Tunable Filtering via Lossy Mode Resonance in Integrated Photonics

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors propose a tunable filter based on a lossy mode resonance (LMR) obtained by depositing a TiOx thin film on a polymeric photonic wire with ITO electrodes. I must advise against the publication of this article as there are no experimental results that support this work. Furthermore, some aspects that are not very relevant are explained in excessive detail, such as the characterization of the permittivity of the materials used in the simulations.

In addition to this, several figures are problematic. In Figure 2, the free carrier distribution only changes at the boundaries, so a zoomed-in view would be required. In Figure 3a, the delta and psi values from ellipsometry are not relevant to the reader, so this figure can be removed, and in Figure 3b, it is not necessary to include a photo with the free carrier concentration predicted by the model. In Figure 4, no significant differences can be observed among Figures 4 a-c when the voltage is varied.

Other issues that should be addressed:

• The authors mention that “For inorganic platforms, such large waveguide dimensions are often impractical to fabricate and may also reduce sensitivity due to their inherently higher refractive indices.” However, in conventional inorganic platforms used in integrated photonics, such as silicon on insulator (SOI), the higher refractive index contrast allows to work with much smaller waveguide dimensions.
• The authors say that “ITO do not interfere with the effect”. ITO is capable of generating LMRs, so this sentence is inaccurate, and varying the thickness of the ITO electrodes may affect the central wavelength of the resonance.
• In real applications, the cladding material must have a fixed refractive index. While it can be chosen as a design parameter, it cannot be varied afterwards. The authors mention several values for the cladding refractive index, and they do not explain to which materials they would correspond in a real application.

Author Response

Comment 1: I must advise against the publication of this article as there are no experimental results that support this work. Furthermore, some aspects that are not very relevant are explained in excessive detail, such as the characterization of the permittivity of the materials used in the simulations.

Response 1: I sincerely appreciate the reviewer’s concern regarding the absence of experimental validation. This study represents the design and optimization phase of a broader research effort in which all key materials (TiOₓ, ITO, and Al₂O₃) have already been fabricated and optically characterized. The experimentally obtained optical parameters were directly used in the COMSOL simulations, ensuring that the modeled device reflects realistic physical conditions rather than idealized data.

The primary objective of this work is to establish a design and optimization framework that guides efficient prototype fabrication. Such pre-fabrication modeling is standard practice in modern photonics research and has been adopted in many high-impact studies on integrated device design. To highlight this more clearly, the following sentence has been added to the Introduction section (page 3, Introduction section, line 103, in red):

“Although the present work focuses on numerical modeling and design optimization, all simulation parameters were obtained from experimentally characterized thin films, and fabrication of the proposed device is currently underway for experimental validation.”

I have extensive experience in both LMR-based modeling and device fabrication, and previous work has shown excellent consistency between simulated and experimental results. For example, in my recent publication (Letko, E.; Bundulis, A.; Vanags, E.; Mozolevskis, G. Lossy Mode Resonance in Photonic Integrated Circuits, Opt. Lasers Eng. 2024, 181, doi:10.1016/j.optlaseng.2024.108387*), FEM-based simulations demonstrated close agreement with experimental results. I am therefore confident that the ongoing experimental validation of the proposed device will confirm the findings presented in this work.

Regarding the level of detail in the material characterization section, it was intentionally included to ensure transparency and reproducibility. Because the LMR phenomenon is highly sensitive to dielectric permittivity, even small deviations can significantly alter resonance conditions. Nevertheless, I am willing to condense this section if the editor or reviewers consider it too extensive.

Finally, I emphasize that the fabrication and experimental testing of the tunable filter are currently underway and will be presented in a follow-up publication. The present manuscript provides a significant and original contribution by extending the LMR concept beyond sensing applications toward actively tunable integrated photonic devices.

Comment 2: In addition to this, several figures are problematic. In Figure 2, the free carrier distribution only changes at the boundaries, so a zoomed-in view would be required. In Figure 3a, the delta and psi values from ellipsometry are not relevant to the reader, so this figure can be removed, and in Figure 3b, it is not necessary to include a photo with the free carrier concentration predicted by the model. In Figure 4, no significant differences can be observed among Figures 4 a-c when the voltage is varied.

Response 2: I thank the reviewer for this valuable suggestion regarding Figure 2. In the  revised version of Figure 2, zoomed-in view of the TiOx layer interface has been added to clearly show the variation in free carrier distribution near the boundaries. This adjustment makes the spatial modulation of carrier concentration under different applied voltages easier to visualize and interpret. This adjustment appears in the revised manuscript on page 6, materials and methods section, line 259, in red font.

In the revised manuscript, the delta and psi ellipsometry curves (previously Figure 3a) have been removed to streamline the presentation and maintain focus on the most relevant results. However, I have retained the dielectric permittivity plot and the corresponding free carrier concentration extracted from the model (former Figure 3b), as these parameters are directly used in the COMSOL simulations and are essential for understanding the electro-optic tuning mechanism. This adjustment appears in the revised manuscript on page 7, results and discussion section, line 275, in red font.

