection, right to left V. Liu, D. A. B.
Miller and S. Fan, Optics Express 20, 28318 (2012).
Slide 20
Mode-to-mode transmission coefficient always symmetric S. Fan
et al, Science 335, 38 (2012) [Comment on Feng et al, Science 333,
729, 2011] Nonreciprocal light propagation in an aperiodic silicon
photonic circuits? V. Liu, D. A. B. Miller and S. Fan, Optics
Express 20, 28318 (2012)
Slide 21
How does one really test non-reciprocity? D. Jalas et al,
Nature Photonics 7, 579 (2013). Device High transmission, left to
rightLow transmission, right to left Send time-reversed output back
into the device Detect asymmetry in transmission between two
modes.
Slide 22
How does one really test non-reciprocity? D. Jalas et al,
Nature Photonics 7, 579 (2013). Device High transmission, left to
rightLow transmission, right to left which is how isolator in
practice will be used in an on-chip setting Single-mode waveguide
Test transmission asymmetry between two single-mode waveguides
Slide 23
Outline of my talk The basics of reciprocity. Options for
on-chip non-reciprocity. Nonlinear optical isolator: fundamental
limitation. Dynamic modulation: effective gauge potential for
photons.
Slide 24
Only ways to achieve on-chip optical isolation Lorentz
reciprocity theorem applies to any electromagnetic system that is:
linear, time-independent, has a symmetric permittivity and
permeability tensor. Therefore, to create optical isolation
on-chip, the only options are: On-chip integration of
magneto-optical materials. Exploit nonlinearity. Consider
time-dependent systems. (e.g. systems where the refractive index
varies as a function of time.)
Slide 25
On-chip integration of magneto-optical materials Silicon
Photonics Platform Yittrium Iron Garnet
Slide 26
Combination of Si and Magneto-Optical Material Y. Shoji, T.
Mitzumoto, R. M. Osgood et al, Applied Physics Letters 92, 071117
(2008). For related experimental developments, See L. Bi, L. C.
Kimering and C. A. Ross et al, Nature Photonics 5, 758 (2011) M.
Tien, T. Mizumoto, and J. E. Bowers et al, Optics Express 19, 11740
(2011).
Slide 27
Only ways to achieve on-chip optical isolation Lorentz
reciprocity theorem applies to any electromagnetic system that is:
linear, time-independent, has a symmetric permittivity and
permeability tensor. Therefore, to create optical isolation
on-chip, the only options are: On-chip integration of
magneto-optical materials. Exploit nonlinearity. Consider
time-dependent systems. (e.g. systems where the refractive index
varies as a function of time.)
Slide 28
Outline of my talk The basics of reciprocity. Options for
on-chip non-reciprocity. Nonlinear optical isolator: fundamental
limitation. Dynamic modulation: effective gauge potential for
photons.
Slide 29
An optical isolator using intensity dependent index Input power
85 nW Input power 85 W L. Fan, A. Weiner and M. Qi, et al, Science
335, 447 (2012).
Slide 30
The idea of a nonlinear isolator: starting point Single-mode
waveguide Start with a linear, reciprocal, spatially asymmetric
structure Single-mode waveguide Weak transmission in the linear
regime Transmission completely reciprocal
Slide 31
Asymmetric distribution of the field Single-mode waveguide
While the transmission is reciprocal, the field distribution in the
structure depends on incident light direction Single-mode waveguide
Weak transmission in the linear regime
Slide 32
Nonlinear structure breaks reciprocity Single-mode waveguide
Forward and backward light now sees a different dielectric
structure Single-mode waveguide High transmission in the forward
direction Low transmission in the backward direction Kerr
nonlinearity So there is a contrast in the forward and backward
direction! Kerr nonlinearity
Slide 33
Nonlinear optical isolators in fact do not isolate Forward
signal When forward signal is present, there is no isolation High
transmission for noise in the forward direction High transmission
for noise in the backward direction Kerr nonlinearity Y. Shi, Z. Yu
and S. Fan, Nature Photonics 9, 388 (2015).
Slide 34
Only ways to achieve on-chip optical isolation Lorentz
reciprocity theorem applies to any electromagnetic system that is:
linear, time-independent, has a symmetric permittivity and
permeability tensor. Therefore, to create optical isolation
on-chip, the only options are: On-chip integration of
magneto-optical materials. Exploit nonlinearity. Consider
time-dependent systems. (e.g. systems where the refractive index
varies as a function of time.)
Slide 35
Outline of my talk The basics of reciprocity. Options for
on-chip non-reciprocity. Nonlinear optical isolator: fundamental
limitation. Dynamic modulation: effective gauge potential for
photons.
