OCIS codes: (070.5753) Resonators; (070.6020) Continuous optical signal processing;
(130.7408) Wavelength filtering devices.
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1. Introduction
RF-photonic processing of microwave signals using passive optical filters can in many cases
replace traditional electrical signal processing while providing higher bandwidth and
potentially lower power consumption [1, 2]. Moreover, as optical delay lines are characterized
by their low-loss that is independent of RF frequency, a much more complex processing
(filtering) network can be constructed. Such all-optical signal processing approaches can be
beneficial for a broad range of applications [3–5] especially at high bandwidths. All-optical
signal processing in optical lattice filters [5‒7] can support the fully reconfigurable optical
transfer function with a large number of zeros and poles synthesized by cascading many
identical unit cells. Preferably, the optical lattice filter design should accompany recursive
algorithms to facilitate synthesis of sophisticated filter functions by reconfiguring many unit
cells of known identical transfer functions.
In addition to scalability and reconfigurability, practical implementations of optical lattice
filters should be based on low loss and compact integration of many unit cells that can be
reconfigured rapidly while consuming low energy. Silicon photonics realization of optical
lattice filters exploiting complementary metal oxide semiconductor (CMOS) fabrication
process [6] can offer high levels of yield, uniformity, resolution, and repeatability while
keeping the fabrication cost relatively low. Recently, such integrated optical lattice filters
have been demonstrated on silicon as well as InP platforms [7–12]. This paper discusses rapid
reconfiguration and synthesis of a fourth-order silicon optical lattice filter that is fabricated
using a commercial silicon CMOS foundry process. The current injections into p-i-n diodes in
silicon photonic unit cells allow lattice filter reconfiguration in less than 10 ns.
2. Device concept and design
Figure 1(a) shows the input coupler (outside the largest rectangle) and the unit cell [13]
(inside the largest rectangle), a basic building block used to construct higher-order filters. The
unit cell takes the form of an incomplete Mach-Zehnder interferometer (MZI) where the input
#146285 - $15.00 USD Received 22 Apr 2011; revised 9 Jun 2011; accepted 15 Jun 2011; published 23 Jun 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. 14 / OPTICS EXPRESS 13246
coupler is separate from the unit cell. The upper arm of the incomplete MZI is coupled to a
ring resonator and the lower arm of the MZI connects directly to the output coupler. All of the
couplers are designed as tunable MZI‘s with 3-dB directional couplers at the input and the
output. Phase shifters (shown as numbered red rectangles in Fig. 1) in each arm control the
output splitting ratio irrespective of the device‘s initial conditions. The ring resonator‘s
perimeter is 8.2 mm resulting in a free spectral range (FSR) of 10 GHz (100-ps lattice
constant). The output coupler of the first unit cell acts as the input coupler for the next stage.
The inset of Fig. 1(a) shows images of the fabricated devices.
The tuning elements used to reconfigure the filter are phase-shifters based on the free-
carrier plasma dispersion effect in silicon [14]. Each phase-shifter is fabricated by embedding
an optical waveguide between n-type and p-type doped regions which are defined by ion
implantation and the required phase shift is induced by injecting current into the resulting p-i-
n diode structure. The length of phase shifters 1 and 6 are 700 µm, and the length of phase
shifters 2, 3, 4, and 5 are 500 µm. These diodes consistently achieved a uniform threshold
voltage of 0.85 V and a DC forward resistance below 12 Ω on measurements on more than
hundreds of unit cells.
Fig. 1. (a) Schematic of a single unit cell, red boxes indicate phase shifter electrodes. (b) Simulation showing the mode size in both the narrow (0.5 µm) and wide (3 µm) waveguides.
(c) Schematic of a four-unit-cell filter.
