Structureless excitation and manipulation of dynamic holographic plasmonic slides

Domain: physics
Published: 2026-02-19
Editorial outcome: minor_revision

Abstract
Surface plasmons are bound modes at metal–dielectric interfaces and enable a wide range of applications. However, holographic plasmonic fields are usually realized with complex nanostructures, introducing diffraction background and limiting flexibility and dynamic reconfigurability. Here, we propose a structureless holographic approach for generating complex plasmonic fields and controlling their energy flow through a reverse-designed algorithm. Both theoretical and experimental results demonstrate that holographic plasmonic fields can be effectively excited and flexibly modulated on a flat metal film. Furthermore, by loading orbital angular momentum onto the holographic plasmonic field, a controllable energy flow aligned with the plasmonic field can be achieved, visualizing through gold particles transporting along the designed trajectory like a surface slide. This work offers a promising structureless pathway for generation and manipulation of holographic plasmonic fields as well as other surface-wave fields, demonstrating significant potential for controllable on-chip optical energy and particle transmission.

Introduction
Surface plasmons are electromagnetic eigenmodes bound to metal-dielectric interfaces, with evanescent fields that decay away from the surface1. By coupling incident light into these surface modes under appropriate wave-vector matching conditions, one obtains a propagating plasmonic wave that runs along the interface and remains tightly confined near it, effectively forming a near-field optical belt2–4. This confined plasmonic field possesses a shorter wavelength compared to the incident light, and enables the concentration of light into a deep subwavelength region through the storage of optical energy within electron oscillations. This phenomenon leads to a substantial enhancement of electromagnetic field at the nanoscale, thereby producing numerous valuable applications, such as plasmonic tweezers, plasmonic sensing, bioimaging, nano-lasers, and photonic circuits5–10. Consequently, the excitation of specifically designed plasmonic fields is essential to meet the diverse requirements of these applications.

The excitation of designed complex plasmonic fields typically necessitate the use of specialized metallic nanostructures11. Through the meticulous arrangement of nanostructures, holographic plasmonic fields with intricate spatial configurations can be generated12–19. For example, by spatially arranging nanostructures on a metallic film, it is feasible to generate specific structured holographic plasmonic fields12,20. To improve its adaptability, the configuration can be simplified to a single ring-shaped groove by merely customizing the excitation phase along the ring19. This approach facilitates the generation of diverse surface plasmonic modes through the excitation of a single nano-ring configuration. However, there are notable limitations associated with the excitation approach based on metallic nanostructures. Primarily, the metallic nanostructures introduce unavoidable diffraction components and significant energy losses, which detract from the fidelity of the generated plasmonic field20. Furthermore, the fixed nature of nanostructures imposes considerable constraints on the dynamic modulation of the excited plasmonic field. Additionally, most previous studies on holographic plasmonic fields have predominantly focused on holographic intensity distributions. Some other properties, such as energy flow, are challenging to manipulate according to desired patterns because the diffraction background perturbs the phase of the plasmonic field12,19–21. These properties are particularly important for the modulation of on-chip optical energy and particle transmission.

In this work, we propose a structureless and reverse-designed methodology aimed at generating desired complex plasmonic fields and controlling their energy flow. This methodology enables the creation and dynamic modulation of complex structured plasmonic fields on a flat metallic surface, eliminating the need for nanostructures. The strong correlation between theoretical and experimental results offers robust evidence for the feasibility of constructing and manipulating holographic plasmonic fields. Furthermore, it is demonstrated that by loading the ring-shaped orbital angular momentum (OAM) onto the incident light, the OAM can be transferred into the excited plasmonic field, resulting in a controllable unidirectional energy flow along the plasmonic field. To visualize the controllable energy flow within the holographic plasmonic fields, gold particles are employed to experimentally demonstrate the particle trapping by the plasmonic field and the particle transmission along the designed energy flow, akin to a surface slide. This research leverages the advantages of a structureless excitation methodology to manipulate holographic plasmonic intensity and energy flow fields, thereby offering a versatile on-chip optical manipulation platform applicable not only to surface plasmon but also to other optical surface waves such as Bloch surface wave22,23.