I appreciate the reviewer’s observation regarding Figure 4. I agree that the visual differences between subfigures (a–c) are subtle; however, this behavior is expected due to the short Debye length in TiOₓ, which limits the spatial extent of carrier modulation to only a few nanometers near the interfaces. Although the affected region remains the same in depth for all applied voltages, the magnitude of carrier concentration within this region increases significantly, as indicated by the color scale and quantitative values shown in the legends. These changes directly influence the average carrier concentration used for subsequent optical modeling (as described in the text) and are therefore essential for understanding the electro-optic response of the device. For clarity, the revised manuscript now includes the following sentence (page 8, results and discussion section, line 279, in red font):

“Although the carrier distribution profiles appear visually similar due to the limited Debye length, the carrier density within the interfacial regions increases with applied voltage, as reflected in the color scale and quantified in the corresponding average carrier concentrations.”

Comment 3: The authors mention that “For inorganic platforms, such large waveguide dimensions are often impractical to fabricate and may also reduce sensitivity due to their inherently higher refractive indices.” However, in conventional inorganic platforms used in integrated photonics, such as silicon on insulator (SOI), the higher refractive index contrast allows to work with much smaller waveguide dimensions.

Response 3: I thank the reviewer for this valuable observation. I fully agree that in conventional SOI platforms, the high refractive index contrast between the silicon core and SiO₂ cladding enables compact waveguide geometries, which is advantageous for single-wavelength or narrowband photonic applications. However, my statement referred specifically to LMR-based configurations, where the physical requirements differ significantly. In LMR devices, the lossy coating must possess a refractive index higher than that of the waveguide core to enable resonance excitation. Consequently, high-index materials such as silicon are unsuitable for this purpose, as this fundamental condition cannot be met. Moreover, LMR-based devices are generally designed for broadband operation using tunable or wide-spectrum sources, whereas SOI technology is typically optimized for narrowband or single-wavelength systems. This distinction highlights why materials with moderate refractive indices—such as polymers or certain oxides—are more appropriate for integrated LMR implementations. For clarity, the revised manuscript now includes the following sentence (page 2, introduction section, line 62, in red font):

“For inorganic platforms, such large waveguide dimensions are often impractical to fabricate and may also reduce sensitivity due to their inherently higher refractive indices. Materials with very high refractive indices cannot support LMR excitation because the lossy coating must exhibit a higher refractive index than the waveguide core. In addition, LMR devices are typically designed for broadband operation with tunable or spectral light sources, unlike many high-index integrated photonic platforms optimized for single-wavelength applications. Polymers, in contrast, allow straightforward fabrication of large waveguides while maintaining favorable refractive-index contrast for LMR sensitivity [6].”

Comment 4: The authors say that “ITO do not interfere with the effect”. ITO is capable of generating LMRs, so this sentence is inaccurate, and varying the thickness of the ITO electrodes may affect the central wavelength of the resonance.

Response 4: I thank the reviewer for this important clarification. I fully agree that ITO is capable of supporting lossy mode resonances and that its thickness can influence the spectral position of the resonance. My intention in the original sentence was to indicate that the inclusion of ITO electrodes in the proposed multilayer structure does not suppress or prevent the occurrence of LMR in the TiOₓ layer. However, ITO can indeed contribute to or slightly shift the resonance depending on its optical properties and thickness. The revised manuscript now includes the following sentence (page 3, materials and methods section, line 125, in red font):

“Our earlier studies showed that LMR can be observed in ITO-coated devices [16]. In the present structure, the inclusion of ITO electrodes therefore does not suppress the LMR phenomenon but may influence the spectral position of the resonance depending on the electrode thickness.”

Comment 5: In real applications, the cladding material must have a fixed refractive index. While it can be chosen as a design parameter, it cannot be varied afterwards. The authors mention several values for the cladding refractive index, and they do not explain to which materials they would correspond in a real application.

Response 5: I thank the reviewer for this relevant observation. The reviewer is correct that, in real applications, the cladding material has a fixed refractive index and cannot be varied after fabrication. In the simulations, the cladding refractive index was treated as a design parameter to ensure the excitation of the first-order TM-polarized LMR at the target wavelength of 1310 nm. As described in device simulations section, this represents a design optimization step rather than a post-fabrication adjustment. In practice, the required refractive index can be achieved by selecting or formulating a polymer cladding material with suitable optical properties. For example, mixing OrmoCore (n ≈ 1.54 at 1310 nm) and OrmoClad (n ≈ 1.52 at 1310 nm) — two optically compatible ORMOCER® materials — allows fabrication of coatings with refractive indices in the range of 1.52–1.54, corresponding to the values used in this work. For clarity, the revised manuscript now includes the following sentence (page 5, results and discussion section, line 188, in red font):

“In practice, the cladding material can be any polymer coating with a refractive index tailored to satisfy the desired resonance conditions. Such tuning can be achieved, for example, by mixing compatible polymers such as OrmoCore (n ≈ 1.54 at 1310 nm) and OrmoClad (n ≈ 1.52 at 1310 nm) to obtain an intermediate refractive index corresponding to the simulated values.”

