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

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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
-lines technique: prism coupling
measurement and discussion of
accuracy for homogeneous
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´
ome, 13397 Marseille Cedex 20,
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
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
presented. Thispaperonlydealswithhomogeneousisotropic
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)and (xr,y
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
0exp x2
0exp y2
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
0)as a sum of
plane waves. As the plane of incidence is the (XOZ) plane,
S Monneret et al
and because the structure is invariant in Ywe obtain
i,0)=exp y2
−∞ ˆ
Ei(σ ) exp(2jπσxi)dσ
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:
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
r)=exp y2
−∞ ˆ
Ei(σ )f (σ )
where the longitudinal spatial frequency of each plane wave
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
p1) 1+λ
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
The electric field distribution of the reflected beam is now
given by
r)=exp y2
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.
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
For a given value zr0of zr,Ir(xr,z
0)is therefore obtained
directly from the one-dimensional inverse Fourier transform
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 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
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
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,
red beam: λ=632.8nm,
Thegreen and thered images ofthe corresponding near fields
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].
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.
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
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].
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
∂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
∂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.
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
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
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
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
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
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.
We are very grateful to Thierry Kakouridis for his precious
help in improving the English.
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... M-line prism coupling can be used to measure material refractive index, optical loss, filmthickness and anisotropy (Monneret et al., 2000). The relationship between the refractive index and the wavelength or the temperature of the sample can also be studied. ...
... For a bulk material, a prism with a known, higher refractive index than the bulk, is brought into contact with the material via a pneumatically operated coupling head. Although a perfect contact will not be achieved, an airgap less than half the wavelength of the coupling light is acceptable (Monneret et al., 2000). The angle (θ) of the incident light on the material is changed while the intensity reflected onto the photodetector is measured. ...
... The location of the first mode will approximately determine the refractive index, whereas the angular difference between the modes can be used to calculate the thickness of the film. These values are calculated by the software provided using the methodology described by (Monneret et al., 2000). ...
Pulsed laser deposition (PLD) is a technique for depositing materials and PLD displays versatility and high growth rates. It can be used to grow active single-crystal materials, which can be used as planar waveguide lasers. During PLD, particulates can be embedded into the growing film, which can reduce the planar waveguide lasers optical-to-optical efficiency and degrade the physical characteristics of a grown film. The experiments presented in this thesis focus on reducing the density of particulates in PLD-grown films and using this knowledge to grow high quality, novel materials.Three particulate reduction techniques were investigated including a shadow-mask, segmented targets and bi-directional ablation. All of these techniques reduced the particulate density and bi-directional ablation was implemented as the new standard ablation regime. This novel technique increased target utilisation by 50%, target lifetime by 100% and demonstrated an average particulate density reduction of 80%. As a direct result of bi-directional ablation, films with losses down to 0.12 dB/cm were realised. The versatility of PLD was exploited to tune the lattice constant of a mixed-sesquioxide film to demonstrate a <0.1% lattice mismatch with sapphire. Waveguiding was realised for the first time in a 3% Yb-doped sapphire waveguide, a material that is impossible to grow via traditional crystal growth methods. A Yb:LuAG laser with cladding layers was demonstrated, for the first time with PLD, with output powers of 3.3 W. Using bi-directional ablation, an Er:YGG film was grown and 3.46 dB of gain was realised in a channel waveguide geometry. Previous attempts had not achieved any such gain due to high losses.The particulate reduction technique demonstrated in this thesis and the subsequent exploitation, pave the way for PLD as a commercially viable technique for waveguide fabrication. Without the drawback of high particulate densities, high quality optical devices can be fabricated via PLD that would compete with other growth techniques.
... Similar to the analogy between the description of a mechanical system using classical equation of motion versus using circuit theory, there is an illuminating analogy between the description of certain optical systems using classical optics versus using transmission-line theory [55]. Examples include dielectric thin-film multilayers, slabs, channel optical waveguides, directional couplers, anisotropic waveguides, etc. ...
... We observe a clear modification of the reflected beam with divergence. In particular, we retrieve the wellknown [55] dark line region, which is characteristic of field cancellation in the detector area, due to destructive interferences (and not to absorption) or shift rays. Also, we notice the shift of the beam from one figure to another, as the result of a Goos-Hänchen [59] effect. ...
... Employing the shape modification of the reflected beam at resonance as a detection criterion is motivated here by the ZAL stacks having negligible absorption. The exact calculation of the output beam shape changes upon reflection of the incoming beam on the ZAL coatings, including m-line [55] and Goos-Hänchen [59] effects, constitutes a robust method for evaluating other potential input beam shapes, albeit with an added complexity. This is evident from the successful comparison of theoretical and experimental data that validate the calculations presented. ...