Results
Principles
To generate a holographic plasmonic field, as illustrated in Fig. 1A, a specifically designed incident light field is utilized in a tight focusing system to illuminate a smooth metallic thin film. The high-NA focusing system provides large incident angles, so that the in-plane wave-vector components satisfy the required wave-vector matching condition for plasmon excitation5. In our approach, the incident light field is produced with a reversal design algorithm, which enables the precise control of the formed plasmonic field as desired. In this approach, the targeted holographic plasmonic field is expressed as a superposition of multiple plasmonic plane wave modes. By determining the expansion coefficients of each mode, which correspond to the initial plasmonic field distribution along an approximately ring-shaped excitation region that satisfies the wave vector matching conditions under tight focusing, the amplitude and phase of the incident light field are derived through the reversal design algorithm (See Methods Section). The amplitude and phase configuration of the reverse designed incident light field are then encoded onto a spatial light modulator (SLM), resulting in the generation of the targeted holographic plasmonic field.

To assess the efficacy of our methodology, experimental mapping for the generated plasmonic field was conducted in a metal nanoparticle-film system24 Moreover, to demonstrate the multifunctionality of the generated plasmonic field, OAM characterized by unidirectional phase gradients is integrated into the incident light field. The OAM is subsequently transferred into the plasmonic field, where the OAM induced energy flux along the plasmonic profile can drive the particles to move along a designed trajectory. Analogous to children’s slides Fig. 1B, the OAM within the surface plasmon field can generate surface slides, as illustrated in Fig. 1C. Detailed experimental configuration is presented in Fig. 1D and described in the Methods section.

Properties of the structureless excitation approach
To compare the performances of the structural and the structureless excitation approaches, Fig. 2 shows the FDTD results of an example of holographic plasmonic helix fields excited by two different methods, including the ring-shaped structural approach utilized in our previous work19 Fig. 2A and the structureless method Fig. 2D. The FDTD simulation methodologies are delineated in the subsequent Methods section and supplementary Note S1. In Fig. 2A, the nano-ring slit in Au film is essential for the excitation of the plasmonic field, thereby circumventing the strict excitation angle matching condition for incident light. The parameters of the ring structure are consistent with ref. 19, and the phase of the incident light is modified by the SLM to produce the helix plasmonic field. Fig. 2B presents the excited plasmonic helix field excited via the ring-shaped slit structure, with the yellow dashed line indicating the slit’s position. Although the predicted plasmonic field can be effectively excited, however, the fabricated ring-shaped slit strictly limit the position of excited plasmonic field within the ring structure, and brings the high requirement for incident beam alignment. Furthermore, the diffraction background induced by the structure significantly degrades the signal-to-noise ratio and accuracy of the generated plasmonic field. In addition, in the absence of the ring-shaped slit, the excitation efficiency of the plasmonic field becomes relatively low due to the rigorous wave-vector matching condition, resulting in a significantly weak and chaotic plasmonic field profile, as shown in Fig. 2C. In contrast, Fig. 2D, E illustrate the schematic and corresponding excited plasmonic helix field produced by our structureless method. The intensity and phase of the incident beam are derived through the proposed reversal design algorithm according to the predicted plasmonic helix field, as depicted in Fig. 2F (details see “Method” section). For a quantitative comparison, the amplitude distributions in Fig. 2B, E are calculated from electric fields that are normalized to an incident beam with an electric-field amplitude of 1 Vm⁻¹.

In the absence of structure-induced diffraction background, the pattern in Fig. 2E exhibits a significantly cleaner background and a higher excitation efficiency than that in Fig. 2B. Quantitatively, we define the coupling efficiency β as the ratio of the power coupled into the excited plasmonic field to the total input power (see supplementary Note S2 for the formal definition). With this definition, the coupling efficiency of our inverse-designed configuration reaches 18.5%, exceeding that of the ring-shaped structural approach (12.3%) by 6 percentage points, corresponding to a 50% relative improvement. Furthermore, it is important to highlight that this approach does not require the alignment between the incident beam and the ring slit, thereby providing great flexibility in shifting and re-shaping of the excited plasmonic field. As a result, with this structureless approach, desired holographic plasmonic patterns can be efficiently achieved with high modulation freedom and flexibility.