Slide 36
Time-reversal symmetry and reciprocity breaking in time-
dependent systems Break time-reversal symmetry and reciprocity as
long as:
Slide 37
Dynamic optical isolators Z. Yu and S. Fan, Nature Photonics,
vol. 3, pp. 91-94 (2009); H. Lira, Z. Yu, S. Fan and M. Lipson,
Physical Review Letters 109, 033901 (2012). See Also: G. Shvets,
Physics 5, 78 (2012).
Slide 38
Static magnetic field breaks time-reversal symmetry for
electrons Can we create an effective magnetic field for photons? B
B
Slide 39
gauge potential for photons K. Fang, Z. Yu and S. Fan, Physical
Review Letters 108, 153901 (2012). Si Metal electrode: applying a
time-dependent voltage
Slide 40
Magnetic field for electrons in quantum mechanics Electron
couples to the vector gauge potential
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1 2 Propagation phase Gauge potential results in a
direction-dependent phase 1 2
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Direct transition Air Silicon z Uniform modulation along
z-direction
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Oscillation between two states
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Direct transition independent of the modulation phase
Slide 45
Modulation phase provides a gauge transformation of the photon
wavefunction Gauge potential that couples to the photon
Slide 46
Downward and upper-ward transition acquires a phase
difference
Slide 47
A Photonic Aharonov-Bohm Interferometer Clockwise roundtrip has
a phase: Counter-clockwise roundtrip has a phase: Phase difference
between two time-reversal related trajectories due to a gauge
degree of freedom
Slide 48
K. Fang, Z. Yu and S. Fan, Physical Review Letters 108, 153901
(2012). A Photonic Aharonov-Bohm Interferometer as an Optical
Isolator silicon air
Slide 49
Experimental demonstration of photonic AB effect
FilterMixerFilterMixerFilter Phase shifter Mixer provides the
modulation K. Fang, Z. Yu, and S. Fan, Phys. Rev. B Rapid
Communications 87, 060301 (2013).
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The Scheme Filter Mixer Phase shifter
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FilterMixerFilterMixerFilter Phase shifter Non-reciprocal
oscillation as a function of modulation phase
Slide 52
AB Interferometer from Photon-Phonon Interaction E. Li, B.
Eggleton, K. Fang and S. Fan, Nature Communications 5, 3225 (2014).
Local oscillator (50MHz) AOM (Acoustic- Optic Modulator) He-Ne
Laser (633nm)
Slide 53
AB interferometer on a silicon platform L. Tzuang, K. Fang, P.
Nussenzveig, S. Fan, and M. Lipson, Nature Photonics 8, 701
(2014).
Slide 54
Electron on a lattice Electron hopping on a tight-binding
lattice Single unit cell Magnetic field manifests in terms of a
non-reciprocal round-trip phase as an electron hops along the edge
of a unit cell.
Slide 55
Two sub-lattices of resonators Coupling constant between
nearest neighbor resonators dynamically modulated. Photons on a
dynamic lattice K. Fang, Z. Yu and S. Fan, Nature Photonics 6, 782
(2012). See also M. Hafezi et al, Nature Physics 7, 907 (2011); M.
C. Rechtsman et al, Nature 496, 196 (2013).
Slide 56
Constructing effective magnetic field for photons Lorentz force
for photons Analogue of Integer quantum hall effects for photons.
K. Fang, Z. Yu and S. Fan, Nature Photonics 6, 782 (2012).
Slide 57
Simple but unusual gauge potential configurations n1n1 n1n1
A
Slide 58
The effect of a constant gauge potential For electrons In
general, a constant gauge potential shifts the wavevector
Slide 59
A constant gauge potential shifts the constant frequency
contour n1n1 n1n1 A A
Slide 60
Gauge field induced negative refraction n1n1 n1n1 A K. Fang, S.
Fan, Physical Review Letters 111, 203901 (2013). A
Slide 61
Gauge field induced total internal reflection n1n1 n1n1 A K.
Fang, S. Fan, Physical Review Letters 111, 203901 (2013). A
Slide 62
n1n1 n1n1 A A single-interface four-port circulator K. Fang, S.
Fan, Physical Review Letters 111, 203901 (2013). Both regions have
zero effect B-field. A B-field sheet at the interface.
Slide 63
A novel one-way waveguide n1n1 n1n1 n1n1 A Waveguide mode
exists only in the positive k y region Light cone of the cladding
Light cone of the core Q. Lin and S. Fan, Physical Review X 4,
031031 (2014).
Slide 64
Summary To create optical isolation on a silicon platform,
Isolators need to suppress all reflections. Therefore, there is no
passive, linear, silicon isolator. The only options for optical
isolations on silicon chip are: Integration of magneto-optical
materials on chip. Significant material science challenges are
being overcome. Nonlinear isolators. Innovative concepts. But does
not provide complete optical isolation. Dynamic isolators from
refractive index modulation. Can completely reproduce standard
magneto-optical isolator functionality. Does require energy input.
There is exciting fundamental physics in on-chip non-reciprocal
photonics.