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m-Lines technique: Prism coupling measurement and discussion of accuracy for homogeneous waveguides

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  • Institut Fresnel - Institut Carnot STAR

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A method is proposed to measure the thickness of the air layer between the prism and the waveguide in a totally reflecting prism coupler. The coupling efficiency of a Gaussian beam from the prism into the waveguide can be calculated when the air-layer thickness (ALT) is known. To perform measurements of the indices and thicknesses of planar waveguides using the m -lines technique, it is necessary to have a good knowledge of the prism's characteristics and to accurately measure the angles. However, we show by means of an example that the small distance between the prism and the guide (i.e. the ALT) should be taken into account in order to achieve accurate measurements.
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m-lines technique: prism coupling measurement and discussion of accuracy for homogeneous
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2000 J. Opt. A: Pure Appl. Opt. 2 188
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J. Opt. A: Pure Appl. Opt. 2(2000) 188–195. Printed in the UK PII: S1464-4258(00)04726-7
m
-lines technique: prism coupling
measurement and discussion of
accuracy for homogeneous
waveguides
S Monneret, P Huguet-Chantˆ
ome and F Flory
Laboratoire d’Optique des Surfaces et des Couches Minces, Ecole Nationale Sup´
erieure de
Physique de Marseille, Domaine Universitaire de Saint-J´
erˆ
ome, 13397 Marseille Cedex 20,
France
E-mail: francois.flory@enspm.u-3mrs.fr
Received 2 June 1999, in final form 4 February 2000
Abstract. A method is proposed to measure the thickness of the air layer between the prism
and the waveguide in a totally reflecting prism coupler. The coupling efficiency of a Gaussian
beam from the prism into the waveguide can be calculated when the air-layer thickness (ALT)
is known.
To perform measurements of the indices and thicknesses of planar waveguides using the
m-lines technique, it is necessary to have a good knowledge of the prism’s characteristics and
to accurately measure the angles. However, we show by means of an example that the small
distance between the prism and the guide (i.e. the ALT) should be taken into account in order
to achieve accurate measurements.
Keywords: Thin films, m-lines, prism coupling, optical waveguides, refractive index
1. Introduction
Thewellknownprismcoupler [1–5] can be consideredasone
of the best ways to couple large amounts of light in planar
optical waveguides. The totally reflecting prism coupler
(TRPC) technique, also referred to as the m-lines technique,
is commonly used to determine the optical properties of
thin films [6, 7]. The refractive index and the thickness as
well as the anisotropy of dielectric planar waveguides can be
determined in this way [8–11].
The m-lines appear for the different incident directions
corresponding to the coupling of light in the waveguide. As
the coupling between the prism and the waveguide increases,
the m-lines are broadened and shifted [1]. For m-lines
measurements,thecouplingisgenerallyconsideredweakand
is neglected as soon as the thickness of the air layer between
the prism and the waveguide is greater than about half the
wavelength of the coupled beam [8,9].
To the best of our knowledge, the study of the prism’s
influence on the m-lines technique has never been treated
because of the difficulty in determining the thickness of the
coupling air layer between the prism and the guide (air layer
thickness (ALT)).
Thus this paper is devoted first to the method we propose
to measure the ALT, then to the study of the prism’s influence
† Present address: ENSIC, DCPR (UMR 7630 CNRS-INPL), BP 451,
54001 Nancy Cedex 01, France.
on the measurements obtained with the m-lines technique.
After a short review of the principle of the TRPC, we
present the experimental method implemented to determine
the ALT. It is shown that this method gives the ALT with
a difference of 1 nm or less for two sets of independent
measurements performed at two different wavelengths.
Numerical results concerning the consequences of prism
coupling on measurements are given afterwards. A general
discussiononhigh-accuracythin-filmcharacterizationisthen
presented. Thispaperonlydealswithhomogeneousisotropic
single-layeropticalwaveguidesforwhichtherefractiveindex
nand the thickness tare the parameters to be determined.
The absorption can be taken into account but we concern
ourselves mainly with weakly absorbing materials.
2. The totally reflecting prism coupler
We shall first briefly review the main properties of the
common TRPC. In this paper, we consider prisms that are
rectangular and isosceles. A schematic representation of the
device is given in figure 1.