Calibration of the generated Plasmonic fields
To visualize and quantitatively assess the excited plasmonic field, a near-field nanoparticle scanning approach is employed to map the excited plasmonic fields25. Fig. 3 presents the comprehensive results of four examples of holographic plasmonic fields, namely Oval, Arc, Helix, and Cycloid, with typically non-centrosymmetric profiles (Corresponding phase distribution, see supplementary Note S3). Specifically, Fig. 3A shows the four targeted plasmonic field patterns (I0), characterized by a well-defined and sharp boundary, with the color depicting its spatial phase distribution. The phase undergoes periodic variations, resulting in a phase gradient along the plasmonic belt; consequently, akin to a plasmonic vortex26,27, it demonstrates OAM along its entire profile. Fig. 3B illustrates the theoretical distribution of the field (I1) excited by the incident field, as calculated using the reversal design algorithm. Due to the interference and diffraction effects, the background is not as clear as the targeted plasmonic field, with the presence of sidelobes. Fig. 3C presents the simulated results obtained by a FDTD solution (I2), verifying the correctness of the theoretical results Fig. 3B. According to the plasmonic field mapping through the near-field nanoparticle scanning approach, Fig. 3D presents the final experimental results (I3), indicating that the measured plasmonic intensity profiles exhibit a notable degree of similarity.

To quantitatively assess the degree of correlation between the pre-designated and the actually excited plasmonic fields, correlation indices of both the intensity and complex amplitude of the plasmonic fields are calculated (see Methods section and supplementary Note S4). The following Table 1 deliver the performances of the four representative fields in Fig. 3. Here, γ is the correlation index of field intensity and η is the correlation index of complex amplitude. To be consistent with the actual physical situations, correction indices of the FDTD simulations (I2) and experiments (I3) results are compared against the theoretical fields (I1). It is noted that only the intensity of the plasmonic field can be mapped in the experimental system; consequently, the index η for complex amplitude is lacking in this case.

The results in Table 1 indicate a strong degree of correspondence across all four scenarios, suggesting effective excitation of the pre-designated plasmonic fields in experiment. Notably, the case of cycloid-shaped plasmonic field performs a non-ideal match with a lower correlation index. This imperfect is mainly affected by the sharp corners of the field, which contains a significant amount of high-frequency spatial information. The spatial frequency of excited plasmonic field on gold film is subject to an upper limit, determined by the wave vector matching condition. Consequently, when addressing highly complex plasmonic field patterns, the required spatial frequency may exceed this limit, resulting in a deterioration of the observed effect.

Furthermore, Table 1 shows that the FDTD results are slightly degraded compared with the ideal theoretical values. This discrepancy mainly arises because the plasmonic field in theory is constructed as a superposition of plane waves, whose complex amplitude weights are prescribed by the inverse-design procedure. During the actual propagation of the plasmonic field, however, Joule losses and other dissipative mechanisms inevitably reshape these complex weights, leading to deviations between the simulated fields and the ideal target pattern, particularly in the high-frequency spatial components.

Particle transportation through plasmonic slide
It is well known that small objects within a plasmonic field experience plasmonic optical force, including both gradient and scattering components28. The gradient force arises from the spatial variation in the intensity of plasmonic field, resulting in the formation of a trapping potential well that attracts particles toward the high intensity region6. For example, Fig. 4A1 illustrates the trapping potential distribution of the Helix plasmonic field (simulation details see Method section and supplementary Note S5), which closely corresponds to its intensity profile depicted in Fig. 3. The scattering force, primarily resulting from the transfer of photon momentum from the light field to particles, is consistently directed along the Poynting vector (i.e, energy flux)18. As illustrated in Fig. 3A, OAM is included in the designed plasmonic fields, leading to a continuous energy flux along the plasmonic field profile, as indicated by the arrows in Fig. 4A2 being derived from FDTD simulations. The OAM-induced energy flux exerts a significant scattering force along the field profile, thereby enabling the dynamic actuation of particles. As a result, within the plasmonic field in a liquid environment, a particle is initially trapped at the plasmonic potential well by the gradient force, and then be transported by the scattering force along the energy flux of the field, acting like a slide for particles. Fig. 4A3 presents experimental results for particle manipulation, where the colored dots denote the motion trajectory of an Au particle (diameter of 0.8 μm) over time, demonstrating a high degree of consistency with the plasmonic field distribution.