As the upper part of Fig. 1(a) indicates, the unit cell design incorporates two types of
silicon rib waveguides, a ―narrow‖ waveguide which is 0.5-μm wide and a ―wide‖ waveguide
which is 3-μm wide. Figure 1(b) shows the mode field profiles calculated for the two different
widths (they have equal rib and slab heights of 250 nm). The ―narrow‖ and ―wide‖
waveguides are connected with a linear taper. The advantages of the narrow waveguide
include single-mode confinement, strong lateral evanescent coupling, and relatively large
phase shifts with low tuning-current [15], while the advantages of the wide waveguide include
lower propagation loss (~0.3-0.5 dB/cm) and lower optical nonlinearity [16]. The bends (300-
μm radius) and the tuning sections use the narrow waveguide and the long runs of waveguide
in the ring resonator use the wide waveguide. This design ensures that the filter supports only
#146285 - $15.00 USD Received 22 Apr 2011; revised 9 Jun 2011; accepted 15 Jun 2011; published 23 Jun 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. 14 / OPTICS EXPRESS 13247
a single mode at wavelengths near 1.55 μm for the TE-polarization and that the bend and
propagation losses are minimized. Figure 1(c) shows a four-unit-cell filter which consists of
four cascaded unit cells.
To understand the optical frequency response of the unit cell filter in Fig. 1(a), we analyze
the transmission from the input (In 1) to the Out 1 (bar) and Out 2 (cross) outputs (H11 and
H21, respectively). The first step is to look at the frequency response of the single-mode
waveguide coupled to the ring through the ring coupler [i.e., the transfer function between
points ‗A‘ and ‗B‘ in Fig. 1(a)]. Using the z-transform notation [17] this can be written as
6
6
1
ring 11
j
r r
j
rr
e z NH
De z
(1)
where z = exp(jωT), T is the round-trip propagation delay in the ring, ρr is the bar field-
coupling ratio of the ring coupler defined as 21 r where r is the cross field coupling
ratio for the case of a lossless coupler, γ is the ring round-trip loss including any excess
coupler loss, 6 is the phase shift in the ring, andrN and
rD denote the numerator and
denominator, respectively.
The two-port transfer function of the unit cell filter is
1
1
1 1 1
cell
2 2 2
1j
o r o r
jr o r o r
N j e DO I IH
O I ID j N e D
(2)
where ρo and κo are the output coupler‘s bar and cross field-coupling ratios, respectively, and
1 is the phase shift through the lower arm of the main MZI. I1, I2 are the two input signals,
O1, O2 are the two output signals, and the subscripts 1 and 2 correspond to the upper and
lower port, respectively. The prime notation is added to the coupling ratios of the output
couplers to indicate the inclusion of a separate loss factor for each arm of the main MZI.
The poles and zeros of the transfer function are simply the roots of the denominator, Dr,
and numerator with respect to z1
. From Eq. (1) and Eq. (2), it is apparent that the unit cell
transfer function has a pole equal to 6j
r e which is the same for both the H21 and H11
transmission and two zeros which are different for the H21 and the H11 transmission. In the
special case of a lossless device these transfer functions are complementary. The two zeros
and the single pole are fully-controllable by four parameters: the ring phase shift (electrode 6),
the coupling strength between the MZI upper waveguide and the ring (electrodes 2 and 3), the
phase shift in the MZI lower waveguide (electrode 1), and the splitting ratio of the output
coupler (electrodes 4 and 5). The magnitude and phase of the unit cell‘s pole is fully defined
by the ring coupler (including γ) and the ring phase shift, respectively, whereas the two linked
zeros are a function of the pole value. They are adjusted by tuning the main MZI‘s lower
waveguide phase shifter and output coupler. Achieving a near-unity pole requires minimizing
the round-trip and excess coupling losses. The general filter tuning procedure is as follows:
first, the pole magnitude and phase are set using the ring coupler and ring phase-shifter, and
then the zero is adjusted by tuning the main MZI lower phase shifter (3) and the output
coupler.