The growing need for classical as well as quantum optical sensing places increasingly stringent requirements upon the desired characteristics of the engendered fields. Specifically, achieving superior field enhancement plays a critical role in applications ranging from chem-bio sensing, Raman and infrared spectroscopies to ion trapping and qubit control in emerging quantum-information science. Due to their low optical losses and ability to exhibit resonant field enhancements, all dielectric multilayers are emerging as an optical material system not only useful to classical photonics and sensing but also of potential to be integrated with quantum materials and quantum sensing. The recently introduced concept of zero-admittance layers [1] within dielectric multilayer materials, enables the creation and control of resonant fields orders of magnitude larger than the exciting field. Here, invoking the zero-admittance concept, we design, fabricate, and characterize an all-dielectric nonabsorbing stack and demonstrate the engendered huge field enhancement. Describing the fields in terms of Bloch surface waves, we connect the surface field to the semiperiodicity in the dielectric domains of the stack. As a specific application of the resonant field, we propose and demonstrate refractive-index sensing for the detection of trace amounts of an analyte. The results include a quantification of the sensitivity of the device with respect to the profile of the exciting field. The experimental results are shown to be in good agreement with theoretical calculations.
... An example of a typical leaky mode optical path is shown in Figure 2a below. In this particular arrangement, the light of TE polarization enters a proton exchanged waveguide via input grating (or via evanescent prism coupling [6,7]). The guided light encounters a counter-propagating surface acoustic wave (SAW), generated by an interdigital transducer (IDT) [8], that couples the guided light from a discrete TE guided mode to a spectrum of TM-polarized leaky modes. ...
... The primary tools for measuring and analyzing leaky mode devices are prism couplers and m-lines [7]. Prism couplers may include Metricon prism couplers, used to determine waveguide index, thickness, and sometimes loss, though the loss may also be measured photographically in beta-phase waveguides [40]. ...
Full-text available
It will soon be a decade since leaky mode waveguide devices were presented as a solution for holographic video displays. This paper seeks to provide a brief, topical review of advances made during that time. Specifically, we review the new methods and architectures that have been developed over this period. This work draws primarily from papers seeking to present dynamic holographic patterns using mode coupling from indiffused waveguides on lithium niobate. The primary participants during this time period have been groups from the Massachusetts Institute of Technology, Brigham Young University, and Draper. We also describe the challenges that remain. The body of work reviewed speaks to the need for further development, but it also reaffirms that leaky mode waveguides continue to hold a unique place within spatial light modulation for holographic video displays.
... Selon la nature du besoin, il existe de nombreuses méthodes de caractérisation de l'indice optique. On peut citer par exemple les m-Lines [104,105], permettant de déterminer la partie réelle d'un indice par l'étude de la réflexion lumineuse à l'interface entre un prisme et l'échantillon. Dans le cas de matériaux polaires, métalliques ou de semiconducteurs dopés, des méthodes basées sur l'excitation de phonons ou de polaritons sont également disponibles [106,107]. ...
La gamme spectrale du moyen infrarouge (MIR : 3-12 μm) s’ouvre aujourd’hui à de nouvelles possibilités d’applications grâce à la maturité des lasers à cascade quantique : communications espace libre, spectroscopie, LIDAR... Or, il n’existe aujourd’hui pas de détecteur rapide fonctionnant à température ambiante dans cette gamme spectrale : tel est l’objectif de ce travail de thèse qui s’appuie sur la technologie des détecteurs à multipuits quantiques, technologie fonctionnant aujourd’hui à des températures cryogéniques pour des raisons thermodynamiques. Pour contourner cette limitation fondamentale, ce travail s’appuie entre autres sur les récents progrès dans le domaine des antennes optiques, qui permettent de redéfinir radicalement l’architecture de détection. Les réalisations dans le MIR restent encore largement à défricher, comparées aux longueurs d’onde visibles. L’ambition de cette thèse est de démontrer la pertinence de la technologie des détecteurs à cascade quantique intégrée aux architectures d’antennes optiques et de tenter de dégager les principaux leviers d’optimisation et les compromis quant aux performances du senseur optique aussi bien en termes de conception que de fabrication.Ce travail s'intéresse aux systèmes de couplage optique utilisés dans les technologies de détection inter-soubande pour palier aux faibles rendements d’absorption ISB. L’absorption optique expérimentale d’un système en géométrie patch, solution retenue dans ces travaux, est étudiée. La description électromagnétique des systèmes en cavité planaire MIM puis des géométries patch menée conduit à la modélisation de l’absorption totale du système selon différents canaux de dissipations via la théorie des modes couplés. La question de l’optimisation de l’absorption est abordée. Les performances DC (courant d’obscurité, réponse et rendement quantique) sont étudiés ainsi que le processus de fabrication développé durant cette thèse. Ces résultats expérimentaux, en accord avec les modèles théoriques, permettent de placer les performances du détecteur à l’état de l’art pour la filière des détecteurs à cascade quantique.Enfin, les performances du système dans un schéma de détection hétérodyne. Une caractérisation expérimentale accompagnée d’un modèle analytique sont présentés. Une bande passante de 30 GHz à température ambiante est démontrée.