 

 

Reviewer 2 Report

Comments and Suggestions for Authors

In the work by E. Letko, the author performs a simulation study on an electro-optically tunable lossy mode resonance (LMR) wavguide, realized by tuning the free carrier concentration in TiOx. The presentation of the results is clear and well-organized. The findings are also of considerable interest to the readers. My major concern on this muscript is the link between the results and the proposed applications.

The author suggests two potential applications for the platform, tunable filter and selectable wavelength sensing, and emphasize on the former. While the tuning rate of 4nm/V is pretty signficant, the linewidth of the filtering is ~100nm and the the extinction ratio is <~10dB. At this level, the tuning is relatively small and the filtering is not very useful. There are plenty of commerical filters and research works that surpass these specifications. The author should discuss more on the advantage of their platform in filtering application or feasible optimizations. Alternatively, the author suggests the platform can be used in sensing by providing wavelength selectivity, but does not provide further details. If the author can show how their platform support this applicaton as well as its signficance, it may be a good idea to focus on this instead.

Some other comments:

1. It will be good to discuss more on how the LMR is modeled and realized in COMSOL simulations.
2. Providing more details on the underlying mechanism of LMR will be helpful to less-familiar readers.
3. Discuss aspects on practical implementation and fabrication of the device as guidance for future work. Provide evidence or reference to previous works to show how much the simulation aligns with experiments in existing platforms. This will make the simulation results more convincing.

Author Response

Comment 1: In the work by E. Letko, the author performs a simulation study on an electro-optically tunable lossy mode resonance (LMR) wavguide, realized by tuning the free carrier concentration in TiOx. The presentation of the results is clear and well-organized. The findings are also of considerable interest to the readers. My major concern on this muscript is the link between the results and the proposed applications.

The author suggests two potential applications for the platform, tunable filter and selectable wavelength sensing, and emphasize on the former. While the tuning rate of 4nm/V is pretty signficant, the linewidth of the filtering is ~100nm and the the extinction ratio is <~10dB. At this level, the tuning is relatively small and the filtering is not very useful. There are plenty of commerical filters and research works that surpass these specifications. The author should discuss more on the advantage of their platform in filtering application or feasible optimizations. Alternatively, the author suggests the platform can be used in sensing by providing wavelength selectivity, but does not provide further details. If the author can show how their platform support this applicaton as well as its signficance, it may be a good idea to focus on this instead.

Response 1: I sincerely appreciate the reviewer’s detailed and insightful comments regarding the practical applications of the proposed LMR-based platform. The reviewer is correct that the simulated device currently exhibits a relatively broad resonance (~100 nm) and a moderate extinction ratio (<10 dB), which may limit its direct applicability as a high-performance narrowband optical filter. However, the main advantage of the proposed approach lies not in achieving the narrowest linewidth, but in introducing a new electro-optically tunable mechanism based on the LMR phenomenon, which has not previously been demonstrated in integrated photonic platforms.

The present design achieves a tuning efficiency of 4.0 nm/V, surpassing most reported electro-optic tunable filter concepts, including those based on Bragg gratings, photonic crystals, and microring resonators. While the current linewidth can be further optimized by refining the refractive index contrast, introducing multilayer coating structures, or precisely controlling TiOₓ stoichiometry, the conceptual novelty of realizing active tuning through free-carrier modulation remains the main contribution of this work.

Furthermore, the platform shows strong potential for single-wavelength sensing. In this configuration, the applied bias can be used to align the LMR resonance with a fixed light source, allowing detection through simple intensity variations without requiring broadband sources or spectrometers. This approach enables compact and energy-efficient sensor systems suitable for chemical and biochemical applications. The Conclusions section has been updated to emphasize these optimization strategies and practical perspectives more clearly (page 12, Conclusion section, line 402, in green font):

“Although the present device exhibits a relatively broad resonance and a moderate extinction ratio, the achieved tuning efficiency demonstrates strong potential for practical implementation. Further optimization of the refractive index contrast, multilayer coating structure, and TiOₓ stoichiometry could lead to narrower and deeper resonances. The voltage-controlled LMR shift can also be utilized in single-wavelength sensing, where tuning the resonance to match a fixed optical source enables detection without the need for broadband illumination or spectrometers, offering a compact and cost-efficient platform for integrated photonic sensors.”

Comment 2: It will be good to discuss more on how the LMR is modeled and realized in COMSOL simulations.

Response 2: I thank the reviewer for the helpful suggestion to elaborate on how the LMR effect was modeled in COMSOL. The modeling approach coupled the optical and electrostatic phenomena using COMSOL’s Multiphysics framework, which enabled simultaneous interaction between the Wave Optics and Semiconductor modules. The Electromagnetic Waves, Frequency Domain interface was used to perform mode analysis in the two-dimensional waveguide cross-section and extract the effective refractive index of the guided modes. In parallel, the Semiconductor module simulated the free carrier distribution in the TiOₓ film under an applied electric field, using Fermi–Dirac carrier statistics. The average free carrier concentration obtained from these simulations was incorporated into the Drude model to determine the corresponding dielectric permittivity, which was then used to calculate the transmittance spectrum according to Eq. (2). To improve clarity, the following explanatory sentence has been added to the Materials and Methods section  (page 6, line 224, in green font):

“The EO tunable LMR behavior was modeled by coupling the optical and electrostatic phenomena using COMSOL’s Multiphysics framework, which enabled simultaneous interaction between the Wave Optics and Semiconductor modules.”

