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(1985).
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EOS Topical Meeting on Diffractive Optics, Delft, Netherlands, 27 Feb.-1 Mar. 2012.
1. Introduction
Resonant diffractive optical elements, like standard DOEs, consist of a surface corrugation or
index modulation modifying and shaping the wave front in the objective of achieving a
desired optical function. The specific characteristic of a resonant DOE structure is the
fulfillment of the optogeometrical conditions for the existence of a surface wave whose field
has a substantial overlap with the corrugation, and that the latter can excite under definite
synchronism conditions. This association between a surface wave and the surface or index
modulation boosts the diffractive effect of the latter and gives it the selectivity properties of
the former. The selectivity which the surface wave confers to the diffraction event concerns
the polarization, the wavelength as well as the local wave vector.
The examples given in the present paper will be listed according to the type of optical
surface wave that concentrates the field in the corrugation region: true guided mode [1], leaky
mode [2] and non-localized plasmon mode [3]. These three basic resonant grating structures
are illustrated symbolically in Fig. 1 with the related surface wave field responsible for the
incident wave field accumulation. Figure 1(a) corresponds to resonant reflection mediated by
the coupled TE0 mode with the transverse electric field represented. Figure 1(b) is for –1st
order resonant diffraction canceling the Fresnel reflection in a metal mirror based corrugated
dielectric layer with the transverse electric field of the fundamental leaky-mode represented.
The figure of 100% is the theoretically achievable efficiency in a single order. Figure 1(c)
represents the effect of resonant light transmission through a continuous undulated metal film
embedded in a homogeneous dielectric medium via the excitation of a TM plasmon mode; the
field profile is that of the longitudinal electric field of the low-loss long range plasmon mode
exhibiting a zero modulus at the middle of the metal film; the figure of 90% corresponds to
the expectable transmission maximum in the red part of the spectrum with a silver or gold
So far the association between a surface microstructure and an optical resonance has been
studied and applied essentially to periodic DOEs, and the present paper will limit its scope to
resonant gratings although much is still to be explored in the objective of generating more
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complex optical functions. As far as the fabrication issue is concerned, the lithography of
resonant structures does not differ notably from that of standard DOEs. It is at the level of the
etching that there are great differences as the surface wave structure may be made of
(multi)layer materials of a wide diversity of refractive index and chemical composition. This
is the reason for the next section devoted to the etching problematics. Sections 3 to 6 give
examples of resonant functional structures all fabricated by wet etching processes. In section
3 is described a resonant grating mirror permitting to filter out transverse modes of order
larger than the dominant mode. Section 4 gives two examples of polarizing laser mirrors
generating a circularly symmetrical polarized mode by grating coupling to a leaky mode of
the mirror’s multiplayer. In section 5 another wet etching process is applied for the definition
of an ultra-shallow seed-grating at a metal surface for plasmon excitation, and, finally, section
6 shows that wet etching can even be applied to diffractive polarizing elements operating in
the 193 nm ArF laser wavelength range.
2. Microetching of optical material surfaces
There are strong incentives in planar photonics to borrow ready-developed microstructuring
processes of microelectronics [4]. One problem with this manufacturing trend is that the
standards are not - and cannot be - generalized to the same extent that the photonics market is
very diverse with a plurality of 3D elements and modules, and thus the mechanism of
economy of scale in microoptics is in many cases far from being effective. This problem is
faced in photolithography, but it is particularly acute in etching where mainly silicon-based
compounds (silica, SiON, silicon nitride) can borrow the well developed reactive ion etching
(RIE) and related equipments provided the substrate size matches that of microelectronic
wafers. The etching of high index metal oxide layers, of fluoride layers, or simply of a glass
surface, requires some variant of reactive ion beam etching (RIBE) where a kinetic energy
component is needed for evacuating the non-volatile decomposition products [5]. RIBE-like
equipments are less standardized and do accept non-standard substrate sizes and materials.
