AlAs multiquantum-well waveguide

15 November 2000

Optics Communications 185 (2000) 325±329

www.elsevier.com/locate/optcom

A tunable ®lter with electrooptical TE±TM mode conversion in a GaAs/AlAs multiquantum-well waveguide B. B^eche a,*, E. Gaviot a, N. Grossard b, H. Porte b a

ENSIM ± Micro_Cap_Ouest, Laboratoire d'Acoustique de l'Universit e du Maine, LAUM ± UMR CNRS 6613, 72000 Le Mans, France b Laboratoire d'Optique P.M. Dueux UMR CNRS 6603, Universit e de Franche Comt e, 25000 Besancßon, France Received 27 July 2000; accepted 19 September 2000

Abstract In this paper, the theoretical study of a new electrooptic tunable ®lter based on TE±TM mode conversion, and the high form birefringence that occurs in a GaAs/AlAs multiquantum-well waveguide is presented. Then TE±TM conversion can be achieved with a relatively low voltage (30 V). Such a ®lter shows o€ a tuning rate voltage ranging around 7 V/channel, and as regards selectivity a 1.3 nm ®lter bandwidth can be obtained. Ó 2000 Elsevier Science B.V. All rights reserved. Keywords: Electrooptic e€ect; Multilayers; Integrated optics; Tunable ®lters

1. Introduction Electrooptical tunable wavelength ®lters are well known as attractive components for wavelength division multiplexing (WDM) network applications. Di€erent ®lter systems based on TE± TM mode conversion and TE±TM phase shift have been developed with birefringent LiNbO3 waveguides [1±5]. The birefringence of the material stands as a mainstay in the design of such ®lters since their selectivity hinges on its value. III±V semiconductors are also an alternative solution for designing new integrated components. Bulk GaAs is widely known as the basic material for integrated optic devices [6,7]: unfortunately, it exhibits a very low birefringence. Recently we have pro-

*

Corresponding author. Fax: +33-243-833-794. E-mail address: [email protected] (B. BeÃche).

posed an acoustically tunable wavelength ®lter based on GaAs/AlAs multiquantum wells (MQW) [8]. The idea is to take advantage of superlattices which feature a high form birefringence [9±12]. Obtaining a high form birefringence implies that the refractive index of the two materials used (GaAs and the alloy Alx Ga1ÿx As) should be strongly di€erent. One of the best solutions to obtaining a strong birefringence, and a high selectivity of the ®lter, is a multilayer core composed of alternate layers of GaAs and AlAs …x ˆ 1†. In this paper, a TE±TM mode conversion relying upon electrooptical interaction is investigated theoretically for designing a new tunable ®lter arranged on a GaAs/AlAs MQW structure. At ®rst, the principle of the device is explained. The following is directed towards investigating the electrooptical interaction leading to TE±TM conversion and phase shift. We conclude with the theoretical performance of such a tunable ®lter.

0030-4018/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 ( 0 0 ) 0 1 0 2 3 - 3

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B. B^eche et al. / Optics Communications 185 (2000) 325±329

2. Design and principle of the device

waveguide projects in the cleavage plane …x01 ; x03 † according to the following expression:

The layout of a generic device is depicted as Fig. 1. R…x1 ; x2 ; x3 † and R0 …x01 ; x02 ; x03 † represent the crystallographic coordinate system of the GaAs/AlAs structure together with the one of the study. The GaAs/AlAs waveguide cut x1 ˆ ‰1 0 0Š relates to a speci®c structure that was realised and characterised in Ref. [12]. This GaAs/AlAs rib optical waveguide features a group birefringence of Dngp ˆ 0:047 at 1550 nm. Three electrodes are evaporated and patterned over the MQW structure as shown in Fig. 1, so as to obtain a TE±TM mode converter electrode, a phase shift electrode and a ground electrode. The TE±TM mode converter electrode consists of a digital electrode with period K, driven by a voltage VMC , that brings 0 about a horizontal electric ®eld E3e . The phase shift electrode located on the top of the waveguide, driven by a voltage VT , creates a vertical electric 0 ®eld E1e . Owing to these ®elds, the refractive index of the crystal along the crystallographic axes is changed via the linear electrooptic tensor of the GaAs/AlAs MQW cut [1 0 0] which exhibits a  42m tetragonal symmetry (that is r52 ˆ r63 6ˆ r41 ) [13]. Considering a 45° rotation applied from the crystallographic axes R…x1 ; x2 ; x3 † to the study axes R0 …x01 ; x02 ; x03 †, the index ellipsoid of the GaAs/AlAs

