Interferometric microscale measurement of refractive index at VIS and IR
wavelengths

Meguya Ryu1, Simonas Varapnickas2, Darius Gailevičius2, Domas Paipulas2,
Eulalia Puig Vilardell2, Zahra Khajehsaeidimahabadi3,4, Saulius
Juodkazis2,3,5$\star$, Junko Morikawa5,6,7$\dagger$, and Mangirdas
Malinauskas3$\ddagger$

1 National Metrology Institute of Japan (NMIJ), National Institute of Advanced
Industrial Science and Technology (AIST), Tsukuba Central 3, 1-1-1 Umezono,
Tsukuba 305-8563, Japan

2 Laser Research Center, Physics Faculty, Vilnius University, Saulėtekio Ave.
10, 10223 Vilnius, Lithuania

3 Optical Sciences Centre, ARC Training Centre in Surface Engineering for
Advanced Materials (SEAM), Swinburne University of Technology, Hawthorn,
Victoria 3122, Australia

4 Aerostructures Innovation Research Hub (AIR Hub), Swinburne University of
Technology, John St, Hawthorn, Victoria, Australia

5 WRH Program International Research Frontiers Initiative (IRFI) Tokyo
Institute of Technology, Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa 226-8503
Japan

6 LiSM, International Research Frontiers Initiative (IRFI) Tokyo Institute of
Technology, Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa 226-8503 Japan

7 School of Materials and Chemical Technology, Tokyo Institute of Technology,
Ookayama, Meguro-ku, Tokyo 152-8550 Japan

$\star$<EMAIL_ADDRESS>, $\dagger$<EMAIL_ADDRESS>,
$\ddagger$<EMAIL_ADDRESS>
## Abstract

Determination of refractive index of micro-disks of a calcinated
($1100^{\circ}$C in air) photo-resist SZ2080TM was carried out using
transmission and reflection spectroscopy. Interference fringes at specific
wavenumbers/wavelengths were selected for determination of the optical
thickness, hence, the refractive index when the thickness of micro-disks was
measured by scanning electron microscopy (SEM). Refractive index of disks of
$\sim 6\pm 1~{}\mu$m thickness were determined at visible and IR (2.5-13
$\mu$m) spectral ranges and where $2.2\pm 0.2$ at visible and IR wavelengths.
Peculiarities of optical characterisation of micro-optical structures are
discussed in view of possible uncertainties in the definition of geometric
parameters, shape and mass density redistribution.

Copyright attribution to authors.
This work is a submission to SciPost Physics.
License information to appear upon publication.
Publication information to appear upon publication. Received Date
Accepted Date
Published Date

###### Contents

  1. 1 Introduction
  2. 2 Experimental
  3. 3 Methods
    1. 3.1 Poly-chromatic interferometry
    2. 3.2 Reflectance
  4. 4 Results and Discussion
  5. 5 Conclusion and Outlook
  6. A Transmittance

##  1 Introduction

Currently, ultrafast laser assisted 3D micro-/nano-fabrication is used for
diverse technological tasks [1, 2, 3, 4, 5]. One of the most promising trends
is the rapid prototyping and manufacturing of various micro-optical components
merging different refractive, diffractive, polarisation, waveguiding and
interconnect applications or even combined functionalities [6, 7, 8, 9, 10].
They are useful for beam collimation [11], shaping [12], imaging [13],
telecommunications [14], sensing [15], hyperspectral imaging [16] and other
applications where miniature dimensions are required [17]. Unique virtue of
fs-laser pulses in 3D polymerisation is a localised ionization of the major
polymerizable component in the photo-resist/resin without the need for photo-
initiators [18, 19, 20, 21]. Direct write production of 3D silica directly
from precursor is a recent example [18, 19, 20].

When the wavelength of light becomes comparable to the thickness of an optical
element, the wave nature of light manifests stronger as compared with macro-
optics [22]. At a larger scale, ray optics and surface curvature of a lens are
the major factors for optical function/performance [23]. Characterization of
material for applications in micro-optics is preferably based on interference,
which has a high sub-wavelength precision in determination of optical
thickness - the phase delay [24, 17, 25].