Dry etching is a passage obligé for corrugations of high aspect ratio. For resonant diffractive
elements, it is not: whereas in a transmission grating of wavelength-scale period a typical
aspect ratio (ridge height/width) is about 2 for the cancellation of the 0th order, that of a
resonant grating can be notably smaller than 1/10 as will be shown in the examples hereunder.
This means that the emerging domain of resonant diffraction may advantageously resort to
wet etching technologies which permit non-vacuum batch processing at room temperature,
chemical surface smoothing, and low investment costs. The chemical processes used here are
toxic for microelectronics – so are they for optoelectronics too - but for passive element
photonics they aren’t, and may therefore represent new reliable and low-cost manufacturing
possibilities for this field.
Some known generalities about spatially resolved surface wet etching will now be
reminded and some hypotheses regarding the selection of the adequate chemistry and
microstructuring process steps of optical material will be made.
Passive microoptic permits to broaden the spectrum of acceptable chemical reactions
beyond acidic solutions. These have the inherent tendency to create bubbles and exhibit a
nonlinear etching rate at the beginning of the reaction which causes non-uniformity and non-
reproducibility in the fabrication of very shallow microstructures. HF can etch SiO2, glasses
and can even decompose some other metal oxides as well like Ta2O5, HfO2, but its use
requires much care and it has the property of easily creeping between a substrate/photoresist
interface which is a practical handicap for microstructuring objectives. Acids tend to render
oxide surfaces hydrophilic, therefore the spreading of photoresist is often difficult and the
resist adhesion is weak. Unlike microelectronics, photonics may opt for basic chemistry
which offers a very wide range of possible solutions. Whereas the wet etching of metal layers
relies upon oxidation-reduction reactions, inorganic dielectric layers (oxides, sulphides,
fluorides, etc.) can be wet etched by designing reactions of the exchange type: it is well
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known that an exchange reaction can take place and be completed only if one of the
compounds leaves the reaction [6]. To that end, the participation of a properly chosen
complex-forming agent is required. A qualitative estimate of the electrochemical process
direction in the substitution of ions is made by using the reactivity series [7]. The lower the
electrode potential, the higher the reduction activity of the element and therefore the lower the
oxidizing activity of its ions. The use of reactions with the participation of sodium and
potassium ions in the role of strong reducers substantially increases the possibility to choose
the most appropriate etching reaction; since most sodium and potassium compounds are water
soluble, the exchange product dissolves in the often used water based solution. Using
photoresist as a microstructuring etch-mask with a basic etchant should a priori be ruled out.
However, there are baking and chemical passivation processes which render the photoresist
etch-mask immune while still allowing an easy hot acetone removal without resist-rest at the
surface [7]. This is an important asset because the advantages of basic etching should not be
offset by the resort to an intermediate mask etching step if for instance a silica or metal etch
mask would be required. Some specific precautions must be taken when using a basic wet
etchant for high spatial resolution microstructuring: the photoresist layer must have a strong
adhesion on the substrate to prevent non-uniformities and edge roughness. This can be solved
by using standard adhesion promoters or some non-acidic surface treatment rendering the
surface to be etched hydrophobic. Another very important precaution is to ensure the
wettability of the groove bottom between photoresist walls. The above requirements of
hydrophobicity of the surface for strong resist adhesion and wettability of the groove bottom
after resist development are contradictory when water-based etch-solutions are concerned;
this can be solved by adding a wetting agent to the etchant. Wet etching processes are very
sensitive to the surface cleanliness and to residual nanolayer at the surface. This nanolayer
can be the native oxide grown at a silicon or aluminum surface or a photoresist rest. Whereas
dry etching is less vulnerable to a residual nanolayer than wet etching and permits to perform
a short plasma cleaning prior to the actual dry etching process, wet etching can also be
preceded by a very short wet treatment which dissolves for instance a native oxide nanolayer.
The next section will describe a number of examples of high efficiency resonant structures
of low aspect ratio and subwavelength dimension.