Similarly, Fig. 4B–G display the energy flux of other three excited plasmonic fields in Fig. 3, along with the corresponding experimental manipulation results of the Au particles. Notably, the trajectories of trapped particles are highly consistent with the field intensity and energy flux distribution (see Supplementary Movie S1), demonstrating effectiveness of the proposed approach in particle transportation.

Ad libitum dynamic plasmonic slides
To further verify the diversity and dynamics of the proposed methodology, additional complex ad libitum plasmonic fields have been designed for particle manipulation. Fig. 5A shows the FDTD results of three designed plasmonic fields characterized by the letters S, Z, and U, with energy flux arrows along the field profiles. In experiment, gold nanoparticles are successfully trapped and guided along the trajectories of the letter S, Z, and U, as presented in Fig. 5B, further proving the reliability and diversity of our structureless holographic plasmonic technique (see Supplementary Movie S2).

Furthermore, due to the inherent advantages of a structureless design, excited plasmonic field can be dynamically adjusted by altering the incident holographic light field. By sequentially modulating a series of incident holograms, one can attain a time-averaged composite plasmonic field. The aforementioned analysis demonstrates that the two plasmonic fields can be easily produced, facilitating the independent trapping and movement of gold nanoparticles. Furthermore, the proposed structureless approach offers significant advantages in the dynamic manipulation of the excited plasmonic fields and the particle movement by simply altering the incident light field. Fig. 5C, D present the superimposed profiles of two distinct plasmonic fields generated successively in time, with their energy flux denoted by different colors. In Fig. 5C, two arc-shaped plasmonic fields are generated to form a heart-shaped field, enabling the guidance of particles along the heart-shaped profile through the successively activation of the two fields Fig. 5E (see Supplementary Movie S3).

Additionally, a specific nodal composite field with the ∞ configuration can also be generated with two S-shaped fields in different times, as illustrated in Fig. 5D. Correspondingly, Fig. 5F presents the final experimental manipulation tracks of the trapped gold particle, demonstrating a high degree of consistency with the predetermined design (see Supplementary Movie S4).

As a result, the navigation of particles along desired complex transmission pathways can be accomplished through the sequential excitation of multiple simple holographic plasmonic fields. This approach significantly improves the capacity for the on-chip transport of targeted microscopic objects.

In contrast to the widely-used structural excitation techniques for plasmonic fields, the proposed structureless approach offers several notable advantages. The structureless configuration demonstrates considerable dynamic benefits, such as the movable excitation position and the flexible profiles of the excited plasmonic fields. Furthermore, despite the stringent excitation conditions, the exciting efficiency remains relatively high and could be further enhanced when the incident light beam is shaped into a ring to perfectly match the surface plasmon resonant angle29. More importantly, the particle trapping process is highly repeatable and can be easily reestablished, thereby providing a stable and powerful tool for particle manipulation.

In particle trapping experiments, the incident laser inevitably introduces heating effect, which always brings thermal force and may cause damage on the trapped samples. To mitigate these adverse effects, a relatively low incident power of 5mW is utilized in experiments, significantly reduces thermodynamic impact compared to previous works30. It is essential to note that the thermal effect is not solely detrimental; previous researches have demonstrated that the plasmonic thermal effect can yield beneficial applications in special optical tweezers systems31, such as the thermoelectric and thermophoretic optical tweezers systems, and many other related technologies32–34. Thus, this approach represents an optimal strategy for plasmonic tweezers system, particularly in structureless configurations.