The transfer function of a higher-order filter composed of several cascaded unit cells is the
multiplication of the two-port transfer function of each stage, which is written as
filter cell,i
i
H H (3)
The denominator of Hfilter is the product of Dr from each stage. Whereas the numerators
are a complex function of each stages Nr, Dr, and κo. Therefore, the poles of the higher-order
filter are independently adjustable (i.e., roots of the denominator) since each relies on the ring
#146285 - $15.00 USD Received 22 Apr 2011; revised 9 Jun 2011; accepted 15 Jun 2011; published 23 Jun 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. 14 / OPTICS EXPRESS 13248
parameters (ring coupler, and ring phase shifter) of a separate unit cell. However, the zeros
depend upon the pole order, all of the output coupler splitting ratios, and all of the lower
waveguide phase shifters. This feature is crucial to consider when developing algorithms for
filter synthesis and reconfiguration. Typically, a recursion algorithm [13] can find the tuning
values of the lower waveguide phase shifters and output couplers for a desired set of zeros.
Control of the unit cell pole magnitude between 0 and 1 enables a filter transfer function
with either a finite impulse response (FIR) or an infinite impulse response (IIR), respectively.
A pure FIR filter requires full coupling into and out of the ring resonator corresponding to a
pole magnitude of zero. In this case, the ring simply acts as a delay line and the unit cell
impulse response contains two impulses spaced by T. When the pole magnitude is greater than
zero, IIR functionality occurs and the optical signal coupled to the ring is stored (i.e.,
circulates the ring many times) resulting in an impulse every T, and hence extending the
length of the impulse response to much longer than the delay provided by the physical path
length of the device. The duration of the impulse response is proportional to the pole
magnitude and the pole magnitude is inversely proportional to the coupling into the ring.
From (2), an IIR filter with a pole magnitude near unity requires a very small coupling to
the ring and a very low ring round-trip loss. Then, light inside the ring circulates many times
before decaying, thereby producing a very long impulse response. In the frequency or
wavelength domain, the pole magnitude controls the finesse of the features in the filter
transfer function. If the pole magnitude is held constant, then changes in the filter‘s zero
engrave filters with very different shapes. The results in Section 5 will demonstrate these
concepts.
3. Optical lattice filter die fabrication and preparation for testing
All device fabrication took place at the BAE Systems CMOS foundry following the various
process steps illustrated in Fig. 2. The fabrication process starts with a commercial 6-inch
silicon-on-insulator (SOI) wafer that has a 3-μm-thick buried oxide (BOX) layer and a 0.5-
μm-thick upper silicon layer. The lithography uses a deep ultraviolet (DUV) scanner,
development, and photoresist reflow [18] to smooth the resist profile. The pattern is
transferred to the dielectric hard mask, and the waveguides are formed by reactive ion etching
(RIE) using the hard mask. A second lithography step defines the waveguide trenches in
which silicon is etched down to the BOX layer for thermally isolating individual p-i-n diodes
designed for current tuning. The trenching regions are filled by silicon dioxide (SiO2) whose
thermal conductivity is two orders of magnitude lower than that of silicon [19].
After the trenches are etched using a RIE process, a thermal oxidation step reduces the
waveguide corrugations and then an oxide deposition step deposits over a micron of oxide.
The wafer surface is then planarized by chemical mechanical polishing (CMP) to facilitate the
subsequent metallization steps. To obtain an accurate 50/50 splitting ratio in the directional
couplers, the fabrication process was optimized through several iterations to find the best
compromise between the counteracting effects of the photoresist reflow, the waveguide
oxidation and the waveguide rib etching depth parameters. These optimizations and
adjustments were necessary to produce directional couplers with splitting errors below 3%,
which helped realize a full range tuning of the pole magnitude.
#146285 - $15.00 USD Received 22 Apr 2011; revised 9 Jun 2011; accepted 15 Jun 2011; published 23 Jun 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. 14 / OPTICS EXPRESS 13249
Fig. 2. An illustration showing the device fabrication process.
To form the p-i-n diodes required for tuning, via openings are made in the cladding SiO2
by a RIE process followed by boron and phosphorus ion implantations to form the p + and n
+ doped regions, respectively. The electrodes comprise aluminum on top of a thin layer of
Ti/TiN (Titanium/Titanium Nitride). The wafer is prepared for testing by diamond saw dicing
followed by facet polishing. The waveguides meet the facets at a 7° tilt angle with respect to
the facet surface normal to suppress the formation of a Fabry-Pérot cavity that would disturb
the filter response. Also, an anti-reflection (AR) coating reduces optical coupling losses and
further suppresses any residual Fabry-Pérot effects. The optical lattice filter die is then
mounted on a chip-carrier and their electrodes were wire-bonded to facilitate simultaneous
tuning of many electrodes on the die. However, this basic wiring technique limits high-
frequency modulations beyond several hundred megahertz.