3. True-mode field enhancement and transverse laser-mode filtering
The resonant structure concerned here is a slab waveguide with a grating coupler between an
incident collimated free-space wave and a waveguide mode corresponding to Fig. 1(a). There
are two main configurations as suggested by Fig. 2: oblique incidence for beam filtering, and
normal incidence when the selectivity of resonant reflection is applied to intra-cavity laser
emission control.
When the coupling synchronism condition is fulfilled, the field in the grating region is
very large and a corrugation depth of a small fraction of the wavelength is efficient enough to
couple an incident beam of usual submillimeter diameter and to exploit the properties of this
0th order diffraction effect, for instance resonant reflection which theoretically reaches 100%.
Since its experimental discovery [8] and its explanation as a waveguide grating feature in
1985 [9] the effect of resonant reflection has been mainly used as a narrow band reflection
filter in biosensor [10] or in laser mirror applications [11]. The remarkable feature of resonant
reflection is its polarization, wavelength and angular selectivity related with the grating
excitation of a mode of a slab waveguide.
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Fig. 2. Grating coupling of a free space wave to a waveguide mode with associated
wavelength, angular and polarization selective resonant reflection, (a) as a free space-wave
filter, (b) as a laser mirror for emission control.
Wet etching is applied here in a 2D waveguide grating structure aimed at ensuring lossless
single transverse mode filtering in a wide surface emitting Yb-, Er-doped microchip laser in
order to achieve all at once high power and high brightness emission [12]. The angular width
of a resonant grating mirror is set between the angular width of the fundamental and of the
second order transverse mode. Such application requires a very shallow depth of hardly 30
nm and an extremely high uniformity of the depth and diameter of the holes in a high index
Ta2O5 waveguide layer with a 2D period of 1100 nm in a hexagonal hole distribution meaning
a groove aspect ratio of about 1/15. This demand can actually hardly be matched by RIBE,
whereas a soft wet etching only can achieve it precisely with high uniformity within 1 or 2
nanometers. Figure 3(a) is an AFM scan of a wet etched hole in a Ta2O5 layer deposited by
ion plating showing a bottom surface as smooth as that of the resist-protected top. Figure 3(b)
is the top view of a hexagonal set of circular holes wet-etched in a Ta2O5 layer showing good
uniformity. The etched Ta2O5 layer is only the waveguide part of the complete transverse
mode selective element which also comprises a standard multilayer providing a non-selective
reflection offset, and also a SiO2 overlay to decrease the modal field confinement in the Ta2O5
waveguide.
Fig. 3. (a) AFM scan of wet etched holes at the surface of an ion plated Ta2O5 layer. (b) SEM
top view of the same with holes of 550 nm diameter.
The grating is transferred photolithographically by hard contact. The alkaline wet etching
is made with an etching rate of 10 nm per hour.
4. Leaky-mode mediated polarization selection in laser mirrors
The surface wave of a resonant structure does not have to be a true guided mode and the
waveguide does not have to be a single slab layer. The waveguide can be a multilayer - as that
of a highly reflective laser mirror for instance - and the resonance can be that of a leaky mode
which permits one of the incident polarizations to tunnel through the multilayer mirror into a
high index substrate by grating coupling to this mode, thus to degrade the reflection
coefficient for this polarization, leaving the reflection of the non-coupled polarization
unaffected, thus imposing the lasing of this polarization. Such a polarization selective mirror
has been developed and fabricated [13] in the objective of checking the theoretical prediction
of a possible 50 to 100% increase of laser machining efficiency [14] in a CO2 laser emitting
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the radially polarized mode in comparison with the currently used circular polarization. A
circular line resonant grating achieving high reflection coefficient for the local TM
polarization and close to zero reflection for the local TE polarization reflects above 99% of
the radially polarized laser mode and almost suppresses the reflection of the azimuthally
polarized mode. Thanks to its resonant character, the almost 100% diffractive transmission
through the highly reflective multilayer mirror is obtained by a corrugation grating of hardly
200 nm deep grooves in a thin germanium layer on top of a multilayer mirror. The radial
period is about 6 µm for the 10.6 µm wavelength of a CO2 laser, meaning that a corrugation
aspect ratio of about 1/15 suffices to almost cancel the TE reflection. Both dry and wet
etchings have been used in the objective of comparing the profile roughness, the
reproducibility as well as the fabrication cost. The dry process was argon ion beam etching
whereas the wet chemistry was an alkaline solution with baked photoresist as an etch-mask.