Calcination and sintering of polymerizable materials can provide new
composites including glasses, porous glasses polycrystalline and crystalline
materials of tailored composition [26, 27, 28, 29, 20, 18]. The uniformity of
such composite is of paramount importance, similar to the homogeneity of
glass, which can only be produced to the high required optical quality for
melts in volumes exceeding $\sim 1$ liter. A challenge to produce micro-
volumes of composite optical materials with micro-dimensions and good surface
optical quality, as well as homogeneous composition and uniform shape, is the
next main focus for micro-optics made by fs-laser polymerization or ablation
[30, 31]. Micro-optics made from polymerizable resists, e.g., SZ2080TM, can be
used in IR applications due to small thickness and still acceptable losses due
to absorption [32]. Furthermore, SZ2080TM is a foreseen candidate material for
micro-optics and nano-photonics applications due to its compatibility with
established functionalization and antireflection coatings for 3D complex
multi-layered structures via Atomic Layer Deposition (ALD), which is
technology of choice for deposition of conformal layers of tens-of-nm using
range of oxides [33]. For such applications, calcination is an interesting
next step that could make such optical elements less lossy and sensitive to
high laser power irradiation [34]. Typical IR materials CaF2 [35] and BaF2
have melting temperatures 1420∘ and 1368∘, respectively, and are acceptable
substrates for calcination up to $1100^{\circ}$C used in this study on SiO2
substrate ($T_{m}\approx 1710^{\circ}$C).

Here, we show the determination of optical retardance and, consequently, the
refractive index at visible (0.4-0.7 $\mu$m) and IR (2.5 -13 $\mu$m)
wavelengths of the same $\sim(6-9)-\mu$m-thick slabs of calcinated (1100∘C in
air) resist SZ2080TM (70-150 $\mu$m in diameter typical for micro-optical
elements). Figure 1 shows the concept of this study where measurements of
reflectance and transmittance spectra were used to determine the optical
retardance. Such measurements can reveal formation mechanisms and surface
tension induced material reflow as well as structural and phase changes
induced by calcination when large portion of initial material $\sim 40\%$ is
removed/oxidised. Having two free surfaces acting onto soft-glass (at high
temperature) between them with lateral dimensions much larger than separation
is a new unexplored scenario of micro-optics formation.

Figure 1: What is the refractive index $n\propto\rho$ ($\rho$ is the mass
density) of the calcinated micro-disks out of SZ2080TM resist? Concept of the
study: spectra of reflectance $R(\lambda)$ and transmittance $T(\lambda)$ are
used to determine the optical retardance $n\times d$ at visible and IR
spectral domains; $d$ is the thickness, $\lambda$ is the wavelength. Surface
tension $\sigma(T,r)$ driven flows on _two_ surfaces are defined by the
gradients $\nabla\sigma$ caused by the local temperature gradient $\nabla T$
varying over position $r$. Different scenarios 1 and 2 of the $\sigma$-induced
mass transport can cause increase or decrease of $n$. Glass transition at
specific temperature, phase separation due to exsolution, and crystalisation
all can contribute to the final refractive index and thickness of the
calcinated micro-optical element.  Figure 2: Calcinated micro-disks out of
SZ2080TM. (a) Optical images of samples polymerised at different laser powers;
the determined retardance $nd$ at the visible 500-700 nm window and IR at
2.5-13 $\mu$m is shown. Inset shows a side-view SEM image of a suspended
micro-disk at the lowest power when the disk acquired a concave shape
recognizable on the top plane. (b) SEM top-view images of the calcinated
micro-disks.