4. Single unit cell characterization and parameter extraction
This section describes the amplitude and phase measurement technique, pole-zero curve
from the pole-zero fit, and characterization of the phase shifters.
Measurement technique and pole-zero fitting
An accurate and fast transmission measurement technique offers both visual feedback and a
means to quickly determine the pole and zero information from the phase and amplitude
transmission. A frequency-domain swept coherent interferometer [20, 21] enables
simultaneous complex spectral transmission measurements (i.e., intensity and phase) across
10 nm with a 100 dB dynamic range and an update rate of 10 Hz. Lensed fibers couple light
into, and out of, the device while preserving only the TE-polarization. The experimental
arrangement provides simultaneous measurement of both outputs (i.e., Out 1 and Out 2 in Fig.
1(a)).
Figure 3(a) shows a phase (red) and amplitude (blue) measurement (grey lines) of a
bandpass filter shape with a 400-MHz, 3-dB bandwidth displayed across four FSRs. We use
the MATLAB System Identification Toolbox to find the best-fit pole and zero to the
measured data [22]. The pole and zero fits [Fig. 3(b)] are overlaid on the measured data in
Fig. 3(a) (red and blue curves). The excellent match between the measurement and fit
indicates that the unit cell provides a pure single pole and single zero without any undesired
features (e.g., Fabry-Pérot fringes). Using the equations that describe the transfer function that
were discussed earlier, we can estimate many of the internal circuit parameters of the filter
#146285 - $15.00 USD Received 22 Apr 2011; revised 9 Jun 2011; accepted 15 Jun 2011; published 23 Jun 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. 14 / OPTICS EXPRESS 13250
(i.e., those that cannot be directly measured) including the ring loss, the directional coupler
coupling ratio, phase shift and attenuation versus injection current.
Fig. 3. Unit cell data. (a) Example amplitude and phase measurement (grey) and fit (blue, red)
of unit cell configured as a bandpass filter with a 400-MHz, 3-dB bandwidth. (b) Fitted pole
and zero. (c) Extracted pole magnitude plotted for independent current sweeps of each phase
shifter electrode in Fig. 1(a).
Figure 3(c) shows the extracted unit cell pole magnitude versus separate sweeps of the
drive current to each phase-shifter in Fig. 1(a). As expected, the data show that the phase
shifters inside the ring coupler [electrodes 2 and 3 from Fig. 1(a)] primarily control the pole
magnitude over a range of 0.08–0.93. This corresponds to 99.4% and 8% power coupled into
the ring, respectively and demonstrates the filter changing from FIR to IIR. It is apparent from
Fig. 3(c), that tuning the zero (electrodes 1, 4) does not affect the pole magnitude and this
indicates low crosstalk between the electrodes. However, due to loss associated with phase
changes from free-carrier absorption, operating the ring phase shifter (electrode 6) and the
ring coupler electrodes simultaneously (electrodes 2 and 3) decreases the pole magnitude.
Although not shown here, similar plots are available for the pole‘s angle, the zero‘s
magnitude, and the zero‘s phase. The detailed analyses of the relationship between these and
the injection current levels will be the subject of a future publication.
Extraction of circuit parameters from the pole-zero fit
From the pole magnitude versus current injected into electrodes 2 and 3 [see Fig. 3(c)], we
can estimate two device circuit parameters: the splitting ratios of the directional couplers
which make up the tunable MZI and the ring round-trip loss. The pole magnitude is the
product of the ring-round trip loss, γ, and 21 r where κr is the ring coupler coupling ratio
[see denominator of Eq. (2)]. We will show the upper limit of the pole magnitude is
proportional to the ring round-trip loss and the lower limit is proportional to imperfect 50/50
splitting ratios of the direction couplers that comprise the tunable MZI.