where nTE and nTM are the e€ective indexes of the two optical modes TE and TM, and r41 , r52 the electrooptical coecients of GaAs/AlAs MQW. Eq. (1) shows that the phase shift electrode modi®es the propagation constant of the TE-mode. 0 Indeed b0TE ˆ k0 n0TE , with n0TE  nTE ÿ …r41 =2†n3TE E1e and k0 ˆ 2p=k0 , according to the vertical electric 0 ®eld E1e , whereas the propagation constant of the TM-mode is unchanged with b0TM ˆ k0 nTM . Moreover the alternate term of the ellipse clearly shows the coupling between both polarised modes TE and TM. Then, these two electric ®elds acting simultaneously allow us to obtain the tunable wavelength TE±TM conversion. Due to the hori0 zontal electric ®eld E3e , each ®nger of the converter electrode behaves like an elementary crystal plate where the working axes …x01 ; x03 † have turned an angle h (Fig. 2) which de®nes both indexes of refraction nx00 and nx00 along the new principal axes 1 3 …x001 ; x003 †:

Fig. 1. Schematic diagram of the tunable electrooptic ®lter integrated in a multilayer GaAs/AlAs waveguide. Crystallographic coordinate systems (R and R0 ).

Fig. 2. Deformation of the index ellipse stemming from the 0 applied electric ®eld E3e . Each ®nger of the converter electrode presents a width …K=2†.

ÿ 0
2   ÿ
2 x1 1 0 e0 ‡ ‡ r41 E1 x03 ÿ 2r52 E3e x01 x03 ˆ 1 n2TM n2TE …1†

B. B^eche et al. / Optics Communications 185 (2000) 325±329

p 8 1  2 ˆ A ‡ B2 ‡ C 2 > > > < nx00 1 p 1 >  2 ˆ A ÿ B2 ‡ C 2 > > :

327

…2†

nx00 3

with,

  1 1 1 e0 ‡ ‡ r41 E1 ; Aˆ 2 n2TM n2TE   1 1 1 e0 ÿ r41 E1 ; ÿ Bˆ 2 n2TM n2TE   1 C e0 C ˆ r52 E3 ; and h ˆ arctg 2 B

When the polarised optical mode proceeds along the waveguide, a series of m such plates is encountered as in an integrated version of bulk S olc ®lter in optics. We have used respectively the Jones matrix formalism and the coupled mode theory in order to analyse the theoretical behaviour of this tunable ®lter, namely, its TE±TM mode conversion, selectivity, and phase shift.

3. Modelling the performance of tunable ®lter According to the Jones matrix approach to analysing the TE±TM mode conversion of such a ®lter, the general matrix P which governs the transmission of the polarised optical mode across this ®lter (m plates) can be expressed as: P ˆ ‰ R…h ˆ 0†D…/; w†R…h ˆ 0†R… ÿ h†  D…/; w†R…h†Šm=2 with,



R… h † ˆ

cos h ÿ sin h

sin h cos h

…3† 

h de®ned in Eq. (2), D…/; w† ˆ e /ˆ

ÿjw

eÿj/=2

0

0

ej/=2

! ;

 p nx003 ÿ nx001 K k0

the relative phase di€erence, and w ˆ …p=2k0 † …nx003 ‡ nx001 †K the mean absolute phase di€erence.

Fig. 3. Wavelength response of TE±TM normalised conversion eciency for a given applied voltage VMC ˆ 30 V.

