As a research fie ld , lith iu m niobate in te g ra te d o p tic technology has reached a ve ry m ature state in the la s t decade. M ost e ffo rt was directed tow ards devices fo r optical com m unication systems^ such as fa st in te n s ity and phase m o d u la to rs , s w itc h a rra y s , w a ve le n g th m u ltip le x e rs , frequency sh ifte rs and po la risatio n controllers. A d d itio n a lly , a v a rie ty o f devices have been dem onstrated fo r sig n a l processing and sensing a p p lic a tio n s ^ . M ore recently, there has also been some in te re s t in the in v e s tig a tio n o f n o n -lin e a r o p tic a l phenom ena in lith iu m n iobate
w a v e g u i d e s 3 as w e ll as la s in g in neodym ium and e rb iu m doped
stru ctu re s^.
The aim o f th is short chapter is to introduce the basic concepts and design s tra te g ie s o f lith iu m n io b a te in te g ra te d m o d u la to rs . F a b ric a tio n techniques and waveguide ch a ra cte ristics are presented in the fir s t section, follow ed by the b rie f d escription o f the ele ctro -o p tic effect in lith iu m nio b a te . In te g ra te d o p tic phase and in te n s ity m o d u la to r configurations are described in the th ird section. In the concluding p a rt, the hig h frequency operation o f the m odulators is discussed.
4.1 Waveguides
In te g ra te d o p tic lith iu m niobate m odulators are e s s e n tia lly electro- o p tic a lly c o n tro lle d single-m ode channel w aveguide devices. The waveguides are form ed by increasing the re fra ctive index o f the substrate w ith in a define volum e through the a d d itio n o f dopants. There are two sta n d a rd techniques fo r waveguide fa b ric a tio n in lith iu m n io bate: tita n iu m in d iffu s io n and proton exchange. B oth o f these techniques are re la tiv e ly sim ple compared to waveguide fa b ric a tio n in sem iconductor
m a te ria ls .
In tita n iu m in d iffu s io n te ch n o lo gy w aveguide s trip e s o r m ore com plicated p a tte rn s are defined u sin g p h o to li to g ra p h ic te ch n iq u e. T ita n iu m is deposited over the e n tire crysta l by RF s p u tte rin g , electron beam d e p o sitio n or th e rm a l e va poration. S u b sequently, th e lif t o f f technique (im m ersing in photoresist solvent) is used to remove photoresist and unw anted tita n iu m . The crysta l is then placed in a d iffu s io n furnace a t tem peratures o f 980^-1050^0 fo r typ ica l diffusion tim es o f 4-10 hours.
The in d iffu s io n o f tita n iu m stripes is often accompanied by a p a ra s itic film waveguide a t the surface o f the c rysta l due to an increase o f the e xtra o rd in a ry index |ig. This is a ttrib u te d to the o u td iffu sio n o f 0 2 /L i2 0 . V arious means fo r the suppression o f th is p a ra sitic film waveguide have been proposed. A t U C L we have in v e s tig a te d tw o te chniques fo r o u td iffu s io n suppression: w et d iffu s io n , and long d ry d iffu s io n in an
atm osphere ric h in L i2Û. The fa b ric a tio n techniques th a t we have
employed are described in more d e ta il in Appendix 2.
T ita n iu m d iffu s io n a llo w s the fa b ric a tio n o f o p tic a l w aveguides su p p o rtin g both TE and TM modes. W aveguide losses below O .ldB/cm have been re p o rte d ^. The mode size o f waveguides can be ta ilo re d by va ryin g the fa b rica tio n param eters, and to ta l fibre-w aveguide-fibre device in se rtio n losses o f Id B have been reported^. However, because o f re la tiv e ly
sm all re fra ctive index changes (Apg<0.04, A|Iq<0.02), bran ch in g angles o f
Y -ju n ctio n s have to be sm all and bend's ra d ii large re s u ltin g in device sizes o f several centim eters.
The photorefractive effect or optical damage in term inology o f in te g ra te d optics severely lim its the optical power in tita n iu m in d iffu se d waveguides a t shorter wavelengths (O.Sp) to several m icrow atts only. A t 1.3-1.5 pm no degradation has been observed up to levels o f tens o f m iliw a tts ^ , so in th a t respect tita n iu m in d iffu s e d waveguide devices are w e ll su ite d to long w avelength o ptical com m unication systems.
