Enhancement of the Shift in the Photonic Spin Hall Effect and Its Application for Cancer Cell Detection

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript utilizes the plasma-enhanced lateral spin-dependent shift (SDS) in the optical spin Hall effect (PSHE) to propose an optical refractive index sensor based on the surface Hertz effect, applied to label-free detection of cancer cells. By introducing silicon nitride as a tuning layer and combining it with plasmonic resonance, effective control over the spin-orbit interaction is demonstrated, elevating the SDS from the nanometer range to 350.82 μm.

This manuscript holds reference value for the spin Hall effect and non-destructive cancer cell detection communities. However, the following issues require resolution before consideration for acceptance.

1. In the introduction, the authors should include a discussion of previous research on SDS enhancement related to PSHE structure.
2. The manuscript mentions that adding silicon nitride significantly enhances SDS; further explanation of the physical mechanism is required. Is this enhancement related to the crystal structure of silicon nitride or interfacial effects?
3. The authors did not provide experimental details in the manuscript. Is this a simulation result? The authors should supplement the experimental or simulation conditions.
4. In the final Table 4 discussion, a comparison regarding LOD should be added.

Author Response

This manuscript utilizes the plasma-enhanced lateral spin-dependent shift (SDS) in the optical spin Hall effect (PSHE) to propose an optical refractive index sensor based on the surface Hertz effect, applied to label-free detection of cancer cells. By introducing silicon nitride as a tuning layer and combining it with plasmonic resonance, effective control over the spin-orbit interaction is demonstrated, elevating the SDS from the nanometer range to 350.82 μm.

This manuscript holds reference value for the spin Hall effect and non-destructive cancer cell detection communities. However, the following issues require resolution before consideration for acceptance.

Comment-1: In the introduction, the authors should include a discussion of previous research on SDS enhancement related to PSHE structure.

Reply -1:  Thanks for the suggestion. The comment is incorporated in the revised manuscript on page no. 2 (line numbers 65 to 75) are as follows:

PSHE refers to a spin-dependent shift,  (SDS) of light caused by SOI. This phenomenon can be utilized to detect minute changes in the RI [12, 15] and to identify cancer cells without the use of labels. A key aspect of this process involves the separation of LCP and RCP light waves in different directions. This separation is highly sensitive to various physical factors [2]. However, the intrinsic PSHE is typically weak, resulting in that range from the nanometer to several micrometers [2, 7, 9, 13, 18]. To enhance the , researchers utilize various techniques and materials, including weak measurement methods, Brewster angle [19], surface plasmon resonance (SPR) [3], guided wave-based SPR [1, 20], metamaterials [21], chiral materials [22], optical Tamm states (OTS) [23], and others [18] to advance extremely sensitive sensors and tunable photonic devices such as RI sensor [14], gas sensors [12], biosensors [14, 15, 20], magnetic field detection [16], image edge detection [24], etc.

Comment-2: The manuscript mentions that adding silicon nitride significantly enhances SDS; further explanation of the physical mechanism is required. Is this enhancement related to the crystal structure of silicon nitride or interfacial effects?

Reply -2: The authors thank the reviewer for this insightful comment. The comment is incorporated in the revised manuscript on page no. 8 (line numbers 257 to 265) are as follows:

The enhancement of the  induced by the introduction of the Si₃N₄ layer is not attributed to its crystal structure, as Si₃N₄ is optically isotropic and non-chiral in the wavelength range considered. Instead, the enhancement originates from interface-mediated SOI of light. The Si₃N₄ layer modifies the RI contrast and phase accumulation at the interface, leading to an increased gradient of the Fresnel reflection coefficients and an enhanced spin-dependent geometric (Pancharatnam–Berry) phase. These interfacial effects strengthen the transverse spin splitting characteristic of the PSHE. Prior research has extensively reported comparable enhancing mechanisms resulting from dielectric multilayers and interface engineering [2, 8].

The manuscript has been revised to clarify that the observed amplification is driven by interfacial optical effects rather than intrinsic crystal anisotropy.