The coupling of an incident laser beam by a prism into a
planar waveguide [1–5] is governed by the incident angle
θpof the beam on the prism base. Under total internal
reflection conditions on this base, strong coupling of light
into the waveguide can occur via resonant frustrated total
1464-4258/00/030188+08$30.00 © 2000 IOP Publishing Ltd
Discussion of the accuracy of the m-lines technique
Figure 1. Schematic representation of the TRPC, and CCD
recording of a m-line.
reflection, i.e. via evanescent waves in the air layer (figure 1).
Such coupling occurs only when resonant conditions inside
the waveguide are met. This leads to a finite number of
discrete incidences of the laser beam, for which the light can
be strongly coupled into the guide. We call these incidences
synchronism angles θsync (figure 1).
In the experiments, the resonant coupling of the laser
beam into the waveguide is observed through the appearance
of a dark line in the reflected beam. The dark line can
be associated with a bright line (figure 1, CCD recording).
According to [1], we call such lines m-lines.
Consequently, the method referred to as the m-lines
technique consists in measuring the synchronism angles
corresponding to the m-lines. The optical parameters nand
tare calculated from the measured θsync [6–9]. Under such
conditions, the propagation constants determined from the
θsync are assumed to be those of the free guided modes.
However, this hypothesis is not perfectly true due to prism
coupling. The coupling is, of course, directly dependent on
the ALT: we shall now consider the measurement of the ALT.
3. Measurement of the ALT
The determination of prism coupling efficiency has been the
subject of several studies. Chilwell [12] proposed a method
basedontheobservationofinterferencefringeslocalized near
the prism’s base. This method is not easy to implement when
it comes to determining the absolute value of the ALT.
A second way to assess the efficiency of prism coupling
is to use m-lines. Midwinter [13] has first shown that there
is a relationship between the intensity profile of a m-line and
the coupling of the incident beam in the waveguide. Falco
et al [14] have then shown experimentally that the near-field
intensity profile of the reflected beam directly depends on the
coupling of the incident beam.
After these studies, this principle was developed to
study nonlinear changes in the refractive index of thin-film
materials[15,16]. This methodoffersseveraladvantages: the
beam itself, coupled in the waveguide, is used; the ALT is
determined at the exact point where light is actually coupled;
such determination is possible in real time; we will see that
the precision of the method is quite high.
Figure 2. Modelling of the reflected beam. Coordinate frames.
Solid arrow: mean incidence of the Gaussian beam. Broken
arrow: one of the incidences of the Gaussian beam.
First we present the modelling of the reflected beam
needed for ALT determination, which has not been presented
in [15, 16]. We then describe the measurement method,
validate it experimentally, and finally give the precision of
the measurement.
3.1. Modelling of the reflected beam
Let us consider the prism coupler schematically drawn in
figure 2. All the media are assumed to be isotropic and
homogeneous. The waveguide and the substrate can be
dissipative, so that refractive indices are complex numbers.
In the coupling zone, interfaces are assumed to be plane and
parallel. A first reference (O,X,Y,Z) is chosen in order
that the boundaries between the media may be parallel to the
(XO Y ) plane. The plane of incidence is the (XOZ) plane.
The system is assumed to be infinite along the Ydirection. E
istheelectricvectoroftheelectromagneticfield. Weconsider
harmonic waves with an exp(iωt) temporal dependence
which will be omitted in the presentation.
This modelling concerns only the particular case of a TE
or TM linearly polarized incident light beam.
Let our system be illuminated by a Gaussian laser beam
focused on the prism’s base and centred on the point O
(figure2). WedenoteOiandOrthe geometrical images of O
through the entrance and exit faces of the prism, respectively.
Two Cartesian coordinate frames (xi,y
i,z
i)and (xr,y
r,z
r)
are centred on Oiand Or(figure 2). These coordinate frames
are such that they are directly associated with the path of the
beam in the air.
Let us first consider the beam propagating in the air
without any prism. In this case, the amplitude of the incident
electric field in the plane (xiOiyi)is given by
Ei(xi,y
i,z
i=0)=E
0exp x2
i
w2
0exp y2
i
w2
0(1)
where w0is the half width at 1/e2in intensity of the Gaussian
beam’s waist in the air and E0the maximum amplitude of Ei.