##  2 Experimental

Micro-disks of the final thickness of $d=7\pm 2~{}\mu$m after calcination of
SZ2080TM with 1% w.t. Irgacure 369 as photoinitiator were fabricated at
different exposure doses using fs-laser (Yb: KGW Pharos, Light Conversion) at
average power range $P_{av}=[70-130]~{}\mu$W (corresponding to estimated
intensity at focus $I=0.33-0.61$ TW/cm2); the wavelength $\lambda=515$ nm,
pulse duration $t_{p}\approx 300$ fs repetition rate $f=200$ kHz. The system
comprises a galvanometric beam scan system with precision translation
stages[36], which can work synchronously ensuring continuous 3D writing
without causing any stitching [37]. The fabrication process was controlled by
3DPoli (Femtika) software at a linear stage scan at high speed $v_{sc}=10$
mm/s, slicing between layers along the optical axis at the step of $\Delta
z=0.2~{}\mu$m, in-plane hatching (radial concentric) was $\Delta r=50$ nm and
corresponded to the in-line separation between neighboring pulses
$v_{sc}/f=50$ nm. Such a condition corresponds to the most uniform exposure of
the focal volume. A Plan Apochromat Zeiss 63x magnification and with numerical
aperture $NA=1.4$ immersion oil objective lens was employed to focus the laser
beam inside the SZ2080TM resist through an oil immersion; resist was on fused
silica glass substrates. It is known that during calcination SZ2080TM
structures shrink by a factor of 0.6[26] and this was taken into account by
making them appropriately larger during initial fabrication. Too small of a
structure after calicnation would have made their characterization more
difficult, therefore the primary design was set to a 120 $\mu$m diameter disk,
expected to become 72$~{}\mu$m, close to experimental observation $\sim
70~{}\mu$m.

The laser power of 100 $\mu$W corresponds to $I_{p}=0.474$ TW/cm2 per pulse;
this condition was used to polymerize micro-lenses directly on a glass
substrate without calcination [22]. The diameter at focal spot was
$2r=1.22\lambda/NA=445$ nm. The support pillars were recorded in raster scan
mode with layer-by-layer separation of $\sim 0.57~{}\mu$m after calcination,
which closely corresponds to the designed $1~{}\mu$m step before calcination
($0.57~{}\mu$m is 60% of the initial size, 100% corresponds to $0.95~{}\mu$m).

In previous study, the required geometry was established to pre-compensate
shape of polymerised posts supporting the micro-optical element in order to
retrieve the final optical element with close-to-normal support pillars after
calcination [38].

Figure 2 shows optical and SEM images of the calcinated micro-disks. Inset of
Fig. 2(a) shows the structure made at the lowest power. Slight changes of
surface-plane of micro-disks with substrate could take place as well as slight
thickness $d$ variations, which were focus of the analysis discussed below.
Micro-disks were suspended above fused silica substrate by 35-37 $\mu$m. After
calcination they were very close to the circular circumference as fs-laser
polymerised, only reduced in size by $\sim 40\%$ due to calcination during
which the organic part of the resist was fully removed (oxidised) at high
temperature of $1100^{\circ}$C for 12 hours [38]. Uniform resizing of
polymerized structures during calcination is the virtue of this method [26].

Figure 3: Actual tilt angle $\theta$ of SEM imaging was determined from the
ellipticity of imaged circular micro-disk. The entire structure was
polymerised out of SZ2080TM with support pillars at angle, which was
straightened towards a vertical orientation after calcination. The average fs-
laser power was 120 $\mu$W. Separation of layer-to-layer for the support
pillars was $567\pm 20$ nm. Thickness of a disk was evaluated at the same
location on the structure as shown here for all the samples from the same SEM
session (same tilt of the sample).  Figure 4: Method. Interferometric
determination of retardance $n_{2}d$. (a) SEM images of polymerised and
calcinated (at 300∘C) SZ2080 structures. (b) Interferometric transmission
imaging of a calcinated prism using $\lambda=632$ nm HeNe laser illumination
of a sample and image formed with Mickelson interferometer. The fringes can be
traced to determine the thickness of the prism which corresponded to optical
retardance of $n_{2}d=n_{2}\times 9(\lambda/n_{2})=5.688~{}\mu$m. (c)
Transmission imaging with iris selection of ROI. Inset shows optical images of
calcinated structures and the retardance $n_{2}d$ measured from selected ROI
and fitting $T$ spectra by Eqn. 6 as shown in (d). Transmittance spectra
$T(\lambda)$ from ROI (c). Calcination at lower temperature and shorter time
yielded in yellow-brown tint of the modified SZ2080TM.