 

Comment-3: The authors did not provide experimental details in the manuscript. Is this a simulation result? The authors should supplement the experimental or simulation conditions.

Reply-3: We thank the reviewer for raising this important point. The results presented in this manuscript are obtained from a theoretical and numerical analysis, not from direct experimental measurements. Specifically, the  associated with the PSHE is calculated using the well-established analytical expressions derived from Maxwell’s equations and the angular spectrum method [3, 9, 13, 15] and finally results in the form of Eq. (1), as mentioned in the revised manuscript. This equation is numerically evaluated using MATLAB software to obtain the transverse  under structural parameters of the proposed structure. The manuscript has been covered to explicitly state that the study is simulation-based and to include the relevant theoretical model, governing equation, and numerical parameters, such as refractive indices, incident wavelength, incident angle range, and layer thicknesses used in the MATLAB simulations.

However, for better understanding, the possible experimentation setup is provided in supplementary materials (SM-1) of the revised manuscript.  

Comment-4: In the final Table 4 discussion, a comparison regarding LOD should be added.

Reply -4: Thank you for suggestion. comment is incorporated in the revised manuscript as suggested on page no. 11 are as follows:

Table 4: Comparative analysis of sensitivity for the proposed PSHE structures with reported PSHE based cancer cell detection

Structure	Sensing Mechanism	Sensitivity	LoDPSHE	Applications	Ref.
Multilayer structure	PSHE	Sensor 1(H): 1029.0 nm/RIU	--	Cancer Cells	[22]
		Sensor 2(V): 750.0 nm/RIU
Multilayer structure (Present study)	PSHE	439.30 µm/RIU	2.28×10-6 deg. RIU/µm	Cancer Cells

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper presents a study on enhancing the photonic spin Hall effect (PSHE) using a plasmonic multilayer structure and applying it for cancer cell detection. The authors propose a structure comprising an SF10 glass prism, gold, silicon nitride , molybdenum disulfide, and an analyte layer. The primary contribution is the significant enhancement of the spin-dependent shift  up to 350.82μm, which is substantially higher than previous reports. The work addresses the limitation of weak PSHE shifts (typically nanometer-scale) by optimizing material layers and leveraging(SPR. The application focuses on discriminating between healthy and cancerous cells based on refractive index (RI) differences, demonstrating high sensitivity. The paper is well-structured, with clear sections on background, methodology, results, and conclusions, aligning with standard scientific reporting.

A more thorough explanation of the challenges in measuring SHE in real-world applications would be helpful. Additionally, the rationale for choosing plasmonic structures to enhance it could be clarified, as this is a key part of the innovation presented.

A more detailed explanation of the material selection process, including how the properties of Si3N4 and MoS2 contribute to improving SHE and the overall performance of the structure, would strengthen the methodology section.

The discussion could benefit from more in-depth analysis and practical considerations regarding the experimental setup, material selection, and real-world application challenges.

Expanding the conclusion to highlight potential future applications and improvements would strengthen the overall impact of the paper.

There are many methods to enhance and tune the Spin Hall Effect (SHE) as well as the Goos-Hänchen (GH) shifts.

[https://doi.org/10.1103/PhysRevA.108.023514;https://iopscience.iop.org/article/10.1088/1367-2630/ad1489]  I think the authors should include a discussion of these methods in the paper.

Beyond scalar light beams, vector beams-particularly those featuring C-point polarization singularities-also exhibit the spin shift, which is accompanied by transformations in their polarization structure upon reflection [https://doi.org/10.1007/s11433-024-2589-6]. Incorporating this aspect into the introduction would help underscore the broader relevance and wide-ranging implications of spin shifts.

Author Response

This paper presents a study on enhancing the photonic spin Hall effect (PSHE) using a plasmonic multilayer structure and applying it for cancer cell detection. The authors propose a structure comprising an SF10 glass prism, gold, silicon nitride, molybdenum disulfide, and an analyte layer. The primary contribution is the significant enhancement of the spin-dependent shift up to 350.82μm, which is substantially higher than previous reports. The work addresses the limitation of weak PSHE shifts (typically nanometer-scale) by optimizing material layers and leveraging (SPR. The application focuses on discriminating between healthy and cancerous cells based on refractive index (RI) differences, demonstrating high sensitivity. The paper is well-structured, with clear sections on background, methodology, results, and conclusions, aligning with standard scientific reporting.