For zi=0 one can express E0exp(x2
i
w2
0)as a sum of
plane waves. As the plane of incidence is the (XOZ) plane,
189
S Monneret et al
and because the structure is invariant in Ywe obtain
Ei(xi,y
i,0)=exp y2
i
w2
0Z+
−∞ ˆ
Ei(σ ) exp(2jπσxi)dσ
(2)
where
σ=sin )/λ0(3)
is the transverse spatial frequency of each plane wave, θ
the angle between the incidence of this plane wave and the
mean incidence of the Gaussian beam, and ˆ
Ei(σ ) the one-
dimensional Fourier transform of Ei(xi,0,0). Its analytical
expression is given by:
ˆ
Ei(σ ) =E0πw0exp(π2w2
0σ2). (4)
Let us now consider the beam propagating in the real
system, i.e. with the prism. After propagating through the
material, the electric field in the air is given by
Er(xr,y
r,z
r)=exp y2
r
w2
0Z+
−∞ ˆ
Ei(σ )f (σ )
×exp(2jπσxr)exp(2jπµzr)dσ(5)
where the longitudinal spatial frequency of each plane wave
is
µ=cos)/λ0.(6)
Thefunction f(σ)isdefinedby f(σ)=t
1(σ )t2(σ )r (σ )
exp(jp(σ )). Values t1(σ ),t2(σ ) and r(σ) are the
transmission and reflection coefficients [17] in amplitude on
the prism’s faces (figure 2) for a plane wave characterized
by the spatial frequency σ.r(σ) is obtained from a classical
plane wave matrix method [18], and is strongly dependent on
σnear a resonance. pis the change of phase of a plane
wave of spatial frequency σas a result of its path inside the
prism. Its expression is given by
p(σ ) =k0Lp
np
(n2
p1) 1+λ
2
0
2sin2i)
n2
psin2i)σ2!(7)
where θiis the mean angle of incidence of the beam on
the prism and Lpthe mean total length of the beam’s path
inside the prism. Lpis easily determined by geometrical
considerations, and obviously depends on θiand on the size
of the prism.
Let us now assume that the incident Gaussian beam has
a small aperture. Hence we can neglect the dependence of
t1and t2on σand assume t1(σ )t2(σ ) =t1(0)t2(0). The
small aperture of the beam implies that σλ1
0, which,
carried into equations (3) and (6), leads to an expression of
the longitudinal spatial frequency µversus the transverse
spatial frequency σ:
2π µ(σ ) k01λ2
0σ2
2.(8)
The electric field distribution of the reflected beam is now
given by
Er(xr,y
r,z
r)=exp y2
r
w2
0Z+
−∞
F(σ,x
r)
×exp(2jπσxr)dσ(9)
Figure 3. Typical calculated evolution of the transverse intensity
profile Ir(xr,zr=1 m) of the reflected light beam. The given
profiles correspond to: (a) No coupling (infinite ALT), (b) weak
coupling (ALT =250 nm) and (c) stronger coupling
(ALT =150 nm). Calculated for λ=514.5 nm with a beam waist
w0=15 µm and a SrTiO3prism, in the case of a waveguide of
refractive index 1.500 and of thickness 1046 nm. Substrate index
1.4616. TE0resonance.
with
F(σ,z
r)=ˆ
E
i(σ )f (σ ) exp(jk0zr)exp(jπσ2zr). (10)
Let Ir(xr,z
r)be the transverse intensity profile of the
reflected light beam. This profile is defined as
Ir(xr,z
r)=|E
r
(xr,0,z
r)|2.(11)
For a given value zr0of zr,Ir(xr,z
r
0)is therefore obtained
directly from the one-dimensional inverse Fourier transform
versusσofthefunctionF(σ,z
r
0). Numerically,afastFourier
transform algorithm is used to compute Ir. The sampling
must be chosen carefully because of the steep slope of the
function exp(πλ0σ2zr)versus σwhen zrincreases.
In figure 3 we provide an example of the dependence
of Ir(xr,z
r)on the ALT. For an infinite ALT, the reflected
beamis Gaussian (figure 3(a)). When the coupling increases,
the m-line appears and becomes more and more contrasted
(figure 3(b), ALT ta=250 nm and figure 3(c), ALT
ta=150 nm). Oscillations appearing in the reflected beam
can also be observed experimentally, especially for low-loss
waveguides. They can be regarded as interferences between
the part of the beam that is almost directly reflected on the
prism’s base and that which has passed through the guide.
