JOlJRNAL OF LIGHTWAVE TECHNOLOGY, VOL. 10, NO. 1, JANUARY 1992 57

Narrow-Band Optical Channel-Dropping Filter Hermann A. Haus, Fellow, IEEE, and Y. Lai

Abstruct- Waveguide couplers are combined with X / 4 shifted distributed feedback resonators to produce narrow-band channel dropping filters. With distributed feedback coupling parameters already realized today, one may construct banks of 40 channel- droppping filters with 10-GHz bandwidths each that do not mutually interfere. Each stage may also inject its own signal or reinject the tapped signal so that other stages can pick it up.

I. INTRODUCTION

PROMISING approach to high bit rate communication A systems is the combination of time division multiplexing (TDM) and wavelength division multiplexing (WDM) [ 11. The TDM would be run at rates compatible with electronic switching rates. The WDM would be used to increase the bit rate by utilizing the very large bandwidth of optical fibers. The hit rates accessible to electronic switching are of the order of 5 Gb/s. If the communication is at a wavelength of 1.53 pm and each channel is to be filtered efficiently, one needs optical filters of the order of 0.5 A bandwidth. These channel-dropping lilters should transfer radiation within the band to the receiver without perturbing the radiation outside the band. It is also desirable that each stage should be able to inject its own signal or reinject the tapped signal so that other stages can pick it up as well. This means, of course, that the filters be active.

The tunable filter invented by Alferness and Cross [2] is not sufficiently narrow band to be used for that purpose. In this letter we propose a filter that utilizes the resonant characteristic of several X/4 shifted DFB resonators so as to achieve an (improved) transfer characteristic. The concept originates from thc narrow-band distributed feedback reflector design [3], [4]. The fundamental structure is illustrated in Fig. 1. An optical waveguide is coupled to an adjacent waveguide made into a X / 4 shifted DFB resonator. The reflection in guide (2) [the transmission bus] is (ideally) perfect if the resonator is lossless. It is clear that the reflection will not be perfect, that part of the incident power will be absorbed, when there are finite losses in the resonator, and/or when power is coupled out of the resonator.

Near the center of the stopband, the structure of Fig. 1 can be represented by the equivalent circuit shown in Fig. 2. Here the conductances G,, Gb represent the losses due to the output coupling of the resonator to both sides. Their values can be adjusted by adjusting the grating lengths. With no output coupling, the resonator reflects perfectly at resonance, which

Manuscript received April 16, 1991. This work was supported in part by the National Center for Integrated Photonic Technology and by the Joint Services Electronics Program DAAL03-89-C-0001.

The authors are with the Department of Electrical Engineering and Com- puter Science and Research Laboratory of Electronics, Massachusetts Institute of Tcchnology, Cambridge, MA 02139.

IEEE Log Number 9103307.

hi4 4L -

input signal \

- 5 -, K waveguide (211 \ \ - Fig. 1. Schematic of one-section structure

G..

Fig. 2. The equivalent circuit near center band.

occurs at the center of the stopband. In this case G, = Gb = 0. If one shortens the length of grating on the right-hand side, Gb # 0, power is delivered to Gb. It is clear from the equivalent circuit that maximum power transfer occurs when Gb = Yo/2. Then half of the incident power is absorbed in Gb, 1/4 is reflected in the feeder waveguide, and 114 is transmitted. This is not necessarily the limit: if another lossless A/4-shifted DFB resonator is coupled to the waveguide as shown in Fig. 3, the equivalent conductance in guide (2) on the right-hand-side of resonator (1) is infinite at resonance. Thus if Gb = Yo, full power transfer from the bus to the output of resonator (a) is possible.

The structure in Fig. 3 can be used also to couple narrow- band signals into the bus (see Fig. 4). This is simply the time-reversed version of the operation we just mentioned.

The two structures in Figs. 3 and 4 can be combined into a compact form as shown in Fig. 5. The central section ensures fulI power transfer between the bus and resonators in the first and third section. The first section takes the narrow-band signal out of the bus while the third section couples the signal from the transmitter into the bus.

If one wants a receiver that can receive and retransmit the same signal at the same time, the structure in Fig. 6 can be used. The first and third sections are now directly connected with a X/4 shift. The signal is taken out from the central section. Of course one needs some gain in the central section to compensate the loss due to the output coupling.

