We investigate the impact of the intrinsic-Q of the resonant poles on the performance of multiring-based optical filters and dispersion-compensating devices. We highlight the role of quality factor by defining figures-of-merit for some specific filter configurations

Hossein-Zadeh, Mani

Vahala, Kerry J.

English

Caltech Authors - Main

IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 19, NO. 14, JULY 15, 2007 1045
Importance of Intrinsic-Q in Microring-Based Optical
Filters and Dispersion-Compensation Devices
Mani Hossein-Zadeh, Member, IEEE, and Kerry J. Vahala, Member, IEEE
Abstract—We investigate the impact of the intrinsic- of the
resonant poles on the performance of multiring-based optical fil-
ters and dispersion-compensating devices. We highlight the role of
quality factor by defining figures-of-merit for some specific filter
configurations.
Index Terms—Dispersive media, optical filters, optical microres-
onators.
I. INTRODUCTION
OPTICAL microring resonators (OMRs) are versatile ele-ments for designing integrated photonic circuits, and can
be used as building blocks for many optical signal processing
devices and systems. It has been shown that OMRs can serve as
poles in multipole add–drop filters [1]–[3] and multistage dis-
persion compensators [4]–[6]. Although significant effort has
been dedicated toward design and fabrication of these devices,
their performance has not been clearly characterized in terms
of the intrinsic quality factor of the constituent microring res-
onators . Note that is limited by intrinsic loss mech-
anisms (i.e., material loss and scattering losses due to surface
roughness) and is a characteristic of different microresonator
fabrication technologies and material systems (polymer, semi-
conductor, hydex, etc.). Hence, -characterization simplifies
the comparison and evaluation of the performance of optical
multiring filters built based on different platforms and technolo-
gies. Here we present an alternative perspective on the theory of
multiring filters that highlights the role of intrinsic quality factor
in over-all behavior of these devices. We show that the inter-
play between coupling and loss makes the attainment of high
intrinsic quality factor an essential requirement for designing
multiring bandpass filters and all-pass filters (dispersion com-
pensators).
II. MICRORING-BASED BANDPASS FILTERS
Fig. 1(a) shows the most common configuration used for
designing microring-based multipole bandpass filters. The be-
havior of the multipole filters is well understood based on their
building blocks, i.e., the single-pole (single-ring) add–drop
Manuscript received December 6, 2006; revised April 17, 2007. This work
was supported in part by the Defense Advanced Research Projects Agency
(DARPA) and in part by Caltech Center for Physics of Information.
The authors are with the Applied Physics Department, California Insti-
tute of Technology, Pasadena, CA 91125 USA (e-mail: mhz@caltech.edu;
vahala@caltech.edu).
Digital Object Identifier 10.1109/LPT.2007.899456
Fig. 1. (a) Schematic diagram of a multiring filter. (b) Single-pole (single-ring)
filter. (c) Dropped power spectrum for a single-pole filter.
filter [Fig. 1(b)]. The single-pole filter has a Lorentzian power
transfer function [Fig. 1(c)] with a bandwidth defined by
, where , and
are external quality factors associated with coupling to bus
and drop waveguides ( ; : microring
radius; : effective refractive index of the optical mode; :
coupling factor for the electric field [1]). The total power
transfer is a function of and the coupling
factors . Note that the magnitude of the coupling factors
control the distribution of the input power among the reflected,
dropped, and throughput powers.
The minimum insertion loss (maximum power transfer from
input to the drop channel) occurs for an asymmetric coupling
configuration in which the input coupling is set at the critical
coupling condition . Note that we assume
all coupling junctions are lossless. It has been shown that the
power transfer for a critically coupled single-ring filter is equal
to [7]. However, here we consider the
symmetric coupling configuration (i.e., or ,
therefore, critical coupling is not perfectly attained) that simpli-
fies insertion loss calculations for higher order filters [1]. For a
single-pole symmetric coupler the power transfer can be written
as . Note that for relatively small values
of , the difference between the symmetric coupler and
critically coupled coupler is negligible. If we define as
, or basically the for a symmetric
single-pole element, for higher order filters can be derived
as a function of . Regardless of the order and the shape