3.2. Measurement method
Let us now study the characteristics of the reflected near-field
intensity distribution INF, defined as
INF(xr,y
r)=|E
r
(xr,y
r,0)|2.(12)
INF corresponds to the transverse intensity distribution of
light. It can be directly recorded on a screen by imaging the
prism’s base around Owith the use of a lens.
Figure 4 gives typical experimental recordings of INF
obtained with a CCD camera in various coupling conditions.
The appearance of such reflected spots can be understood as
follows: the first spot represents the part of the incident beam
that is directly reflected on the prism’s base; the second one
representsthe light leaking out afterhavingbeen coupled into
190
Discussion of the accuracy of the m-lines technique
Figure 4. Typical experimental recordings of reflected near-field
images, obtained with a CCD camera. (a) no coupling, (b) weak
coupling, and (c) strong coupling.
the waveguide. Therefore only the first spot is visible when
no coupling occurs (figure 4(a)), and for strong coupling
(figure 4(c)) the second spot is much brighter than the first
one. Because the coupling efficiency cannot be more than
81% [3,13], the first spot is always visible. We denote by I1
the first relative maximum of the INF(xr,0)profile and by
I2the second one, according to the propagation direction of
the light.
Values of I2depend on the coupling, on the waveguide
absorption, and on the beam waist. Dependence on the
beam’s waist is due to the filtering effect of the function ˆ
Ei
on the spatial frequencies, which depends on the ALT [16].
Figure 5 represents typical changes of the near-field
ratio (NFR) I1/I2with the ALT tafor a single-layer
waveguide, showing a one-to-one relationship between these
parameters for each configuration (i.e. prism and waveguide
characteristics, beam wavelength, waist and polarization,
resonance order). Thus, this one-to-one relationship implies
that, for a given configuration, the measurement of the NFR
I1/I2gives the ALT. Moreover, our calculations show that
the value of I1/I2corresponding to the optimal coupling
efficiency depends neither on the resonance order nor on the
polarization state.
3.3. Validation of the method
In order to validate the method described above, we have
determined the values of the ALT tasimultaneously by
performing two independent sets of measurements with two
different laser beams (figure 6).
The waveguide we have used is a single thin film of
SiO2deposited by ion-assisted deposition on a fused silica
substrate. The two incident beam spots are superimposed on
thebaseof the SrTiO3prism. Theexperimentalconfiguration
is defined by
green beam: λ=514.5nm,
w
0=46.4±0.5µm,TE0resonance,
red beam: λ=632.8nm,
w
0=34.7±0.5µm,TM0resonance.
Thegreen and thered images ofthe corresponding near fields
ofthereflectedbeamsareobtainedbymeansofthesinglelens
Figure 5. Typical evolutions of the NFR versus the ALT and
influences of the beam waist w0and of the imaginary part κof the
waveguide refractive index. (a)κ=0; w0=15 µm.
(b)κ=7.8×105;w0=15 µm. (c)κ=7.8×105;
w0=30 µm. Calculated for λ=514.5 nm and a SrTiO3prism, in
the case of a waveguide of refractive index 1.500 and of thickness
1046 nm. Substrate index 1.4616. TE0resonance.
Figure 6. Experimental two-beam set-up used for validating the
determination of the prism coupling efficiency.
L2(figure 6) because with this waveguide the two resonances
are very close together. Values of the green and the red NFRs
are measured simultaneously with a CCD camera connected
to a digital image processing system. Curves such as those
given in figure 5 are used to obtain the value of the ALT as
measured with the green and the red beams. The extinction
coefficientκof the waveguide, determined by a photothermal
deflection technique [19] is considered:
λ=514.5 nm: κ7.8×105,
λ=632.8 nm: κ3.4×105.
In order to verify our results, five thorough independent
measurements with various coupling efficiencies have been
performed. TheALThasbeentunedbychangingthepressure
usedtopresstheguideagainsttheprism. Theresultsare given
in figure 7. Values of the ALT obtained either from the red
or the green beam are the same, within approximately 1 nm.
As the ALT can be measured, the coupling efficiency
of the incident beam into the waveguide can be calculated as
wellas the electricfield distribution in thewhole system [16].