Comment 3: Providing more details on the underlying mechanism of LMR will be helpful to less-familiar readers.

Response 3: I thank the reviewer for this helpful suggestion to provide additional explanation of the underlying mechanism of the LMR phenomenon. In the revised manuscript, a concise description has been added to the Introduction to clarify the physical origin of LMR and highlight its distinction from related effects such as surface plasmon resonance (SPR). The new paragraph explains that LMR can be described through a Fabry–Perot interference model, where partial reflections at both interfaces of the lossy thin film create resonant coupling between guided modes, and that it can be observed with both TE and TM polarizations in a variety of coating materials. This addition appears on page 1, Introduction section, line 34 (in green font):

“The LMR phenomenon can be described through a Fabry–Perot interference model, where partial reflections at both interfaces of the lossy thin film create resonant coupling between guided modes [7]. In contrast to surface plasmon resonance (SPR), which occurs only for transverse magnetic (TM) polarization at metal–dielectric interfaces, LMR can be excited with both transverse electric (TE) and TM polarized light and can support multiple resonances. Moreover, it can be realized using a wide range of coating materials, including polymers [3], semiconductors [8], and dielectrics [9], which makes it a versatile and cost-effective approach for integrated photonic applications.”

Comment 4: Discuss aspects on practical implementation and fabrication of the device as guidance for future work. Provide evidence or reference to previous works to show how much the simulation aligns with experiments in existing platforms. This will make the simulation results more convincing.

Response 4: I thank the reviewer for this valuable suggestion to discuss the practical implementation and fabrication feasibility of the proposed device, as well as to relate the simulations to experimental results. The revised manuscript now includes a statement clarifying that the simulated multilayer architecture can be fabricated using established thin film deposition methods such as sputtering for TiOₓ and ITO and atomic layer deposition for Al₂O₃. In addition, a reference to our earlier experimental work (Letko et al., Opt. Lasers Eng., 2024) has been added, where LMR behavior in integrated devices was experimentally verified and shown to align well with FEM simulations. This addition appears in the Materials and Methods section (page 4, line 160, in green font):

“From the perspective of future device fabrication, both ITO and TiOₓ can be deposited by magnetron sputtering, while ultrathin Al₂O₃ layers can be grown using atomic layer deposition. These coatings are mutually compatible and can be sequentially deposited without adhesion or interfacial issues. The author has already developed OrmoCore waveguide patterning methods suitable for LMR applications, as detailed in previous work [6]. Furthermore, the same study experimentally demonstrated that depositing these thin films onto polymer waveguides generates LMR consistent with numerical modeling.”

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript reports on the design and numerical modeling of a tunable filter based on lossy mode resonance (LMR) in non-stoichiometric TiOₓ thin films integrated within polymer-based waveguides. The study leverages electro-optic modulation of free carrier concentration to shift the LMR spectral position under applied bias, achieving a reported tuning efficiency of 4.0 nm/V. The work positions LMR as a promising mechanism for active integrated photonic devices beyond its conventional sensing applications. The research is timely and relevant, given the growing demand for compact, efficient, and tunable optical components in integrated photonics. The manuscript is clearly structured, methodologically sound, and well contextualized with prior literature. However, several aspects require further elaboration, clarification, and discussion before the paper can be considered for publication.

1. The manuscript convincingly demonstrates LMR tunability in TiOₓ films. However, the novelty claim would benefit from a clearer comparison with other emerging approaches, such as phase-change materials, hybrid plasmonic-photonic structures, and flat-profile resonant architectures. Without this, the relative advantages of the proposed approach remain insufficiently highlighted.
2. The introduction should explicitly include a section on tuning strategies for flat-profile resonant structures (e.g., “New microwave photonic filter based on a ring resonator including a photonic crystal structure,” In 2017 19th International Conference on Transparent Optical Networks (ICTON) (pp. 1-4). IEEE, 2017; “Tunable bandpass microwave photonic filter with largely reconfigurable bandwidth and steep shape factor based on cascaded silicon nitride micro-ring resonators,” Opt. Express, 31, 25648–25661, 2023; “Silicon photonic Vernier cascaded microring filter for broadband tunability,” IEEE Photonics Technol. Lett. 2019, 31, 1503–1506, 2019; “Fully reconfigurable photonic filter for flexible payloads,” Applied Sciences, 14(2), 488, 2024) Such approaches are relevant benchmarks because they allow broad, uniform passbands with reduced spectral distortion, which could directly contrast with the relatively broad resonances of LMR devices.
3. The use of averaged permittivity via the Drude model is reasonable; however, the limitations of this approximation should be discussed. In particular, spatial inhomogeneities in carrier distribution may lead to deviations in experimental performance, especially for ultrathin films where the Debye length becomes comparable to film thickness.
4. The choice of OrmoCore as the waveguide material is well justified, yet no sensitivity analysis is provided for variations in its refractive index or propagation losses. This could be critical for practical fabrication.
5. While the materials deposition is described, the transition from simulation to experimental realization is not sufficiently elaborated. For example, the feasibility of maintaining 2 nm Al₂O₃ insulating layers without defects, or the reproducibility of carrier concentration in TiOₓ films, should be discussed. Reliability under continuous operation and possible degradation effects (e.g., oxygen vacancy migration in TiOₓ) are not addressed but may strongly impact device longevity.
6. The reported tuning efficiency of 4.0 nm/V is significantly higher than in many reported devices. However, a balanced discussion of trade-offs is necessary: resonance linewidth broadening, reduced extinction ratio, and voltage requirements should be discussed against application-specific performance benchmarks.
7. A direct comparison in tabular form with other tunable filter technologies (e.g., Bragg gratings, micro-ring resonators, photonic crystals, phase-change based filters) would strengthen the manuscript and allow readers to rate the unique position of LMR-based devices.
8. While sensing is mentioned as a possible application, the work would benefit from a deeper exploration of potential roles in telecommunications, RF photonics, and quantum photonics.
9. Figures are clear, but quantitative analysis of resonance depth and quality factor evolution with bias is missing.

