of 5
Metawaveguide for Asymmetric Interferometric Light-Light Switching
Han Zhao,
1
William S. Fegadolli,
2
Jiakai Yu,
1
Zhifeng Zhang,
1
Li Ge,
3,4
Axel Scherer,
2
and Liang Feng
1
,*
1
Department of Electrical Engineering, The State University of New York at Buffalo, Buffalo, New York 14260, USA
2
Department of Physics and Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California 91125, USA
3
Department of Engineering Science and Physics, College of Staten Island, CUNY, Staten Island, New York 10314, USA
4
The Graduate Center, CUNY, New York, New York 10016, USA
(Received 4 May 2016; published 31 October 2016)
Light-light switching typically requires strong nonlinearity where intense laser fields route and direct
data flows of weak power, leading to a high power consumption that limits its practical use. Here we report
an experimental demonstration of a metawaveguide that operates exactly in the opposite way in a linear
regime, where an intense laser field is interferometrically manipulated on demand by a weak control beam
with a modulation extinction ratio up to approximately 60 dB. This asymmetric control results from
operating near an exceptional point of the scattering matrix, which gives rise to intrinsic asymmetric
reflections of the metawaveguide through delicate interplay between index and absorption. The designed
metawaveguide promises low-power interferometric light-light switching for the next generation of optical
devices and networks.
DOI:
10.1103/PhysRevLett.117.193901
Effective light-light switching promises optical informa-
tion processing, which has been a long-standing driving
force for high-speed and energy-efficient optical networks.
Strong optical modulations are initiated in nonlinear
optical media by intense laser fields to enable switching
of a weak signal, for example, intensity modulation of light
by light has been demonstrated based on the all-optical
Kerr effect
[1
6]
. Nevertheless, the high power require-
ment for the intense control or pump light becomes a
significant barrier for practical applications. While cavity
quantum electrodynamics displays nonlinear optical effects
on a few-photon level
[7,8]
, its application as a robust
optical element operating in the classical regime remains
still unclear. On the other hand, a recent pioneering
investigation of exploiting photonics absorption offered
a unique linear scheme to efficiently control light by
light utilizing mutually coherent interaction of light
beams and absorbing matters
[9,10]
, by which coherent
perfect absorption (CPA) was demonstrated
[11
14]
.
While this linear strategy reduces the power requirement,
the control beam still has a similar amount of power as the
actual source signal in these previous works, due to the
rather symmetric optical scatterings in the optical
implementations.
The recent emergence of non-Hermitian photonic meta-
materials offers a new paradigm to explore nanophotonics
and metamaterials research in the entire complex dielectric
permittivity plane, based on parity-time (PT) symmetry
[15
20]
. Attractive physical phenomena including phase
transitions and exceptional points are emulated with
photonics, consequently, leading to novel effective
manipulation of cavity lasing modes
[21
26]
and unidi-
rectional light transport
[27
32]
. Here, we will show a
unique metawaveguide of potential for on-demand control
of interferometric light-light switching can be realized
through non-Hermitian metamaterial explorations.
An intriguing characteristic of non-Hermitian photonic
metamaterials is their intrinsic asymmetry near an excep-
tional point. For PT symmetric systems, in particular, these
exceptional points can either represent asymmetric trans-
mission resonances
[27
30]
or a violation of energy con-
servation in the scattering eigenstates, depending on the
formulation of the scattering matrix
[30]
. Here, we delicately
design the interplay between index and absorption to con-
struct a metawaveguide by exploring the former type of
exceptional points. An asymmetry in reflection arises near
the exceptional point and is further utilized to facilitate
asymmetric light-light switching in a linear regime, where a
weak control beam can be interferometrically exploited to
controlanintenselaser signal, resulting intwo distinct modes
of operation, i.e., CPA or strong scattering. The experimental
results show the metawaveguide enables low-power inter-
ferometric weak-intense light-light control of an extinction
ratio up to approximately 60 dB, promising highly efficient
integrated photonic switches for data guiding, routing, and
switching around optical communication networks.