Comment-1: A more thorough explanation of the challenges in measuring SHE in real-world applications would be helpful. Additionally, the rationale for choosing plasmonic structures to enhance it could be clarified, as this is a key part of the innovation presented.

Reply-1:  The authors thank the reviewer for this insightful comment. 

In practical applications, the PSHE generates a transverse SDS () that is usually much smaller than the wavelength of light due to the inherently weak SOI of light, making direct measurement challenging [1, 2].

To overcome these limitations, plasmonic structures are employed due to their strong field confinement and enhanced SOI at metal-dielectric interfaces. SPR generates significant electromagnetic field gradients that improve spin-dependent light–matter interactions, thereby amplifying the magnitude of the PSHE to levels that can be empirically observed [1].

The comment is incorporated in the revised manuscript on page no. 2 (line numbers 69 to 75) are as follows:

However, the intrinsic PSHE is typically weak, resulting in that range from the nanometer to several micrometers [2, 7, 9, 13, 18]. To enhance the , researchers utilize various techniques and materials, including weak measurement methods, Brewster angle [19], surface plasmon resonance (SPR) [3], guided wave-based SPR [1, 20], metamaterials [21], chiral materials [22], optical Tamm states (OTS) [23], and others [18] to advance extremely sensitive sensors and tunable photonic devices such as RI sensor [14], gas sensors [12], biosensors [14, 15, 20], magnetic field detection [16], image edge detection [24], etc.

Comment-2: A more detailed explanation of the material selection process, including how the properties of Si₃N₄ and MoS₂ contribute to improving SHE and the overall performance of the structure, would strengthen the methodology section.

Reply-2:  The authors thank the reviewer for this insightful comment. The comment is incorporated in the revised manuscript on page no. 4 (line numbers 150 to 154) and page no. 8 (line numbers 257 to 265) are as follows:

“Furthermore, the use of MoS₂ is advantageous due to its direct bandgap, significant spin–orbit coupling, and larger light absorption [1, 36]. Therefore, it interacts with light more strongly than conventional materials. This strong interaction modifies the refractive index variation gradient, which can effectively enhance the PSHE [1].”

“The enhancement of the  induced by the introduction of the Si₃N₄ layer is not attributed to its crystal structure, as Si₃N₄ is optically isotropic and non-chiral in the wavelength range considered. Instead, the enhancement originates from interface-mediated SOI of light. The Si₃N₄ layer modifies the RI contrast and phase accumulation at the interface, leading to an increased gradient of the Fresnel reflection coefficients and an enhanced spin-dependent geometric (Pancharatnam–Berry) phase. These interfacial effects strengthen the transverse spin splitting characteristic of the PSHE. Prior research has extensively reported comparable enhancing mechanisms resulting from dielectric multilayers and interface engineering [2, 8].

”

 

Comment-3: The discussion could benefit from more in-depth analysis and practical considerations regarding the experimental setup, material selection, and real-world application challenges.

Reply-3: The authors thank the reviewer for this insightful comment. The comment is incorporated in the revised manuscript on page no. 4 (line numbers 150 to 156) are as follows:

The SF10 prism is chosen for its high RI, which aids in effective momentum matching and enhances . Si₃N₄ is a high-RI material employed to reduce radiative losses and enhance the confinement of the evanescent field at the metal–dielectric interface [35]. Furthermore, the use of MoS₂ is advantageous due to its direct bandgap, significant spin–orbit coupling, and larger light absorption [1, 36]. Therefore, it interacts with light more strongly than conventional materials. This strong interaction modifies the refractive index variation gradient, which can effectively enhance the PSHE [1]. The supplementary materials (SM-1 and SM-2) depict the potential experimental setup as well as possible deposition and characterization techniques for the proposed work.

