Reflectionless multichannel wavelength demultiplexer in a transmission resonator configuration
ABSTRACT A wave demultiplexer system with N channels in a two-dimensional photonic crystal is proposed. The demultiplexer is realized by the coupling among an ultra-low-quality factor microcavity and N resonators with high-quality factor. The coupling mode theory is employed to analyze the behavior of this system. The analytic results reveal that the reflection is fully absent at the peak frequencies for all channels. The simulations obtained by multiple-scattering method and experimental results in the microwave region show that the analysis is valid. This method might also be valuable for the design of other all-optical functional circuits.
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ABSTRACT: The use of computational electromagnetics (CEM) techniques has greatly advanced nanophotonics. The applications of nanophotonics in turn motivates the development of efficient highly tailored algorithms for specific application domains. In this paper, we will discuss some specific considerations in seeking to advance CEM for nanophotonic design and discovery, with examples drawn from the design of aperiodic nanophotonic structures for on-chip information processing applications.Proceedings of the IEEE 01/2013; 101(2):484-493. · 6.91 Impact Factor
160IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 1, JANUARY 2003
Reflectionless Multichannel Wavelength
Demultiplexer in a Transmission
Chongjun Jin, Shanhui Fan, Shouzhen Han, and Daozhong Zhang
Abstract—A wave demultiplexer system with
two-dimensional photonic crystal is proposed. The demultiplexer
is realized by the coupling among an ultra-low-quality factor
resonators with high-quality factor. The
coupling mode theory is employed to analyze the behavior of
this system. The analytic results reveal that the reflection is fully
absent at the peak frequencies for all channels. The simulations
obtained by multiple-scattering method and experimental results
in the microwave region show that the analysis is valid. This
method might also be valuable for the design of other all-optical
channels in a
Index Terms—Microcavity, photonic crystal, resonant couple,
Commercially available wavelength demultiplexer systems,
such as planar lightwavecircuit-based arraywaveguide gratings
– and fiber gratings , tend to occupy a footprint of
at least one centimeter square. There is therefore tremendous
interest in developing devices that are more compact.
Recently, photonic crystal based wavelength demultiplexers
attracted much attention – as potentially viable schemes
for device miniaturization. Photonic crystals are artificial struc-
tures composed of periodically arrayed dielectric media ,
. These structures have been found to be very useful in
the design of all-optical devices . For wavelength demul-
tiplexer applications, photonic-crystal-based mechanisms that
have been proposed include the channel-drop tunneling scheme
–, the super-prism effect , and the frequency-selective
media –. Among all of these mechanisms, the most com-
pact configurations involve the interactions of waveguides with
it is crucial that the reflection be eliminated. Previously, the
elimination of reflection is achieved by side coupling the cavity
to the waveguides, and by adjusting the symmetry properties of
AVELENGTH demultiplexers play an important role
in enhancing the capacity of optical communications.
Manuscript received January 31, 2002; revised August 13, 2002. This work
was supported by the NNSFC, by the Chinese National Key Basic Research
Special Fund (CNKBRSF), and by the National Research Center for Intelligent
Computing Systems under Grant 99104.
of Physics and Center for Condensed Physics, Chinese Academy of Sciences,
Beijing, 100080, China.
S. Fan is with the Department of Electrical Engineering, Stanford University,
Stanford, CA 94305-4085 USA.
Digital Object Identifier 10.1109/JQE.2002.806188
multichannel. (b) Schematic electronic circuit of the multichannel filter.
(a) Schematic optical circuit for realizing a wave demultiplexer with
the cavity modes . Doing so, however, tends to require de-
tailed tunings of the cavity properties, which represent a chal-
lenge in device designs and fabrications.