191
S Monneret et al
Figure 7. Simultaneous determination of the ALT with two laser
beams. Five independent measurements with various coupling
efficiencies are reported. Waveguide: thin film of SiO2deposited
by ion assisted deposition (deposition conditions: deposition
rate 1.0nms
1, ion energy 250 eV, current
density 200 µAcm
2. Film properties: n=1.494 at
λ=632.8 nm, n=1.500 at λ=514.5 nm, κ=7.8×105at
λ=514.5 nm, κ=3.4×105at λ=632.8 nm, t=1046 nm).
Substrate: fused silica (ns=1.4570 at λ=632.8 nm,
ns=1.4616 at λ=514.5 nm). Prism: SrTiO3. Green beam:
λ=514.5 nm, w0=46.4±0.5µm, TE0resonance. Red beam:
λ=632.8 nm, w0=34.7±0.5µm, TM0resonance.
3.4. Discussion
Because of the limited dynamics of the CCD camera, the
coupling efficiencies that can be measured with this method
are restricted to values greater than 30% of the maximum
coupling efficiency. This corresponds to NFRs typically
between 0.1 and 10.
Such a range is not convenient for determining the ALT
in the case of weak coupling as is usually considered for
typical m-lines measurements. A two-beam set-up (like that
presented in figure 6) can be used to remove this constraint.
A first beam is weakly coupled for the measurement of
each m-line by searching a dark line as thin as can be visible
to the naked eye. A second beam, at a different wavelength,
is used at the same time to measure the NFR. By combining
the two wavelengths and the mode orders, both beams can be
coupled with the same ALT, each into its own mode, which
make weak coupling of the first beam possible and permits
us to measure the NFR of the second one.
4. High-accuracy m-lines measurements
As mentioned previously, the m-lines can be broadened and
shifted when the coupling efficiency increases [1,2]. This
means that the synchronism angles θsync depend on the ALT.
The weak coupling hypothesis is commonly used to neglect
thisdependencebecause of the former difficultyinmeasuring
the ALT. However this hypothesis limits the accuracy of the
waveguide parameter measurements [20]. The aim of what
is presented below is to assess such a limitation and also to
compare it with the other sources of inaccuracy inherent in
the m-lines technique.
First we recall the differences in the conditions of
light propagation between the free waveguide (i.e. the weak
coupling hypothesis) and the waveguide coupled to a prism.
Numericalsimulationsoftheprism’sinfluencearethengiven.
Finally, an example shows that for accurate measurements,
the effect of the very small distance between the prism and
the guide could lead to non-negligible errors in the recovery
of the waveguide parameters.
4.1. The weak coupling regime
4.1.1. Theory. Let us recall some general results concern-
ing guided optics, in order to clarify the main changes occur-
ring in the light propagation whether the waveguide is free
or coupled to a prism.
We first consider the free waveguide. Guided modes
occur when the fields are evanescent in the air and the
substrate [18, 21]. Then, we need to find the solutions
to Maxwell’s equations, which can satisfy the boundary
conditions at the waveguide–substrate and waveguide–air
interfaces. We know that there exists only a finite number of
discreteguidedmodesthat can propagate in a free waveguide.
Each guided mode is then characterized by its polarization
stateandanintegermwhichistheorderofthemode. Besides,
each mode can be associated with the propagation of one
single wave inside the structure, of propagation constant
βm;βmis invariant inside the waveguide and represents
the projected part of the wavevector on the guided wave
propagation axis [21]. For more convenience, the effective
index αm=βm/k0can also be used, where k0is the modulus
of the wave vector of the light beam in vacuum.
In a prism–film coupler, the resonant modes are not
the modes of the free guide. In this case, a continuum of
propagating waves exists in the guide; and the propagation
constant β[22] depends only on the incidence of the input
beam on the prism, independently of any of the guide’s
parameters. Because of this fundamental change, for a
Gaussian incident beam, one can no longer associate the
beam propagating inside the waveguide with a single wave
but with a continuous set of waves [23]. The aperture of such
a wavepacket strongly depends on the ALT [16].
Nevertheless, the different resonances of the waves
correspond to the modes of the waveguide coupled to the
prism [3]. When increasing the ALT, these resonances
grow sharper and change notably. For an infinite ALT, they
correspond, of course, to the free guided modes. Therefore,
each resonance is labelled with the same mode order mas
the corresponding free guided mode. We call βmr the mean
propagationconstantof the resonant beam propagating inside
the coupled waveguide, and αmr the corresponding effective
index.