... As a planar waveguide, we used a five modes ion-exchanged waveguide [15] on K8 optical glass [16]. The effective indices of refraction of the corresponding TE-guided modes were measured with a goniometer by the well-known prism-coupling technique [2,17,18]. Their values were found to be equal to n 0 = 1.531, n 1 = 1.525, n 2 = 1.520, n 3 = 1.514, and n 4 = 1.510. On the basis of these preliminary obtained data the coupling prism was designed. ...
... As a planar waveguide, we used a five modes ion-exchanged waveguide [15] on K8 optical glass [16]. The effective indices of refraction of the corresponding TE-guided modes were measured with a goniometer by the well-known prism-coupling technique [2,17,18]. Their values were found to be equal to n 0 = 1.531, n 1 = 1.525, n 2 = 1.520, n 3 = 1.514, and n 4 = 1.510. On the basis of these preliminary obtained data the coupling prism was designed. ...
... The SLGW1 was optically characterised by means of prismcoupling technique and dark-line spectroscopy in order to measure the effective indices (i.e. the propagation constants) of the modes supported by the guiding structure so obtained [46,47]. This was performed at the excitation wavelength of 635 nm by means of a home-made semi-automatic instrument, named COMPASSO, located at the IFAC-CNR Labs [48]. ...
Ion-exchange in molten nitrate salts containing metal ions (i.e. silver, copper, etc.) represents a well-established technique able to modify the chemical-physical properties of glass materials. It is widely used not only in the field of integrated optics (IO) but also, more recently, in plasmonics due to the possibility to induce the formation of metal nanoparticles in the glass matrix by an ad hoc thermal post-process. In this work, the application of this technology for the realisation of low-cost and stable surface-enhanced Raman scattering (SERS) active substrates, based on soda-lime glass microrods, is reported. The microrods, with a radius of a few tens of microns, were obtained by cutting the end of an ion-exchanged soda-lime fibre for a length less than 1 cm. As ion source, silver nitrate was selected due to the outstanding SERS properties of silver. The ion-exchange and thermal annealing post-process parameters were tuned to expose the embedded silver nanoparticles on the surface of the glass microrods, avoiding the use of any further chemical etching step. In order to test the combined SERS/fluorescence response of these substrates, labelled molecular beacons (MBs) were immobilised on their surface for deoxyribonucleic acid (DNA) detection. Our experiments confirm that target DNA is attached on the silver nanoparticles and its presence is revealed by both SERS and fluorescence measurements. These results pave the way towards the development of low-cost and stable hybrid fibres, in which SERS and fluorescence interrogation techniques are combined in the same optical device.Graphical abstract
... This technique therefore makes it possible to selectively excite the modes of a waveguide according to the synchronous angles. From the measurement of the angular position of the synchronous angles, with a turntable and a photo-detector placed on the path of the light beam reflected on the prism, one can determine the index of the guided mode [13]. ...
Conference Paper
Great interest is devoted to electro-optic (EO) polymers since they allow the fabrication of very high performance microwave photonic components, such as optical modulators and analog-to-digital converters, due to a much better velocity matching between microwave and optical signal as well as a higher EO coefficient than the very popular inorganic LiNbO 3 material. This paper studies the influence of nanoparticle loading on optical properties of EO polymers. We are interested in the host-guest system. A proof of concept is investigated by using a polymer matrix in which we add Disperse Red One (DR1) chromophores. Our first investigations are realized with TiO 2 nanoparticles, which are transparent at the telecommunications wavelength of 1.55 μm. The m-lines technique allows measuring the refractive index of the films. As expected, the refractive index increases when weight-weight percentage of DR1 to PMMA increases from 3.5 wt.% to 14 wt.%. The refractive index increase tends to saturate at high DR1 percentages, which suggests that DR1 aggregation occurs. By adding TiO 2 nanoparticles, a further increase is observed that we discuss by considering both the refractive index of TiO 2 and the possibility to decrease the DR1 aggregation.
