Design of epitaxial AlGaAs multilayer structures: interference filters and optically controllable reflection modulators

Design of epitaxial AIGaAs multilayer structures: interference filters and optically controllable reflection modulators H. FOUCKHARDT, M. WALTHER, TH. HACKBARTH, K.J. EBELING Dielectric interference filters incorporating an epitaxial anti-reflector structure and a concept for an all-optical reflection modulator are introduced. They are suitable for two-dimensional digital optical signal processing in an AIGaAs system employing molecular beam epitaxy. The reflection modulator concept uses dynamic band filling in multiquantum wells to obtain a bleachable absorption type optical non-linearity and promises more than 80% modulation depth. The numerical investigations are carried through with the help of two equivalent mathematical approaches which are explained in detail. Calculated results show satisfying agreement with experiments. KEYVVORDS: integrated optics, signal processing, interference filters, optical switching, reflection modulators, semiconductor devices

Introduction Optical data processing using integrated optics has gained growing attention because it shows a reduced necessity for conversions between optics and electronics j. To exploit fully the potential of optics two-dimensional signal processing with 2-D arrays of devices (for example, modulators or amplifiers) should be employed ~. Thus waveguide-based structures should be avoided. Semiconductor material is favourable due to its compatibility to active optoelectronic devices. Epitaxial growth techniques have to be used to achieve good homogeneity of the growth parameters over the entire wafer and thus for all elements of the array. Molecular beam epitaxy is well-suited for high structural resolution of the growth process in the zdirection normal to the layers. Moreover, it offers the possibility to integrate multilayer antireflection coatings or high reflectivity groups of layers into the structure. AIGaAs is the material of choice as far as long haul signal transmission with glass fibres is not necessary. The band gap can be tailored and changed from layer to layer without variations of the lattice constant and subsequent lattice mismatch strain. Since the band gap of the GaAs substrate is lower than that of the epitaxial AIGaAs layers, for The authors are in the Institut for Hochfrequenztechnik, Technische Universit~t Braunschweig, Schleinitzstrasse 2 1 - 2 4 , D-3300 Braunschweig, FRG. Received 20 July 1988. Revised 30 October 1989

devices operated in transmission the substrate has to be removed or the elements have to be operated in reflection and designed appropriately. The purpose of this paper is to introduce concepts for a dielectric interference filter incorporating an epitaxial anti-reflector structure for suppression of secondary reflectivity maxima and for an all-optical reflection modulator. First experimental results are compared with numerically calculated expectations and results of numerical design optimization. The calculations are based upon two mathematical approaches, which are described in detail. Although the approaches are physically and mathematically equivalent, one of them stems from the theory of electromagnetic waves at dielectric boundaries, the influence of which is characterized by matrices, while the other is based on the theory of electrical transmission lines and uses wave impedances instead of refractive indices.

Calculation of the optical properties of dielectric multilayers Matrix approach A one-dimensional model of the wave propagation in the multilayer structure is used considering plane waves with incidence in the z-direction normal to the optical boundaries 3. The relative permeabilities ~/r of the materials are assumed to be unity (Pr = 1).

0 0 3 0 - 3 9 9 2 / 9 0 / 0 1 0 0 2 3 - 0 8 © 1990 Butterworth 6~ Co (Publishers) Ltd Optics ~" Laser Technology Vol 22 No 1 1 9 9 0

23

The light waves are considered to be linearly. polarized with sinusoidal time dependence e TM, where i is the imaginary unit, o9 the angular frequency of the light wave, and t time. The timeindependent wave equation for the y-component of the electric field Ey(z) is

(7) +

with the matrix Q(zm) belonging to the ruth boundary (m = 0, 1, 2, 3. . . . )

02ey

km + 1 + krn e - i ( k , "

Oz 2 + k2Ey

= 0

(1)

Q(zm) =

x = ~a

I

km+ 1 -- km 2k,. + 1

where k = k(z) = (og/c)rI = (o9/c)(n - ix) is the complex propagation constant with 1/as complex refractive index and c the velocity of light in a vacuum; n is the real refractive index a n d the extinction coefficient x accounts for attenuation or amplification a n d is connected to the intensity absorption coefficient a by

+i-

ei(k,n + l +

k,.)z,,,

k,.)z,..

km+ 1 -- km ,,.~ kmTU e-'(k" + '+ k.)z km + l + k m 2kin + !