Such dependence of βmr on the ALT is directly
responsible for the intrinsic limit on the accuracy of the m-
lines technique. In order to suppress such a limit and because
of the difficulty in determining the ALT in the TRPC, it
is usually assumed that the measurements are made in a
weak coupling regime. Calculations have shown that the
ALT should be greater than half the wavelength in order
not to disturb the guided modes [8,9]. The weak coupling
approximation then allows us to consider the free guided
modes as corresponding to the m-lines. In this condition
it is easy to recover nand tfrom the measured propagation
constants [24].
192
Discussion of the accuracy of the m-lines technique
4.1.2. Accuracy of the m-lines measurements. Let us
define several parameters concerning the evaluation of the
errors made during m-lines experiments and calculations:
th =|α
mr αm|
=error due to the coupling to the prism.
exp =uncertainty on the measurement of αmr .
On the one hand, the uncertainty exp stems from the
uncertainty on both the refractive index npand the angle
Apof the prism (see figure 2). On the other hand, it results
fromtheuncertaintyonthemeasured synchronism angle. Let
1np,1Apand sync be these uncertainties. The maximum
absolute error exp of αmr is then given by
exp =∂αmr
∂Ap
1Ap+∂αmr
∂np
1np+∂αmr
∂θsync sync.(13)
The refractive index of the prism can generally be
determined from the common minimum deviation method,
giving in our case 1np=2×105†. The angle Apof the
prism is measured with 1Ap=1×103degrees and the
synchronism angles with sync =5×103degrees.
Calculatingthedependenceofexp onthesynchronism
angle θsync for realistic values of npand Ap, the values of the
multiplicative coefficients of equation (11) ∂αmr
∂Ap,∂αmr
∂npand
∂αmr
∂θsync imply that exp varies only weakly around 1×104.
One can therefore assume that the weak coupling hypothesis
is satisfied as long as th is negligible in comparison with
exp. We assume this condition is met when th <
lim =1×105.
We must now calculate the error th versus the
coupling in order to define experimental conditions in which
the coupling has no significant bearing on the measurements.
For this purpose, we shall first study the influence of the
coupling of the prism.
4.2. Numerical simulations of the prism’s influence
The ALT that corresponds to a given coupling efficiency
depends a lot on the characteristics of the coupled beam
(i.e. wavelength, polarization, mode order, beam waist) [16].
Consequently, the ALT is not the most suitable parameter
to define the weak coupling regime. On the other hand, for
a given beam waist, the NFR associated with the maximal
coupling efficiency depends neither on the mode’s order nor
on the polarization state. The NFR can therefore be used as
a typical parameter of the coupling regime.
Severalremarkscanbemadeabouttheevolutionofth
relative to the NFR. First, th clearly tends to zero for an
infinite NFR (that is for an infinite ALT). Additionally, the
TM resonances are much more sensitive to the coupling than
the TE ones in all the calculations we performed with various
waveguide parameters, wavelengths, beam waists or prism
indices (an example is shown in figure 8). To satisfy the
criterion th <1α
lim, the NFR should be greater than
several hundreds, corresponding to extremely weak coupling
conditions.
This implies corrections 8 and 10 indicated below.
Figure 8. Evolution of th versus NFR for the TE2and TM2
resonances. Calculated for λ=514.5 nm with a beam waist
w0=15 µm and a SrTiO3prism, in the case of a waveguide of
refractive index 2.27 and of thickness 427 nm, with an extinction
coefficient κ=5×105. Substrate index 1.4616.
4.3. High accuracy determination of optical properties
of light guiding thin films
4.3.1. m-line detection. With the m-lines technique, the
purpose is to measure the angles for which dark lines appear
in the reflected beam. These dark lines, when thin, can be
efficiently detected by the eye, whereas for a coherent laser
beam, the speckle makes the detection of these lines difficult
to perform with a photodetector. To be in a weak coupling
regime, it is necessary to measure the angles for lines as thin
as possible, i.e. on the limit of visibility.