A precise analysis of the structures requires a full analysis of the coupled mode equations and the DFB structure. In particular, the simple equivalent circuits of Figs. 2-4 do not

0733-8724/92$03.00 0 1992 IEEE

58 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 10, NO. 1, JANUARY 1991

n_h L 2 4 ..

signal to recetver

t

" G 2 - I f

to receiver from transmitter

t i Input signal ___) ------b output signal

input signal output signal - - I I I

3b I I I

hi4 I 3a

(a)

Equivalent Circuit

+ 2 4:

T + ( b)

Fig. 3. Schematic of two-section structure that couples signal out

from tla"sm,ttel

i IS1 ! hi4

Fig. 5. Schematic of three-section structure that can be used to receive signal and inject new signal.

hi4 hi4 AJ4 ! L1a I I I t I I

I

I I active layer

I \ to receive1

Fig. 6. Schematic of three-section structure that retransmit the received signal.

Option 2) is attractive because it does not require two different waveguide dispersions. Very high ti values have already been reported in the literature [5]. By picking 6 large enough one can make the stopband wide; by choosing the coupling between the two waveguides small enough one can achieve a sufficiently narrow filter bandwidth.

Unavoidable waveguide losses prevent high Q values and hence narrow filter bandwidths. Therefore, any narrow band filter of the type discussed here will have to have gain compensating for the loss. Technically, this is not a serious constraint, because the structure is merely a modification of a X/4 shifted DFB laser coupled to another waveguide.

, ,

In this paper we take up all the issues discussed in the introduction. We solve the coupled-mode equations exactly to calculate the response of the structure. We show that, with distributed feedback coupling parameters already realized

Fig. 4. Schematic of two-section structure that couples signal in.

give any information about the of the resonators on the two sides of the stopband that cause spurious responses. These spurious responses lie at the edge and outside the stop- band of the grating. In order to avoid performance degradation

today, One may construct banks Of 40 channel-dropping With 10-GHz bandwidths each that do not mUtUalIy interfere. Each stage may so that Other reinject the tapped stages can pick it up as well. caused by the spurious, one has two options:

1) The filter is designed so as to suppress the spurious

2) The stopband of each filter is made wide enough so that all channels can be accommodated within one half of the stopband. In this case none of the spurious need appear within one of the other channels.

Option 1) can be realized if one coupled waveguides of different dispersion characteristics, similar to the Alferness- Cross filter. If the coupled waveguides are sufficiently detuned at the edge of the stopband, the spurious can be suppressed.

response. 11. COUPLING EQUATIONS AND AN APPROXIMATE ANALYSIS

We donote by Ai and Bi the forward and backward ampli- tudes of the waves in guide i(= 1, a) , from which the spatial dependences exp[fj(~/h)z] have been removed. ti is the coupling coefficient of the DFB structure, p is the coupling between the two waveguides. Then the equations for the waves are:

(2.1) d

dz -Ai = - j S A I + KBI - j p A 2

HAUS AND LAI: NARROW-BAND OPTICAL CHANNEL-DROPPING FILTER 59

where h = (w - wo)/ ug is the detuning parameter, wo is the frequency at band center, wg is the group velocity, and 6 is real. A real K implies that the reference planes have been picked at a 90 distance from the peak of the index perturbation. We use the parameter o(# 1) to allow for a difference of group velocities in the two guides.

Before solving the equations exactly, it is useful to set up approximate relations for the filter structure, as has been done in [O], in order to lay out a design to zeroth order. The equiv- alent circuit of Fig. 2 is characterized by three parameters; the resonance frequency of the filter, the impedance or the external Q , Q c , and the conductance G = Gb(G, = CO) or the internal Q , Q0. The resonant frequency w, is the Bragg frequency of the DFB structure.

(2.5) , ,

where is the phase velocity and A is the grating period. The external Q of the lossfree resonator in Fig. 1 is easily computed by evaluating the power escaping from the initially excited resonator P,, and the energy W in the resonator [6]:

The inverse internal Q is given by the dissipated energy per radian divided by the internal energy. The dissipated power is, in fact, absorbed in the load (receiver).

Here we have assumed that Llb >> I&, so that the power escaping through the port on the left-hand side can be ignored. For the structure in Fig. 3, full power transfer occurs when G = Y,,. This gives a relation for the resonator length and the coupling parameter p:

(2.8) e - 2 K L 2 ~ - - 4 1 ~ / t 4 ~ .

For the structure in Fig. 3, the total Q is

and therefore the filter bandwidth is given by:

The width of the stopband, Aw, is given by

Aw, = 2v,n. (2.11)

0.6

-0.04 -0.02 0.00 0.02 0.04

8 I K

I I I I -0.04 -0.02 0.00 0.02 0.04

Fig. 7.