... Therefore, the combination of both materials in multilayer films is ideal to tune the birefringence and the refractive index dispersion within a wide range. The occurrence of index matching in the multilayer waveguides was studied by measuring the effective refractive index dispersion of transverse electric (TE) and magnetic (TM) waveguide modes with the mline technique [37][38][39]. The experimental investigations were accompanied by transfer matrix calculations allowing TE-TM index matching to be predicted and the influence of interdiffusion between adjacent organic layers in the theoretical modeling to be estimated. ...
Index matching of guided modes in birefringent multilayered organic waveguides opens new prospects for the design of mode coupling and mode switching devices. We demonstrate index matching of guided modes in two multilayered structures, in (a) a PTCDA-Alq3-PTCDA three-layer and (b) a PTCDA-Alq3 effective medium multilayer waveguide. The optical waveguides were grown on a Pyrex substrate by organic molecular beam deposition. The occurrence of index matching was investigated both experimentally by measuring the effective refractive index dispersion of transverse electric and magnetic modes using the m-line technique and theoretically by modelling the index dispersion with a transfer matrix algorithm.
Full-text available
Guided wave techniques are powerful to study the properties of different optical coatings. The latest results are presented to illustrate the interest of these techniques: the dependence on ion energy of the anisotropy of ion assisted TiO2 films is given; the measurement of losses during propagation permits to study the origin of losses in multilayer coatings and in particular to demonstrate that absorbing transition layers have to be introduced in the model; properties of ion implanted Ta2O5 layers are also investigated. The refractive index profile of Ta2O5 layers implanted with Ti is determined by using the m-line technique; coupling a pump beam at 488 nm in different guided modes, the photoluminescent properties around 1.53 mm of Er implanted Ta2O5 layers are also shown.
This work presents advances in thin films for applications in the fields of integrated optics, micro-optics, optical telecommunications and optoelectronics. It delineates the performance characteristics needed for graded coatings, damage-resistant laser coatings and many others. Basic theory and applications are illustrated.
A laser beam can be coupled with high efficiency into a light-guiding thin film by means of a prism-film coupler. Basically this device is a totally reflecting prism, the light-guiding film being separated from the reflecting prism face by a narrow gap of reduced refractive index. This coupling scheme is analyzed in detail by the method of plane-wave expansion. It is shown how the coupling efficiency is determined by the competition between the desired coupling effect and the reverse effect of leakage. A general condition is derived under which the transverse profile of the input beam continues undistorted into the guide. The theory is illustrated for a gaussian beam, which allows a maximum coupling efficiency of 0.80.
We report quantitative evidence of the slight anisotropic behavior of several Ta2O5 dielectric thin films. Refractive indices and thickness have been determined by using the prism-film coupler setup. In order to obtain dispersion values for the refractive indices, the measurements have been realized at four different wavelengths, 632.8, 514.5, 488.0 and 457.9 nm. We have checked the results by measuring the layers with two different prisms. A new numerical approach to the problem has been useful to determine the parameters of the layers.
An optical characterization of thin semiconducting multilayers in the infrared range, using a combination of m-lines and reflection spectroscopy techniques is exposed. Such a method, non-destructive, allows to determine the thickness and the refractive index of each component of a multilayer multimodal planar waveguide.
A description of the prism-film coupler, with use of the ray picture, was introduced by Tien and Ulrich [J. Opt. Soc. Am. 60, 1325–1336 (1970)]. Here a discussion of this model is given, and it is argued that the effect of the Goos-Hänchen shift cannot be neglected in general. Further, relatively simple expressions are given for the computation of the coupling efficiency of a prism-loaded planar structure as a function of the angle of incidence of the incoming beam. Computational results are presented and compared with those of other methods.
A prism-film coupler has been discussed recently by Tien, Ulrich, and Martin as a device to couple efficiently a laser beam into thin-film dielectric light guides. This coupler also allows an accurate measurement of the spectrum of propagating modes from which the refractive index and the thickness of the film can be determined. We present here a theory of the prism-film coupler. The physical principles involved are illustrated by a method that combines wave and ray optics. We study the modes in the thin-film light guide and their modification by the effect of coupling. We also calculate the field distributions in the prism and the film, the power transfer between the prism and the film, and derive a condition of optimum operation. In one example, 81% of the laser power can be fed into any desired mode of propagation in the film.
In a previous paper we demonstrated a simple yet accurate method for determining the thickness and refractive index of thin SiO2 films on silicon substrates, the only equipment required being an Abbe refractometer. The films were assumed to be isotropic. In the present communication we show that the method described, used with s- and p-polarized light, also permits to determine the optical anisotropy of the films which are optically uniaxial with their optic axis oriented normally to the film. The measured ordinary and extraordinary refractive indices of 2–10 μm thick SiO2 films are reported. The anisotropy is induced photoelastically by compressive stresses in the SiO2 films. From the measured anisotropy the stresses are determined to be σ‖∑−290 MPa.