JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 11, NO.

9, SEPTEMBER 1993 1447

Energy Loss in a Planar Waveguide Caused

by a High Refracting and Absorbing Overlay
B. Gotz, K. Hehl, W. Karthe, and B. Martin

Abstract-In this paper we give an explanation of the mode be- alr n = l k=O
4 4
~ _ _ _
havior in dielectric waveguides with an absorbing, high refractive
index cladding. By consideration of the total waveguiding system WL2 lossy overlay n3= 4.1 O B k 2 0.21 Osd34 0.4prn
as two separate waveguides we are able to explain the behavior of ~

the oomplex refractive index of the guided modes by the mixing WL1 dielectric wavegulde n = 1.588 k = 0 d = lprn
2 2
of the modes of both waveguides. For systems with absorption
we observe so called quasi-leaky waves in the total system for tubatrate nl= 1.510 kl= 0
finite thicknesses of the overlay. For absorptionless systems these
leaky waves can be found only for infinite thicknesses of the Fig. 1. Setup parameters of the investigated dielectric waveguide with
overlay. The occurrence and the behavior of these quasi-leaky absorbing overlay.
waves versus the increasing overlay thickness are interpreted. We
present a method to calculate the coupling efficiency of modes
at the junction unclad waveguide-clad waveguide taking into losses at the junction. All calculations and measurements
consideration waveguides with absorption. Finally we developed are done for the wavelength A = 633 nm, otherwise, it is
an experimental method to measure the absorption coefficient mentioned separately.
for the guided modes in the cladded waveguide and the coupling
losses at the unclad-clad waveguide junction. The measured
values are in a good agreement with our theoretical calculations. 11. MODE BEHAVIOR
IN CLAD WAVEGUIDES
The geometrical arrangement of the whole waveguide sys-
I. INTRODUCTION tem is shown in Fig. 1. The values of the optical and
geometrical parameters assumed to be fixed for the following
S EMICONDUCTOR-clad or metal-clad optical waveguides
are useful as cutoff polarizers [2] or waveguide controlled
photodetectors [l],modulators, and switches. Such integrated
calculations are indicated too. The two changeable parameters
d and k are the thickness and the absorption index of the
cladding.
optical devices are of increasing interest for optical commu-
The physical principle of the waveguide with a semicon-
nications.
ductor overlay consists in the occurrence of extra overlay
To optimize such integrated optical devices it is of interest to
modes. These occur even for thin films because of their high
investigate the mode behavior in semiconductor clad dielectric
refractive index and their resonant or nonresonant coupling to
waveguides versus the overlay thickness and versus complex
the waveguide modes associated with the dielectric waveguide.
refractive index of the overlay. For the transmission character-
Our description follows the lines in previous papers [3]-[6],
istics of polarizers [2] it is necessary to know the propagation
[16] for these special waveguiding systems. But in contrast to
constants and the attenuation of both TE and TM modes and
the perturbative effect in the weak absorption case discussed in
their dependence on various setup parameters. To produce an
the literature, the mode coupling is influenced itself for higher
effective working waveguide controlled photodetector [ 11 it is
absorption. For this reason we have calculated the effective
also of fundamental interest to know the mode behavior of
mode ( n , ~ and) absorption indexes (keff) as a function of
the guided waves in the gap (semiconductor clad) region. On
the thickness d3 of the waveguide cladding. The well known
the other side, such an integrated optical circuit consists of
matrix method, discussed in detail in previous papers [SI,
a section guiding the light without absorption and an other
[9], was used for the calculations. To summarize the known
section absorbing the light.
literature results for our configuration we start with the lossless
So it is necessary to know the coupling coefficient for
system in Fig. 2.
the guided waves at the junction unclad-clad waveguide. In
The behavior of the mode index n,ff can be interpreted
Section I1 we have investigated the mode behavior of a silicon
by the coupling of the modes of two waveguides called
clad waveguide, in Section I11 we determine the coupling
WL1 and WL2 in the following. WL1 represent the system
losses at the junction unclad-clad waveguide. In the last section
air-waveguide-substrat, WL2 the system air-overlay substrat.
we represent our experimental results. Here we have measured
The two dashed horizontal lines in Fig. 2 represent the two
both the attenuation of the guided modes and the coupling
modes of WL1 which of course do not depend on the overlay
thickness d. The dotted and nearly vertical lines show the mode
Manuscript received June 16, 1992; revised January 8, 1993. behavior of WL2 versus the increasing overlay thickness d.
The authors are with Friedrich Schiller University Jena, Institute of Applied
Physics, Max-Wien Platz, DO-6900 Jena, Germany. Because of the high refractive index of WL2, the propaga-
Log Number 9209874. tion constants n , increase
~ drastically for thicknesses larger
0733-8724/93$03.00 0 1993 IEEE