The comment is incorporated in the revised manuscript on page no. 2 (line numbers 59 to 62) are as follows

The various sensing applications have been documented in the scientific literature, including gas sensing [12, 13], refractive index (RI) sensing [14], haemoglobin sensing [15], cancer cell detection [14], magnetic field detection [16], and air quality index (AQI) sensors [17].

Comment-4: Expanding the conclusion to highlight potential future applications and improvements would strengthen the overall impact of the paper.

Reply-4: We thank the reviewer for this valuable suggestion. The comment is incorporated under conclusion section in the revised manuscript on page no. 12 (line numbers 365 to 371) are as follows

Further, the authors believed that the proposed work also has potential future applications, such as secure encoding and encryption [43], and hardware-level security systems [44]. The proposed work can be further enhanced by integrating it with compact on-chip photonic platforms. This integration would allow for its application within the wider framework of ongoing developments in PSHE-based sensing, security, and information processing, ultimately strengthening the overall impact and future prospects of the study.

 

Comment-5: There are many methods to enhance and tune the Spin Hall Effect (SHE) as well as the Goos-Hänchen (GH) shifts.

[https://doi.org/10.1103/PhysRevA.108.023514;https://iopscience.iop.org/article/10.1088/1367-2630/ad1489] I think the authors should include a discussion of these methods in the paper.

 

Reply-5:  The comment is incorporated under conclusion section in the revised manuscript on page no. 2 (line numbers 75 to 82) are as follows

The optical vortex pair can also can manipulate the amplitude and polarity of the PSHE, facilitating improved and tunable transversewithout necessitating alterations to the material interface [25]. A 2024 study revisited the longitudinal  process and elucidates the physical relationship between longitudinal  and the Goos–Hänchen effect, resolving prior interpretative uncertainties [26]. These studies enhance the tunability of spatially varying  by integrating both transverse and longitudinal  into a cohesive framework based on the principles of angular momentum conservation.

25. Zhen, W., Wang, X.L., Ding, J. and Wang, H.T., Controlling the symmetry of the photonic spin Hall effect by an optical vortex pair. Physical Review A, 108(2), p.023514, 2023.
26. Zhen, W., Wang, X.L., Ding, J. and Wang, H.T., 2024. Revisiting physical mechanism of longitudinal photonic spin splitting and Goos-Hänchen shift. New Journal of Physics, 26(1), p.013045, 2024.

 

Comment-6: Beyond scalar light beams, vector beams-particularly those featuring C-point polarization singularities-also exhibit the spin shift, which is accompanied by transformations in their polarization structure upon reflection [https://doi.org/10.1007/s11433-024-2589-6]. Incorporating this aspect into the introduction would help underscore the broader relevance and wide-ranging implications of spin shifts.

Reply-6: The authors gone through the https://doi.org/10.1007/s11433-024-2589-6 and found that Zhen et al. examine how polarization singularities, specifically those at C points, change during optical refraction. The study demonstrates how reflection at interfaces can alter the polarization structure of C-points, altering their spatial distribution and topological characteristics. The authors demonstrate that these transitions are controlled by an interaction between the incident polarization state and the phase and amplitude changes brought on by reflection by examining the underlying polarization dynamics. These results provide more insight into polarized singular optics and may have implications for advanced photonic devices controlled by polarization, photonic spin-orbit interactions, and precise optical manipulation.

We thank the reviewer for bringing this work to our attention. However, due to the already extensive reference list and the inclusion of two closely related references from the same group, we have chosen not to include this additional citation. In future, we will cite this reference also. 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript proposes a multilayer plasmonic structure for the enhancement of spin dependent shift or photonic spin Hall effect and implements this enhancement for cancer cell detection via refractive index sensing. The topic is potentially relevant; however, the manuscript lacks serious conceptual and methodological shortcomings that undermine the credibility of these results. The experimental claims made in the manuscript are not physically convincing. More rigorous analysis is required for the publication of these results. Therefore, I would not recommend this article for the publication in Quantum reports.