This is very well suited for wet etching, the more so as the polarizing function of the element
is little dependent on the duty cycle. Figure 4(a), resp. (b) are the AFM picture of Ge grooves
made by dry and wet microstructuring.
Fig. 4. AFM pictures of 200 nm deep, 3 µm wide grooves etched in a layer of amorphous
The wet etched grooves are somewhat smoother; the groove bottom is flat because of the
presence of an etch-stop layer guaranteeing a prescribed depth. The reflection spectrum of
Fig. 5 is the result of the exact optimization of the resonant polarizing mirror. It exhibits a
double TE dip whereas the typical signature of leaky-mode mediated transmission is a single
dip while the TM polarization still experiences quasi 100% reflection.
Fig. 5. (a) Symbolic representation of leaky mode mediated TE tunneling into the substrate
through the multilayer of a CO2 laser mirror. (b) Double-dip TE and TM reflection spectra of
(a)
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This double-dip character illustrates how interestingly the resonant coupling mechanism
can be tailored: in order to broaden the tolerances on the ZnSe/ThF4 multilayer, the multilayer
was engineered so as to bring two TE leaky modes in coalescence which considerably widens
the reflection dip. As a matter of fact, the reproducibility in index and thickness of the
multilayer is much more critical than the corrugation profile; the latter is very tolerant and
essentially relies upon the amplitude of its first Fourier harmonic. Figure 5(a) is a symbolic
representation of the resonant leak of the TE polarization through the multilayer mirror; in a
radial polarization generating mirror the grating shown has circular lines. Experimental
results and donut beam profiles can be found in [13].
An alternative polarizing principle was also developed which is more appropriate for
obtaining the lasing of the azimuthally polarized mode whereby the local TM polarization
leaks through the multilayer mirror and the TE polarization is highly reflected. This
polarization distribution has been shown to permit the machining of deep uniform diameter
holes in metals whereas the radial polarization is better suited for cutting thick metal plates
[15]. This new scheme was also demonstrated at the CO2 laser wavelength, but it is its
implementation in the 1.0 to 1.1 µm range which is particularly interesting here. As shown in
the reflection spectra of Fig. 6, the reflection differential between TE and TM is very wide
band and extends over about 70 nm.
Fig. 6. TE and TM reflection spectra in the near IR of a wide band polarization selective laser
mirror with moderate reflection differential for a high Q laser resonator. Inset: experimentally
obtained donut mode with radial polarization, resulting in the typical bow-tie shape after a 45°
linear analyzer.
The laser mirror consists of a SiO2/HfO2 multilayer with a last high index thin layer of
hydrogenated amorphous silicon of about 50 nm thickness which, unlike single crystal
silicon, is highly transparent in this wavelength range. With a radial period of 900 nm, the
requested aspect ratio is about 1/10 which is again very well suited for wet silicon etching.
The etching was made by a basic solution (30% water-diluted KOH at room temperature)
with a baked photoresist etch-mask at a rate of 6 nm per minute. Figure 7 is the AFM scan of
a few grating lines showing high smoothness and uniformity.
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Fig. 7. AFM picture of a small aspect ratio wet etched amorphous silicon grating showing the
450 nm wide, 50 nm deep grooves of the polarization selective laser mirror of Fig. 6.
The experimental TE and TM reflection spectra of Fig. 6 are measured under close to
normal incidence to shun a beam splitter. The inset is the picture of the characteristic donut
beam of azimuthal polarization distribution emitted by a Nd:YAG laser equipped with a
circular line grating mirror.