The p roto n exchange technique is based on an ion-exchange re a ctio n
between Li"^ from the L iN b 0 3 substrate and fro m some a ppropriate
source. P ro to n exchange can be achieved by im m e rs in g the lith iu m niobate substrate in benzoic acid a t tem peratures in a range between 150® to 250®. The im m ersion tim es va ry w ith tem perature and can be from m inutes a t higher tem peratures to hours a t low er tem peratures.
P roton exchanged waveguides have a step re fra ctive index p ro file w ith a la rg e , p o s itiv e e x tra o rd in a ry change (Apg<0.12) and s m a ll negative o rd in a ry re fra c tiv e in d e x change (Apg<-0.04). Due to th is in h e re n t anisotropy, proton exchanged waveguides support only T M modes in z-cut m a te ria l and TE modes in x and y-cu t m a te ria ls. Because o f the b e tte r o p tica l confinem ent proton exchanged waveguides are m ore su ite d to g ra tin g based devices, w aveguide bends and rin g resonators th a n tita n iu m diffused waveguides. However, u n til re ce n tly proto n exchange w aveguides suffered fro m a num ber o f disadvantages in c lu d in g la rg e propagation losses and a much reduced electro-optic a c tiv ity .
Two m ethods fo r im p ro vin g the proton exchange technique have been established. The firs t one is based on the use o f buffered benzoic acid and re su lts in long im m ersion tim es. The second, more p ra c tic a l m ethod is annealing and i t involves heating the substrate a fte r the proton exchange. W aveguides produced by proton exchange and annealing can e x h ib it low propagation loss (0.15dB/cm ), can be w e ll m atched to single-m ode fib re (to ta l fib re -to -fib re in se rtio n loss o f 1.2dB a t 0.8pm) and can have to ta lly restored electro-optic coefficients®.
4.2 E lectro-O ptic E ffect in L ith iu m Niobate
The lin e a r electro-optic (Pockels) effect, w hich is th e basis fo r active w aveguide device c o n tro l, p rovides a change in re fra c tiv e in d e x p ro p o rtio n a l to the a pplied e le ctric fie ld . The lin e a r change in the coefficients o f the index ellipsoid due to an applied electric fie ld (E j) along
the p rin c ip a l crystal axes is y = £ TijEj IM i / j = i
(4.1)
or a lte rn a tiv e ly 3 3 (Ap)i = ~ X rijE j H i (4.2)where i= l,6 and ry is a 6x3 electro-optic te n so r.T h is re la tio n can be contracted to 3x3 m a trix form :
A -1^ = y - -r22 Ey+riaEz T22Ex rsiE x T22 Ex r22E y+ri3E z rsiE y rsiE x rsiE y 1*33 Ez (4.3)
where p is e ith e r o rd in a ry or e xtra o rd in a ry value. F or lith iu m niobate a t
24.50 C and a t 1.439pm, Pg=2.151 and Pg=2.143.
U tiliz a tio n o f diagonal m a trix elem ents re su lts in an in d e x and phase change fo r the proper in cid e n t fie ld orientation. The o ff diagonal elements re p re s e n t e le c tro -o p tic a lly induced conversion or m ix in g betw een orthogonal p o la riza tio n components.
F or the purpose o f m o du la tio n i t is desirable to u tilis e th e strongest
electro-optic coefficient rgg (~ 30.8 x 10“^^m V "^). In th is case
A -K c
Ape = — rggE; (4.4)
F igure 4.1 shows the standard cuts o f c rysta l and o p tica l p o la risa tio n s
electrode v N \ \ V . X W - X \ \ ^ X-cut LiNbOa horizontal qI fie ld TE optical mode a) S102 buffer electrode nWWWWWXW' Z-cut LiNbOa z TM optical mode
vertical el. fie ld
X
b)
F ig u re 4.1 Electrode and waveguide configurations in lith iu m niobate w hich u tilise the m axim al electrooptic coefficient rgg
a) X-cut LiNbOg for TE polarized lig h t: m odulators
b) Z-cut LiNbO g for TM polarized lig h t: directional couplers and phase reversal m odulators
4.3 Phase and In te n s ity M odulators
A n in te g ra te d optic phase m odulator is shown in F igure 4.2a. Electrodes are placed on the sides o f the waveguide in case o f X or Y -cu t lith iu m niobate or on the top o f the waveguide in case o f Z-cut m a te ria l. In the la tte r case, an in s u la tin g b u ffe r la ye r is required to e lim in a te loss to TM p o la riz a tio n .