There is a possibility of slight changes of the surface inclination of micro-
disks during calcination. SEM imaging was used (Fig. 3) to determine the angle
(normal to the surface of silica substrate, which is $0^{\circ}$ for the top-
view imaging in SEM). With the $\theta$ angle determined from the elliptical
profile of circular disks (Fig. 3), the thickness $d$ of micro-disks was
determined for calculations of refractive index $n_{2}$ of the calcinated disk
from the retardance $n_{2}d$.

##  3 Methods

###  3.1 Poly-chromatic interferometry

The optical path length of the sample was measured by the poly-chromatic
interferometry in the reflection or transmission geometry. When a normally
incident polychromatic plane wave transmits a thin transparent layer (sample)
of refractive index $n_{2}$ and thickness $d$ surrounded by transparent media
having lower refractive index $n_{1}$ such as air, the amplitude of the
transmitted light after several inter-reflection in the gap will be a series
of complex amplitudes $E_{1}$, $E_{2}$, $E_{3}$,…, expressed as follows (the
Stokes’ treatment [39]):

$\displaystyle E_{1}$ $\displaystyle=$ $\displaystyle E_{i}tt^{\prime}$
$\displaystyle E_{2}$ $\displaystyle=$ $\displaystyle
E_{i}tt^{\prime}r^{2}e^{i(2\phi+\delta)}$ (1) $\displaystyle E_{3}$
$\displaystyle=$ $\displaystyle
E_{i}tt^{\prime}r^{4}e^{i(4\phi+2\delta)}\dots$ (2)

here, $E_{i}$ is the incident light amplitude, $r$ is the reflection
coefficient at the surface of the sample, $\phi$ is the phase change
associated with a single reflection, $\delta=2\frac{2\pi}{\lambda}nd$ is the
phase change due to the optical path difference, and $t$ and $t^{\prime}$ are
the transmission amplitude coefficient for the substrate-sample and sample-
substrate interface, respectively. By neglecting terms in $r$ of higher order
than 4, transmitted light amplitude $E_{t}$ can be written as follows:

$E_{t}=E_{i}tt^{\prime}\left(1+r^{2}e^{i(2\phi+\delta)}\right).$ (3)

The intensity $I_{T}=E_{t}\cdot E_{t}^{*}$ can be written as:

$I_{T}=E_{t}\cdot E_{t}^{*}=E_{i}\cdot E_{i}^{*}t^{2}t^{\prime
2}\left[1+r^{2}\left(e^{i(2\phi+\delta)}+e^{-i(2\phi+\delta)}\right)+r^{4}\right],$
(4)

and, by using the Euler’s formula
$\left(e^{i\delta}+e^{-i\delta}\right)=2\cos\delta$, the equation can be
further simplified:

$I_{T}=I_{in}t^{2}t^{\prime 2}\left[1+2r^{2}\cos\left(\frac{4\pi
nd}{\lambda}\right)+r^{4}\right]=I_{in}(1-r^{2})^{2}\left[1+2r^{2}\cos\left(\frac{4\pi
nd}{\lambda}\right)+r^{4}\right],$ (5)

here identify $tt^{\prime}=1-r^{2}$ is used; $r^{2}$ is the portion of
intensity reflected by one interface. Transmitted intensity is complimentary
to reflection at negligible absorption $I_{T}+I_{R}=1$. This Eqn. 5 was
validated to fit experimental results of low-temperature 300∘C calcinated
micro-disks with prisms (see Fig. 4). To account for the actual dispersion of
sample transmittance, the fit function was chosen with a Gaussian preform
multiplier to reproduce the spectral form factor:

$T(\tilde{\nu})=a_{G}\exp\left(-\frac{(\tilde{\nu}-b_{G})^{2}}{2c^{2}_{G}}\right)\times[1+a_{t}\sin(2\pi
b_{t}\tilde{\nu}+c_{t})],$ (6)

here $a_{G},b_{G},c_{G}$ are the Gaussian form factor parameters to reproduced
spectral form factor, $\tilde{\nu}=1/\lambda$ is the wavenumber,
$b_{t}=2n_{2}d$ is the retardance, which is the major fit parameter, $a_{t}$
is related to $r^{2}$ and $c_{t}$ is the phase angle of the fit (a constant
related to the Fresnel coefficients and anisotropies of $n$ and $\kappa$). The
fit is shown in Fig. 4(d). This procedure to determine $n_{2}d$ was used for
transparent micro-disks calcinated at high 1100∘C temperature; Figure 4(d)
illustrates the method’s applicability to similar samples calcinated at
$300^{\circ}$C.

###  3.2 Reflectance

Reflection from a medium with a higher refractive index $n_{2}$ for light
incident from the medium of lower refraction index $n_{1}$ (air) at an
incident angle $\theta_{i}$ is used to measure retardance $n_{2}d$ of the
dielectric slab (micro-disk in this study). Importantly, the medium below the
sample has a lower refractive index $n_{3}<n_{2}$; this is required since
there would be a $\pi$ phase change for reflected light at the boundary 3-to-2
if $n_{3}>n_{2}$ as for the front surface 1-to-2 interface (marked in Fig. 1).

Interference maxima and minima in reflected spectra from a slab/film of
thickness $d$ are determined by the conditions for the phase retardance for a
double pass in the slab $2nd\cos\theta_{2}$ [40]:

$2nd\cos\theta_{2}=m/\tilde{\nu}~{}~{}~{}~{}~{}(\mathrm{Minima}),$ (7)
$2nd\cos\theta_{2}=\left(m+\frac{1}{2}\right)/\tilde{\nu}~{}~{}~{}~{}~{}(\mathrm{Maxima})$
(8)

where $\theta_{2}$ is the refraction angle in the slab/film (medium 2), $m$ is
the order of interference, and $\tilde{\nu}=1/\lambda$ is the wavenumber
($\lambda$ is the wavelength). From Snell’s law we have
$\cos\theta_{2}=\sqrt{1-\sin^{2}\theta_{1}/n_{2}^{2}}$. By combining this
expression with conditions of either minima or maxima (Eqn. 7;8) one finds
[40]:

$n_{2}=\sqrt{\frac{(\Delta
m)^{2}}{4d^{2}(\Delta\tilde{\nu}_{if})^{2}}+\sin^{2}\theta_{1}},$ (9)

where $\Delta m=m_{i}-m_{f}$ is the number of fringes between the initial and
final fringes counted,
$\Delta\tilde{\nu}_{if}=\tilde{\nu}_{i}-\tilde{\nu}_{f}$ is the difference
between the corresponding fringes. This Eqn. 9 was used to determine the
refractive index at IR spectral ranges at close to normal incidence
$\theta_{1}\approx 0^{\circ}$. Slight changes of $\theta_{1}$ due to sample
tilt can be modeled using Eqn. 9.

Figure 5: (a) Principle of interference method in reflection at angle of
incidence $\theta_{i}$. (b) IR image of a micro-disk. (c) IR spectrum measured
from the region of interest in (b); markers are in wavenumbers $\tilde{\nu}$.
The wavenumbers $\tilde{\nu}_{i}=\frac{1}{\lambda_{i}}$ at reflection maxima
used for calculation by Eqn. 9. Normalisation of reflectance $R$ was carried
out using Au mirror. (d) Visualisation of Eqn. 9 for two thickness settings of
10 and 9.5 $\mu$m determined from two adjacent peaks (one dark fringe)
$\tilde{\nu}_{1-2}$, $\tilde{\nu}_{1-4}$ (3 dark fringes) and from minima
$\tilde{\nu^{\prime}}_{1-4}$ (3 bright fringes); the window of analysis
$\lambda=3-5~{}\mu$m.