In this paper, we introduce a photonic crystal demultiplexer
structure based upon the coupling among a microcavity with an
ultra-low-quality factor and transmission resonators with high-
quality factors, as shown schematically in Fig. 1(a). The config-
uration consists of
a microcavity with low-quality factor. Each resonator possesses
a resonant frequency at a particular signal frequency channel,
to allow for a frequency-selective transmission of the frequency
channel into the corresponding waveguide. In general, in trans-
mission resonator configurations, signals at frequency channels
away from the resonant frequency are reflected. Here, however,
we introduce a theoretical criterion to show that by appropriate
design of the waveguide branches, the overall reflection from
the demultiplexer device can, in fact, be completely eliminated
for all frequency channels. We substantiate our theoretical anal-
ysis with numerical and experimental work. In such, our design
represents an optical analog of a classic electronic filter circuit,
as shown in Fig. 1(b), where
inductance–capacitance (LC) resonant circuits with
near 100% efficiency and no reflections .
channels can be perfectly sepa-
0018-9197/03$17.00 © 2003 IEEE
JIN et al.: REFLECTIONLESS MULTICHANNEL WAVELENGTH DEMULTIPLEXER IN A TRANSMISSION RESONATOR CONFIGURATION161
composed of two-dimensional photonic crystal. (b) Corresponding straight
(a) Cross section of the wave demultiplexer with two channels
Let us start by considering the case with only two channels
before we generalize the analysis to
a structure consisting of an input waveguide split into two out-
going waveguides at a T-branch, as shown in Fig. 2(a). Within
each outgoing waveguide, we place a resonator, labeled
cylinders at either side of the defect cylinder. Furthermore, the
as an ultra-low-quality factor microcavity, labeled as
Therefore, we can describe the whole optical system in terms
of the coupling among the three microcavities, and deduce its
properties using coupled mode theory. As the losses of the cavi-
ties can be designed to be very small, and the coupling between
and is negligible, the coupling equations can
be written as 
channels. We consider
of the resonant modes for
the decay rate of the microcavity
through the port
the input and output waves at the port
represents the coupling coefficient between resonant cavities.
Using (1)–(4), the transmittivity
, respectively, and the reflectivity , can be determined as in
(5)–(7), shown at the bottom of the page.
For a full demultiplexing operation in a wavelength-divi-
sion-multiplexing (WDM) system, we would like to completely
transmit each frequency channel to an appropriate corre-
sponding output waveguide without any reflection or crosstalk.
In this two-channel WDM device, therefore, we will be pri-
marily interested in the response function of the system in
the vicinity of the resonant frequencies
we would like the reflectivity to vanish, i.e.,
and. Also, at each frequency channel
or, we would like the corresponding transmittivity,
, respectively, to reach 100%, while the other transmittivity
becomes zero, in order to eliminate crosstalk. From (5)–(7),
shown at the bottom of the page, one could easily check that
this ideal behavior can be achieved provided that the following
three criteria are satisfied:
and aretheresonant frequenciesand theamplitudes
due to the power escape
,and denote the field amplitudes of
), respectively, is
, respectively, and
andat the portsand
, for both
Here, in (8) and (10),
cavities in the outgoing waveguides.
Let us give a brief physical discussion of each of these three
criteria above. Equation (8) indicates that the frequency chan-
nels of the signals should fall within the resonant line shape
represents the label for the
162IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 1, JANUARY 2003
Fig. 3.Schematic picture of the coupling between two resonators.
of the branch; this should hold true for any broad-band splitter
structures . Equation (9) requires that the microcavities
andshould possess sufficiently high-quality factors in order
to provide the necessary distinction between nearest neighbor
microcavity filter structure. The key designing consideration is
then encapsulated in (10). Simply put, this equation relates the
coupling constants between the cavities to the decaying rate of
the cavities to each individual port.
coupling constant between two cavities that are connected with
a waveguide, as shown in Fig. 3. Our treatment closely follows
Fig. 3 are
time of the two cavities, respectively,
coming and outgoing waves for the th cavity at either the input
or the output waveguide, while
and outgoing waves for the th cavity in the connecting wave-
guide. Furthermore, due to the wave propagation within the
waveguide, we have
and,are the frequencies and the decaying
and are the in-
and are the incoming
Combining (14), (16)–(18), we have
fective coupling constant between the two cavities. In this way,
one could write the coupling constant between the two cavities
Comparing (21) with (10), we see that the criterion outlined
above can indeed be achieved with
, and. Therefore, it can be deduced that
. Thus, ideal performance for our
demultiplexer can be realized by using a symmetric waveguide
and a symmetric branch, and by choosing the appropriate phase
shift between the branch and the high-Q cavities.