In an in te g ra te d optic m odulator, the effective e le ctro -o p tica lly induced index change o f the optical waveguide mode can be w ritte n as
3
= (4.5)
4 g
where V is the d riv in g voltage, Ç is the interelectrode gap and is the
overlap in te g ra l between the applied electric fie ld and the o p tica l mode (ty p ic a lly 0.3-0.5). The to ta l phase s h ift over the in te ra c tio n le n g th Lj^ is then
ApL„ = -7tn3r33r„il^L!ii (4.6)
g
XFor a phase s h ift o f tc, a voltage o f n e a rly lO V is re q u ire d i f X = 1.5pm , L ^ = lc m , Ç=10|im and r^ = 0 .5 . T his gives an in d ic a tio n o f the re la tiv e weakness o f the electro-optic effect w hich imposes fu rth e r re s tric tio n s on the m in im a l size o f lith iu m niobate m odulators. F or the same applied voltage, the re s u ltin g phase s h ift is reduced a t h ig h frequencies. The b a n d w id th o f a m odulator w ill be introduced and discussed in the fin a l section o f th is chapter.
A n in te n s ity m o du la to r is shown in F ig u re 4.2b. I t consists o f a Y- ju n c tio n s p litte r, phase s h iftin g electrodes and Y -ju n ctio n recom biner. I f
the optical paths o f tw o arms are equal, tw o components combine in phase
lig h t in waveguide electrode a) b) c)
F ig u re 4.2 Standard m odulator configurations a) Phase M odulator
b) Mach-Zehnder In te n sity M odulator
c) D irectional Coupler In te n sity M odulator/Sw itch
lig h t out
introduced by electro-optic effect the combined mode is n o t supported by the o u tp u t single-mode waveguide, and the lig h t is radiated in to the
substrate. A three electrode co nfiguration can be used to achieve push- p u ll operation in w hich the required voltage is halved w ith respect to the case o f a single branch phase m odulator. In the case o f a p u s h -p u ll in te n s ity m odulator, the v a ria tio n o f the o u tp u t in te n s ity is given by the re la tio n
^ o u t ” ^ o u t ( m a x ) C O S ^ ( A ( j ) / 2 ) ( 4 . 7 )
where A(|) is the difference between the phase s h ifts in troduced in each arm , and lout(max) is the o u tp u t lig h t in te n s ity when th e tw o waves recom bine in phase. I f we neglect Y -ju n ctio n and waveguide propagation
losses, l o u t ( m a x ) equals the in p u t in te n sity. From the E quation 4.7 i t can be
seen th a t the lin e a r region o f operation is positioned around the in te n s ity
i o u t " i o u t ( m a x / ^ '
A d ire ctio n a l coupler sw itch/m odulator (Fig.4.2c) consists o f tw o p a ra lle l waveguides separated by a sm all distance so th a t the lig h t propagating in one guide can couple in to the other. A voltage applied across one o f the w aveguides changes its propagation ch a ra cte ristics and m odifies the coupling between the tw o guides. For a length o f in te ra c tio n equal to one coupling len g th , the lig h t in itia lly launched in one guide comes o ut from the other guide when no voltage is applied. On a p p lica tio n o f an e lectric fie ld , the lig h t can be sw itched back to the o rig in a l waveguide. The DC ch a ra cte ristic o f a d ire ction a l coupler, a t the o u tp u t o f the second guide, can be expressed as
I o u t = I o u t ( m a x ) ^ ^ 2 % ^ ( 4 . 8 )
where p =
V
(APLm/Jt)^+l , Ap is the difference in the effective propagationfo r a M ach-Z ehnder m o d u la to r, th e lin e a r re g io n is centered a t
^out“ ^ o u t(m a x /2 *
4.4 H ig h Frequency O peration
The lum ped electrodes, shown in Fig.4.3a, act as a ca p a cito r in the e le c tric a l c irc u it. I f the electrode le n g th is sm all com pared to the RF w avelength and i f the sta tic resistance is n o t to large, the frequency o f operation o f the m odulator is lim ite d by its RC constant:
A f = - 1 - (4.9)
where A f is the 3dB bandw idth and !^ is u su a lly a 50Q te rm in a tio n . As the