##  4 Results and Discussion

Figure 5 shows the principle of measurement of refractive index from
retardance in reflection (a). Equation 5 was used for the reflection spectra
at normal incidence, hence $\theta_{i}\equiv\theta_{1}=0^{\circ}$. The IR
image of the micro-disk, which is close in thickness to the IR wavelengths is
shown in (b) and the corresponding IR spectra in (c). By selecting several
orders of interference maxima, a more precise determination of refractive
index $n_{2}$ can be made (assuming negligible dispersion within that range).
Using the initial and final wavenumbers $\tilde{\nu}_{i,f}$, Eqn. 9 was used
to determine $n_{2}$ from experimentally determined $d$ from the rim of the
disk imaged at large tilt angle $\theta\sim 82^{\circ}$ (Fig. 3). The method
is sensitive to the definition of spectral positions of the maxima as
illustrated in the inset of (c). If only two adjacent maxima (one fringe [40])
are selected, there is a large difference in thickness determination when it
is changing by only $5\%$ (10 vs. 9.5 $\mu$m) as shown in the inset of Fig.
5(c). If four peaks (three fringes) are used, the difference in the thickness
determination is much smaller regardless minima (bright fringes) or maxima
(dark fringes) are used. Also, the $n_{2}$ values are strongly different for
the 1 vs. 3 fringes. It is noteworthy, that the second term of
$\sin^{2}\theta_{1}$ in Eqn. 9 can affect the determined $n_{2}$ value. This
is of particular importance for structures that might lose alignment of the
surface plane of the disk with the substrate after calcination (see, inset in
Fig. 2(a)). The center-line of oscillating reflectance spectra is close to the
expected value of $n=1.7$ as evident from normal incidence (from air)
$R=\frac{(n_{2}-1)^{2}}{(n_{2}+1)^{2}}=6.7\%$, which was close to
experimentally observed $R$ values.

Poly-chromatic interferometry (Sec. 3.1) was used for the determination of
retardance $n_{2}d$ (and $n_{2}$ for the measured $d$) at visible spectral
range using the white light illumination of a microscope. The region of
interest (ROI) was selected over the micro-disk (see the condition in Fig.
4(c)) and transmitted spectra was fitted by Eqn. 5 as shown in Fig. 4(d).
Fitting over the spectral range of 500-700 nm provided high fidelity of
fitting due to many periods of oscillating spectra. Figure 6 has a summary of
results of $n_{2}d$ determination at visible and IR spectral wavelengths made
by two complementary methods of polychromatic interferometry (visible) and
reflectivity (IR) for the same calcinated micro-disks. Closely matching
$n_{2}d$ values were obtained for the $0.5-0.7~{}\mu$m as well as $3-5~{}\mu$m
ranges. Interestingly, thinner disks polymerised at lower powers were easily
characterised at IR wavelengths due to low absorbance, however, at visible
wavelengths, the consistent fringe pattern was not always observed, most
probably, due to wedge formation, concave center, etc. (see, scenarios 1 and 2
in Fig. 1) which affect shorter wavelengths considerably stronger.

Figure 6: Retardance $n_{2}d$ of three samples: B, A1, A2 measured in
transmission for the visible spectral range (Eqn. 6) and in reflection for IR
(Eqn. 9) vs. fs-laser power. Lines are showing a global trend as an eyeguide
for the same sample. Insets show optical images of arrays of micro-disks all
at the same scale . Laser polymerisation at average power of 100 $\mu$W
corresponded to $I_{p}=0.474$ TW/cm2 per pulse at $f=0.2$ MHz laser repetition
rate; the focusing was carried out with $NA=1.4$ objective lens. Arrows in the
inset show the sequence of decreasing powers used in laser printing of micro-
disks.