/

ei(k" + t -

(8)

k.,)z,. /

(2)

In the case of M layers (M + 1 boundaries; M + 2 segments, m = 0. 1. . . . . M, M + 1) the incident wave is characterized by the complex amplitude

where (3)

A = 2nc/o9

is the vacuum wavelength. Fig~ 1 gives a schematic to illustrate the notation for the z-coordinate and the amplitudes Am and Bm of the forward and backward travelling waves in the ruth segment of the structure. The general solution of the wave equation (l) in each segment is the sum of two counterpropagating exponentially increasing or decreasing plane waves with complex amplitudes

AM + 1 = 1

(9)

No light is incident from the other side: B0 = 0

(10)

With (7), (9), a n d (10) the final matrix equation is \

1

Q(zM)Q(zM_ , ) . . . Q(z,,)Q(zm_ l ) . . .

)

BM+ I /

(4)

Eym(Z) = Am eik''z +Bm e-ik"z

,,,,

Since Thus, the amplitude reflection coefficient r is curl/~ = -POP,- d--t

(5) r = BM+ - -

with P0 as magnetic permeability of the vacuum, the corresponding equation for the x-component of the magnetic field is =

nxm(z)

kmAmeik,.z km Bme_ik,. z ido0 9 -- Ido0 9

(6)

1 e - 2 s k"u +

AM+I

*zM = BM+ I e-2ikM+ ,zM

(12)

a n d the amplitude transmission coefficient t is t-

e-iku.,zu

A°

+ ikozo

=

Aoe-iku+,zu + ikozo

(13)

AM + 1

At the optical boundaries gm the tangential components of/~ a n d / t have to be continuous. In matrix notation this condition is written

The (intensity) reflectivity R and transmissivity T are R =

Irl:

(14)

and due to the law of energy conservation

ko

"r/i

"r/z ~3

kt

I k2 k3

"qM "qN÷I kM k M + l Incident light 41

itl 2

no HM+

I

"--5_

T-

(15)

1

respectively. Self-oscillation in the structure can be accounted for simply by setting

J

AM+

Ao Zo

Fig. 1

24

Z1

Z 2 Z3

...

ZM

Illustration of the notation used in the matrix approach

1 = 0

(16)

Of course (12) and (13) are not valid in this case and BM + j and A0 are the results of the calculation. In this model spontaneous emission and gain Optics 8" Laser Technology Vol 22 No 1 1990

saturation are neglected; therefore absolute values for the wavelength d e p e n d e n t output power c a n n o t be predicted.

"r/I

"q2

"% " "'%-,

~u

%

Wave impedance approach The second mathematical a p p r o a c h uses the wave impedances instead o f the refractive indices 4. The wave i m p e d a n c e z is related to the field c o m p o n e n t s Ev and H x o f plane waves propagating in z-direction by

n.

From Maxwell's equations the relation between H~ and Ev is given by Hx =

Zo,ro

e0er k/t0 /

Ev = q •

Ev

(18)

~

', z,,r,

I

I

I I

I I

(17)

Z = ~Ev

X

c

[2

-i-

/3.,../M_l-I-

/M

-I

1 ZoYo

zb

Fig. 2 Sketch of a multilayer structure interpreted as a concatenation of electrical transmission lines in the wave impedance approach. (a) Multilayer structure; (b) equivalent circuit; (c) transformed equivalent circuit

where 0 = ~

(19)

= n-ix

with eo and er as absolute a n d relative dielectric constants respectively. With these equations a h o m o g e n e o u s m e d i u m can be described as an electric transmission line o f length l, wave impedance Z, and propagation constant 7 defined by a 2rr y = ~ + i~-n

(20)

A,

The wave impedance Zb at the beginning of a h o m o g e n e o u s transmission line is obtained from that at the end of the line (Ze) using the transformation s Zb = Z

Z~ + Z t a n h ( y l ) Z + Z e tanh(yl)

(21)

For the multilayer structure depicted in Fig. 2(a) the equivalent circuit of Fig. 2(b) is obtained with the wave incident from the left side. With (21) the wave impedance ZM + I at the right side is transformed along the lines Z M , Z M - I . . . . . and Z t to the left side. The resulting transformed equivalent circuit is depicted in Fig. 2(c). From the theory of electrical transmission lines the amplitude reflection coefficient r is given by ~ r -

Zb -- Z~ Zb + Zo

(22)

where Z0 is the wave i m p e d a n c e of the vacuum. Since both approaches use Maxwell's equations without any approximations and Z = __Z° = Evo/H~.o.