The tuning range of the coupling coefficient of the tunable MZI, κr, and thus the pole
magnitude is a function of the splitting ratios of its two directional couplers. For example,
100% power coupling into the ring occurs only when the two directional couplers in the MZI
have either a 50/50 splitting ratio or opposite splitting ratios (e.g., 60/40 for the first coupler
and 40/60 for the second). When the two couplers in the MZI have equal but imperfect 50/50
splitting ratios, the coupling into the ring can always tune to 0% (i.e., a pole magnitude of 1.0)
but can never tune to 100%. Since the two directional couplers are fabricated identically they
will have near equal coupling ratios and the MZI can always weakly couple to ring (i.e.,
achieve pole magnitude near unity). Therefore, the lower limit of the pole magnitude (i.e., less
than 100% coupling into the ring) is primarily due to an imperfect 50/50 splitting ratio of the
direction couplers in the MZI. In our case, 99.4% max power coupling into the ring
corresponds to a 3% directional coupler splitting ratio error (i.e, 47/53 or 53/47 splitting
ratio).
Likewise, since κr can be tuned to 0, the upper limit of the pole magnitude is limited by
losses (i.e., γ < 1). In the measured device, the total ring round trip loss is estimated at 0.6 dB
which includes excess coupler, bending, and waveguide losses. This is consistent with our
measured waveguide loss of 0.3-0.5 dB/cm.
#146285 - $15.00 USD Received 22 Apr 2011; revised 9 Jun 2011; accepted 15 Jun 2011; published 23 Jun 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. 14 / OPTICS EXPRESS 13251
Characterization of the phase shifters phase and amplitude response
The total phase shift resulting from current injection into each tuning element (phase-shifter)
in the device is the result of two counteracting physical effects; the free-carrier plasma
dispersion [14] and the thermo-optic effect [23]. The plasma dispersion effect decreases the
refractive index with increasing carrier density and it is accompanied by free-carrier
absorption (undesired), whereas the thermo-optic effect increases the refractive index and
depends on the power absorbed in the diode structure.
The phase shift and amplitude response of the phase shifter are extracted from
measurement of the pole magnitude and pole phase versus sweep of the ring phase shifter
(electrode 6) [see Fig. 3(c)] and the mathematical form of the pole, 6j
r e . The phase shifter
phase response and amplitude response versus injection current are simply the angle of the
pole and magnitude of the pole, respectively, normalized to the pole value without injection
current. Figure 4 shows the phase induced in a typical phase-shifter and the associated optical
loss versus the drive current. At low current densities, the plasma dispersion effect is
dominant and at high currents the effect is weakened—most likely due to thermal power
dissipation. The loss versus current curve shows an almost exponential behavior since it
depends only on free-carrier absorption and not heating. Despite the increase of the loss
versus phase shifter current, it is evident from Fig. 3(c) that the unit cell provides a pole with
a large tuning range due to the low-loss waveguides and the large range κr.
Fig. 4. Measured ring phase-shifter phase shift and loss versus driving current.
Characterization of the phase-shifters speed
Figure 5(a) shows the modulator test structure used to examine the device tuning speed. The
modulator is fabricated on the same chip with the filter and its input and output waveguides
are extended for direct access at the device facets. For the measurement, a single-frequency
laser is coupled into the structure using a lensed fiber. The phase shifter is driven by a 0–5
mA 15-MHz square wave and the output light is measured with a 20-GHz sampling
oscilloscope. Figure 5(b) shows the optical response of the modulator where the measured
optical output rise and fall times are less than 10 ns (10%–90%). The limitation in speed is
partly due to the electrical connection to the chip and the carrier lifetime inside the p-i-n
structure. Figure 5(c) shows the measured optical modulator response when it is driven by a
1-kHz square wave current signal. This shows the device‘s slower heating and cooling effects
which have a time constant on the order of 20 μs. For fast reconfiguration of the filter shape,
the drive signals must include pre-emphasis that account for the time dependent response of
the phase shifter.