1 .o g 0.8

0.0 I I I I I I I -3 -2 -1 0 1 2 3

81 K

(c)

The resDonses of single resonator; the Darameters are: a = 1,

Thus, if the filter bandwidth Awf is given, and a certain width of the stopband is to be achieved, one has the constraint:

awf = 4 ~ ~ , 1 ~ / ~ 1 ~ . (2.12)

This analysis shows clearly that there is only one degree of freedom left in the design, the value of K . When K is chosen, the ratio of is fixed, and with it the resonator length. Of course, P / K must be much less than unity to start with, in order to satisfy the high-Q criterion of the approximate analysis on which it is based.

The preceding simple analysis gives the order of magnitude of the design parameters. Typically, ps of the order of 5-10 cm- are easily achievable. A K value of the order of 300 cm- has been reported [5]. Thus it appears that the designer has sufficient freedom for a wide range of filter characteristics. If one chooses K = 200 cm-I and p = 5 cm-, then the stopband is of the order of 4000 GHz and the filter bandwidth is about 10 GHz. To avoid the spurious response outside the stopband, only the central half portion of the stopband can be used (i.e., 2000 GHz). This bandwidth can

60 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 10, NO. 1, JANUARY 1992

Fig. 8.

I -0.04 -0.02 0.00 0.02 0.04

c

2 0.2 0.0

-0.04 -0.02 0.00 0.02 0.04

$ 0.6 2 0.4 c

2 0.2 0.0 EIz -3 -2 -1 &/K 0 1 2 3

(c)

The responses of single resonator with different group velocities in the two guides; the parameters are: a = 1.3, li = 200 cm-, ki = 5 cm-, L1, = 250 pm, Llh = 150 pm.

accommodate 40 channels (each with a 10 GHz bandwidth) spaced 5 times the channel width apart (i.e., 50 GHz). These results show that the design of such a filter bank is realistic

In the sequel we investigate the problem exactly as described by the differential equations.

111. RESULTS FROM EXACT ANALYSIS

Equations (2.1)-(2.4) can be integrated easily by computer, under suitable boundary conditions. Fig. 7 shows the exact evaluation of the response of the single resonator, whose approximate equivalent circuit is shown in Fig. 2. At and near resonance, the equivalent circuit is a good representation of the transmission and reflection characteristic of the structure. Indeed, at resonance, 1/2 of the power is transferred to the resonator when the Qs are adjusted optimally, as has been done for the plot; 1/4 of the power is reflected, 1/4 transmitted in the transmission bus. The plot of the response over the entire grating bandwidth shows spurious response near the edge of the stopband that is not represented by the equivalent circuit. If this response is considered deleterious,

n

I -0.02 -0.01 0.00 0.01 0.02

0.2

0.0

\ / -0.02 -0.01 0.00 0.01 -0.02

8 / K

( b)

0.4

0.2

0.0 -2 1 0 1 2

&lK

(c)

Fig. 9. The filter characteristic of the structure in Fig. 3 . The parameters are: (I = 1, K = 200 cm-, p = 5 cm-, L1, = Lz0 = Lst, = 250 pm. and Lit, = 1.50 pm.

one may remove it by changing the dispersion characteristics of the two guides, by setting a # 1 in (2.3) and (2.4). When this is done, the plot of Fig. 8 results. The spurious response has been removed at the cost of a design compli- cation.

This complication may be avoided, if one puts all channels within the stopband of the grating, within which the spurious response may be of acceptable magnitude. We shall assume that to be the case when analyzing the more complicated structures below that transfer (practically) all the power from the bus to the channel dropping filter and are capable of retransmitting the signal.

Fig. 9 shows the response functions of the two-section structure in Fig. 3 for the case a = 1, K = 200 cm-, p = 5 cm-, L1, = Lsa = L36 = 250pm, and Llb = 150 pm. One can see clearly the correspondence with the prediction of the equivalent circuit of Fig. 2 although the correspondence is not perfect. One also sees the spurious response outside the grating stopband (Fig. 9(c)). The spu-

UAUS AND LAI: NARROW-BAND OPTICAL CHANNEL-DROPPING FILTER 61

0.0 -0.04 -0.02 0.00 0.02 0.04

u.u , I I I I -0.04 -0.02 0.00 0.02 0.04

-1 0 1 I -2

(c)

Fig. IO. The filter characteristic of the structure in Fig. 6. The parame- ters are: ( I = 1.0, K = 200 cm-l, p = 5 cm-I, L1, = 300 pm, I , , , , z L:,,, = 173 pm and L3b = 75 pm, The gain constant in the central DFR section is 0.38 cm-I.

rious response could be suppressed without affecting the response at band-center if the group velocity in the two guides is different. However, for our purposes, we do not need it because we have already had enough bandwidth to spend.