The optical transfer matrix describes the related scatter-
ing eigenstates of an optical system. For a two-port system
of length
L
, a transfer matrix
M
links the scattering
eigenstates of both ports as

A
ð
L
Þ
B
ð
L
Þ

¼

M
11
M
12
M
21
M
22

A
ð
0
Þ
B
ð
0
Þ

;
ð
1
Þ
where
A
ð
0
Þ
and
B
ð
L
Þ
are inputs in the left and right ports,
while
B
ð
0
Þ
and
A
ð
L
Þ
denote outputs in left and right ports,
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=
16
=
117(19)
=
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© 2016 American Physical Society
respectively. To facilitate interference-enhanced absorption
for switching, the CPA condition
M
11
¼
0
is desired, which
corresponds to input light being completely absorbed
[10,11,21]
. The goal we set to achieve, i.e., using a weak
control beam
B
ð
L
Þ
to bring a strong signal beam
A
ð
0
Þ
into
CPA, is satisfied when
j
M
21
j
1
, which corresponds to a
strongly
asymmetric reflection
, i.e.,
j
r
L
j
j
r
R
j
[33]
. This
condition requires a non-Hermitian system since reciproc-
ity of light propagation in a Hermitian system implies
j
r
L
j¼j
r
R
j
. Here to create an asymmetry in light reflection,
we take the approach inspired by asymmetric transmission
resonances
[27
30]
in a PT symmetric metawaveguide.
More specifically, we manipulate the spatial index-
absorption modulation of the metawaveguide in the vicinity
of the exceptional point, i.e., the quasi-PT symmetry phase
transition point, where
r
L
¼
0
j
r
R
j
, satisfying the
requirement of asymmetric reflection mentioned above.
Figure
1(a)
shows the schematic on a silicon-on-insulator
(SOI) platform. The metawaveguide is designed to be
800 nm wide and 220 nm thick, embedded in a background
of SiO
2
, supporting a fundamental mode with an effective
wave number of
k
1
¼
2
.
69
k
0
at the wavelength of 1550 nm,
where
k
0
is the wave number in free space. The non-
Hermitian optical potential is enforced along the length of
the metawaveguide with the index-absorption engineering,
and reads
Δ
ε
¼
Δ
ε
0
½
cos
ð
qz
Þþ
i
δ
sin
ð
qz
Þ
;
ð
2
Þ
where
Δ
ε
0
¼
0
.
317
denotes the modulation amplitude,
δ
is
larger than 1 (
δ
¼
1
corresponds to the exceptional point
[27
29]
) to have the device operating in the symmetry
breaking phase, and
q
¼
2
k
1
, and the modulation regions
are located at
4
n
π
=q
z
4
n
π
=q
þ
π
=q
(
n
¼
1
;
2
;
3
...
).
Because of the coupling between forward and backward
propagating light by the modulated dielectric constant, the
metawaveguide supports two degenerate Bragg modes of
different absorption coefficients. To maximize the extinc-
tion ratio for switching in the device, the length of the
device is designed to be approximately
21
.
9
μ
m corre-
sponding to 38 periods
[33]
, such that one degenerate mode
satisfies the CPA condition, i.e.,
M
11
¼
0
, where coherent
light inputs from the left and right ports are perfectly
absorbed with zero output scatterings [see Fig.
1(b)
,
upper panel]. The other degenerate mode has much less
absorption and thus generates strong output scatterings [see
Fig.
1(b)
, lower panel]. Assuming the incident phase of the
signal remains 0, efficient switching between these two
FIG. 1. Asymmetric interferometric light-light switching:
(a) Schematic of a metawaveguide with asymmetric reflection,
i.e.,
j
r
L
j
j
r
R
j
. The intrinsic reflection asymmetry in the vicinity
of the quasi-PT exceptional point facilitates asymmetric inter-
ferometric light-light switching of a strong source signal (forward
input) by a weak control field (backward input). (b) Electric field
distributions of interferometrically controlled asymmetric light-
light switching, where the power ratio of the weak control to the
strong source signal is set to
1
3
. If the incidenct phase of the
control is
φ
¼
π
=
2
(upper panel), the CPA mode is achieved with
no scattering, validated by the vanishing of interference patterns
between inputs and outputs in both ports outside the modulation
region, whereas if the incident phase of the control is
φ
¼
π
=
2
(lower panel), the degenerated mode of less absorption is
demonstrated, leading to strong output scatterings in both ports
that can be seen by the interference patterns outside the
modulation region.
FIG. 2. Metawaveguide for asymmetric interferometric
light-light switching: (a) Design of the non-Hermitian metawa-
veguide to create a spatial modulation equivalent to that in
Eq.
(2)
: The real index modulations of are shifted
2
π
=q
along the
length of the waveguide and emulated using sidewall modula-
tions with a transverse modulation depth cosine-varying from
þ
71
to
48
.