#146285 - $15.00 USD Received 22 Apr 2011; revised 9 Jun 2011; accepted 15 Jun 2011; published 23 Jun 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. 14 / OPTICS EXPRESS 13252
Fig. 5. (a) An illustration of the modulator structure used to measure the device reconfiguration
speed. (b) The modulator response for a 15-MHz square wave current signal (0-5mA). (c)
Modulator response for a 10-kHz square wave current input (0-5mA).
5. Single unit cell measurement and tuning
This section shows amplitude and phase measurement examples of a single-unit cell‘s
complex transfer function which demonstrate large pole tuning range, and control over the
zero. Attached movies show how the filters change from one shape to another.
Bandpass filter bandwidth tuning
Figure 6 shows simultaneous measurements of the transfer function from the ‗In 1‘ port of
Fig. 1(a) to both outputs (Out 1 and Out 2 or H11(f) and H21(f), respectively) of a single-unit
cell when it is tuned to act as a bandpass filter optimized for Out 2 with pole magnitudes of
0.11, 0.53, and 0.88, respectively. The filter‘s impulse response‘s (i.e., h11(t) and h21(t)) are
displayed along the top of Fig. 6 and they are equal to the inverse Fourier transform of the
corresponding measured complex spectral transmission [i.e., H11(f) and H21(f)]. The increase
in duration of the filter‘s impulse response, and the corresponding narrowing of the filter
shape in the frequency domain as the pole‘s magnitude increases is evident in Fig. 6.
The change in the filter‘s bandwidth is inversely proportional to the filter‘s pole
magnitude and the zero helps adjust the filter shape (e.g., bandpass vs. notch). To create a
symmetric bandpass filter shape there must be a relative π rad phase difference between the
unit cell‘s pole and zero and the filter rejection is maximized (approaching infinite) when the
filter‘s zero is located on the unit circle. The complimentary output transmission, H11(f),
shows a notch filter shape and has the same pole as H21(f). The shape difference between
H21(f) and H11(f) is from the position of its zero which shares the same angle as its pole.
Figure 6(a) illustrates the impulse response and spectral transmission of the filter when it
is configured for a near ideal FIR response. Such a filter is equivalent to a delay
interferometer and has sinusoidal transmission versus frequency. The impulse response
contains two peaks of almost the same magnitude; the first peak comes from the lower arm of
the main MZI and second peak is delayed by T and comes from the ring. The remaining
unwanted peaks in the FIR filter‘s response constitute less than 1% of the energy passed by
the filter‘s transfer function.
Figure 6(b,c) show the impulse response and transmission functions of the filter when it is
configured as IIR bandpass filters with 3 dB bandwidths of 2 GHz and 400 MHz,
respectively. The transfer functions for the cross and bar states (H21 and H11) are bandpass and
notch, and the impulse responses have the same duration for both outputs. The difference in
the impulse response between the two outputs is that the energy of the first peak is smaller for
the bandpass filter and higher for the notch filter. In the spectral domain, the energy of the
#146285 - $15.00 USD Received 22 Apr 2011; revised 9 Jun 2011; accepted 15 Jun 2011; published 23 Jun 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. 14 / OPTICS EXPRESS 13253
first peak corresponds to the background level of the filter which is large for a notch filter and
small for the bandpass filter.
Fig. 6. Measured impulse response (top) and transmission (bottom) for bandpass filters with (a)
small pole (Media 1) (b) medium pole (c) large pole created from a single unit cell. Red curves indicate H11 transmission and blue curves indicate the H21 transmission. Insets show the drive
currents to electrodes 1, 2, 3, 4 and 6 (bar plot) for each measured response and the
corresponding pole and zero fit around the unit circle.
The narrow bandpass filter impulse response in Fig. 6(c) rolls off at about 1 dB per peak
and extends beyond 5 ns before reaching the measurement noise floor. The 14-dB decrease in
peak transmission between the 400-MHz filter and 2-GHz filter occurs because of the
resonant enhancement of the ring loss. However, this filter still achieves a clean bandpass
shape with a pole and zero near unity. Media 1 associated with Fig. 6 shows the single-unit
cell filter switching between FIR [see Fig. 6(a)] and IIR [see Fig. 6(b,c)] including
intermediate stages when the zero is not positioned optimally. In addition to the filter shapes
shown in Fig. 6, Media 1 includes bandpass filters with pole magnitudes of 0.11, 0.28, 0.53,
0.62, 0.71, 0.8, 0.85, and 0.89.