We note that, in general, the phase
However, since the entire signal bandwidth is typically only on
the order of a few percent of the carrier frequency, the variation
over the entire signal bandwidth should be small. Also, in
general the phase shift can only determined by detailed electro-
magnetic simulations. The analytic calculations above however
establish the basic criteria for the design procedure. Finally, for
our purposes here, the choice of phase factor at
avoids the diverging point of the coupling constant
the coupling constant between the cavities diverge, and it is no
longer appropriate to describe the system in terms of the cou-
pling coefficients . However, even in this case, there is still a
valid physical solution to (11)–(16). Such a physical solution
corresponds to the situation where the resonant amplitudes in
the two resonators oscillates exactly in phase.
We shall emphasize that a symmetric branch, as character-
ized by equal decay of the resonance to each of the branches,
generates a finite reflection  by itself. In this design, it is
precisely this finite reflection from the branch that cancels the
reflected amplitude from the high-Q resonances, resulting in an
overall reflectionless operation at every frequency channel for
To visualize the behavior of our analytic theory, we plot the
), (,), and (,
and (0.96, 0.0005), respectively. It can be found that
indeed approach 100% at the resonant frequencies, while the
reflection vanishes at these frequencies. Thus, our theory does
indeed predict the presence of an ideal demultiplexer.
We can generalize the results, as described above for a two-
channel demultiplexer, to a system with
structure is shown in Fig. 5, where each port outputs a spe-
cific frequency channel. Using similar theoretical derivations,
is frequency dependent.
) as (1.0, 0.5), (1.04, 0.0005),
output ports. The
JIN et al.: REFLECTIONLESS MULTICHANNEL WAVELENGTH DEMULTIPLEXER IN A TRANSMISSION RESONATOR CONFIGURATION 163
in Fig. 2(a). assuming that (? , ??? ), (? , ??? ) and (? , ??? ) are (1.0, 0.5),
(1.04, 0.0005 ), (0.96, 0.0005) respectively.
Transmission spectra for a two-channel wave demultiplexer, as shown
the transmittivity at a particular port
(22), shown at the bottom of the page.
Equation (22) describes a system that is represented in
Fig. 1(a). To apply (22) to a system as shown in Fig. 5, we note
that the essence of the derivation is the presence of a symmetric
branch with the reflection amplitude equal to the transmission
amplitude into the each of the branch. It is, therefore, conceiv-
able that such a branching structure can be built with a tree-like
structure. We will investigate this further in later works.
From (22), it can be clearly seen that, at a frequency channel
, when the criteria as described by (8)–(10) are satisfied,
thetransmittivitiesofallportsare zeroexceptfor port
it reaches 100%. No reflection can be found at the input port
for all frequency channels. In order to visualize the prop-
agation properties described by (22), the transmission spectra
of each port in a 16-channel wave demultiplexer are plotted in
Fig. 6, where assuming that
is 0.0001. It is clear that the transmittivity at each port does ap-
To test the validity of the above approach, the multiple
scattering method ,  is employed to simulate the
propagation of waves in these structures. An experiment in
setup can be found elsewhere . Here, we adopt the structure
as shown in Fig. 2(a), the parameters of this photonic crystal
wave demultiplexer are chosen as follows. The photonic crystal
with a lattice constant
is composed of 0.182 radius dielectric
cylinders imbedded in a background dielectric medium. The
dielectric constants of the cylinders and background are 8.0
can be expressed as in
is 0.5, ()
in two-dimensional photonic crystal.
Schematic optical circuit for realizing ? channels wave demultiplexer
that ??? is 0.5 and ??? (? ? ? ? ??) is 0.0001.
Transmission spectra for a 16-channel wave demultiplexer assuming
and 1.03. respectively. The first band gap of this crystal for
S-polarized waves is in the range of 0.36 0.46
is the light velocity in vacuum. Point defect is created by
replacing a selected cylinder with a dielectric cylinder with
different radius and dielectric constant.
special cylinders and serve as two point defects, and their
radius and dielectric constants are 0.182 , 1.0 and 0.273 ,
8.0 respectively. In the simulation, we integrate the energy
fluxes at two outlets respectively. Meanwhile, the energy flux
at the outlet of a corresponding straight waveguide shown in
transmission spectrum, which is a ratio of the flux at the outlet
of the demultiplexer to that of the straight waveguide from
each outlet. From the spectrum. one can confirm whether the
reflection from the input port exists at the peak frequencies.