Some of the major concerns in the manuscript are:

1. No information is provided on the techniques used for the deposition. The thickness of each layer (< 1 nm) shown in the manuscript are not physically acceptable, since it is quite challenging to make a uniform layer of MoS₂ and Si₃N₄. These tend to grow as flakes. How can the authors assure homogeneity in the layers. The thickness seems to be an highly under-estimated. Also, there is a typo in the thickness (0.65 x 10^-9 nm), this is completely unrealistic. Authors need to provide details on the deposition technique used for the deposition of these multilayers and discuss about their characterization (especially the thickness determination) at least in supplementary information.
2. Since it is the property of these layers to grow as flakes, how would the authors include the defects such as grain boundaries etc. into their analysis of photonic spin Hall effect.
3. The authors have reported the enhancement of spin dependent shift using the multilayers. However, the physical mechanism involved for such enhancement using the multilayers is lacking in the manuscript.
4. The quantification made on the spin-dependent shift (350 µm) is orders of magnitude larger than that reported in the PSHE literature (typically few nm to few microns). The authors need to make serious clarifications for such a high spin-dependent shift.
5. The manuscript does not clearly distinguish between mathematical amplification in Fresnel coefficients and a measurable spatial displacement.
6. Numerous grammatical errors and typographical artifacts are present throughout the manuscript.

Comments on the Quality of English Language

Numerous grammatical errors and typographical artifacts are present throughout the manuscript.

Author Response

Comment from reviewer #3:

The manuscript proposes a multilayer plasmonic structure for the enhancement of spin dependent shift or photonic spin Hall effect and implements this enhancement for cancer cell detection via refractive index sensing. The topic is potentially relevant; however, the manuscript lacks serious conceptual and methodological shortcomings that undermine the credibility of these results. The experimental claims made in the manuscript are not physically convincing. More rigorous analysis is required for the publication of these results. Therefore, I would not recommend this article for the publication in Quantum reports.

Comment-1: No information is provided on the techniques used for the deposition. The thickness of each layer (< 1 nm) shown in the manuscript are not physically acceptable, since it is quite challenging to make a uniform layer of MoS₂ and Si₃N₄. These tend to grow as flakes. How can the authors assure homogeneity in the layers. The thickness seems to be an highly under-estimated. Also, there is a typo in the thickness (0.65 x 10^-9 nm), this is completely unrealistic. Authors need to provide details on the deposition technique used for the deposition of these multilayers and discuss about their characterization (especially the thickness determination) at least in supplementary information.

Reply-1: The authors thank the reviewer for this insightful comment. In this work authors performed the simulation work.

However, atomic layer deposition (ALD) can make thin films of Si₃N₄ that are very uniform and conformal with atomic-level accuracy. For monolayer MoS₂, technologies such as chemical vapor deposition (CVD) or transfer procedures from exfoliated flakes can provide thicknesses below one nanometer.

Further, the typo error in thickness of MoS₂ is corrected in the revised manuscript.

A separate section of supplementary information (SM-1: Possible Deposition and Characterization Techniques for Multilayer Structure) has been prepared that outlines possible deposition and characterization techniques for multilayer structures, such as MoS₂ and Si₃N₄.

The comment is incorporated under conclusion section in the revised manuscript on page no. 4 (line numbers 154 to 156) are as follows:

The supplementary materials (SM-1 and SM-2) depict the potential experimental setup as well as potential deposition and characterization techniques for the proposed work.

 

Comment-2: Since it is the property of these layers to grow as flakes, how would the authors include the defects such as grain boundaries etc. into their analysis of photonic spin Hall effect.

Reply-2:  I appreciate your suggestions. In this work the authors performed the simulation work. Most theoretical analysis and simulations often assume ideal, homogeneous layers. During the experimentation, imperfections like grain boundaries can greatly affect the optical characteristics and result in performance degradation of the device. The previous work of the authors' group demonstrated the effect of the surface roughness and grain size [A, B] on the sensing applications.