For the mid-range power of 100 $\mu$W polymerisation, the difference in
retardance is from $n_{2}d=13\pm 1~{}\mu$m (sample B) with $d_{SEM}=6~{}\mu$m
with $n=n_{2}d/d_{SEM}=2.17$. Larger retardance $n_{2}d=19\pm 1~{}\mu$m was
determined for the approximately twice larger microdisks (two regions on
sample A). The difference of $\sim 32\%$ in retardance was not expected due to
the same laser exposure protocol and a total dose. A slight difference in
sample’s preparation and development could be the reason, which led to
different material photo-sensitivity, degree of cross-linking, and density
[24, 25] – all further influencing the evolution of calcination. Smaller
samples (B) tend to be over-developed since it is judged by a naked-eye
observation of 3D structures on glass. Over-exposed samples are more nano-
porous on the surface which helps the removal of organic components during
calcination. Larger disks were slightly thicker and less porous, which led to
a slightly different evolution of calcination yielding disks of a larger
retardnce and larger thickness $\frac{n_{2}d}{d_{SEM}}=\frac{19~{}\mathrm{\mu
m}}{8.5~{}\mathrm{\mu m}}\approx 2.24$.

Both, $n_{2}$ and $d$ can be affected by calcination at high temperatures due
to compositional changes of glass-ceramic (silica-zirconia). In the case of
suspended micro-opitcs (disks here), the surface tension-driven mass transport
(Fig. 1) of lower viscosity regions (higher temperature) can also contribute
to the final state of processing [41]. At temperatures above the annealing
point of glass, the surface tension is changing by $4\times 10^{-5}$ N/m per
1K degree for typical $\sigma=0.23-0.36$ N/m for different glasses [42].

As shown above, the determination of $n_{2}$ is strongly dependent on the
measurement of micro-slab thickness $d$, which was carried out using a tilted
view in SEM (Fig. 3). Higher power of fs-laser during 3D polymerisation,
hatching, scan speed at selected repetition rate and numerical aperture of the
focusing lens all contributed to the 3D accumulated exposure dose, hence, to
the final cross-linking, mass density and, consequently, refractive index
$n_{2}$. This is evident from Fig. 6. Mass redistribution inside micro-disks
during thermal cooling stage could be expected with gradients of less viscous
glass phase (higher local temperature) pulled towards the colder regions
(larger surface tension), e.g., support pillars [41]. Thermal morphing of
laser processed 3D structures made out of glass was demonstrated by changing
shape of 3D object cube-to-sphere depending a temperature-time protocol [43].
Since the micro-disks are suspended, two surfaces can affect the liquid glass
between two colder surfaces, which is very different from the known cases of
observed mass redistribution by re-solidification front on a molten phase
after laser ablation (one surface with air). Glasses are known for the low
atomic packing $C_{g}$ and can experience significant densification under
pressure [44]. For amorphous silica, Poisson’s ratio $\nu=0.15$ is low and is
correlated with $C_{g}$ as it is typical for glasses [44]. Hence a lateral
compaction is not causing significant out-off-plane expansion due to low
Poisson’s ratio, however, densification can occur (a larger refractive index).
Interesting opportunities in metal oxide reduction and mixing could be
explored using exsolution at high temperatures using polymerised materials
during the calcination step [45].

It is noteworthy that homogeneity of the shape of a micro-disk, as well as
interferometric transmission measurements, showed that the entire thickness of
the calcinated small 3D prisms (at 300∘C) have the same mass density
distribution (same pattern of interference fringes; Fig. 4(b)). The higher
refractive index of a silica-zirconia calcinated resist is expected due to
very different melting temperatures of SiO2 at 1710∘C, SiO at 1705∘C and
zirconia at $2750^{\circ}$C; silica sublimation rate at 1700K is $\sim
10^{-4}$ g/cm2/s [46]. Partial loss of silica as compared to zirconia could
contribute to the increase of refractive index of calcinated micro-optics. The
variation in exact refractive index value could be influenced by environmental
conditions such as ambient humidity.