1 -
1448 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 11, NO. 9, SEPTEMBER 1993

d/n rn
1 2 5 JO 2g,nm 40 loo zoo 400
50 100 150 200 250

Fig. 2. Propagation constants (represented by n,ff--values) for a cladding Fig. 4. Imaginary part kefi of the modes of the total system for absorption
without absorption versus the thickness of the cladding; k = 0 {-}{-}{-}{-}{-} index of the cladding k = 0.01 in dependence on the thickness of the
WL1 modes, . . . . . WL2 modes {-}{-}{-} modes of the total system. cladding ......... TEO-TOT mode, {-}{-}{-}{-}{-} TE1-TOT mode, {-}{-}{-}
TE2-TOT mode, TE3-TOT mode.
Amplitude (arb.un.)
I 1
I 1
I
But this is only correct for the case of d3 greater than the first
crossover value and less than the next framed area, because

_.--
'
- TEO-WL1
the behavior of the TE1-TOT mode of the total system is more
complicated and in general the mode is a three mode mixed
state.
Starting from the pure TE1-WL1 mode, at first a symmetric
mixing with the TEO-WL2 mode occurs. Because of the
nl n2 n4 strong steepness of the TEO-WL2 mode an additional but now
TEO-WL2 antisymmetric mixing with the TEO-WL1 mode occurs.
In the horizontal region between the two framed areas, the
TE1-TOT mode corresponds to a weakly perturbed pure TEO-
-1 -0.5 0 0.5 1 1.5 2 WL1 mode. In the second framed region this mode will be
coupled in a symmetric way to the TE1-WL2 mode.
The higher TE(N)-TOT modes have cutoff values larger
than the TE(N-2)-WL2 modes and their dependence on the
thickness of the cladding can be interpreted by the subsequent
mixing of the TE(N-2)-WL2 mode, TE1-WL1, TE(N-l)-WL2,
TEO-WL1, TE(N)-WL2, respectively. For infinite thickness
than the cutoff values for the different WL2 modes. Therefore of the cladding, the modes of WL1 can only be seen as
cross over occurs between the two uncoupled waveguide resonances, called as leaky modes, with n,tf values 1.56652
systems. We have marked the regions for the cross over of and 1.5113, corresponding to the TEO or TE1 values of WL1.
the two lowest overlay modes by the framed areas in Fig. 2. Let us now discuss the influence of the absorption in the
The behavior of the modes of the coupled system represented cladding but at first for small absorption coefficients, were the
by the full lines can be understood in terms of the mixing behavior of n,ff in Fig. 2 is more or less unchanged due to
of the modes of the uncoupled waveguides. Mixing is most the weak absorption.
effective in the cross over regions due to the match of mode The effective absorption of the total systems is represented
index values combined with the superposition of the field by the calculated imaginary part k , of ~ the effective refractive
distributions between dielectric waveguide modes and overlay index n,ff for the corresponding mode shown in Fig. 4.
modes. Considering for example the first framed region, we The result can be understood by a perturbative treatment
find the following: The coupling of the TEO-WL1 mode and starting with the result for the absorptionless case discussed
the TEO-WL2 mode leads to the TEO-TOT mode of the total before, because the calculated n,ff curves do not differ from
system. The corresponding n,R curve shows the transition Fig. 2. The mixing of WL2-modes to the total modes is a
from the horizontal line of WL1 to the nearly vertical line measure of the total absorption. Therefore definite maxima of
of WL2 caused by a symmetric mixing of both waveguide k , ~occur in the crossover regions. This effect corresponds
modes from one to another pure state. to the resonant coupling of the lossless system WL1 to the
Symmetric mixing means a superposition of both field distri- absorptive system of WL2. Behind the last crossover, the
butions with the same sign, i.e., no extra node in the resulting TE(N)-TOT mode corresponds completely to the TE(N)-WL2
combined function. The opposite and so called antisymmetric mode with increasing nee and kee with increasing thickness d.
mixing occurs for the TE1-TOT mode where a node occurs Both results can be summarized in Fig. 5 where the represen-
due to the destruction character of the superposition. Fig. 3 tation of neff and k,ff in the complex area as a one-parametric
shows this effect for d = 11 nm. function of d3 for the different total modes is shown.
G6TZ et al.: ENERGY LOSS IN A PLANAR WAVEGUIDE

0.005 0.03 7 -
I
/93 nm
keff keff I
0.OOL I t TE1-TOT
92Lnrn "