5
nm; the imaginary absorption modulations remain
unchanged at their original locations, mimicked using bilayer
sinusoidal shaped combo structures of 9.8 nm chrome
ð
Cr
Þ
=
8
nm
germanium (Ge) deposited on top of the Si waveguide. (b) SEM
picture of the device consisting of 38 periods for strong signal
light switching by a weak control. (c) Zoom-in picture of the
metawaveguide. The profile of the waveguide sidewall along with
Ge
=
Cr combo structures on top, respectively, realizes the
designed real and imaginary modulation.
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modes of operation can be achieved by tuning the incident
phase of the control field from
π
=
2
to
π
=
2
, with an
extremely remarkable extinction ratio.
The interferometric light-light switching is facilitated by
the asymmetric reflection of the designed metawaveguide
attributed to the exceptional point. However, operating too
close to the exceptional point leads to a low transmission
efficiency
[33]
and is also challenging in fabrication. Here,
a relatively small value of
δ
¼
2
was chosen to obtain a
reasonable transmission efficiency and ensure that fabri-
cation imperfections do not make the system deviate
strongly from the designed CPA condition. We find that
the intensity ratio
ξ
is given by
ð
δ
þ
1
Þ
=
ð
δ
1
Þ
, leading to
ξ
of
3
1
between the strong signal beam and the weak control
beam
[33]
, which is in contrast to the previous approaches
of controlling light with light using both linear and non-
linear strategies
[1
14]
.
To demonstrate the metawaveguide with the desired
intrinsic scattering asymmetry, an equivalent guided-mode
modulation has been designed to realize the virtual non-
Hermitian function modulation with in-phase separation of
real index and imaginary absorption modulations, as
illustrated in Fig.
2(a)
. The equivalence to the original
quasi-PT modulation was validated by the consistent mode
effective indices of guided light for both the real index and
imaginary absorption modulations, respectively, enabling
the same asymmetric reflection. The sample was then
fabricated using overlay electron beam lithography, fol-
lowed by electron beam evaporation and lift-off of sinus-
oidal shaped Cr/Ge combos and dry etching to form the Si
waveguide with cosine shaped sidewall modulations,
respectively
[33]
. The pictures of the metawaveguide
before deposition of SiO
2
as top cladding are shown in
Figs.
2(b)
and
2(c)
.
In our experiments, coherent laser beams, split from the
same laser source, were coupled from free space to tapered
polarization-maintaining fibers to deliver light into the
waveguide from both ports, by means of specifically
designed mode converters. The experimental validation
of the asymmetric interferometric light-light switching
required precise measurements of the ratio of outputs to
inputs consisting of both reflection and transmission. We
implemented two on-chip waveguide directional couplers
to separate the inputs and outputs and route them to 4
respective grating couplers [Fig.
3(a)
]. The grating couplers
efficiently scattered input and output light to free space,
FIG. 3. Characterization of asymmetric
interferometric light-light switching:
(a) Configuration of the experiment setup.
(b) Spectra of maximum (red) and mini-
mum (blue) output scattering coefficients
as a function of wavelength detuning (
Δ
)
to the resonant waveglength. Insets: mi-
croscope snapshots of the scattering (top)
and CPA (bottom) modes at the resonance
under an exposure time of 15 ms. While
the designd resonance is located at
1550 nm, the measurement results show
a resonant wavelength of approximately
1540 nm. The overall detection loss due to
the light splitting at the directional coupler
is estimated to be 6 dB at 1540 nm.
Nevertheless, the experimental results (tri-
angles) of asymmetric interferometric
light-light switching remain the same with
respect to the wavelength detuning, show-
ing an extinction ratio of approxmiately
60 dB at the resonance.
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which was collected by a microscope objective and further
imaged onto a highly sensitive charge-coupled device
(CCD) camara for final evalutions
[33]
. As a result, the
output scattering coefficient from the device was charac-
terized by
Q
s
¼
10
log
½ð
O
1
þ
O
2
Þ
=
ð
I
1
þ
I
2
Þþ
C;
ð
3
Þ
where
O
1
and
O
2
are scattered light from two output
grating couplers,
I
1
and
I
2
are scattered light from two
input grating couplers, and
C
is a constant, denoting the
overall detection loss to the output scatterings by the
directional couplers. The incident phase of the control
field was well controlled by an optical delay line con-
structed in free space. The intensity ratio
ξ
of the signal
beam to the control beam was manipulated to the designed
value of 3 (corresponding to
δ
¼
2
) by adjusting the
coupling efficiency of the control beam, confirmed by
imaging the scattered light from the corresponding input
grating couplers. The spectra of the output scatterings of the
fabricated non-Hermitian waveguide have been measured
for both minimum and maximum
Q
s
, corresponding to the
CPA mode and the other degenerate mode of less absorp-
tion, respectively, as shown in Fig.