Author Response

Comment 1: The manuscript convincingly demonstrates LMR tunability in TiOₓ films. However, the novelty claim would benefit from a clearer comparison with other emerging approaches, such as phase-change materials, hybrid plasmonic-photonic structures, and flat-profile resonant architectures. Without this, the relative advantages of the proposed approach remain insufficiently highlighted.

Response 1: I thank the reviewer for this valuable comment highlighting the need for a clearer comparison with other emerging tunable photonic approaches. In the revised manuscript, a new paragraph has been added to the Introduction to briefly compare the proposed LMR-based tuning mechanism with phase-change materials, hybrid plasmonic–photonic structures, and flat-profile resonant architectures. The addition clarifies that the present approach offers comparable or higher tuning efficiency while maintaining simplicity, low power requirements, and compatibility with standard materials and fabrication processes. A corresponding sentence emphasizing these advantages has also been added to the Introduction section (page 2, line 76, in blue font):

“In recent years, several alternative approaches have been explored for achieving tunability in integrated photonic devices. Phase-change materials such as Ge₂Sb₂Te₅ (GST) and Sb₂S₃ can provide large refractive index contrast upon switching, but they typically require thermal or optical activation, which limits modulation speed and introduces device degradation over repeated cycles [17]. Hybrid plasmonic–photonic structures have also demonstrated strong confinement and tunability, yet their fabrication often involves nanoscale patterning and complex alignment steps that complicate large-area integration [18]. Flat-profile resonant architectures, including microring resonators incorporating photonic crystal structures [19], cascaded silicon nitride microrings with reconfigurable bandwidths [20], Vernier-coupled microrings [21], offer sharp spectral features and high Q-factors [22]. However, their tuning range is generally restricted by narrow modal overlap and strong dependence on geometry precision. In contrast, the LMR-based approach proposed in this work enables efficient wavelength tuning through modulation of free carriers in TiOₓ, employing a simple multilayer stack of commonly available materials. This configuration achieves high tuning efficiency without phase-change transitions, thermal activation, or submicron structuring, making it attractive for scalable and low-cost integrated photonic implementations.”

Comment 2: The introduction should explicitly include a section on tuning strategies for flat-profile resonant structures (e.g., “New microwave photonic filter based on a ring resonator including a photonic crystal structure,” In 2017 19th International Conference on Transparent Optical Networks (ICTON) (pp. 1-4). IEEE, 2017; “Tunable bandpass microwave photonic filter with largely reconfigurable bandwidth and steep shape factor based on cascaded silicon nitride micro-ring resonators,” Opt. Express, 31, 25648–25661, 2023; “Silicon photonic Vernier cascaded microring filter for broadband tunability,” IEEE Photonics Technol. Lett. 2019, 31, 1503–1506, 2019; “Fully reconfigurable photonic filter for flexible payloads,” Applied Sciences, 14(2), 488, 2024) Such approaches are relevant benchmarks because they allow broad, uniform passbands with reduced spectral distortion, which could directly contrast with the relatively broad resonances of LMR devices.

Response 2: I thank the reviewer for highlighting the importance of including a discussion of tuning strategies in flat-profile resonant structures as relevant benchmarks. In the revised manuscript, a new sentence has been added to the introduction section to summarize key technologies in tunable photonic filters based on microring and photonic crystal architectures. These approaches indeed offer broad and uniform passbands with low spectral distortion, but they typically rely on complex cascaded designs or thermo-optic modulation, whereas the present work introduces a simpler and fully solid-state EO tuning mechanism based on LMR. This addition helps position the proposed concept within the broader context of tunable integrated photonic filters.  The new text appears in the Introduction section (page 2, line 83, in blue font):

“Flat-profile resonant architectures, including microring resonators incorporating photonic crystal structures [19], cascaded silicon nitride microrings with reconfigurable bandwidths [20], Vernier-coupled microrings [21], offer sharp spectral features and high Q-factors [22].”