of the filter, always increases for larger values of .
Practically, this means that the insertion loss can be reduced by
either increasing the operational bandwidth (through waveguide
loading) beyond the bandwidth already set by the resonator it-
self, or increasing the intrinsic- .
In the multiring configuration the spectral response of the
transfer function is determined by the relation among the cou-
pling factors. Photonic counterparts of the well-known RF filter
1041-1135/$25.00 © 2007 IEEE
1046 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 19, NO. 14, JULY 15, 2007
Fig. 2. (a) Insertion loss plotted against Q =Q for three filter orders with
Butterworth transfer function. (b) Insertion loss plotted against 3-dB bandwidth
for three values of Q in a third-order Butterworth filter. The intrinsic-Qs are
chosen based on available microring technologies: semiconductor and polymers
(10 ) [8], [9], Hydex (10 ) [2], and silica microtoroids (10 ) [7].
functions such as Chebyshev and Butterworth (maximally flat)
can be realized by carefully tuning the mutual coupling factors
with respect to and [1]. Here we consider a sym-
metric multiring coupler with Butterworth (maxi-
mally flat) response. For any filter order , this response can
be achieved by setting the proper relation between and .
Fig. 2(a) shows the insertion loss plotted against for
and . As evident from the graph a large value of
is even more important as the filter order increases. In-
sertion loss scales as , where dB,
14 dB, 32 dB, for and , respectively. Note that
is inversely proportional to and basically carries the sig-
nature of all coupling strengths for a specific filter function.
In order to illustrate the effect of insertion loss compensation
by over-coupling (decreasing ), the insertion loss of a third-
order Butterworth filter is plotted against its 3-dB bandwidth for
three values of [Fig. 2(b)]. As shown in the plot, a low inser-
tion loss is accompanied with a bandwidth penalty and clearly
a lower bandwidth requires larger intrinsic- s. An equally im-
portant figure-of-merit in a bandpass filter is the roleoff slope
that represents the strength of the out-of-band signal rejection.
For any filter shape, this slope is proportional to the order of
the filter , where is the determined by the specific filter
function). One of the challenging tasks for photonic filter de-
sign is building a narrow bandwidth box-like (large slope) filter
with low insertion loss. These three characteristics are essential
in many optical communication and RF-photonic signal pro-
cessing systems where narrowband, low loss, and high rejec-
tion of closely spaced frequency components is required [10],
[11]. Although the exact -dependence of insertion loss and
roleoff varies in different filter designs, it is useful to define a
figure-of-merit that highlights the role of quality factor in the
overall performance of a filter. Knowing that insertion loss ap-
proximately scales as , bandwidth scales as , and
the slope scales as , the figure-of-merit can be written as
This figure-of-merit illustrates the extreme importance of high
intrinsic- in the design of box-like multipole bandpass filters.
Fig. 3. (a) Multiring APF architecture. (b) Single-pole microring APF. (c) GD
and insertion loss spectrum of a single-pole APF. (d) Four-pole APF with con-
stant dispersion. (e) Four-pole APF with constant delay over a passband.
III. MICRORING-BASED DISPERSION-COMPENSATING STAGES
It is well known that microrings can be used to build all-pass
optical filters (APFs) [4], [5]. Ideally, APFs have a constant am-
plitude response and a phase response that can be made arbi-
trarily close to any desired response. It has been shown that pho-
tonic all-pass filters can be realized by side coupling a series of
OMRs to a waveguide [4], [5]. Fig. 3(a) shows the schematic di-
agram of a multiring optical APF. The group delay (GD) spec-
trum of a single-pole ring filter [Fig. 3(b)] has a Lorentzian
shape [Fig. 3(c)] and its maximum GD is proportional
to [12]. Note that due to absence
of the drop port, in this configuration, . The power
transfer spectrum of this filter can be characterized
by an inverted Lorentzian with a minimum transmission of
[Fig. 3(c)].
It is desirable to maintain a unity amplitude response over
the bandwidth of an APF. In a ring-resonator-based APF, this
requirement translates to operation in the over-coupled regime,
where should be large. Since large GD is also
desirable and , high intrinsic- operation becomes
a critical aspect of APF filter design (to increase
without sacrificing ). By adjusting the coupling factors
and the relative resonant frequency of the constituent mi-