The response curves of the structure in Fig. 6, with the parameters as indicated, are shown in Fig. 10. One can see that the signal is indeed successfully retransmitted. However, due to the coupling, the resonances of the X/4- shifted DFB resonators in the first and third section are split. They are responsible for the sharp dips in Fig. 10(b). The dips do not degrade the performances because they are off the signal frequency. By keeping the adjacent channels far apart (say, 50 GHz in our example), the dips will not interfere with the adjacent channel either. The side peaks in Fig. l0(a) are caused by the same effect. Since they are already very small (and off the signal frequency), one may be able to ignore them. The examples we chose are intended for illustration, not as examples of optimum design.

IV. CONCLUSIONS We have shown the possibility of using coupled waveguides

and X/4 shifted DFB resonators to arrive at a narrow-band channel-dropping filter. The bandwidth of the filter can be made much narrower than the stopband of the grating. Even if todays technology is not quite ready to realize a filter of the ideal characteristics shown, it is only a matter of time that it will catch up.

It is possible to remove the spurious responses of the grating filter by appropriate dispersion characteristics for the coupled waveguides. However, in some practical applications it may not be necessary to do this, if all channels can be accommodated within half the grating bandwidth of the filters.

In another paper [7], we have studied side-coupled cascades of resonator structures. One may be able to use cascade structures to achieve desirable filter responses.

ACKNOWLEDGMENT

H. A. Haus gratefully acknowledges stimulating discussions with Dr. K. Utaka of KDD, Japan.

REFERENCES

[ l ] For example, see H. Toba et al., A 100-channel optical FDM trans- missionidistribution at 622 Mb/s over 50 km, J. Lightwave Technol., vol. 8, pp. 1396, 1990.

[2] R. C. Alferness and P. S. Cross, Filter characteristics of codirection- ally coupled waveguides with weighted coupling, IEEE J. Quantum Electron., vol. QE-14, pp. 843, 1978.

[3] R. F. Kazarinov, C. H. Henry, and N. A. Olsson, Narrow-band resonant optical reflectors and resonant optical transforms for laser stabilization and wavelength division multiplexing, IEEE J. Quantum Electron., vol. QE-23, p. 1419, 1987.

[4] For experimental demonstration, see N.A. Olsson et al., Narrow linewidth 1.5 pm semiconductor laser with a resonant optical reflector, Appl. Phys. Lett., vol. 15, p. 1141, 1987.

[5] H. A. Haus and Y. Lai, Narrow-band distributed feedback reflector design, to be published in J. Lightwave Technol.

[6] H. Hillmer, S. Hansmann, and H. Burkhard, Realization of high coupling coefficients in 1.53 p m InGaAsP/InP first order quarter-wave shifted distributed feedback laser, Appl. Phys. Lett., vol. 57, p. 534, 1990.

[7] H.A. Haus and Y. Lai, Theory of cascaded quarter wave shifted distributed feedback resonators, submitted to IEEE J . Quantum Electron.

Hermann A. Haus (S50-A55-SM58-F62) was born in Ljubljana, Yugoslavia, in 1925. He attended the Technische Hochschule, Graz, and the Technische Hochschule, Vienna, Austria He received the B.Sc degree from Union College, Schenectady, NY, in 1949, the M S. degree from Rensselaer Polytechnic Institute, Troy, NY, in 1951, and the Sc.D. degree from the Massachusetts Institute of Technology, Cambridge, in 1954 He received honorary doctors degrees from Union College and the Technical University of Vienna.

He joined the Faculty of Electrical Engineering at MIT, Cambridge, in 1954, where he is an Institute Professor He is engaged in research in electromagnetic theory and lasers He is the author or coauthor of five books and over 200 journal articles

Dr. Haus is a member of the American Physical Society, the National Academy of Engineering, the National Academy of Sciences, and a Fellow of the Optical Society of America, and the American Academy of Arts and Sciences.

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 10, NO. 1, JANUARY 1992

Y. Lai received the B.S. degree in electrical engi- neering from National Taiwan University, Taiwan, in 1985 and the M.S. and Ph.D. degrees in elec- trical engineering from Massachusetts Institute of Technology (MIT), Cambridge, in 1989 and 1991, respectively. He joined the Faculty of the Institute of Electro-Optical Engineering at the National Chiao- Tung University, Taiwan, in 1991, where he is an Associate Professor. His research interests include nonlinear optical pulse propagation, quantum optics, short optical pulse generation and applications, and optoelectronics.