.

(23)

where the subscript '0' denotes 'in vacuum', they are physically and mathematically equivalent. But one Optics El- Laser Technology Vol 22 No 1 1990

or the other might be favoured depending on whether the reader is used to optical or microwave argumentation. The matrix .approach has the additional advantage that the amplitude transmission coefficient comes out in a natural way.

Comparison with experiment These approaches give identical results. Also, the calculated data show good agreement with the measurements. Fig. 3 demonstrates the agreement between theory and experiment for a structure with a 300pm thick GaAs substrate (real part o f the refractive index n = 3.56, fundamental absorption edge at a wavelength of2, e = 0.874pm), a 1 p m thick GaAs buffer layer (n = 3.56, Ae = 0.874/2m) to lower the dislocation density, and 20 AlAs/A10.08Ga0.92As (n --- 2.95, Ae = 0 . 6 0 0 p m / n = 3.47, 2,e = 0.780pro) pairs o f dielectric quarterwave layers. For the computation the absorption coefficient in every layer is chosen to be 2 X 1 0 4 c m - | above and 1 X 103 cm -t below the fundamental absorption edge at wavelength ~ . A linear transition between these extreme values is assumed to occur in an interval o f _+12.5 n m a r o u n d the edge wavelength ~-e. The absorption coefficients are effective quantities; they are assumed to be much higher than those of corresponding bulk material in order to take account of losses due to scattering at the not ideally flat optical boundaries and to take thickness variations into consideration which reduce the overall reflectivity o f the structure as higher material absorption would do. In Fig. 3 the reflectivity is plotted against the wavelength o f the m o n o c h r o m a t i c light wave with normal incidence. Fig. 3(a) gives the c o m p a r i s o n between the experimental result (solid curve) and the expectation (dashed curve) calculated with the matrix a p p r o a c h neglecting the wavelength d e p e n d e n c e o f the real part o f the refractive index. In Fig. 3(b) the measured reflectivity (solid line) is c o m p a r e d with the results o f the calculation (dashed curve) based on the wave i m p e d a n c e concept in a version which includes dispersion in the AIGaAs layers. The

25

I'OIs-B-(L-H)~

1.0 t Matrix approach No dispersion

Sample 113 0.8 ee

-£ 0.6 Experimental >

l

i

^

~ l l l l j ~ l l l / ~|kI l l ~

I"'~'I

I

a

O.BO

I

I

0,0

I

0.90 1.00 Vacuum wavelength, k (p.m)

I.lO

1.0 Wave impedance approach

Dispersion

0.8

0.6 >

-$

0.4

rr

',y

0.2 ~

b

0 0.70

Experi mentaI

~ I 0.80

i i 0.90 1.00 Vacuum wavelength, k (p.m)

i I. I0

Fig. 3 Reflectivity R = ]rl 2 as a function of vacuum wavelength ,t.. Comparison of the experimental results (solid curves) and the calculations (dashed curves) using the matrix approach (a) and the wave impedance concept (b). Dispersion is neglected for Fig. 3(a), while considered for Fig. 3(b). The parameters of the layers are given in the text

L(X/n)/4 H(X/n)/4

0.4

w"

0.2

0.70

Substrate S 500 p.m n=3.56 Buffer B I p.m n=5.56 n= 2.95 n= 3.56 X=935 nm, a #0

>

0

/ ~ ~

5

/ I

I

I0 15 Number of layer pairs, #

I

20

25

Fig. 4 Calculated reflectivity R = Irl 2 at the mean vacuum wavelength Z as a function of the number, #, of pairs of quarterwave layers. The upper trace is for O, 1, 2, 3 . . . . . the 1 1 1 " lower for 5' 15' 25' 351 . . . . pairs of layers. 251 pairs of layers form a very effective anti-reflector structure