In addition to trapping metallic nanoparticles, our method is also applicable to the micromanipulation of dielectric particles (see Supplementary Note S6). To demonstrate its generality, we further perform trapping experiments with SiO₂ microspheres, showing that these dielectric particles can likewise be guided along trajectories prescribed by the holographic plasmonic fields. These results confirm the universality of our approach for microparticle trapping and transport.

Methods
Reversal design algorithm
Similar to the beam shaping methodology utilized for generating free-space structured optical fields, here a reversal design algorithm is built for the generation of targeted plasmonic fields. The expression for any targeted plasmonic field can be derived as35:

E0(x,y) = 1/π ∫ exp[ik ∫ √(X'(θ)²+Y'(θ)²) dθ] exp[iΘ(x,y,θ)] dθ (1)

where, (x,y) represent the Cartesian coordinate system on the metallic surface where the targeted plasmonic field located, as shown in Fig. 6A; θ=atan(x/y) is the azimuthal coordinate on the metallic surface; Θ∈[−π,π] defines the integrating range of θ for the target plasmonic field; X(θ) and Y(θ) are the parametric functions that describe the two-dimensional trajectory of the targeted plasmonic field; X'(θ) and Y'(θ) are the derivatives of X(θ) and Y(θ), respectively; k is the wavenumber of plasmonic field, and w0 represents the beam waist. In Eq. 1, the initial exponential term denotes the Gaussian-decaying amplitude distribution of the plasmonic field, while the subsequent term illustrates the phase distribution along the field profile. For example, in Fig. 6A, X(θ)=−Sθcos(θ) and Y(θ)=−Sθsin(θ) describe a helix curve, with S is a real number that controls the size of the curve.

Since all initially excited plasmonic waves are focused towards the center to form the final plasmonic field on the metal surface, the desired holographic plasmonic field E0(x,y) can be treated as the superposition of plasmonic plane waves propagating in various directions. In accordance with the experimental scenarios, it is necessary to employ a discretization approximation of the azimuthal angle θ with a chosen step size of π=500. This step size offers a pragmatic balance between computational efficiency and the resolution of the plasmonic field. Accordingly, the targeted plasmonic field is expressed as a sum of plane waves:

E0(x,y) ≈ ∑ u(θ)ϕθ(x,y) = ∑ u(θ)exp[ikxsin(θ)] exp[ikycos(θ)] (2)

where E(x,y) represent the actual superimposed field of plane plasmonic waves on the metal surface; ϕθ(x,y) represent the plasmonic plane wave propagating with the azimuthal angle θ at the targeted plasmonic field location, and u(θ) is the complex amplitude function of the initially excited plasmonic plane wave. Therefore, the goal is to calculate u(θ), which can be expressed as:

u(θ) = 〈ϕθ(x,y)|E0(x,y)〉 (3)

where the symbol 〈·|·〉 represent the inner product of two fields, and the detailed simulation procedure is provided in Supplementary Note S7. From Eqs. (1–3), the amplitude and phase distribution of initial excited plasmonic plane waves at different angle θ can be calculated, as shown in Fig. 6B.

The above process explains how to use the targeted plasmonic field to reversal-calculate the initially excited plasmonic plane waves propagating in various directions. Since the above solution involves a discretization approximation, the final distribution of the focused plasmonic field exhibits a slight discrepancy with the designation. Furthermore, as the longitudinal component (Ez) shows an absolute predominance in the plasmonic field5, the above Eqs. 1 and 2 are adopted for the Ez component in a scalar format. Moreover, the Joule loss associated with plasmonic propagation is negligible, as the propagation distances of different plasmonic plane waves towards the center exhibit slight variations.

Distinct from conventional inverse-design techniques, such as Gerchberg–Saxton–type phase retrieval or adjoint-based gradient optimization, which typically require numerous iterations, rely on convergence checks, and are prone to local minima, our method avoids these issues, offers significantly higher computational efficiency, and retains a clear physical interpretation.