0.02
0.003

0.002
0.01

0.001

0
152
' E l WLl
1.3 1.56 1TEO WL1
l.Sneff
I

1.6
0
1.5 I 1.52
TEO \nl
1.54 1,50 1,60

"eff
Fig. 5. Trajectories of the total modes in the complex nee plane. The leaky wave
numbers correspond to the thickness d in nm. The absorption of the cladding
is k = 0.01. Fig. 7. n,E-values of the total system for strong absorption k = .0.09 in
the cladding TEO-TOT mode, {-}{-}{-}{-}{-} TE1-TOT mode, {-}{-}{-}
TE2-TOT mode, .- TE3-TOT mode.
I
I
At first, crossing of the different trajectories does not occur
I
I
1.58 - TE 0-TOT also in correspondence to Fig. 2 and Fig. 5. But the main
I
changes occur for the region where in Fig. 5 all trajectories
_ --
_ _ _ _TEl-TOI_---,
_-- ---...I._-___
\ _ _ _ _ _ _ _ _ _ _ - -
reach small k,tf values. Let us consider the TEO WL1 region
1.56 - ! in Fig. 5 . Because of the increased resonance values at the left
I I
II
I and the larger steepness of the overlay modes at the right, from
I
1.54 I this marked region for increasing k , the trajectories touch in
- I,!
I
I this region. Therefore for example, in our case the TE2 value
I TE 2 - TOT TE3-ITOT exhibit a spiral characteristic reaching a fix point for infinite
7:
1.52

1.51 .- 4 r
L A
1
. - . _._-
L"A
Lil
values of d3.
This point corresponds to the leaky wave resonance in
the waveguide occurring for an infinite overlay thickness
1,so I I I I I I I I I

at a certain n,tf and k,tf value near the TE1-WL1 region.

From this representation it is easy to understand why the
Fig. 6. n,s-values of the total system for strong absorption k = .0.21 in
the cladding. TEO-TOT mode, {-}{-}{-}{-}{-} TE1-TOT mode, {-}{-}{-} minimum absorption region for all trajectories occurs in the
TE2-TOT mode, .- TE3-TOT mode. weak absorption case. For vanishing k all trajectories have
to be placed below the leaky wave resonance. For increasing
absorption only a certain number of trajectories show the same
The trajectory of the TEO-TOT mode starts at the TEO- behavior. At a mode number determined strongly by k , the
WL1 mode index for d = 0 and changes to the TEO-WL2 corresponding trajectory approaches the leaky wave character.
mode for larger thicknesses. The higher mode trajectories start For infinite d3 the trajectory reaches the leaky wave character.
for netf larger than the TE1-WL1 mode showing strong res- In Fig. 7 this critical trajectory is the TE2 one whereas in Fig.
onance absorption for the different thicknesses corresponding 5 this critical trajectory is not reached in our calculation.
to crossover regions in Fig. 2. But behind this resonance all For trajectories above the critical one, the typical transition
trajectories reach a fixed region with weak absorption k e and ~ from resonance character to small k,tf values and then the
neff values near by the TEO-WL1 mode for different d . After approximation to the WL2 trajectories with high absorption
this point all mode trajectories approach the normal overlay indices, shown in Fig. 4 for k values, and in Fig. 5 for n,tf
WL2-modes corresponding to the same mode index. But there and k,f~ values for TE1 trajectory is changed.
is, in correspondence to Fig. 2, no crossing of the different For example, the trajectories beginning with the TE3 mode
trajectories. (not shown in Fig. 7) exhibit a nearly continuous increase
Let us now discuss the high absorption case. At first we of the trajectory from TE1-WLl to the corresponding WL2
show the calculated neE values in Fig. 6. The characteristic trajectory and no resonance effects due to TEO-WL1 mode
curves change in comparison to Fig. 2 with the n,tf-curves coupling occur.
for the different modes now crossing each other. This shows From this point of view, the misunderstanding in the oc-
clearly that the perturbative treatment in the weak absorption currence of the level crossing in Fig. 6 is only an artifact
case fails completely. The change is not so dramatic if we look due to the projection of the trajectories in Fig. 7 on the real
at the trajectories in the complex netf and ketf plane in Fig. 7. axis n , ~ As . a characteristic new result of our calculations the
1450 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 11, NO. 9, SEPTEMBER 1993

n 3 + ik lossy c l a d d i n g
assume I T - / << 1 and solve (l), ( 2 ) similar to [6]. We use the
4

lorless waveguide wL< wL> n2 multimade

orthogonality of the modes given by:
monomode 2

n I
' z=o
e p ( s ) h , ( x )d s - S,,, (3)
Fig. 8. Geometry of the waveguides at the junction of both waveguides.