In practical set-ups the wavelength o f the incident light or the wavelengths of the reflectivity extrema often c a n n o t be adjusted precisely to the desired values. Thus, secondary maxima close to the central one can deteriorate the operation of the dielectric interference filter considerably. With an additional special anti-reflector structure secondary maxima can be suppressed on purpose, as the next two figures drawn from calculated data demonstrate. Fig. 4 shows the reflectivity at a v a c u u m wavelength of 0.933 p m used for determination of the thickness of the quarterwave layers as a function of the n u m b e r of layer pairs o f a similar structure as considered for Fig. 3: instead of 3.47 now the high refractive index is n = 3.56 corresponding to vanishing Ai-content which leads to a fundamental absorption edge at I e = 0.874 pm. Solid lines are drawn, although the data are inherently noncontinuous. The top curve gives the reflectivity of

1.0 dispersion function used is n(1) = n(0.933 pro) - 0.5 ( t - 0.933 pro); the linear approximation is justified by the results in Ref. 6, while the coefficient is chosen in order to get a close fit to the measurements. The agreement between theory and experiment is much closer, when dispersion is taken into account, even with the coarse approximation described above. W h e n dispersion is neglected in the wave i m p e d a n c e concept, too, both mathematical approaches give identical results.

E x a m p l e : i n t e r f e r e n c e filter w i t h an additional anti-reflector A filter curve of a dielectric mirror has already been shown in Fig. 3. Typical are the central reflectivity m a x i m u m and secondary m a x i m a on both sides. O f course, the centre wavelength of the central m a x i m u m depends on the thickness of the 1/4 layers.

26

a 0,8

i

0.6 11 jp'

~ 0.4

I

0.2

0

0.70

I

0.80

I

I.O( 0.90 Vacuum wavelength, X ~m)

I.IO

Fig. 5 Reflectivity R = I r l 2 as a function of vacuum wavelength I . Comparison of the reflectivity of a quarterwave stack with 20 pairs of layers (dashed curve a) with that of a structure with additional 2~1 pairs on top designed to suppress side maxima and a thin protection layer (solid curve b). The parameters of the layers are given in the text Optics 8" Laser Technology Vol 22 No 1 1990

the structure at the centre wavelength of 0.933 pm with 0, 1, 2, 3 . . . . pairs of layers. The m a x i m u m reflectivity does not change drastically above 12 pairs anymore. The bottom curve is for structures • with i,l i i,1 2i,l 3iI . . . . pairs of layers. With all the parameters mentioned a n u m b e r of 2½ pairs of layers leads to a nearly vanishing reflectivity. Curve b (solid) in Fig. 5 gives the result of a calculation combining the structure with 20 pairs of layers designed as a quarterwave stack for 0.933 pm vacuum wavelength with an additional 2½ pair antireflector on top designed for a wavelength of 1.025 pm corresponding to the first m a x i m u m on the long wavelength side and a 10 nm thick GaAs layer with n = 3.56 necessary to prevent the last low index layer from rotting. For comparison, curve a (dashed) shows the result for the ordinary structure without the antireflection layer sequence on top. The first m a x i m u m on the long wavelength side is reduced by a factor of 6.2, corresponding to -7.9 dB. The side maxima suppression between this first and the central m a x i m u m increases from -2.1 dB to -9.9 dB, which is a considerable improvement. The maxima on the left side are smoothed by the high absorption of the high index layers with an absorption edge wavelength of 0.874 pro. Usually simple antireflection coatings are made up of a single quarterwave layer with the real part of its refractive index corresponding to the arithmetic mean of the refractive indices of the adjacent dielectric materials: ZnO with a refractive index of n ~ 2.0 is a typical material for antireflection coatings. A separate technological step is necessary for its deposition onto the semiconductor structure. Filter concepts like the one described above, which incorporate an additional anti-reflector structure and use the material absorption at wavelengths lower than the band gap wavelength ,t,e for smoothing of the low wavelength side of the filter curve, are advantageous, because they can easily be realized by molecular beam epitaxy (MBE) without the need for additional processing steps of different type.