According to this model, the tunable ®lter consists of a stack of m elementary plates arranged between two perpendicular polarisers. The ®lter transmission T is then de®ned by the quantity 2 jP21 j . According to the electrooptic coecients of the GaAs/AlAs MQW r52 ˆ 1:295  10ÿ12 m/V and r41 ˆ 1:260  10ÿ12 m/V, and considering that the ®lter includes m ˆ 1400 elementary plates related to a whole length of the component (L  3 cm), the voltage VMC for a 100% TE±TM conversion can be estimated. To this end, Fig. 3 brings out the normalised conversion eciency of the electrooptic ®lter, assuming a distance dMC ˆ 16 lm and a converter electrode period K ˆ 43 lm. Hence, a 100% TE±TM conversion is obtained at an optical wavelength k0 ˆ 1542 mm, with an applied voltage VMC ˆ 30 V. Moreover, as regards selectivity of the ®lter, the linewidth value at full-width at half maximum (FWHM) is typically 1.3 nm. The expressions accounting for the mode coupling and phase shift regarding such a birefringent structure can be inferred from the coupled mode theory. Therefore the signi®cant parameters characterising the tunable electrooptic ®lter can be assessed. The wave equation describing the electric ®eld of the optical modes interacting with the electrooptic interaction in the coordinate system R0 is:  2   2  o o0 o 0 2 o0 E DP ˆ l0 …4† r E ÿ l0 e0 e ot2 ot2

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B. B^eche et al. / Optics Communications 185 (2000) 325±329

where e is the second-rank tensor describing 0 the relative permittivity, Eo the optical ®eld vec0 0 o o and E3o ˆ ETE in R0 †, and DP0 ˆ tor …E1o ˆ ETM o0 e0 ÿe0 e…r:E †eE is the vector of the induced polari0 sation by the electrooptic e€ect. Ee represents the applied electric ®eld vector and r is the third-rank electrooptic tensor. In order to simulate the electrooptic interaction in the working coordinate system R0 , it is ®rst important to consider a 45° rotation to the GaAs/AlAs MQW tensors. In this con®guration, both components of the induced polarisation changing respectively the propagation of the TM- and TE-optical modes are given with: (

0

0

DP10 ˆ ÿe0 e11 e22 r52 E3e E3o 0 0 0 0 DP30 ˆ ÿe0 …e11 e22 r52 E3e E1o ‡ …e22 †2 r41 E1e E3o †

…5†

According to these expressions, one notice that TE±TM (and TM±TE) mode conversion should be 0 obtained by applying a horizontal electric ®eld E3e , 0 0 via the element …ÿe0 e11 e22 r52 E3e E3o or 1 †. Moreover, the electrooptically adjustable phase delay between the TM- and TE-modes naturally result from an 0 applied vertical electric ®eld E1e considering the 0 0 2 term …ÿe0 …e22 † r41 E1e E3o †. Only the e€ective index 0 of the TE optical mode E3o (that is its constant of propagation bTE ) could be changed by the vertical electric ®eld so as to obtain the phase shift. It should be noted that the coupled mode theory yields the same behaviour of such devices that has been explained previously according to said ellipse model. Assuming a slowly varying envelope approximation, TM and TE optical modes yield the two classical coupled amplitude di€erential equations: 8 o0 0 ÿ
> > < dE1 …0 x2 † ˆ jjEo0 x0 eÿj…Db0 †x02 2 3 dx2 …6† 0 ÿ
dE3o …x02 † 0 0 0 > > : dx0 ˆ jj E1o x02 ej…Db †x2 2

where, jˆ

p p VMC e11 e22 r52 CTM=TE k0 dMC

is the TE±TM coupling constant, and

CTM=TE

R R o0 0 0 e0 o0 0 0 E …x ; x †E E …x ; x †dx0 dx0 dMC R R 1 o0 1 0 3 0 3 o0 3 0 1 0 3 0 1 0 3 ˆ VMC E1 …x1 ; x3 †E3 …x1 ; x3 †dx1 dx3