TE-Pol.: e,, = ey,,; h, = h,,

occurrence of such a helix like trajectory can be stated. For
a given absorption and above a certain thickness a mode is TM-Pol.: e,, = e Z p ;h, = h,,
found which shows a relative small k e values
~ in comparison
where ,S is the Kronecker symbol for guided modes and the
to k itself. This can be understood as a resonance softening of 6-Dirac function for radiation modes.
the damping due to the waveguiding layer.
The orthogonality using the integrand e,(x) . h:(s) is not
The mode structure of this helix like curve does not differ so
given because of the absorption in WL>.For the transmission
much from the TEO-WL1 structure inside the WL1. Only the coefficient of the guided modes we have:
small evanescent part of the field in the superstrat changes to
an oscillating but also exponentially decaying behavior in the
overlay region. This is seen by the relative magnitude of the (e'lh<)(e<lh')
Ti = (4)
effective complex refractive indexes of the modes themselves. (e'lh<) + (e<Jh')
This similarity of the structure is a good argument for an where:
effective coupling of the guided wave between cladded and
uncladded regions, as discussed in the next section.
. h,>,(x)
111. COUPLING OF WAVEGUIDES WITH DIFFERENT
CLADDINGS
[,{ e,'(.)
00

e,<(.)
TE-Pol.
.hGi(x)}dxTM-Pol.

Now let us discuss the influence of a junction (see Fig. The transmitted power is given by:
8) between a monomode waveguide WL< and a multimode
waveguide W L > which has an absorbing cladding.
At the junction z = 0 for both waveguides the transition
conditions of the tangential components of the electric and
magnetic fields should be satisfied. with:
Reflection and transmission in guided modes (with the
coefficients Ri Ti, respectively; a gives the number of guided
modes in W L > ) and in radiation and evanescent modes
t ( y ) ) occur. The mode matching condition
(coefficients ~(y), The second term of (5) does not vanish for waveguides that
becomes: include absorption. This term describe a collective guided
E-Field: power of the modes of W L > .Pradrepresents the transmitted
power into the radiation modes of W L > including also the
corresponding mixing terms.
In order to compare theoretical with experimental results,
given in the next section we have to calculate the insertion
losses CY^,,^^ for the power PI coupled into the quasi-leaky
wave of waveguide W L>.

= C Tih,>,b)+
i=l
1 00

t(r)rlj(Y> d r (2) IV. EXPERIMENTAL

RESULTS
We have measured the losses of waveguides with a a-Si
where e,<(e,>)and h,<(h,>) represent the field components in cladding using a special structure (Fig. 9). Using a second
the ranges z < 0 ( z > 0),y2 = kng - ,B>2. The integration structure, we were able to measure the coupling losses at
should be done for the complete range of y for the radiation the junction between unclad-clad waveguide. The waveguides
and evanescent modes. Equivalent calculations are done for used here, were fabricated by ion exchange (K+ c-f Na+)
TM-Polarization. [13]. These monomode waveguides can be described by an
In general, the solution of (1) and ( 2 ) is difficult and should +
exponential profile: n ( s ) = n, d n exp ( -x/deXp) with 12,-
be done by numerical methods [lo], [11]. Because of the substrate index; dn-maximum of refractive index at the surface
similar field distributions of the guided wave in waveguide of the waveguide. The approximation of the exponential profile
W L < and the quasi-leaky mode in waveguide W L > we can leads to a good agreement with the refractive index profile,
 I

&E! et al.: ENERGY LOSS IN A PLANAR WAVEGUIDE 1451

Srep- Polarisation TABLE I

C ALCULATED AND MEASUREDLOSSESOF THE C LADDED
THEORETICAL
WAVEGUIDE AND THE COUPLING E FFICIENCY, 633.nm

L3

L. 10
0.6
0.8 l l C a lcul a t ion

Kopp I .
Measurement

Nr .
Prob.J

Fig. 9. Geometry of the a-Si structure onto the waveguide for measuring ldBcm IdB ldBcm ldB
I
absorption losses of the cladded system.
6iE TE 21.1 26.1 0.022 20.5 -
...........................
163E TE 12.9 f1.I 0.03 13.0 -
...................
64E TE 19.1 f2.9 0,026 19.6 -
..................
6iM TM 266 f45 0.052 253 -
...........................
63M TY 282 f85 0.246 335 0.13
............................
64M TM 323 f76 0.066 328 -