5. Non-localized plasmon field enhancement
The surface wave used in a resonant grating can also be the surface plasmon propagating at
the interface between a metal surface and a dielectric overlay, or simply air. The remarkable
features of a resonant grating relying upon the electromagnetic field concentration in a non-
localized plasmon wave are total absorption of an incident TM wave [16] and resonant
transmission through a continuous undulated thin metal film [17] as illustrated in Fig. 1(c). A
weak TM resonant reflection can also be observed in symmetrical structures in the presence
of the long range surface plasmon mode [18].
The example chosen here of wet etched subwavelength resonant grating is not application
driven: it is part of a scientific endeavor to identify and analyze the role of surface plasmons
in the formation of ripples at the surface of a metal submitted to high energy femtosecond
laser pulses [19]. A number of very shallow sinusoidal undulations (about 10 nm depth) of
different period (from 440 to 800 nm every 10 nm) were made on a nickel surface to act as a
seed for plasmon excitation, the aim being to find out the period at which the ripple formation
under normal incidence of femtosecond pulses is enhanced.
Fig. 8. (a) Picture under white light illumination of the Ni test-nanogratings of differing
periods. (b) AFM scan of a 560 nm period, 10 nm deep undulation at the surface of a Nickel
plate. (c) Histogram of ripple formation versus the period of the seed grating.
So shallow a corrugation cannot easily be made uniformly by dry etching. The alternative
wet process was preceded by a resist photochemistry adapted to permit grating exposure on a
high-reflectivity metallic substrate. A difficulty faced with a metal surface is that the electric
field at the surface is close to zero since the TE polarization must be used to create a high
contrast interferogram. The risk is therefore high that there still are some nanometers of
unexposed and undeveloped photoresist at the groove bottom after development which
prevents the wet etching of the metal substrate in the grooves to take place. To get round this
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difficulty one first makes a preliminary uniform exposure with non-structured light to deliver
small but non-zero energy dose everywhere within the resist layer. This dose offset is
adjusted to remain just below the photomodification threshold of the resist. The sample is
then placed in the interferogram of a conventional Mach-Zehnder scheme. In the presence of
the initial dose threshold all points of the resist layer located where an interference fringe is
created get photomodified however small the dose delivered by the interference fringe. Thus
all grooves are open down to the nickel substrate. The physical transfer of the grating from
the resist layer to the nickel substrate was made by wet etching using an acidic solution.
Nickel requires an acid plus an oxidizer to etch properly. Diluted nitric acid (HNO3) contains
both. A 10:1 dilution gives an etching speed of 1 nm/sec. Figure 8(a) is the picture of the
complete set of etched Nickel test samples with differing periods under white light
illumination. Figure 8(b) is the AFM profile of one of the shallow Nickel surface
corrugations; the relatively large roughness is an effect of the Nickel surface being unpolished
as laminated. Figure 8(c) shows the scientific result obtained with single 150 fs pulse of 0.97
J/cm2 fluence in the form of an histogram demonstrating first that the surface plasmon does
mediate the formation of ripples, and revealing secondly that a seed of ca 750-760 nm period
enhances the ripple formation instead of the 790 nm expected from the bulk permittivity of
Nickel which means that a femtosecond pulse modifies the electron density of the electrons
participating in the plasmonic collective oscillation. The interested reader is invited to refer to
Ref [19].
6. Resonant grating for the control of deep-UV laser sources
The wide application field of DUV is still an observation and exploration field for diffractive
optics technologies. The required periods are well below 200 nm and the materials to be
microstructured are difficult to etch. Some are aluminum-based like the high index LuAG,
and most of them used in multilayers are fluorides such as LaF3, MgF2. One application that
attracts industrial interests is certainly the control of the spatial and temporal coherence of
KrF, and especially ArF excimer lasers, for instance the polarization control which is so far
made by means of a cascade of intra-cavity prismatic Brewster elements [20]. In principle the
type of solutions described above at a larger wavelength could be implemented. One of the
problems is the etching of, e.g., 150 nm period gratings at a depth of hardly 10 nm. The use of
standard RIBE is not appropriate since the first nanometers would be etched during the first
seconds where a stable plasma regime is not established yet. Again, wet etching offers its
solution which might even be here a passage obligé. Figure 9 shows 11 nm deep grooves
obtained by wet etching in a LaF3 layer at a rate of 20 nm per minute. Here an exchange
reaction was used with a complex-forming agent for taking off the fluorine from the reaction
as a soluble compound. The etchant is basic (30% water-diluted NaOH at room temperature):
Na combines with fluorine to form NaF which is soluble in water. During the present phase of
etch-process setting up, the period is here larger than that required for a functional element at
193 nm wavelength.