Comment 3: The use of averaged permittivity via the Drude model is reasonable; however, the limitations of this approximation should be discussed. In particular, spatial inhomogeneities in carrier distribution may lead to deviations in experimental performance, especially for ultrathin films where the Debye length becomes comparable to film thickness.

Response 3: I thank the reviewer for this valuable and technically relevant comment. I fully agree that using an averaged dielectric permittivity derived from the Drude model is an approximation, particularly for ultrathin films where the Debye length becomes comparable to the film thickness. In such cases, spatial inhomogeneities in carrier concentration may cause local variations in the optical response that are not entirely captured by this approach.

In the present study, this simplification remains valid because the guided modes in LMR devices interact with the thin film through an evanescent field extending over hundreds of nanometers. This field not only penetrates the entire coating but also extends into the surrounding medium, which is the fundamental mechanism enabling LMR-based sensing. Therefore, the averaging of dielectric permittivity is physically consistent with how the optical field couples to the lossy layer in both simulations and experiments. Nonetheless, I acknowledge that for films thinner than approximately twice the Debye length, small deviations between modeled and experimental resonance characteristics may occur.

To clarify this point, the following paragraph has been added to the revised manuscript (page 6, Results and Discussion section, line 252, in blue font):

“It should be noted that using an averaged dielectric permittivity is an approximation, as spatial variations in carrier concentration may locally affect the optical response, especially when the TiOₓ thickness approaches the Debye length. However, in LMR-based structures, the evanescent field extends beyond the coating into the surrounding medium, averaging local optical variations and allowing interaction with the environment, which is fundamental to LMR-based sensing.”

Comment 4: The choice of OrmoCore as the waveguide material is well justified, yet no sensitivity analysis is provided for variations in its refractive index or propagation losses. This could be critical for practical fabrication.

Response 4: I thank the reviewer for highlighting the importance of material tolerances. The LMR response is primarily determined by the relative refractive index contrast within the multilayer stack and by the dielectric permittivity of the lossy coating. Consequently, moderate variations in the OrmoCore core index mainly shift the required cladding index to satisfy the same resonance condition, with only a minor influence on tuning efficiency. Similarly, realistic propagation losses primarily affect the absolute transmission level rather than the spectral position of the LMR. To clarify this point, the revised manuscript now includes a short explanatory note in the Materials and Methods section indicating that such variations would mainly result in small spectral shifts without altering the overall tuning behavior (page 5, Materials and Methods section, line 209, in blue font):

“It should be noted that moderate variations in the refractive index or propagation losses of the individual layers are not expected to significantly affect the simulated response, as the LMR condition primarily depends on the relative refractive index contrast within the multilayer stack. Such deviations would mainly lead to minor spectral shifts without altering the overall tuning behavior of the device.”

Comment 5: While the materials deposition is described, the transition from simulation to experimental realization is not sufficiently elaborated. For example, the feasibility of maintaining 2 nm Al₂O₃ insulating layers without defects, or the reproducibility of carrier concentration in TiOₓ films, should be discussed. Reliability under continuous operation and possible degradation effects (e.g., oxygen vacancy migration in TiOₓ) are not addressed but may strongly impact device longevity.

Response 5: I sincerely appreciate the reviewer’s thoughtful remarks regarding the transition from simulation to experimental realization and long-term device stability. All materials and deposition techniques described in this work were selected based on their proven compatibility and reproducibility in thin-film and integrated photonic fabrication. The formation of uniform, pinhole-free Al₂O₃ layers with thicknesses around 2 nm is routinely achievable by atomic layer deposition. The carrier concentration in TiOₓ can be precisely tuned through oxygen flow control during reactive sputtering, as confirmed by our ellipsometric characterization.

Regarding reliability, it is acknowledged that oxygen vacancy drift under prolonged electric fields may influence long-term stability. However, the applied voltages and current densities in the present configuration are relatively low, minimizing electrochemical degradation. Future work will include bias cycling and accelerated aging experiments to assess long-term performance.

To address this comment, the following clarifying paragraph has been added to the end of the Materials and Methods section (page 4, Materials and Methods section, line 167, in blue font):

“Uniform Al₂O₃ insulating layers with thicknesses down to 2 nm can be reliably achieved using ALD, and the free carrier concentration in TiOₓ can be reproducibly tuned through oxygen flow control during sputtering. Although TiOₓ may experience gradual oxygen vacancy migration under prolonged bias, the operating voltages in the proposed device are moderate, and future work will include reliability testing to assess long-term stability under electrical cycling.”

Comment 6: The reported tuning efficiency of 4.0 nm/V is significantly higher than in many reported devices. However, a balanced discussion of trade-offs is necessary: resonance linewidth broadening, reduced extinction ratio, and voltage requirements should be discussed against application-specific performance benchmarks.