Design of the incident light field
To excite the initial plasmonic plane wave u(θ) above, an appropriate hologram can be designed and loaded onto the SLM. Since the amplitude of the initially excited plasmonic field is proportional to that of the excitation light field in free space36,37, the complex amplitude distribution of the light field in free space can be written as U(θ)=Cu(θ), where C is the plasmonic excitation coefficient. In this focusing system, to ensure that the incident light can be approximately perfectly matched to the plasmonic excitation angle29, consequently, the incident light field is designed as a ring-shaped field as shown in Fig. 6C. Accordingly, the incident light field is expressed as:

Ein = rect(r2−R1,R2) · Cu(θ), with (R2−R1) ≪ R2+R1 (4)

where, R1 and R2 represent the inner and outer radii of the ring (Fig. 6C), respectively; the rect(·) function represents the rectangular function, which describes an annular aperture with radius r∈[R1, R2] that covers the excitation angle.

To get the designed incident light field Ein, a holographic mask on SLM (Fig. 6C) that incorporates amplitude-phase modulation can be expressed as38:

Tmask = rect(r2−R1,R2) · |Cu(θ)| exp iangle[u(θ)] + 2πix/d (5)

where, |.| and angle(.) define the amplitude and phase angle of the field u(-θ). The term 2πix/d within the exponential function signifies a blazed grating with d is the grating period, which works in conjunction with the 4-f system. The light field diffracted by the mask, as shown in Fig. 6D, ultimately excites a plasmonic focus field on the metallic surface that closely matches the desired plasmonic field (Fig. 6A).

Calculation of correlation indices of the field
In order to quantitatively assess the quality of excited plasmonic field, it is important to calculate the correlation indices to the predetermined plasmonic field. Here, the mode purity coefficient index η, which indicates the correlation index of field complex amplitude, is defined as:

η = |〈E0(x,y)|Ej(x,y)〉|² (6)

where E0(x,y) and Ej(x,y) are complex amplitude of targeted and generated plasmonic fields, respectively. As a result, a value of 100% signifies that the two fields are exactly same in complex amplitude, whereas a value of 0% indicates that the two optical fields are entirely dissimilar.

The intensity distribution of plasmonic fields is also very important in various applications. Therefore, the intensity correlation index γ is evidently suitable for calibrating the efficacy of the generated plasmonic field, being defined as:

γ = |〈I0|Ij〉|² = |〈(E0(x,y))²|(Ej(x,y))²〉|² (7)

where, I and E are the intensity and complex amplitude of the plasmonic field, respectively. Here, the mode purity index η is used to evaluate the shaping capability of the reversal design methodology applied to the plasmonic field, while the intensity correlation γ assesses the experimental outcomes.

Experimental configuration
The structureless holographic plasmonic system is established on an inverted microscopic system (Olympus IX73), as schematically shown in Fig. 1D. In the configuration, a linearly polarized 532-nm laser beam (Changchun Leishi Photoelectric Technology Co., Ltd) initially passes through a polarizer (P) and a rotatable half-wave plate (HWP) to modulate the power. It is then expanded using a telescope system composed of two convex lenses (L1 and L2) to match the mask size of the hologram loaded on the SLM (PLUTO-2.1, 60Hz, HOLOEYE). A polarizer (P2) is employed to adjust the polarization orientation to align with the SLM. The incident polarized beam is then modulated by the holographic mask loaded on the SLM, which is achieved based on the reversal design algorithm. The encoded +1st-order diffraction from SLM is converted to radially polarized by a vortex plate (VP), and passes through a 4f-system (L3 and L4) to align with the back aperture of the oil-immersed objective lens (Olympus, 100×, NA=1.49). The encoded exciting light is then tightly focused onto a 35-nm thick gold film coated on the glass substrate to accommodate plasmonic field excitations. The gap between the objective lens and glass substrate is filled with oil, and a high-speed CMOS camera (Pointgrey, GS3-U3-23S6M-C) is used to capture the experimental process.