the normalised overlap parameter of the applied electric ®eld with the two optical ®elds. The requirement Db0 ˆ bTE …k0 † ÿ bTM …k0 † ÿ …2p=K† ˆ 0 is a phase-matching condition relevant with the optical wavelength k0 ˆ Dnph …k0 †K, since Dnph …k0 † stands as the phase birefringence of the MQW structure at k0 . A most ecient conversion is allowed at the ®xed optical wavelength k0 , but a slight variation of the constant propagation bTE via the vertically 0 applied electric ®eld E1e only shifts the zero of the phase condition, given with the close wavelength k0 ‡ Dk. The theoretical 0 conversion 2 eciency 0 is then given by g ˆ E3o …x02 †=E1o …0† ˆ …jjj2 =b2 † 2 1=2 sin 2 ‰bx02 Š with b ˆ …j2 ‡ …Db0 =2† † . The optical mode conversion bandwidth is inversely proportional to the overall interaction length L, and to the group birefringence of the MQW structure. Typically, for the GaAs/AlAs MQW structure characterised in Ref. [12] showing o€ a group birefringence Dngp ˆ 0:047 at 1550 nm, and considering the whole interaction length L ˆ 3 cm, the calculated value of the FWHM representing the selectivity of the ®lter, reaches dk  0:8…k20 = Dngp L† ˆ 1:3 nm. The study of the phase shift leads to express the di€erence of the two changed propagation constants DbTE±TM ˆ …p=k0 †…e22 †3=2 r41 CTE …VT =dT † characterising the delay between the TE- and TM-optical modes. CTE

dT ˆ VT

R R o0 ÿ 0 0
e0 o0 ÿ 0 0
0 0 E x ; x E E x ; x dx dx R R 3 o0 1 0 3 0 1 o0 3 0 1 0 3 0 1 0 3 E3 …x1 ; x3 †E3 …x1 ; x3 †dx1 dx3

represents the normalised overlap coecient of the vertically applied electric ®eld with the TE optical mode. Considering the electrooptic coecient r41 ˆ 1:260  10ÿ12 m/V, dT ˆ 4 lm the distance between the ground electrode and the phase shift electrode, an overlap coecient CTE ˆ 0:6, and p nTE ˆ e22 ˆ 3:1420 the e€ective index of the TE mode at a wavelength k0 ˆ 1550 nm, it is clear that a maximal applied tuning voltage VT ˆ 50 V brings forth a phase-matching Dbmax ˆ 594 rad/m. Then for a component featuring typically a whole length

B. B^eche et al. / Optics Communications 185 (2000) 325±329

L ˆ 3 cm, the centre transmission peak of the ®lter is shifted with jDkj ˆ

k20 Dbmax k0 VT ˆ …e22 †3=2 r41 CTE Dngp …k0 † p Dngp …k0 † dT

ˆ 9:7 nm: According to the selectivity dk, and owing to the above mentioned parameters yielding Dk, this GaAs/AlAs MQW tunable ®lter exhibits a tuning rate voltage of …Dk=VT † ˆ 0:19 nm/V, equivalent to 7 V/channel. 4. Conclusion The theoretical study of an electrooptic tunable ®lter on a GaAs/AlAs MQW structure for WDM network applications has been presented. This device resorts to two acting electrodes together with the ground electrode. The TE±TM mode converter electrode consists of a digital electrode with period K, driven by a voltage VMC entailing the horizontal electric ®eld. The phase shift electrode located on top of the waveguide is driven by a voltage VT , and creates the vertical electric ®eld. Taking advantage of these two ®elds allows us to obtain a tunable phase-matching condition regarding both optical modes and thereby a ®lter function. Calculations show that TE±TM conversion is then possible with a voltage VMC ˆ 30 V.

329

Such an electrooptic ®lter presents a tuning rate voltage of 7 V/channel and should be instrumental in multipurpose optoelectronic devices.

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