10. Agarwal, Y. K. Prajapati and J. B. Maurya, "Effect of Metallic Adhesion Layer Thickness on Surface Roughness for Sensing Application," IEEE Photonics Technology Letters, vol. 28, no. 21, pp. 2415-2418, 1 Nov.1, 2016, doi: 10.1109/LPT.2016.2597856.
11. Agarwal, P. Giri, Y. K. Prajapati and P. Chakrabarti, "Effect of Surface Roughness on the Performance of Optical SPR Sensor for Sucrose Detection: Fabrication, Characterization, and Simulation Study," IEEE Sensors Journal, vol. 16, no. 24, pp. 8865-8873, 15 Dec.15, 2016, doi: 10.1109/JSEN.2016.2615110. 

Comment-3: The authors have reported the enhancement of spin dependent shift using the multilayers. However, the physical mechanism involved for such enhancement using the multilayers is lacking in the manuscript.

Reply-3: The authors thank the reviewer for this insightful comment.  The comment is incorporated in the revised manuscript and highlighted.

 

Comment-4: The quantification made on the spin-dependent shift (350 µm) is orders of magnitude larger than that reported in the PSHE literature (typically few nm to few microns). The authors need to make serious clarifications for such a high spin-dependent shift.

Reply-4: The authors thank the reviewer for this insightful comment.  The comment is incorporated in the revised manuscript and highlighted as follows:

“Furthermore, the use of MoS₂ is advantageous due to its direct bandgap, significant spin–orbit coupling, and larger light absorption [1, 36]. Therefore, it interacts with light more strongly than conventional materials. This strong interaction modifies the refractive index variation gradient, which can effectively enhance the PSHE [1].”

“The enhancement of the  induced by the introduction of the Si₃N₄ layer is not attributed to its crystal structure, as Si₃N₄ is optically isotropic and non-chiral in the wavelength range considered. Instead, the enhancement originates from interface-mediated SOI of light. The Si₃N₄ layer modifies the RI contrast and phase accumulation at the interface, leading to an increased gradient of the Fresnel reflection coefficients and an enhanced spin-dependent geometric (Pancharatnam–Berry) phase. These interfacial effects strengthen the transverse spin splitting characteristic of the PSHE. Prior research has extensively reported comparable enhancing mechanisms resulting from dielectric multilayers and interface engineering [2, 8].

 

Comment-5: The manuscript does not clearly distinguish between mathematical amplification in Fresnel coefficients and a measurable spatial displacement

Reply-5: Thank you for mentioning this point. The amplification in the Fresnel coefficients is a purely mathematical effect at the field level, whereas a measurable spatial displacement is a real-space observable that arises only after propagation and evaluation of the beam’s intensity distribution. Corresponding clarifications have been added in Section X, and the wording has been revised to avoid any ambiguity between mathematical amplification and experimentally observable beam shifts.

The comment is incorporated under conclusion section in the revised manuscript on page no. 6 (line numbers 205 to 212) are as follows

Eq. (1) presents the formula for calculating the mathematical amplification of the shift induced by the Fresnel reflection coefficients. It is crucial to understand that this shift is distinct from the physically measurable spatial displacement. The amplified shift outlined in Eq. (1) arises from the rapid phase variation of the Fresnel coefficients at the resonance angle, which enhances the computed beam shift; however, it does not, by itself, indicate a spatial displacement. A measurable displacement occurs only after the convolution of the finite beam profile with the detector's response [9, 11].

 

Comment-6: Numerous grammatical errors and typographical artifacts are present throughout the manuscript.

During the technical check of this manuscript, we noticed that a high
proportion of the cited references belong to the authors (Refs.
2,3,7,9,13,18,35,36,37,42) which is a authors' self-citation rate of about
22.73%. Authors should not engage in excessive self-citation of their own
work (https://www.mdpi.com/ethics#_bookmark20). Please delete some of your.

Reply-6: The grammatical errors and typographical artifacts have been removed from the manuscript. Further self-cited references are reduced as per journal guidelines.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The author has addressed the raised questions, and this version may be considered for acceptance.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have incorporated appropriate changes in the manuscript. The manuscript may now be accepted for publication.