The measured and simulated transmission spectra are plotted
164IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 1, JANUARY 2003
outlets of the demultiplexer.
Measured and simulated renormalized transmission spectra at the
in Fig. 7, where diamond and solid circles are the experimental
values obtained from
solid and dashed lines are the corresponding simulations. It
is found that the transmission to the
Lorentzian peak at a resonant frequency of 0.4420 (
the transmission to
port also shows a single Lorentzian
peak at a resonant frequency of 0.4068 (
both peaks have their maximal transmissivity approaching
100%. Because both simulations and experiments presented
in this paper incorporate the reflection from the interfaces
at the edges of the crystal and therefore does possess some
error that over 100% transmission appears at the peak of the
port–3 spectrum. However, the presence of large transmitted
amplitudes at both frequencies is a strong and clear evidence
that the cancellation of reflection amplitude is at work here.
From energy-conservation considerations, the existence of a
near-complete transmission at these two frequencies indicates
that the reflection is small for both frequencies for the structure.
Furthermore, both the experimental and simulated results agree
well with each other, except that there exists a little peak in
andports which might be caused by very small
interaction between microcavities
reveal that directly coupling resonant tunneling effect can be
used to design wavelength demultiplexer with no reflection
at the peak frequencies.
In conclusion, we introduce a wavelength demultiplexer
microcavities with high-quality factors. This optical circuit
is similar to the low-frequency multichannel filter electronic
circuit. The merit of this optical circuit is that the design
of such a circuit is very simple because one might build
a defect to extract a peak frequency and the technological
wave demultiplexer. Furthermore, the reflection at the peak
frequencies can be fully eliminated compared with the other
method where considerable reflection appears. Eventhough our
simulation and experiment are working in a two-dimensional
photonic crystal, our theory based on the coupling theory
can be valid for both two- and three-dimensional photonic
ports, respectively, while the
port exhibits a single
and. These facts
crystals. This method might also be valuable for the design
of other all-optical functional circuits.
The authors would like to thank Prof. Z. Zhang from HKUST
for his program of multi-scattering method. They also thank the
National Research Center for Intelligent Computing System for
use of the Dawning-2000A parallel computer.
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Englewood Cliffs, NJ:
JIN et al.: REFLECTIONLESS MULTICHANNEL WAVELENGTH DEMULTIPLEXER IN A TRANSMISSION RESONATOR CONFIGURATION 165
Chongjun Jin was born in Zhejiang Province, China, in 1969. He received the
Ph.D. degree in physics from Harbin Institute of Technology, Harbin, China, in
jing, China, since 1997, where he is currently an Associate Research Scientist.
He is also a Research Assistant at the Department of Electrical and Electronics
Engineering, University of Glasgow, Glasgow, U.K. His main research interests
are as follows: applications of photonic crystals in the fields of optoelectronics,
preparation of three-dimensional photonic crystals through the self-assembly
method, nonlinear effects of photonic crystals, simulation of the propagation of
photonic crystals using wet and dry etching.
Shanhui Fan received the Ph.D. degree in physics from the Massachusetts In-
stitute of Technology (MIT), Cambridge, in 1997.
Hehas beenanAssistant ProfessorofElectrical EngineeringatStanfordUni-
versity since 2001. Previously, he was a Research Scientist at the Research Lab-
oratory of Electronics, MIT. His research interests are in computational and the-
oretical studies of the basic properties and applications of micro- and nano-pho-
tonic structures. He has published 47 journal articles, has given more than 20
invited talks at U.S. and international conferences, and holds 11 patents.
Shouzhen Han was born in Hebei Province, China, in 1976. He received the
Master’s degree from Beijing Polytechnic University, Beijing, China, in 2002.
He is currently working toward the Ph.D. degree at the Institute of Physics,
Chinese Academy of Sciences, Beijing, China.
Daozhong Zhang was born in Sichuan Province, China, in 1943. He graduated
from the Chinese University of Science and Technology in 1965.
Since then, he has been with the Institute of Physics, Chinese Academy of
Sciences, Beijing, China, where he is currently a Research Scientist and the
Director of the Optical Physics Laboratory. His research interests include laser
spectroscopy of atoms and molecules, nonlinear optics, photonic crystals, and
light localization. He has published more than 100 papers.