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Thermo-optical bistability in silicon micro-cantilevers
by Basile Pottier, Ludovic Bellon
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We report a thermo-optical bistability observed in silicon micro-cantilevers irradiated by a laser beam with mW powers: reflectivity, transmissivity, absorption, and temperature can change by a factor of two between two stable states for the same input power. The temperature dependency of the absorption at the origin of the bistability results from interferences between internal reflections in the cantilever thickness, acting as a lossy Fabry-Pérot cavity. A theoretical model describing the thermo-optical coupling is presented. The experimental results obtained for silicon cantilevers irradiated in vacuum at two different visible wavelengths are in quantitative agreement with the predictions of this model.
Submission & Refereeing History
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Reports on this Submission
- Cite as: Anonymous, Report on arXiv:2101.12157v1, delivered 2021-03-23, doi: 10.21468/SciPost.Report.2730
1. The work is a thorough study of thermo-optic bistability in silicon cantilevers, which are widely applied and basic systems.
2. There is excellent support of experimental findings with theory.
3. The findings are interesting, especially given the high optical loss of these silicon 'resonators'
4. The paper is very well written and comprehensive.
I have very little weaknesses to report. A minor comment is that
1. even though cantilevers are widely employed in e.g. force microscopy, it is not specified concretely which, if any, current applications would immediately benefit from the understanding gained in this work: at least, there are no citations to works that pose outstanding questions that are answered by this work. This is however not necessary, and it may very well be that such connections will be recognized later.
I read this manuscript with pleasure. I believe the criteria for publication are met; see my strengths and weaknesses assessment.
At the very end of the paper, the authors speculate about using the bistability for sensing with 'infinite sensitivity'. Here, it would be good to acknowledge that the usefullness of bistabilities to enhance practical sensing applications is not as clear-cut as they make it seem: At a bistability, the sharp threshold for a small parameter change is also greatly amplifying any noise mechanism. As such, it is not self-evident that the bistability would make it easier to discern a signal on top of noise - as any useful sensor should aim to do. I recommend that the authors discuss this aspect in a more nuanced fashion.
- Cite as: Anonymous, Report on arXiv:2101.12157v1, delivered 2021-03-17, doi: 10.21468/SciPost.Report.2713
1- Excellent combination of theoretical model and experimental confirmation of developed thermo-optical bistability in silicon cantilevers
2- Clear structure
3- Well written and understandable
4- Good use of visualisations
1- Potentially too little emphasis on possible applications of the observed bistability regarding the necessary high optical powers
In their manuscript titled “Thermo-optical bistability in silicon micro-cantilevers”, the authors discuss the occurrence of thermo-optic bistability in a fundamental single-material system of a micron-sized silicon cantilever. They construct a simple theoretical model to combine the modulation of optical absorption due to interference in Fabry-Pérot cavities with the temperature-dependent changes of the complex refractive index of the material, resulting in a parameter range of incident laser power that allows for bistable temperature operation.
The article is very well written, with a nice read thread following through the whole text. I specifically also want to commend the authors for their clear language and well selected visualizations. During the reading of the manuscript, some questions that were triggered by certain text blocks were instantly answered in the following section, highlighting the clear message of the authors.
In general, I only have minor comments to the authors, which go mostly towards comparing their results with existing concepts of optical bistability in silicon microring resonators, but might lead away from the currently well thought out and concise storyline:
• The only point where I would have hoped for a slightly more in-depth explanation was for the connection between the positive/negative thermo-optic coupling of the system and the positive feedback/stability regarding temperature variations due to absorption. I think the authors look here in section II at their full system, but if one conceptually thinks about on which side of a Fabry-Pérot resonance for a given cantilever geometry the excitation wavelength will be, shouldn’t there be both, positive feedback and stability possible by just tuning the excitation wavelength to the other side of the resonance? Or is this exactly what the authors want to state here?
• While their best fit in Figure 9 is indeed in excellent agreement with their experimental data, I was wondering how the used thicknesses H were determined? In essence, I can’t fully follow the authors how they ended up at a 2% difference of the chosen value with respect to SEM measurements. This variation is indeed fully within the measurement accuracy of the SEM images, I was only wondering how this adaption was done.
• For the choice of using a 18%/15% lower thermal conductivity than bulk silicon, I was wondering if this was a constant, temperature-independent change, or if a different thermal response curve would fit the data equally well?
• It would be interesting to state the Q factor of the cantilever resonance and the minimum threshold power to observe the bistable operation. This would put the work in context to thermo-optic bistability in microring resonators. While the authors clearly state that the investigated system is not designed for its fast switching times or utilization as optical memory (and thus a comparison with these specifically designed systems is not really fair), it could allow readers from that background to more easily understand the system’s operation point.
• One question that somehow remained unanswered was what the optimum cantilever height for one given wavelength is so that thermo-optic bistability occurs at minimum input powers.
• At the beginning of section II, the authors state that due to the poor reflectivity of silicon of only 37%, the material thus absorbs a significant fraction of visible light. I am not sure if I would really combine these two aspects without stating the bandgap position of silicon. For example, AlAs exhibits only significant absorption below 570nm, while still retaining a high refractive index of 3.1, meaning a reflectivity of also around 26%. I agree with the authors that due to Kramers-Kronig relations, the high refractive index is linked to a wide band of absorption, but this could be shifted outside of the spectral region of interest. This is just nit-picking here, I don’t think a real change is required, maybe just a small reformulation of the statement.
With these very minor points in mind, I can nonetheless fully recommend publication in SciPost Physics.
1- In the figure caption of Fig. 3, it should read “green area” instead of “grey area”
2- On page 5 before equation (10), I think “is a solution of” is correct
3- In the figure caption of Fig. 8, it should read “vertical dashed line”, and in Fig. 9 “black dashed curves correspond”
- Cite as: Anonymous, Report on arXiv:2101.12157v1, delivered 2021-03-08, doi: 10.21468/SciPost.Report.2666
The authors report on a thermo-mechanical bi-stability in a microfabricated cantilever. The effect results in a large variation of the transmitted and reflected laser power. The bi-stability is described in an accurate way by a model based on the temperature dependence of the refractive index and the thermal expansion of the cantilever. The manuscript is written in a precise way. I recommend publication.