Mach Zehnder Interferometer for Wavelength Division Multiplexing

Ary Syahriar

Pusat Pengkajian dan Penerapan Teknologi Informasi dan ElektronikaBadan Pengkajian dan Penerapan Teknologi

e-mail : ary@inn.bpPt.go.id

AbstractA theoretical analysis of multiplexing based on Mach-Zehnder interferometer is presinted.

The output characteristics and ITU channel separation variation of an equal arm-length

interferometer are analyzed. The theory and numerical simulation results have some direct

fu n c t i o n fo r p r a c t i c a I fab r i c a t i on of t h e d ev i c e s

1. Introduction

In modern communication systems narrow band information services and high-speed data

and video information services are expected to be integrated in one-cofiununication networks Il].Wavelength Division Multiplexing (WDM) is believed to be one of the most practical ways to

achieve transmission capacities of a few tera bit per second (Tb/s). Devices such as optical filters

and wavelength multiplexers (MUXER) and demultiplexers (DEMUXERS), which manipulate

optical properties in wavelength domain, are essential to WDM optical communication systems.

One of the most useful device is the Mach Zehnder Interferometer (MZI) l2l.It consists of two 3-dB coupler which has been butt spliced to build the interferometers.

The most important parameters in MZI is the difference in path length which basically will

determine the MZI's characteristics.In this paper the analysis of MZI based on coupled mode theory and matrix transmission

method is presented. A number of its features will also be explained.

2. The MZI Structure

A Mach-Zehnder device consists of two 3 dB fused couplers, between which a phase

difference is introduced in the two paths by increasing one of the path lengths with respect to the

orher as shown in Figure 1. The fused couplers are wavelength sensitive; hence the characteristics

of the device are determined by the 3 dB crossover wavelength of the couplers, the coupling

strength and the introduced path difference.

Co ler 2

Input 1

Input 2

Output I

Outout 2

up

Iv

Figure I. Schematic diagram of Mach-Zehnder intederometer

For modeling purposes the device can be divided into three constituent parts: the two 3 dBcouplers and a phase shifting section between them. The characteristic of each of the comporiBnts

parts of the device can be represented by the operation of matrix in a vector which represents the

amplitude of the signals in each of the two fiber at the input to that section based on the coupled

mode theory as [3]:

I cos(@) -7sin(o)-lM : l ' J--- \

| ( l )' - couPter [- ysin(O) cos(O) I

here (D = KZ t r= coupling coefficient, and z: 3 dB coupler length'

The field in the two differential path lengths introduces a phase shift represented by [4]

A-46 Proceedings, Komputer dan Sistem Intelijen (KOMMIT 2002)Auditorium Universitas Gunadarma, Jakarta, 2l -22 Agustus 2002

f eio o IM rn,*-stt, =1,

"-r, )where d = f M, and pis the effective index of the optical fiber. AI is the phase different between

the two arms. As is well known, the pvalue can be calculated by solving the characteristic equation

for LPor mode [3]:

wJ, (u ) K | (w ) = uJ | (u ) K " (w ) (3)

the

(2)

where Jo and J1 areBessel functions and K, and K1 are modified Bessel functions. For single mo&

operation V<<2.4048. U and Whave its usual meanings [3]'

For fiber couplers the coupling coefficient ris given by [3]:

o rr2 x"(Y!)/L \J A_ e)K =

27Tq a'zY2V@

here dis the separation between the fiber axes, d is fiber diameter, / is a normalized frequency, 'l fo

the wavelength and n1 is core refractive index of the fiber'

The response of Mach-Zehnder then is given by [5]

l7f = M "orrlerM

phase'shiftM "ouPI"'

and the output amplitude can be described by

Eou,ou,=ME,nou, tut

Where the input amplitude is represented by a vector

l-t l"*'

= Lo.J c'D

In this calculation a perfect 3 dB coupler has been assumed and that the fiber has no propagarb

loss.