Modulator concept The devices proposed for and realized in 2-D digital optical signal processing should be all-optical, that means it should be possible to control the light output of the elements of the arrays by other light beams. Different kinds of optical non-linearities can be used. A very promising scheme is bleachable absorption based on d y n a m i c band filling 7. For amplifying devices, arrays of surface emitting laser diodes optically pumped and operated close to the lasing threshold are favourable ~. Active devices have to show strong photoluminescence a n d switching devices suitable for digital optical signal processing have to exhibit strong optical non-linearities. For both of these purposes m u l t i q u a n t u m well material 9' 10 is very promising. Multiquantum well (MQW) structures are sequences of thin layers with alternating values of the b a n d gap energy and of the real part of the refractive Optics 8" Laser Technology Vol 22 No 1 1 9 9 0

index. On account of their low density of states a n d high excess carrier density their non-linearities due to dynamic b a n d filling are more distinct than in bulk material• Since the substrate material GaAs has a lower b a n d gap energy t h a n the ternary c o m p o u n d AJGaAs it is adequate to incorporate stacks of A/4 layers into the structure and operate the devices in reflection. With molecular b e a m epitaxy (MBE) the structures can be tailored in a unique way in order to combine M Q W structures with dielectric mirrors and Fabry-Perot resonators. A reflection modulator has been prepared with a Yarian Gen I! MBE system and consists of a M Q W structure stacked upon a dielectric mirror. The layer thicknesses are 70 nm AlAs and 60 nm A10.08Ga0.92As for the quarterwave stack with 20 layer pairs and 80 nm AlAs and 20 nm GaAs for the M Q W with 20 layer pairs. The cross-section of the device is shown in Fig. 6. All layers are slightly Si-doped in the low 1015 cm -3 region. The lowest possible transition energy between the quantized states of the q u a n t u m wells is 1.43 eV matching the centre vacuum wavelength of 0.860 pm of the central reflectivity m a x i m u m of the dielectric mirror. The device works as an all-optical modulator. The reflection of a test beam from a tunable dye laser (Styryl 9, Ar-pumped) with photon energies slightly below 1.43 eV is controlled by a semiconductor laser beam at a wavelength of 0.790 pm. Both test and control beam are focused onto the same spot of the modulator surface with normal incidence. In Fig. 6 the test beam is drawn slightly tilted for ease of lettering. The attenuation of the test beam in the GaAs wells is lowered by the strong absorption of the control beam via bleachable absorption due to dynamic band filling 7. The modulation depth rn of the device is defined as Ron -- Rof f Ron m

, ifRon > Rorr (24)

=

Roff - Ron

Roff

, ifRorr > Ron

The reflectivities Ran and Roff are obtained at two different attenuations aon and aof~ respectively in the active q u a n t u m well layers. The intensity absorption

Substrdte

Dielectric

/ Buf0r reflector

(

MQW

I

/

I

) t )

GaAs

/\ 20 x

v 20 x

s

t

beam rol beam

Reflected test beam

I --v

~

/

AlAs 7Onto AlAs 80nm AIGaAs 60 nm GoAs 2Onto

Fig. 6 Cross-section of the reflection modulator structure used in the experiments

27

1.0

coefficient aon corresponds to Ro, in the so-called 'on' state, aoff = aon + Aa to Roff in the 'off state with an additional attenuation Aa. A maximum modulation depth of m = 60% is found at a test beam wavelength of 0.862 pm. The reflectivity changes from 7.5% without control beam to 19% at a control beam power of 4.1 mW. Spot size is about 5pm. The measured spectral response in the case without control beam is shown in Fig. 7(a). Deep dips are found in the high reflectivity region between 0.820/Jm and 0.900 pm of the quarterwave stack reflector. They are caused by the MQW filled cavity between the quarterwave stack and the device-air interface at the surface. Fig. 7(b) shows the result of the numerical calculation for this structure using the matrix approach. For the reflector layers and the barriers a constant (wavelength independent) intensity absorption coefficient of 1000 cm-1 is chosen to account for scattering losses due to surface roughness and non-ideal layer boundaries. For the well layers an absorption edge at about 860 nm is assumed with a linear change of the absorption coefficient over 25 nm from 1000 cm -I (boundary imperfections) below the band gap energy to 10 000 cm -1 above. The modulation depth measurements show a reflectivity change from 7.5% to 19% at a wavelength of 0.862/Jm corresponding to an absorption change from 4500 cm-r to about 1800 cm -1. With these values of the intensity absorption coefficient there is a close agreement between theoretical and experimental results. The lower trace in Fig. 7(b) is for the case without control beam (a = 4500 cm -1 for the test beam), the upper one is for the situation with control beam (a = 1800 cm-I). The separation of modulator and mirror in this concept has the advantage that the light passes the modulator section twice and hence the necessary modulator thickness is reduced. Both the measurement and the calculation confirm that high modulation depths can only be achieved at relatively low reflectivities and within a small bandwidth. At the peak at 0.840 pm the calculation does not give any reflectivity change, and the measurements show a modulation depth of a few percent only. The problem arises due to the existence of a FabryPerot resonator between the mirror structure and the GaAs-air boundary at the surface. This leads to a reflectivity curve with sharp dips. The wave impedance approach is used to optimize the modulator concept. For the refector layers a linear change o f the absorption coefficient from 1000 cm -I to 20 000 cm -1 over a range of +12.5 nm around 600 nm and 780 nm respectively for the band gap wavelength is assumed. The multiquantum wells are considered to have the same absorption coefficient for all wavelengths within the range used for the computations. In reality the absorption edge wavelength of the wells can be tailored precisely by the composition of these layers. The computations (for Figs 8 and 9) are just supposed to show the device behaviour with a given reflector structure at a