Measurements performed on the limit of visibility yield
a contrast and a width of the line one metre from the prism
of 20% and 0.025, respectively. The contrast is defined as
ImaxImin
Imax+Imin with Imax andImin the maximum and theminimum of
the m-line intensity profile respectively; the width of the line
is defined as the apparent angle between Imax and Imin as seen
from the prism. This is in good agreement with the reference
results [25] about human eye mean contrast sensitivity. It
can be considered that the width of the line on the limit
of visibility, 1 m from the prism, does not change with the
polarizationor the mode’sorder. Nordoesitchange in a wide
range of waveguide, prism or beam characteristics. Hence,
thecontrastaccountsdirectlyforthevisibility. Consequently,
with this contrast, the ALT in the m-lines conditions can be
evaluated without measuring the NFR.
4.3.2. Accuracy of the m-lines technique. Considering
that the approximate values of the refractive index and of the
thickness of the guide are known, the contrast on the limit of
visibility (i.e. 20%) allows the calculation of the ALT, then
of th.
For example, figure 9 shows the differences th
between the effective indices corresponding to the guided
modes of the free waveguide and those corresponding to the
associated resonances of the coupled waveguide. The layer
considered has a refractive index of 2.27 and a thickness of
427 nm. One can notice that non-negligible errors (1αth >
lim =1×105)occur in the TM resonances.
On the other hand, our experimental uncertainties on
the prism’s angles or index and on the synchronism angle
measurements prove more significant than the effect of non-
weak coupling. The accuracy we currently obtain in the
193
S Monneret et al
Figure 9. Example of calculation of th for the resonances of a
guide with the conditions of m-lines measurements. Calculated for
λ=514.5 nm with a beam waist w0=15 µm and a SrTiO3prism,
in the case of a waveguide of refractive index 2.27, of extinction
coefficient 5 ×105and of thickness 427 nm. Substrate index
1.4616.
index and thickness measurements of thin-film dielectric
waveguides is of 1 ×103for the index and 1 nm for the
thickness. In order to reach higher accuracy, the first step
would be to improve the accuracy of the measurements of the
prismparameters and ofthe synchronism angles. Thesecond
stepwouldthenbetocorrectαmr with th by taking account
of the coupling with the prism. In this way, an accuracy
of 1 ×104for the refractive index and of 0.1 nm for the
thickness of a homogeneous and isotropic waveguide could
be expected.
5. Conclusion
Onecandeterminethe indexand the thickness of a waveguide
using the m-lines technique on the assumption of weak
couplingwith the prism. This hypothesis allowsonetomatch
the measured effective indices to the effective indices of the
guided modes of the free waveguide. The necessity for this
hypothesis is warranted mostly by the difficulty in measuring
the coupling of the incident beam in the guide.
We propose a general experimental method to measure
the thickness of the air layer between the prism and the
guidewhich determines the couplingefficiency. This method
is based on an electromagnetic model of the TRPC with
a Gaussian beam. It offers several advantages: first the
precision of the ALT measurement is of the order of 1 nm;
then the beam actually coupled in the guide is used; lastly,
the measurement can be made in real time.
As one can measure the ALT, it then becomes possible
to test the validity of the hypothesis of weak coupling
used by the m-lines technique. Using the model of the
TRPC mentioned above, we have studied the behaviour of
the difference th between the effective indices of the
resonances of the guide coupled to the prism on the one hand
and the effective indices of the associated guided modes of
the free waveguide on the other.
We have shown by means of an example that in m-lines
conditions, the ALT can be such that th becomes non-
negligible by contrast to the other sources of uncertainty,
as regards TM resonances especially. However, in our
experiment, these sources of uncertainty are conducive to
an accuracy of no better than 1×103for the index and 1 nm
for the thickness. Such an accuracy is immune to the effect
of non-weak coupling.
However, if the angles were measured with an accuracy
better than 1 ×103degrees, by taking into account the
presenceoftheprism,onecouldreachanaccuracyof1×104
for the refractive index and of 0.1 nm for the thickness,
respectively, for homogeneous and isotropic waveguides.
The method proposed here for single layer waveguides
can easily be extended to multilayer waveguides and
consequently to inhomogeneous waveguides which can be
approximated by multilayers.
Acknowledgment
We are very grateful to Thierry Kakouridis for his precious
help in improving the English.