croring resonators, the phase response of multiring APFs can be
tailored to serve as linear dispersion compensators [Fig. 3(d)]
that can be used in wavelength-division-multiplexed commu-
nication systems [13], or as optical delays [Fig. 3(e)] that are
useful in applications like RF-photonic signal processing and
RF-phased arrays [14].
Assuming all rings to have an intrinsic quality factor of ,
adjusting the coupling factors determines the and
for each pole and, therefore, the overall GD spectrum.
There is always an undesired frequency-dependent loss asso-
ciated with any GD or dispersion response. To generate an
amplitude response close to an ideal APF filter, the response
should be small enough so that the spectral
variation of the insertion loss becomes negligible over the
HOSSEIN-ZADEH AND VAHALA: IMPORTANCE OF INTRINSIC- IN MICRORING-BASED OPTICAL FILTERS 1047
Fig. 4. Minimum transmission plotted against maximum GD for a single-ring
APF and for three different values of Q .
operational bandwidth. Fig. 4 shows the minimum transmis-
sion plotted against maximum GD for a single ring at three
values of . As evident from the plot when increases both
the maximum insertion loss and the decrease
significantly at a given .
Consequently, the intrinsic quality factor of the constituent
microring resonators in an optical APF filter play a critical role
in achieving large dispersion or delays with a low insertion loss
and flat response. Dispersion is defined as (or
, where is the delay and and are optical wave-
length and frequency). For a linear dispersion over a bandwidth
[Fig. 3(d)], . So, for a linear dispersion-com-
pensating APF, a figure-of-merit can be defined that combines
large dispersion with low loss and a flat response
In an APF that generates a constant GD within a bandwidth
BW [Fig. 3(e)], large dispersion should be replaced with a large
delay so, in this case, the figure-of-merit can be written as
IV. CONCLUSION
We have investigated the importance of intrinsic- in mi-
croring-based optical bandpass and all-pass filters using a
simple analysis based on the fundamental properties of these
filters. Insertion loss characterization of multiring filters as
a function of is a practical approach for evaluating
the performance of these filters regardless of their transfer
function and design details. Similarly using the versus
behavior of the constituent microrings of a compensator
enables a quick evaluation of the overall behavior of the filter
without involving the details of multipole interactions. Gen-
erally speaking, for most applications, the of constituent
rings in these designs should be made to be as high as possible,
even in designs where the operational quality factor
is low. High- operation is also important from a fabrication
point of view since the magnitude of the coupling factor for
a given amount of the coupled power to the ring is inversely
proportional to . So monolithic multiring filters with high-
rings can be designed with larger coupling gaps (smaller cou-
pling factors) that are easier to fabricate. We should note that
thermal and nonlinear effects may impose an upper limit on the
circulating optical power inside the ring resonators. However,
this limit is related to the operational- and not the
intrinsic- of the system. Furthermore, to obtain low
insertion loss, will be much less than and hence high
of the constituent elements of a compound filter does not
necessarily impose a power handling limitation on the filter
design.
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Importance of Intrinsic-Q in Microring-Based Optical Filters and Dispersion-Compensation Devices

A tutorial on microwave photonic filters,”

Active semiconductor microdisk devices,”

General optical all-pass filter structures for dispersion control in

Implications of fiber grating dispersion for WDM communication systems,”

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Multistage high-order microring-resonator add-drop filters,”

Optical delay lines based on optical filters,”

Optical transmission characteristics of fiber ring resonators,”

Polymer microring filters and modulators,”

Simultaneous filtering and dispersion compensation in WDM systems using apodised gratings,”

Ultralow loss, highQ, four port resonant couplers for quantum optics and photonics,”

Very highorder microring resonator filters for WDM applications,”

Wavelength-controlled photonic true time delay for wide-band applications,”

https://authors.library.caltech.edu/8859/1/HOSieeeptl07.pdf

Importance of Intrinsic-Q in Microring-Based Optical Filters and Dispersion-Compensation Devices

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