Response 6: I thank the reviewer for this valuable observation. While the achieved tuning efficiency of 4.0 nm/V exceeds most reported electro-optic tunable filters, it is indeed associated with a relatively broad resonance and moderate extinction ratio. These trade-offs are intrinsic to LMR-based devices. The applied voltages in this work remain moderate and compatible with integrated photonic platforms. Further optimization of refractive-index contrast, TiOₓ stoichiometry, and electrode configuration could improve the balance between tuning efficiency and spectral selectivity. A clarifying note on this has been added to the Conclusions section (page 12, Conclusions section, line 382, in blue font):

“Although the obtained tuning efficiency of 4.0 nm/V exceeds most reported EO tunable filters, it is associated with a relatively broad resonance and moderate extinction ratio, which are inherent characteristics of LMR-based devices. Such trade-offs can be mitigated by optimizing the refractive index contrast, TiOₓ stoichiometry, and electrode configuration to achieve improved balance between tuning efficiency and spectral selectivity.”

Comment 7: A direct comparison in tabular form with other tunable filter technologies (e.g., Bragg gratings, micro-ring resonators, photonic crystals, phase-change based filters) would strengthen the manuscript and allow readers to rate the unique position of LMR-based devices.

Response 7: I appreciate the reviewer’s constructive suggestion. A comparison table has been added to the revised manuscript to clearly summarize the performance of various tunable filter technologies, including Bragg gratings, long-period gratings, photonic crystals, microring resonators, and the proposed LMR-based device. The table highlights the main performance metrics such as tuning efficiency, FWHM, and FOM. This addition helps clarify the unique position of LMR-based devices as a simple and efficient approach for broadband EO tunability. The table is included in the Results and discussion section (page 11, Results and discussion section, line 373, in blue font). Additional introductory text for this table can be found in the Results and discussion section (page 11, Results and Discussion section, line 369, in blue font):

“To highlight the relative performance of the proposed device, Table 3 summarizes key characteristics of representative EO tunable filter technologies reported in the literature, together with results obtained in this work.”

Comment 8: While sensing is mentioned as a possible application, the work would benefit from a deeper exploration of potential roles in telecommunications, RF photonics, and quantum photonics.

Response 8: I thank the reviewer for this helpful suggestion. The proposed LMR-based structure can indeed find applications beyond sensing. Its voltage-controlled wavelength tuning enables signal adjustment and reconfiguration in telecommunication and RF photonic systems. The moderate operating voltages and material compatibility with integrated platforms make it suitable for practical implementation. A short paragraph describing these possibilities has been added to the Conclusions section (page 12, Conclusions section, line 409, in blue font):

“Beyond sensing, the proposed LMR-based device can also be applied in telecommunication and RF photonic systems, where voltage-controlled tuning of the resonance wavelength enables adjustment of signal transmission or attenuation. The achieved EO control allows reconfigurable operation without thermal tuning, while the use of polymer and oxide materials ensures compatibility with existing integrated photonic platforms.”

Comment 9: Figures are clear, but quantitative analysis of resonance depth and quality factor evolution with bias is missing.

Response 9: I thank the reviewer for this helpful comment. The present study primarily focused on the spectral shift of the LMR with applied voltage. The resonance linewidth remains nearly constant across the simulated voltage range, while the resonance depth decreases slightly due to bias-induced changes in the TiOₓ permittivity. This effect can be interpreted through the Fabry–Perot interference model of LMR formation, where variations in phase and amplitude conditions reduce interference contrast and consequently the resonance depth. A clarifying note has been added to the Results and Discussion section (page 8, Results and Discussion section, line 308, in blue font):

“This behavior can be described through the Fabry–Perot interference model, where voltage-induced changes in the real and imaginary parts of the TiOₓ permittivity modify the internal phase conditions and reflection balance within the coating, reducing interference contrast and leading to a shallower resonance.”

 

Reviewer 4 Report

Comments and Suggestions for Authors

The reviewed paper deals with an interesting aspect of lossy mode resonance in TiO_x thin films. Some points need to be clarified in the work:

1. For Fig.2, it is better to highlight the carrier concentration variation features at the edge regions. Some references that are also concerned with carrier concentration distribution and dielectric permittivity are important for the basis of this paper, which should be mentioned here, such as Refs. Journal of Applied Physics, 118(6), 063102 (2015); Nature Nanotechnology, 12, 866-870 (2017); Surfaces and Interfaces, 65, 106428 (2025).
2. The paper mentions that the evanescent field extends to all layers in the stack, hence considering the averaged optical properties of TiO_x. Would it be more reasonable to average the carrier concentration only within the Debye length?
3. The bottom region of TiO_x is a depletion zone, while the top region with stronger evanescent field shows increased carrier concentration. Would applying reverse bias voltage lead to improved modulation performance?
4. Please provide the Drude model parameters used for calculating the dielectric permittivity of TiO_x.

 

Author Response

Comment 1: For Fig.2, it is better to highlight the carrier concentration variation features at the edge regions. Some references that are also concerned with carrier concentration distribution and dielectric permittivity are important for the basis of this paper, which should be mentioned here, such as Refs. Journal of Applied Physics, 118(6), 063102 (2015); Nature Nanotechnology, 12, 866-870 (2017); Surfaces and Interfaces, 65, 106428 (2025).

