# 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:**A novel approach is proposed to design super narrowband DWDM Filters consisting of multiple quantum wells (MQWs) by employing photonic crystals. Numerical investigations prove that the closed-cavity MQWs are more suitable for DWDM systems compared with the open-cavity MQWs. It is shown that different confined states could emerge from photonic band gap, which can be used as high-frequency carriers one-to-one. It is also found that these proposed MQWs could split the single spectral lines into multiples based on the effect of spectral splitting, and the number of the splitting is just equal to the number of the wells. In this way, the density of carriers can be increased multiplicatively in the same wave band, and thus the spectral efficiency can be improved multiplicatively. These results provide the prospects of channel density maximization and effective bandwidth optimization for optical communication.Journal of Physics Conference Series 03/2011; 276(1):012066. - SourceAvailable from: David A. B. Miller[show abstract] [hide abstract]

**ABSTRACT:**We present an extremely compact wavelength division multiplexer design, as well as a general framework for designing and optimizing frequency selective devices embedded in photonic crystals satisfying arbitrary design constraints. Our method is based on the Dirichlet-to-Neumman simulation method and uses low rank updates to the system to efficiently scan through many device designs.Optics Letters 02/2011; 36(4):591-3. · 3.39 Impact Factor - SourceAvailable from: Kiazand Fasihi03/2012; , ISBN: 978-953-51-0170-3

Page 1

160IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 1, JANUARY 2003

Reflectionless Multichannel Wavelength

Demultiplexer in a Transmission

Resonator Configuration

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

microcavity and

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.

channels in a

Index Terms—Microcavity, photonic crystal, resonant couple,

wavelength-demultiplexer.

I. INTRODUCTION

W

Commercially available wavelength demultiplexer systems,

such as planar lightwavecircuit-based arraywaveguide gratings

[1]–[3] and fiber gratings [4], 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 [5]–[11] as potentially viable schemes

for device miniaturization. Photonic crystals are artificial struc-

tures composed of periodically arrayed dielectric media [12],

[13]. These structures have been found to be very useful in

the design of all-optical devices [14]. For wavelength demul-

tiplexer applications, photonic-crystal-based mechanisms that

have been proposed include the channel-drop tunneling scheme

[5]–[7], the super-prism effect [11], and the frequency-selective

droppingofphotonsfromwaveguidechanneltothesurrounding

media [8]–[10]. Among all of these mechanisms, the most com-

pact configurations involve the interactions of waveguides with

microcavities[5]–[10].Forpracticalimplementations,however,

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.

C.Jin,S.Han,andD.ZhangarewiththeOpticalPhysicsLaboratory,Institute

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

(a)

(b)

Fig. 1.

multichannel. (b) Schematic electronic circuit of the multichannel filter.

(a) Schematic optical circuit for realizing a wave demultiplexer with

the cavity modes [5]. 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

transmission resonators,

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

rated by

inductance–capacitance (LC) resonant circuits with

near 100% efficiency and no reflections [15].

branches, and

channels can be perfectly sepa-

0018-9197/03$17.00 © 2003 IEEE

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JIN et al.: REFLECTIONLESS MULTICHANNEL WAVELENGTH DEMULTIPLEXER IN A TRANSMISSION RESONATOR CONFIGURATION161

(a)

(b)

Fig. 2.

composed of two-dimensional photonic crystal. (b) Corresponding straight

waveguide.

(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

,respectively.Eachoftheresonatorsissymmetricalwithtwo

cylinders at either side of the defect cylinder. Furthermore, the

T-branchwaveguideandthebentwaveguidescanbeconsidered

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

the cavities

and is negligible, the coupling equations can

be written as [17]

channels. We consider

and

[16].

(1)

(2)

(3)

(4)

where

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.,

frequency channels

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

and. Ideally,

, for both

or

(8)

(9)

(10)

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

(5)

(6)

(7)

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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 [14]. Equation (9) requires that the microcavities

andshould possess sufficiently high-quality factors in order

to provide the necessary distinction between nearest neighbor

channels.SucharequirementistypicallysatisfiedforanyWDM

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.

Weshallnowseehow(10)canbesatisfied,byconsideringthe

coupling constant between two cavities that are connected with

a waveguide, as shown in Fig. 3. Our treatment closely follows

HausandLai’stheoryoncoupledcavitystructures[18].Briefly,

thecoupled-modetheoryequationsthatdescribethestructurein

Fig. 3 are

(11)

(12)

(13)

(14)

(15)

(16)

Here,

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

(17)

and

(18)

Combining (14), (16)–(18), we have

(19)

and

(20)

whichcanbepluggedbackinto(11)and(12)todetermineanef-

fective coupling constant between the two cavities. In this way,

one could write the coupling constant between the two cavities

as

(21a)

(21b)

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

of

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

foreleadstoasimplifiedformalism.Inthecaseswhere

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 [16] 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

the demultiplexer.

To visualize the behavior of our analytic theory, we plot the

resultsofequations(5)–(7)inFig.4,intheregimewherethecri-

teria(8)–(10)aresatisfied.Forconcreteness,wehavearbitrarily

chosenthenormalizedresonantfrequenciesanddecayrates(

), (,), 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.

and there-

,

,

) as (1.0, 0.5), (1.04, 0.0005),

and

output ports. The

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JIN et al.: REFLECTIONLESS MULTICHANNEL WAVELENGTH DEMULTIPLEXER IN A TRANSMISSION RESONATOR CONFIGURATION 163

Fig. 4.

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-

proach100%atresonantfrequency.Thatisan

demultiplexer.

To test the validity of the above approach, the multiple

scattering method [19], [20] is employed to simulate the

propagation of waves in these structures. An experiment in

themicrowaveregionisalsocarriedout,thedetailedexperiment

setup can be found elsewhere [21]. 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

,where

is 0.5, ()

channelswave

Fig. 5.

in two-dimensional photonic crystal.

Schematic optical circuit for realizing ? channels wave demultiplexer

Fig. 6.

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

Fig.2(b)isalsocalculated.Forclarity,wedefinearenormalized

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

, where

andare two

(22)

Page 5

164IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 1, JANUARY 2003

Fig. 7.

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

and

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

both of

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

operatingbythecouplingamongalow-qualityfactorcavityand

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

complexityisreducedcomparedwiththechanneldroptunneling

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

), while

). Moreover,

and. These facts

crystals. This method might also be valuable for the design

of other all-optical functional circuits.

ACKNOWLEDGMENT

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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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

1997.

HehasbeenwiththeInstituteofPhysics,ChineseAcademyofSciences,Bei-

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

electromagneticwavesinphotoniccrystals,andpreparationoftwo-dimensional

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.

Dr.FanisamemberoftheAmericanPhysicalSocietyandtheOpticalSociety

of America.

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.