28

Sample 109 Reflectivity without control beam 0.8

0.6-

>

tY

0.4

0.2

a

0 0.75

I I 0.85 0.95 Vacuum wavelength, X (/.Lm)

,.05

oI 0.8

t~J

-£

0.6

>,

o, 0.4

0.2

0 0.75

b

0.85 vocoum

0.95 wovelength

1.05

X (f.cm}

Fig. 7 Reflectivity of the structure depicted in Fig. 6. (a) Measured reflectivity R = I r l 2 as a function of the vacuum wavelength ~; (b) Calculated reflectivity R = ]rJ 2 as a function of the vacuum wavelength ,,1.for t w o different absorption coefficients of the active GaAs quantum wells

certain wavelength, when an absorption coefficient is assumed for the wells, which is typical for modulator operation around the band edge. The mirror, designed for ~ = 0.835 pm vacuum centre wavelength in the calculation, consists of 20 pairs of layers with 70 nm thick AlAs and 59 nm thick A10.1Ga0.gAs. Upon this mirror a MQW Optics Et Laser Technology Vol 2 2 No 1 1 9 9 0

I.OO ,.

I.OC

A a =4000 cm -I

~on = I00 c m - I \

~off = ( i o n

075

+ A~ ea

~, 0.5C

n-

0.7 a

(Ion = I000 cm -I

0.5C

f777;,

"G oJ 0.25

0.7.=

>

0.2~ rr (~

0.9 0.8 Vacuum wavelength, X(~m)

1.0

0.7

a

1.00

0.8 0.9 Vacuum wavelength, X (p.m)

1.0

1.00 ~E

0.75 0.50

g

0.75 0.50

L~

=7 b

o

0.25

=7 0 0.7

0.8 0.9 Vacuum wavelength, X(H.m)

1.00~~ . ~~ . . < ~ ~ .

I.O

b

X = O.841 ~ m

0.25 0 0.7

1.00

i

i

0.8 0.9 Vacuum wavelength, X (/zm)

1.0

f

X= 0.835 p.m

0.75

o.7~

o_= o.5a

=7 025 U

o.,00

~/ (-iF

-0 C

~o. = =on+ I

s 0.25

ACt

C l o f f = C l a n + Z~Ot

1

5000 I0000 Attenuation change, A a (crn-I)

15000

Fig. 8 Results o f the calculation o f a structure with separate m o d u l a t o r and mirror sections. (a) Reflectivity R = I r l 2 as a function of v a c u u m w a v e l e n g t h A for t w o different absorption coefficients aon (solid line) and aoff (dashed line) Eespectively in the active q u a n t u m wells; (b) m o d u l a t i o n depth rn as a function of v a c u u m wavelength/1.; (c) modulation depth m as a function of attenuation change A a for different v a c u u m w a v e l e n g t h s A. There are sharp dips in the reflectivity curve due to the FabryPerot resonator b e t w e e n the mirror section and the GaAs-air b o u n d a r y at the surface