Response 1: I thank the reviewer for this valuable suggestion. In the revised version, Figure 2 has been updated with a zoomed-in view of the TiOₓ interfaces to better highlight the carrier concentration variation at the edge regions. Additionally, the discussion accompanying Figure 2 has been expanded to emphasize the importance of these interfacial effects and to cite relevant studies on carrier redistribution and its influence on optical properties in semiconducting oxides. The following sentence has been added after the description of carrier distribution (page 8, Results and Discussion section, line 288, in purple font):

“The carrier accumulation near the interfaces significantly influences the local optical properties of TiOₓ, as variations in carrier density within these narrow regions modify the permittivity and, in turn, affect the observed LMR behavior. Similar interfacial carrier redistribution and its impact on optical response have been reported in electrostatically tuned semiconducting oxide films [Journal of Applied Physics 118, 063102 (2015); Nature Nanotechnology 12, 866–870 (2017); Surfaces and Interfaces 65, 106428 (2025)].”

Comment 2: The paper mentions that the evanescent field extends to all layers in the stack, hence considering the averaged optical properties of TiOₓ. Would it be more reasonable to average the carrier concentration only within the Debye length?

Response 2: I thank the reviewer for this insightful observation. The suggestion to limit the averaging to the Debye length is physically valid; however, in LMR-based structures, the evanescent field extends across the entire lossy coating and interacts with all layers of the stack. As a result, the effective optical response depends on the cumulative interaction rather than solely on the interfacial region. To clarify this point, the following addition has been made to the Materials and methods section (page 6, Materials and methods section, line 248, in purple font):

“Therefore, the LMR behavior is governed primarily by the averaged dielectric permittivity, making the averaged optical properties of TiO_x​ along the y-axis the relevant parameter, even though the strongest carrier modulation occurs within the Debye length near the interfaces.”

Comment 3: The bottom region of TiO_x is a depletion zone, while the top region with stronger evanescent field shows increased carrier concentration. Would applying reverse bias voltage lead to improved modulation performance?

Response 3: I thank the reviewer for this valuable comment. In the proposed structure, reversing the bias would interchange the accumulation and depletion regions at the two TiOₓ interfaces. However, since the LMR behavior depends on the averaged dielectric permittivity of the whole TiOₓ layer rather than local interfacial changes, the overall modulation efficiency is expected to remain nearly the same for opposite bias polarities. Minor differences could appear due to built-in potential or work-function asymmetry, but their impact should be small.

Comment 4: Please provide the Drude model parameters used for calculating the dielectric permittivity of TiO_x.

Response 4: I thank the reviewer for this helpful suggestion. The Drude model parameters used for calculating the dielectric permittivity of TiOₓ have been added to the Results and Discussion section (page 7, line 265, in purple font). The revised text now reads:

“The dielectric permittivity of TiOₓ was calculated using the Drude model with parameters obtained from ellipsometry fitting shown in Figure 3: free carrier concentration 3.83 × 10¹⁹ 1/cm³, carrier mobility  13.08 cm²∙V^-1∙s^-1, and effective electron mass , where  is the free electron mass.”

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I appreciate the authors’ responses but I must advise against the publication of this article as it still lacks experimental results. Although I agree that simulation tools are necessary in optimizing prototype designs, this process should be complemented by the experimental implementation of the optimized design to validate the simulation results in the same work.

Author Response

Comment: I appreciate the authors’ responses but I must advise against the publication of this article as it still lacks experimental results. Although I agree that simulation tools are necessary in optimizing prototype designs, this process should be complemented by the experimental implementation of the optimized design to validate the simulation results in the same work.

Response: I thank the reviewer for taking the time to review my work again and for emphasizing the importance of experimental validation. I fully agree that experimental implementation represents a valuable continuation of this research.

As explained in my previous responses and already clarified in the manuscript, the present work focuses on the design and optimization stage of an ongoing experimental project. The material parameters used in the simulations were obtained from experimentally characterized thin films, which ensures that the presented results reflect realistic physical conditions. The fabrication and testing of the proposed device are currently in progress and will be described in a separate publication once completed.

I would like to emphasize that this study provides a complete and original contribution at the design stage by establishing a validated numerical framework for tunable integrated LMR devices. Simulation-based investigations of this type are regularly published in Photonics and other peer reviewed journals when they present new concepts, physical insights, or design methodologies that directly support future experimental realization.

I appreciate the reviewer’s perspective, but I believe the manuscript, in its current form, meets the standards of Photonics as a significant modeling and design study that is firmly grounded in experimentally measured material properties.

Reviewer 2 Report

Comments and Suggestions for Authors

The author has addressed my concern satisfactorily. I now recommend publication.

Author Response

Comment: The author has addressed my concern satisfactorily. I now recommend publication.

Response: I sincerely thank the reviewer for the positive evaluation and for recommending the manuscript for publication.

Reviewer 3 Report

Comments and Suggestions for Authors

The Authors have modified the manuscript according to the Reviewers' suggestions.

Author Response

Comment: The author has modified the manuscript according to the reviewers’ suggestions.

Response: I thank the reviewer for acknowledging the revisions and for the positive assessment of the manuscript.