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Fig. 9. AFM scan of an 11 nm deep wet etched corrugation in a layer of LaF3.
Figure 10 gives the reflection spectra of the grating mirror structure under development.
The element is a shallow grating etched into the last LaF3 layer of a AlF3/LaF3 multilayer
mirror. The period is 136 nm with a corrugation depth of 15 nm. It is difficult to achieve a
diffractive polarization dichroism in a multilayer system in the deep UV as there are no high
index materials available in a layer form. In the present AlF3/LaF3 system the index contrast
is 1.39/1.66. This limits the possibilities of obtaining a high reflection differential between the
TE and TM polarizations. The principle which is most adequate in this low index contrast
system is to combine a standard quarter wave submirror composed here of 17 pairs of low and
high index with a superstructure of a few layers comprising a corrugated last high index LaF3
layer playing the role of a close to 100% reflective grating waveguide of 52 nm thickness.
This resonant grating is the second submirror of the complete mirror structure; it is a mirror
for the TE polarization only since the waveguide thickness is adjusted to propagate the
fundamental TE0 mode at the wavelength of 193 nm. The TM polarization does not couple to
the TM0 mode of this waveguide whose resonance is located elsewhere in the spectrum, and
only “sees” the multilayer submirror. Below the last high index waveguiding layer are a few
layers whose role is to define a spacing between the multilayer submirror and the resonant TE
submirror corresponding to a Fabry-Perot filter in its first resonant transmission peak at 193
nm wavelength. As a result, the TE reflection spectrum exhibits a deep reflection dip whereas
the TM reflection spectrum is hardly affected and remains close to 100%. The reason why the
± 1st orders of the grating do not lead to diffraction losses for the TM polarization is that with
a grating period of 136 nm and a wavelength of 193 nm the field of the 1st order in the low
index layers is evanescent which forbids their transmission through the multilayer.
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Fig. 10. Reflection spectra of a polarizing grating mirror for an ArF excimer laser
The development of the technology of this deep UV polarizing laser mirror is still in
progress. The optical lithography used for the definition of the needed 136 nm period grating
pattern is the 272 nm period phase-mask transfer under normal incidence exposure of a TE-
polarized ArF laser beam at 193 nm wavelength [21]. The main technical message of the
present example is that the wet etching of such non-conventional layer material as LaF3 is
under control.
6. Conclusion
The present paper illustrates phenomenologically, technologically and experimentally that
resonant gratings can be defined all through the optical spectrum and perform optical
functions which conventional elements or modules don’t, or only with difficulties. The
association of a corrugation and a surface wave gives the diffraction event a high contrast and
high selectivity with surface reliefs having an aspect ratio of a small fraction only of the
wavelength. While such characteristic does not necessarily ease the microstructuring by high
etching rate standard dry etching technologies, it permits to resort to the very wide and
diverse potential of well known and documented wet chemistry solutions.
The examples shown are limited to periodic gratings. This is however not a technological
limitation; it is rather an indicator of the present development stage of R&D on resonant
diffraction. Besides, the application examples given above mainly refer to the processing of
highly coherent light waves and beams. This is not a limitation either. The availability of high
and very high index layer materials permits an extent of the applicability domain of resonant
functional elements to light beams of wider wavelength and angular spectra [22].
Acknowledgment
The authors are grateful to Mrs. S. Reynaud for the AFM scans. They thank Mr. Deyan
Gergov of Laserproduct company, Sofia, Bulgaria, for making the CO2 and Nd:YAG lasers
available for the testing of the grating mirrors.
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