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Interferometric microscale measurement of refractive index at VIS and IR wavelengths
by Meguya Ryu, Simonas Varapnickas, Darius Gailevicius, Domas Paipulas, Eulalia Puig Vilardell, Zahra Khajehsaeidimahabadi, Saulius Juodkazis, Junko Morikawa, Mangirdas Malinauskas
Submission summary
| Authors (as registered SciPost users): | Mangirdas Malinauskas |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2402.15249v2 (pdf) |
| Data repository: | https://vult-my.sharepoint.com/:b:/g/personal/mangirdas_malinauskas_ff_vu_lt/Ef2W_gayBopLpDIZrPerCVYBWBK1n7tzVESkuPlUI6Ck-A?e=KTqd9F |
| Date submitted: | 2024-06-04 09:14 |
| Submitted by: | Malinauskas, Mangirdas |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Experimental, Observational |
Abstract
Determination of refractive index of micro-disks of a calcinated ($1100^\circ$C in air) photo-resist SZ2080$^\mathrm{TM}$ 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.
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
Answer. Thank you for the very good questions. Indeed, this was issue we checked thoroughly. Among different fabricated samples there were structures with tilted disk in respect to the substrate as well as slightly different disk-substrate distances. We looked for the difference in fringe pattern as well as made numerical predictions what periodicity to expect in the measyred reflection spectra. This allowed us to exclude the possibility of those resonant features to change and influence current interpretation. Revisions were made to better reflect this.
Minor:
1. This is a subjective opinion, but it would be beneficial to juxtapose reflection and transmission data to illustrate the correlation in the interference pattern. Currently, the primary focus seems to be on reflection alone. Two graphs put together can be very useful.
Answer. Good point. It was not possible to measure both R and T spectra from the same point in the used setup due to mechanical constraints of the condenser and objective positions and scanning range. Since reflection is always a simpler method and can be applied at visible and IR wavelength for thin and absorbing samples we focused on R measurements. The appendix shows all formulae applicable to transmittance.
2. Again, this is subjective. While Equation 9 is undoubtedly correct, the message surrounding it and Figure 5d is somewhat confusing. It intuitively suggests that the refractive index is dependent on the incident angle (which is a fundamental property of materials), whereas the real significance lies in the importance of knowing the incident angle with high precision to determine the refractive index from the data. Perhaps some rewording could clarify the uncertainty and the dependence on the incident angle.
Answer. Figure 5d shows measured spectra from the selected region by an aperture. The interference pattern is caused by the polymerized membrane, which the actual form factor of the spectra is also affected by rest of objects and structures inside selected region (ROI). This is why, the fit is taken to make qualitative match, while the main information is in the spectral positions of the peaks. Rewording is made to better reflect this.
1. Although the interferometric determination of the optical properties might be rather standard, no details about the measurement setup is given. Perhaps for the general reader, it could be helpful to describe the experiments leading to the transmission and reflection spectra.
Answer. Thank you for the remark. Description added.
Authors describe their spectra with only a single slab problem assuming that the disk is sandwiched in between air. However, I think the situation is more complex than this, as there should be multiple reflections between the sample and the silica substrate, as well as the substrate itself (especially in the IR region, where the silica is only partially transparent, at least in some portion of the measurement range). The situation is also visible in the reflectance curve in Fig.5, where one can see multiple shoulders to the peaks, etc. I think the correct determination of the peak positions is also important for the correct determination of the refractive index.
Answer. Good point. We measured several samples with different geometries with inclined polymerised membrane also when membranes were at different heights. This was compared with expected Fabry-Perot fringes. This analysis allowed us to make assignments we use in the description. Shoulders in the IR spectra are caused by absorption rather competing resonators. Description improved.
Minor comments:
a. It should be Michelson interferometer (in Fig.4 it is given as Mickelson interferometer!)
Answer. Corrected. Thank you.
b. Sometimes the information on the figures are not described (or it is not immediately visible) for instance, in Fig.1, Transmittance spectrum is given with green and red dashed lines defining something, which is not very clear what. In Fig. 2, Sample A and B are given but their difference becomes clear only after careful reading and it is not immediate. I realize that the authors put the scale, but it feels like only belongs to Sample B.
Answer. Thank you. Improved.
c. In the text, authors mentioned that they fit the Transmittance with Eq.5 (Last paragraph of page 8), while in the Figure4 caption, it is mentioned that it was Eq.6 (which is probably the one).
Answer. Thank you for showing the overlooked mistake. Corrected.
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Extra Fig 1 was created to introduce into the fabrication protocol of the samples. Additional text marked in blue was inserted in Introduction section: “We use a route for obtained optical-grade 3D inorganic-structures employing ultrafast laser direct writing multi-photon lithography technique followed by high-temperature annealing. The sequence of the procedure is visually depicted inf Figure. 1”. We believe it gives more clarity regarding the motivation and preparation of the 3D crystalline-ceramics glass microstructures.