m o d u l a t o r is to be grown with 230 pairs of 12 n m thick AlAs q u a n t u m barriers and 10 n m thick active GaAs q u a n t u m wells (corresponding to the lowest energy transition at a wavelength of 0.835 pm). As in the experimental case the reflectivity curve shows sharp dips as depicted in Fig. 8(a) calculated with ao. = 100 cm -I and A a = 4000 cm -I. Here aon is assumed to be much lower than t h r o u g h o u t this contribution in order to exaggerate the fundamental conclusion to be drawn from Fig. 8. High modulation is achieved in the reflectivity m i n i m a only as shown in Fig. 8(b). The sharp m a x i m a with high modulation indicate a small m o d u l a t o r bandwidth. Over such a small wavelength region the modulation depths m are plotted as functions o f the absorption difference A a in the active q u a n t u m wells. Only for very low aon is this resonant modulator effective. Over a b a n d w i d t h o f only 2 n m the m o d u l a t o r reaches a modulation depth o f more than 80%. Within this range the wavelength o f the indicent test beam would have to be set for o p t i m u m Optics 8" Laser Technology Vol 22 No 1 1 9 9 0

aon = I 0 0 0 cm -~

5o~o C

,o6oo

,5ooo

Attenuation change, A a (cm-I)

Fig. 9 AS for Fig. 8; but there is an additional antireflection coating on top of the structure. Thus the curves of the reflectivity and the modulation depth are flat over more than 8 0 nm; within this range the modulation depth is about 8 0 %

modulation, and as the existence o f a m a x i m u m in the curves in Fig. 8(c) verifies the value o f aoff has to be adjusted for higher modulation. For higher attenuation changes and other wavelength regions the m o d u l a t i o n depth saturates to about 65%. To avoid the dips caused by the resonator a single quarterwave layer antireflection coating with n = (3.6 × I) 1/2 = 1.9 is added in the numerical calculations. The epitaxial anti-reflector structure proposed in an earlier section of this p a p e r is not employed here, since a b r o a d b a n d antireflection is necessary in this concept. As shown in Fig. 9(a) this results in a relatively flat reflectivity curve with an insertion loss o f about - 3 dB in the spectral range between 0.800 p m and 0.880/~m; here ao, = 1000 cm -t and A a = 4000 cm -1 such that aoff = 5000 cm -I. Such high absorption changes were already experimentally obtained by d y n a m i c b a n d filling for control b e a m power levels below 10 m W (see Ref. 11). Fig. 9(b) demonstrates that in addition the curve of the modulation depth is also nearly fiat in the whole reflecting region. In Fig. 9(c) again the modulation at 0.835 p m is shown; a m o d u l a t i o n depth o f 80% is reached for about A a = 3200 cm -j,

29

and the modulation depth does not decrease for higher attenuation changes anymore. The flat modulation curve indicates that this structure is tolerant against thickness variations due to the fabrication process. Thus, this concept is very promising for use in integrated optics and 2-D digital optical signal processing.

Conclusion Optically controllable modulators are of growing interest for all-optical signal processing A1GaAs multiquantum well devices employing band filling with integrated dielectric reflector have been shown to be very efficient for two-dimensional all-optical light control. The paper presents two detailed models that allow calculation of the wavelength dependent reflection characteristics of various composed A1GaAs multilayer structures where interference filter sections and optically non-linear multiquantum well sections interact. Close agreement with experiment is obtained when material absorption and dispersion is included appropriately. Simple anti-reflector structures realizable in the AIGaAs material system and used for filter tailoring are investigated in detail Reflectivity changes due to band filling in quantum wells can be predicted with satisfactory accuracy. Given a maximum near band gap absorption change of Aa = 4000 cm-I an optimized modulator structure is proposed that attains a modulation depth of about 80% over a wavelength range of 80 nm. To conclude, the models presented have proven very useful for design of A1GaAs multilayer interference filters and modulators.

Acknowledgement The authors wish to thank J. M~thnB for helpful

discussions concerning the mathematical approaches and P. Krause for time consuming operation of the program. Part of the calculations were carried out on the facilities of the computer centre of the Technical University of Braunschweig, FRG. This work was supported by the Stiftung Volkswagenwerk, the Bundesministerium ftir Forschung und Technologie, and the Deutsche Forschungsgemeinschaft.

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Optics 8 Laser Technology V o l 2 2 No 1 1990