##  5 Conclusion and Outlook

Calcination of micro-disks at high 1100∘C for 12 hours in air resulted in high
refractive index slabs of $\approx 2.2\pm 0.2$ at visible and IR (2.5-13
$\mu$m) wavelengths. Transmission (visible) and reflection (IR) modes of
spectroscopic determination of optical retardance was closely matched each
other. However, there was strong heterogeneity of optical retardance between
disks which had twice different diameters and were developed for different
times (longer development for smaller 3D structures). Calcination evolution
was affected by the development and surface nano-porosity. This calls for a
dedicated investigation to establish reliable protocols for defined refractive
index, which can be also affected by structural and material changes [47]. The
increase of refractive index from 1.6 (visible) in a polymerised state can be
related to the partial sublimation of silica and enrichment of calcinated
material by zirconia. Also, densification of composite during calcination by
two free surfaces (Fig. 1) open new avenues for better compaction of glassy
composite which usually has a low atomic packing. The low Poisson’s ratio of
glasses facilitates their predictable size rescaling during calcination.
Creation of composition-tailored glasses and glass-ceramics via calcination is
promising for realization of high durability micro-optical [48] components
suitable for intense light non-linear microscopy applications [49] as well
operational in diverse harsh environments [50].

## Acknowledgements

D.G, D.P., S.J. and M.M. acknowledge the „Universities‘ Excellence Initiative”
programme by the Ministry of Education, Science and Sports of the Republic of
Lithuania under the agreement with the Research Council of Lithuania (project
No. S-A-UEI-23-6). E.P.V. participated as part of her master thesis project in
the EuroPhotonics (International Master in Photonics program) scholarship.
S.J. was supported by the DP240103231 grant from Australian Research Council.
Z.K. is supported by the Aerostructures Innovation Research (AIR) Hub at
Swinburne University of Technology for this research project and for PhD
scholarship. M.R. and J.M. were partially supported by JST CREST Grant Number
JPMJCR19I3, Japan.

##  Appendix A Transmittance

The very same method presented above for the reflectance spectra
$R(\tilde{\nu})$ can be applied for the transmittance $T(\lambda)$ with the
exchange of the minima and maxima conditions as one would expect for the
optically thin slab with $T=1-R$ (for negligible absorbance $A\rightarrow 0$)
[51]:

$2nd\cos\theta_{2}=m\lambda~{}~{}~{}~{}~{}(\mathrm{Maxima}),$ (10)
$2nd\cos\theta_{2}=\left(m+\frac{1}{2}\right)\lambda~{}~{}~{}~{}~{}(\mathrm{Minima}).$
(11)

The optical losses due to absorption through a slab of thickness $d$ are
accounted by [52]:

$T(\lambda)=\frac{(1-R(\lambda))^{2}e^{-\alpha(\lambda)d}}{1-R^{2}(\lambda)e^{-2\alpha(\lambda)d}}I_{in}(\lambda),$
(12)

where $I_{in}$ is the intensity of incident light,
$\alpha(\lambda)=4\pi\kappa/\lambda$ [cm-1] is the absorption coefficient; the
second term in denominator become negligible only for the strong absorption
$\alpha d\geq 1$.

Since $r^{2}<1$ (Eqn. 3.1), it is possible to calculate all the infinite sum
of the transmitted fields (Eqn. 3) [39]:

$I_{T}=I_{in}\frac{(1-r^{2})^{2}}{1-2r^{2}\cos\delta+r^{4}}\equiv\frac{I_{in}}{1+[4r^{2}/(1-r^{2})^{2}]\sin^{2}(\delta/2)}.$
(13)

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