Supporting Online Material for
An All-Silicon Passive Optical Diode
Li Fan, Jian Wang, Leo T. Varghese, Hao Shen, Ben Niu, Yi Xuan, Andrew M. Weiner,
*To whom correspondence should be addressed. E-mail: email@example.com
Published 22 December 2011 on Science Express
This PDF file includes:
Materials and Methods
Materials and Methods
We fabricated the microrings on a silicon-on-insulator wafer (from SOITEC) with a
250 nm-thick top silicon layer and 3 μm of buried oxide. The single-crystalline Si
microrings and waveguides have a rectangular cross-section of 250 nm in thickness and
500 nm in width, which supports a low-loss single-mode quasi-transverse magnetic (TM)
mode for the filters at near infrared. The device was patterned with high resolution
electron-beam lithography (Vistec VB6) which has a beam step size of 2 nm. The diode
was formed after reactive-ion etching with chlorine/argon gas mixture in an inductive-
coupled plasma tool. No cladding was applied over the silicon waveguides or microrings.
Titanium micro-heaters with 5.3 kΩ resistance were evaporated on top of the buried
dioxide next to only the micro-ring resonator in the NF. Fabricated chip was manually
cleaved and has a width ~5 mm. No polishing or other treatments were applied to the
The key prerequisite for our optical diode is the matching of the resonant
wavelengths of the two high-Q filters when they are operating in linear regime, i.e. with
very low incident power. It is well known that as-fabricated high-Q microrings cannot
match exactly in their resonant wavelengths due to limited precision in nanofabrication.
We targeted the radii of the two microrings in the NF and ADF at 5 μm and 5.002 μm,
respectively. In most cases, this will make the resonant wavelength of the NF slightly
shorter than that of the ADF. A titanium micro-heater was then placed to the side of the
microring in the NF so that we can red-shift the resonant wavelength of the NF to match
that of the ADF, through thermo-optic effect (19) of silicon. Compared to the
conventional way of placing the heater above the microring and cladding, depositing the
heater to the side of the microring reduces the heating efficiency. However, it preserves
the high Q and the thermal isolation of the microrings, which are critical for low-power
Experimental Setup and Measurement Details
A continuous-wave tunable laser source with 1 pm resolution was guided into the
device with the help of single mode tapered lensed fiber and the output was coupled out
using another single mode tapered lensed fiber and fed into an optical power meter. The
fibers were position on xyz nanopositioned stages and butt coupled to the waveguides on
either facets of the device. Even though the fabricated device and method of coupling has
a rather high insertion loss of ~21.4 dB due to the facets, no amplifiers were used since
optical nonreciprocity was achieved at low power. A fiber-based polarization controller
was used to control the polarization of light input into the device to obtain maximum
extinction of the NF. A fiber based variable power optical attenuator was used to control
the amount of optical power fed to the device.
To tune the resonance of the NF to the ADF, the microheater to the side of the NF
was heated using a constant voltage source so that the dip of the NF overlaps the peak of
the ADF. Forward and backward spectra were obtained by switching the input and output
fiber connectors. Two scan modes were used to fetch the spectra: continuous-mode scan
where the laser sweeps from the beginning wavelength to the end wavelength without
stops while the power meter takes a moving average of the received optical power, and
stepped-mode scan where the laser goes to each wavelength and stops while the power
meter averages for a reasonably long time.
For point measurements, the wavelength was fixed at the desired operating
wavelength, which typically is the resonance wavelength of the NF in the backward
direction, and transmitted power was taken 10 seconds after the laser was turned on. The
standard deviation of the nonreciprocal transmission ratio includes contributions from
both the forward and backward transmissions and a Fabry-Perot uncertainty of ±0.4 dB.
Optical diode performance for different laser source power levels at 1630.011 nm.
5 ~270 -49.8 ± 1.5
10 ~850 -51.7 ± 1.5
at the diode
-27.5 ± 1
-24.8 ± 1
22.3 ± 1.8
26.9 ± 1.8
14 ~2,100 -52 ± 1.5 -23.6 ± 1 28.4 ± 1.8
A model based on coupled mode theory (21, 22) was developed to describe the
nonlinear response of the side coupled microring resonator. Nonlinear effects considered
include third order nonlinearity χ(3), such as two-photon absorption(TPA) and Kerr effect;
free carrier effect (FCE); and thermal effect resulted from Joule heating from TPA
process, FCE and linear absorption process. In our case, the thermal effect dominates all
other effects and caused the red-shift of the resonance at elevated temperature. With
various coefficients taken from literature, including an estimated thermal dissipation time
of 2 μs (21-23), as well as effective nonlinearity volumes calculated accurately through
finite-difference time domain (FDTD) simulation (20, 24), we can simulate the nonlinear
responses of the NF and ADF using MATLAB.
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