#146285 - $15.00 USD Received 22 Apr 2011; revised 9 Jun 2011; accepted 15 Jun 2011; published 23 Jun 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. 14 / OPTICS EXPRESS 13254
Fig. 7. Single unit cell configured as a (a) notch filter (Media 2) and (b) bandpass filter. Insets
show the drive currents to electrodes 1, 2, 3, 4 and 6 (bar plot) for each measured response and the corresponding pole and zero fit around the unit circle.
Figure 7 shows a tuning example optimized for the H21 transmission where the filter shape
is changed from notch to bandpass without changing the filter‘s pole. The difference between
the two shapes is the location of the zero at either 1 or +1. Changing the phase of the main
MZI phase shifter (electrode 1) by π rad changes the filter from notch to bandpass. Adjusting
the output coupler (electrode 4) helps to position the zero on the unit circle in presence of
additional losses. Fine adjustments to the zero in Fig. 7(a) (Media 2) shows the shape of the
filter in intermediate states between bandpass and notch. Note that only the magnitude of the
optimized for the H21 transmission. (b) 2 GHz 1-dB bandwidth bandpass filter optimized for
the H11 transmission.
#146285 - $15.00 USD Received 22 Apr 2011; revised 9 Jun 2011; accepted 15 Jun 2011; published 23 Jun 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. 14 / OPTICS EXPRESS 13255
Figure 9 displays the transmission of the four-unit-cell filter optimized for the H21 (cross)
transmission [(a)] and the H11 (bar) transmission [(b)]. The four-unit-cell structure has 26
phase shifters to control 18 independent filter parameters: the amplitude and phase of the four
poles, the four zeros, and the complex gain of the filter. (a) shows the filter manually tuned
for a flat-top bandpass shape with a sharp roll-off for the H21 transmission. The filter has up to
30-dB of rejection and its flat-top 1-dB bandwidth is 600 MHz. Figure 9 shows this filter
shaped measured across 95 FSRs. Across this range the filter has uniform transmission and
shape and near 30-dB extinction. (b) shows a filter optimized for the H11 transmission. As
expected, the four unit-cell devices achieved more complex and versatile filter shapes when
compared to the single unit cell filter.
Fig. 9. Measured transmission across 95 FSRs. Inset shows filter shape within two FSRs.
Currently, these filter shapes are obtained through manual adjustment of the electrodes.
The tuning procedure follows the theory presented in Section 2. First, since each unit cell
uniquely defines a pole, the poles were positioned in their proper locations using the pole
tuning electrodes. The zero values are a function of the pole values, the pole order (i.e., which
unit cell provides the pole value) and all of the zero tuning electrodes. The adjustment of the
zeros tuning electrodes finalizes the filter shape. This procedure is challenging because
adjusting a single zero tuning phase shifter changes every zero‘s value (14 zero phase shifters
total). Currently on-going studies include an automated procedure to switch between filter
shapes including a detailed calibration of the four-unit cell filters.
7. Conclusion
In this work we demonstrate a fully-reconfigurable fourth-order silicon optical lattice filter
built by cascading identical unit cells consisting of a Mach-Zehnder interferometer (MZI) and
a ring resonator. The filter is fabricated using a silicon (CMOS) foundry process and its
reconfiguration is achieved by current injection into p-i-n diodes. This demonstration of
higher-order optical lattice filters with a reconfiguration speed of under 10 ns will enable
many new applications. Employing the recent achievements which provide optical gain in
silicon photonic devices would allow the implementation of similar filters with much higher
orders; a key step in realizing all-optical processing system for a broad range of RF and
microwave applications.
Acknowledgments
This work was supported in part by DARPA MTO Si-PhASER project Grant No. HR0011-
09-1-0013.
#146285 - $15.00 USD Received 22 Apr 2011; revised 9 Jun 2011; accepted 15 Jun 2011; published 23 Jun 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. 14 / OPTICS EXPRESS 13256