References
[1] Tien P K, Ulrich R and Martin R J 1969 Modes of
propagating light waves in thin deposited semiconductor
films Appl. Phys. Lett. 14 291–4
[2] Tien P K and Ulrich R 1970 Theory of prism-film coupler
and thin-film light guides J. Opt. Soc. Am. 60 1325–37
[3] Ulrich R 1970 Theory of the prism-film coupler by
plane-wave analysis J. Opt. Soc. Am. 60 1337–50
[4] Tien P K 1971 Light waves in thin films and integrated optics
Appl. Opt. 10 2395–412
[5] HoekstraHJWM,vantSpijker J C and Klein
KoerkampHMM1993 Ray picture for prism-film
coupling J. Opt. Soc. Am. A10 2226–30
[6] Flory F 1995 Guided wave techniques for the
characterization of optical coatings Thin Films for Optical
Systems (Optical Engineering Series 49) ed F Flory
(USA: Marcel Dekker) pp 393–454
[7] Flory F, Rigneault H, Massaneda J and Monneret S 1996
Optical waveguide characterization of thin films Rev.
Laser Eng. 24 94–102
[8] Ulrich R and Torge R 1973 Measurement of thin film
parameters with a prism coupler Appl. Opt. 12 2901
[9] Kersten R T 1975 The prism-film coupler as a precision
instrument Part I Accuracy and capabilities of prism
couplers as instruments Opt. Acta 22 503–13
[10] Falco C, Botineau J, Azema A, de Micheli M and
Ostrowsky D B 1983 Optical properties determination at
10, 6 µm of thin semiconducting layers Appl. Phys. A30
23–5
[11] Lukosz W and Pliska P 1995 Determination of thickness,
refractive indices, optical anisotropy of, and stresses in
SiO2films on silicon wafers Opt. Commun. 117 1–7
[12] Chilwell J T 1982 Prism coupler jig: interference fringes
enable observation of the coupling gap Appl. Opt. 21
1310–9
[13] Midwinter J E 1970 Evanescent field coupling into a
thin-film waveguide IEEE J. Quantum Electron. 6583
[14] Falco C, Azema A, Botineau J and Ostrowsky D B 1982
Infrared prism coupling characterization and optimization
via near field m-line scanning Appl. Opt. 21 1847–50
[15] Rigneault H, Flory F and Monneret S 1995 Nonlinear totally
refecting prism coupler: thermomechanic effects and
intensity-dependent refractive index of thin films Appl.
Opt. 34 4358–68
[16] Monneret S, Tisserand S, Flory F and Rigneault H 1996
Light-induced refractive index modifications in dielectric
thin films: experimental determination of relaxation time
and amplitude Appl. Opt. 35 5013–20
[17] Born M and Wolf E 1965 Principle of Optics 3rd revised edn
(Oxford: Pergamon) pp 36–51
194
Discussion of the accuracy of the m-lines technique
[18] Abel`
es F 1948 Sur la propagation des ondes
´
electromagn´
etiques dans les milieux stratifi´
es Ann. Phys.,
Paris 3505–20
[19] Commandr´
e M, Roche P, Borgogno J P and Albrand G 1995
Absorption mapping for characterization of glass surfaces
Appl. Opt. 34 2372–8
[20] Bosacchi B and Oehrle R C 1982 Resonant
frustrated-total-reflection technique for the
characterization of thin films Appl. Opt. 21 2167–73
[21] Marcuse D 1991 Theory of Dielectric Optical Waveguides
2nd edn (NewYork: Academic)
[22] Benech P and Khalil D 1995 Rigorous spectral analysis of
leaky structures: application to the prism coupling
problem Opt. Commun. 118 220–6
[23] Rigneault H and Monneret S 1996 Modal analysis of
spontaneous emission in a planar microcavity Phys. Rev.
A54 2356–68
[24] Massaneda J, Flory F, Bosch S, Martorell J and Monneret S
Multispectral measurements of slightly anisotropic thin
films by guided optics methods Proc. Soc. Photo-Opt.
Instrum. Eng.: Lasers, Optics and Vision for Productivity
in Manufacturing vol 2782 (Optical Inspection and
Micro-Measurement)
[25] Miller D 1991 Optics and refraction Textbook of
Ophthalmology vol 1, ed S M Podos and M Yanoff
(Gower Medical Publishing)
195
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