3(b)
. At the resonant
wavelength of the non-Hermitian waveguide, the CPA
mode was achieved with almost no output scatterings when
the incoming phase of the control was
φ
¼
π
=
2
, as shown
in the lower panel inset of Fig.
3(b)
. In contrast, the mode of
less absorption was excited and strong outputs were
observed when the phase of the control was modulated
to
φ
¼
π
=
2
[upper panel inset of Fig.
3(b)
], demonstrat-
ing a weak-to-intense optical switching with an extinction
ratio up to approximately 60 dB in the metawaveguide.
Because the metawaveguide was operated in the vicinity
of the exceptional point, such asymmetric interferometric
light-light switching in output scatterings remained as a
function of wavelength detuning
Δ
[Fig.
3(b)
]. However,
the phase response of output scatterings was different if
moving away from the resonance. At the resonant wave-
length, i.e.,
Δ
¼
0
, two output grating couplers manifested
consistently in-phase on-off light scatterings for
O
1
and
O
2
in spite of interferometic control [Fig.
4(a)
], whereas if
Δ
0
, output light scatterings became out of phase as
different on-off relations were observed for
O
1
and
O
2
[Figs.
4(b)
4(c)
]. This was because an additional phase
shift was inherently associated with the Floquet-Bloch
periodic boundaries due to the periodic nature of the
modulation in the waveguide. Moreover, the Floquet-
Bloch periodic boundaries caused the sign of the phase
shift reversed if the operating wavelength crossed over the
boundary of the Brillouin zone. Hence, output light
scatterings showed opposite out-of-phase on-off responses
with respect to interferometric control of the control at
Δ
<
0
[Fig.
4(b)
] and
Δ
>
0
[Fig.
4(c)
].
The asymmetric interferometric light-light switching we
have accomplished utilizing a non-Hermitian metawave-
guide promises new approaches to optical information
processing. Operating in the vicinity of an exceptional
point, the metawaveguide allows a weak control light field
to strongly modulate the outputs of a large optical source
FIG. 4. Phase responses of outputs in interferometric light-light
switching. (a) When operated at the resonant wavelength, two
outputs oscillate in phase and reach their minimum simulta-
neously at
φ
¼
π
=
2
, where almost no light is scattered from the
two grating couplers of outputs. As the phase difference is flipped
to
φ
¼
π
=
2
, peak output scattering is obtained from both
grating couplers. (b) When operated at off-resonance wavelength
Δ
¼
4
.
2
nm, due to extra phase shift, the two output oscil-
lations move forward. Since the output
O
2
accumulates more
phase than
O
1
, the responses are no more in phase and thus the
two outputs reach minimum or maximum asynchronously.
(c) When operated at off-resonance wavelength
Δ
¼
4
.
6
nm,
the extra phase shift changes sign and results in a shift of output
oscillations in the opposite direction. Note that neither of the
output powers can be completely eliminated at
Δ
0
regardless
of the phase tuning. The output power is normalized to the total
incident power
I
1
þ
I
2
in the plots.
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signal through interference-enhanced absorption.
Interferometric control of the weak control beam demon-
strates light switching in output scatterings with an extinc-
tion ratio of approximately 60 dB. In principle, the control
power can be further engineered to be much weaker than
the signal power by reducing the modulation depth
δ
of
Im
½
Δ
ε

responsible for the asymmetric reflection. Although
the proposed metawaveguide does not break Lorentz
reciprocity, further consideration with nonlinearity
[34]
may promise novel optical isolators
[35]
and highly
integrated all-optical transistors gates
[36]
. Integration of
Kerr nonlinearity may also enable an approach to flexibly
manipulate the metawaveguide towards or away from the
exceptional point
[37]
, proving an additional freedom in the
interferometric light-light switching. This interferometric
light-light switching effect may be enhanced if the material
absorption is further magnified using optical metamateri-
als
[38]
.
The work is supported by the U.S. Army Research
Office (Grant No. W911NF-15-1-0152) and National
Science Foundation (Grant No. DMR-1506884). L. G.
acknowledges the support by National Science
Foundation (Grant No. DMR-1506987). W. S. F. and A. S.
acknowledge Boeing for their support under their SRDMA
program and also thank the NSF CIAN Engineering
Research Center (ERC) (Grant No. EEC-0812072).
H. Z., W. S. F., and J. Y. contributed equally to this work.
*
fengl@buffalo.edu
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