3. The MZI Characteristics

To optimize the design of I'{rZI, it is important tocalculate and

performance. The first calculation is to find the effective refractive indexpredict

of fiber optics

Mach Zehnder Interferometer for Wavelength Division Multiplexing A-47

function of wavelength. Figure 2 shows the effective refractive index of fiber as a function ofwavelength. This is derived by finding root of Equation (3) which can easily be done usingbisection method. The linear response of refractive index shows that the fiber acting in single moderegion. Furthermore it can be used to predict the change of output characteristic as function of*'avelength.

r.46733r.46732r.4673rr.4673

r.467291.46728r.46721r.46726r.4672sr.467241.46723

I 528 1536 1s44 1552

Wavelength (nm)

Figure 2. Effective refractive index as afunction ofwavelengths

Figure 3. shows AI change as function of 1" on n phase shift different of the nvo arms. Itshows that M change as linear function which can be used to predict exact path difference indesigning multi/demultiplexing devices.

C)

. l iHc)li

C)

(),!2.*r r l

2.14118

2.I4TI6

2.I4t t4

E 2.raII2S z. t4t l{{ z.t+ros

2.r4t06

2.t4r04

2.t4t021528 1536 ts44 T552

Wavelength (run)

1560

Figure 3. Arm length different of MZI asfunction of Wavelengthfor d2 phase shift

A48 Proceedings, Komputerdan Sistem Intelijen (KOMMIT 2002)Auditorium Universitas Gunadarma, Jakarta, 2l -22 Agustus 2002

The typical output spectra'of an MZI are shown in Figure 4 with different path length. Aswe can see, this bi directibnal multi-window WDM acts as a special multiplexer whichcombine/separates two sets of wavelengths, which are interleaved by each other. Because thetransfer function is actually perio$ic in the frequency domain, once the first and the last desiredwavelengths are set at the ITU frequency, the rest of the wavelength peaks in between willautomatically sit at their respective ITU wavelengths. Because the 3-dB couplers have a broadbandwidth, this device also shows superior uniformity on the insertion loss of the wavelength peak.

r528 1552 1560

-60

-10

^ -20

b -30

- -40

1536 1544

Wavelength (nm)

(a)

-10

^ _20

b -30

F< -40

-50

1536 t544 1552

Wavelength(nrt

A,L=0.15 pm

L,L:0.3 pm I I

1528

(b)

1560

Mach Zehnder Interferometer for Wavelength Division Multiplexing A-49

0

-10

-20

-30

-40

-50

-601528

0

1536 r544 r552 l 560

(c)

E

ti

B

-10

-20

-30

-40

-50

-60t528 1536 1544 1552

Wavelength (nnr)

(d)

Figure 4. MZI spectra with dffirent AL length

1560

i i It r Ila

II

la

,IIIt '

ut l

r fa lt t

t

(T,I

I

l !

I t

l l

II

t

tII

output i I l

LL--0.5 pm

\ lt lt t

III

I

I

1tl l

t l

II

I{

I tt l

lrIttIItII

LL:0.78 pm

I I

l l

t l

I

a

I

I

I

t

I

I

t l

l l

I II

IItIIIIIf

A-50 Proceedings, Komputer dan Sistem Intelijen (KOMMIT 2002)Auditorium Universitas Gunadarma, Jakarta, 2l - 22 Aeustus 2002

4. Conclusion

We have demonstrated a WDM device based on fiber optics Mach Zehnder interferometer.We investigated the spectral change as a function of wavelength in S-band region. Additionally toimprove device performance a phase length different can be tuned to comply with ITU grid.

Reference

R. Ramaswami, "Optical fiber communication: from transmission to network", IEEE.Commun. Mag., 50'h Anniversary comm.Issue, 138-147,2002.M.J. Yadlowsky, E.M. Deliso, v.L. Da Silva, "opticar fibers and amplifiers for wDMsystems", Proc. IEEE, vol. 85, 1765-1779,1997.D. Marcuse, Theory of dielectric waveguides, Academic press, New york 1990.R. Adar, C.H. Henry, M.A. Milbrodt, R.C. Kistler, "Phase coherence of optical waveguide''.IEEE J. of Lighwave Technol., vol. 12, 603-606,1994.T. Erdogan, T.A. strasser, M.A. Milbrodt, E.J. Laskowski, c.H. Henry, G.E. Kohnke."Intergrated Mach-Zehnder add-drop filter fabricated by a single UV-induced gratingexposure", Appl. Optics. Vol. 36, 783 8-78 45 , 1997 .

t l l

L2)

t3ll4l

l5l