For a good approximation we can assume equal coupling

coefficients for the step unclad-clad waveguide and for the
step clad-unclad waveguide. The theoretical predicted and ex-
Fig. 10. Experimental setup for measurement of absorption and coupling
coefficients of the waveguide system.
perimental measured results are shown in Table I for different
probes.
The precision of the measured values is Aasi = f0.9
measured by the RNF-technique [15] and the measured
dB/cm (TE-Pol.) and Ass; = f 1 8 dB/cm (TM-Pol.) and for
values.
the coupling losses AaLoUpl= f O . l dB. The accuracy of the
By comparing the measured losses of different steps of
calculated absorption losses Acu, is determined by varying the
the cladding, one can easily determine losses in the cladding
parameters of the overlay. These different parameters of the
region asi. To determine the coupling losses another structure
overlay were measured by the above mentioned reflection and
was used, which consists of a different number of coupling
transmission measurements. They are caused by slightly dif-
steps to get a higher precision of the measurement.
ferent parameters of the sputtering processes. The calculations
To measure the absorption and coupling losses of the
were done with the same matrix formalism [SI, [9] used in
waveguides with the overlay we have developed a special
Section 11.
2-prism method (Fig. 10).
In Table I it is shown that only for the sample 63M we
For the analysis of the losses there was taken into account
could measure a coupling coefficient different from zero. This
the incident and reflected intensities in the coupling prism. We
coupling coefficient is only slightly greater than the precision
also considered the reflection coefficients at the given angles
of our experiment but we found this coefficient different times
at the different prism surfaces.
repeating the measurement.
By a careful alignment of the experimental setup it can be
For all other samples, the measured coupling losses are zero
shown that the measured absorption coefficients of the cladded
within the levels of the errors of the measurement.
waveguide do not depend on the coupling efficiencies of the
prism.
V. CONCLUSION
We described the mode behavior in dielectric waveguides
(7) cladded by a high refractive index overlay including absorp-
tion. The representation of the complex refractive index for dif-
IT^; IT,-output intensities by measuring various steps of ferent overlay thicknesses shows that “unphysical” crossovers
the structure (see Fig. 9); L,; L,-length of the steps; O W L - of various modes does not occur. In waveguide systems with
absorption coefficient of the pure waveguide in dB/cm. absorption we found the propagation of so called quasi-leaky
The refractive index and the absorption coefficient of the waves for finite thicknesses of the overlay. This wave is not
semiconductor overlay were determined by direct reflection able to penetrate from one to the other boundary of the overlay,
and transmission measurements at various incident angles its propagation constant and field distribution in the region of
(without waveguide coupling). WL1 are similar to the propagation constant of the wave of
As expected in Section I1 we found the most effective the uncladded waveguide.
coupling into the quasi-leaky wave of the cladded waveguide In the next section we described a method to calculate
because of the similar field distributions of the two guided the coupling efficiency at the junction of an uncladded and
waves. On the other hand all higher modes are damped a cladded waveguide including absorption.
very strongly because of their propagation constants and the With our experimental setup we were able to measure both
high absorption coefficient of the overlay. Thus they do not the absorption of guided waves in the clad waveguide and the
influence the output intensity. As a result we were able to coupling losses at the junction from uncladded to the cladded
neglect the terms P,,(z,g> 0) and PIad by calculating the waveguide. We found a good agreement of calculated and
coupling efficiency a&,plof the guided waves. measured values.

1 -
1452 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 11, NO. 9, SEPTEMBER 1993

As a result of Section I1 we expected an effective coupling C. Vassallo, JOSA A5(1988), 1918.

T. E. R o u i , IEEE Trans. Microwave Theory Tech., vol. MlT-26, p.
into the quasi-leaky wave of the cladded waveguide. This
758, 1987.
prediction was completely confirmed with our experimental B. Gotz, thesis, Friedrich Schiller University Jena.
results (see Table I). Our investigations are of fundamental W. Jost and K. Hauffe, Difision, Dr. Dietrich Steinkopf, Ed. Darm-
stadt: Verlag, 1972, chap. 1, p. 27-31.
interest for the creation and optimization of integrated optical B. Gotz, W. Karthe, and B. Martin, In?. J. Optoelectron., vol. 712, p.
circuits consisting of a multilayer system including absorption 281-284, 1992.
so as polarizers and switches. On this basis we created an R. Goring and M. Rothardt, J. o f o p t . Commun., vol. 7, p. 82-85, 1986.
T. E. Batchman and M. C. McCarson, Appl. Opt, vol. 18, p. 2796,
integrated optical switch (Auston switch) with a high switching June 1990.
efficiency. The results of the switch are published in [12], [14].

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