In this work, we perform two types of experiments: a field-mapping measurement to verify the generation of the holographic plasmonic field, and an optical-tweezing experiment to demonstrate its applicability to nanoparticle manipulation. Both experiments share the same optical setup; the main difference lies in the role of the nanoparticle. In the field-mapping experiment, the particle is immobilized on the metal film and used as a nanoscale probe that scatters the holographic plasmonic field for reconstructing its spatial distribution25. In the optical-tweezing experiment, the particle initially undergoes unrestricted motion within a liquid medium before being confined and manipulated by the holographic plasmonic field.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript demonstrates a novel and fully reconfigurable method to excite arbitrary surface‐plasmon patterns on a flat metal film by encoding both amplitude and phase at the pupil plane of a focusing objective. An inverse‐design algorithm computes the required ring‐shaped holograms. The authors validate their approach using four target patterns (oval, arc, helix, and cycloid), quantify efficiency improvements, and demonstrate dynamic particle transport along complex trajectories using orbital angular momentum.\nWe recommend this paper for publication, after the authors address the following concerns:\n1. The discussion beginning with “In contrast, Figs. 2 (D and E) illustrate … high modulation freedom and flexibility.” appears verbatim in both lines 116–126 and 133–142. Please remove the redundant copy so that the explanation appears only once.\n2. The colorbars in Figs. 2(B), 2(E), and 4(A1) are not specified properly. What do the values 30 in Fig. 2(B), 44 in Fig. 2(E), and -60 in Fig. 4(A1) represent? Are these normalized quantities?\n3. The authors report correlation indices larger than 0.8 between the designed and measured plasmonic fields, but it is not clear how sensitive this metric is to the choice of region of interest (ROI) based on equations 6 and 7. Could you please clarify how the spatial ROI used for the correlation calculation was defined? Was it the entire scanned area or only the high-intensity belt? Have you examined how the correlation index changes with different ROI bounds?\n4. The Inverse-Design Algorithm section provides a high-level description of the plane-wave decomposition of the target field. Please add: a) a step-by-step outline or flowchart detailing the computation of the inner product over the ring aperture\nb) the number of sampling points/angles used, and c) an estimate of the computational cost of the algorithm.\n5. Did the inverse design procedure involve an iterative solver or optimization loop? A brief paragraph comparing your inverse-design approach with other numerical techniques would help the reader to understand its novelty, performance advantages, and limitations.\n6. The manuscript reports improved “efficiency” compared to etched rings, but the metric is not explicitly defined. If efficiency refers to the fraction of input optical power coupled into the target plasmonic mode, please specify how it is measured and include the formula used in the calculation.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "This manuscript developed a method to generate plasmonic files on a metal film without using pre-fabricated nanostructures. It also demonstrated an energy flow control to control particles along the plasmonic intensity profiles. This work is interesting and novel by providing a versatile and flexible platform for controlling nanoscale particles, which might be interesting for the many single particle based quantum applications. I would recommend this paper to be accepted by Nature Communications.\nHere are some more detailed questions:\n1. In figure2, the comparison between the structureless method and the conventional methods is clearly shown. However, it would be better to have a quantitative comparison. For example, the author can define a FoM of the generated pattern. How much do they differ? Or for some other particle trapping profile, to achieve similar trapping depth, how much input energy differs? A quantitative comparison here might be interesting to see.\n2. In figure3, it was not clear to me why the simulation looks worse then the theory, especially for the high-spatial-frequency patterns. Also, why does the experimental results look worse than the simulation result? Is it due to misalignment of the lenses?\n3. In the experiment, a gold particle was used. May I ask why using gold particles? Is it because gold has a very strong plasmonic response? How does this technique apply for other particles with weaker plasmonic responses?", "reviewer_4": "The authors of the manuscript \"Structureless Excitation and Manipulation of Dynamic Holographic Plasmonic Slides\" present a way to manipulate the phase, intensity and properties of plasmon excited on a flat metal-dielectric interface, to produce a holographic image. I found the paper interesting and engaging, with the experimental results showing improvement on current methods used. However, I'm unsure if the progress on the method is significant enough for publication in Nature Communications. I believe that this work will be more suited in a more specialised journal, such as Nanophotonics.\nNevertheless, I have a couple of points that the authors can improve on, before submitting the paper in a more specialized journal:\n1) I'm a bit puzzled why the authors chose to do their experiments by optically trapping nanoparticles. Would a probe-tip not be a better choice, since it won't suffer from Brownian motion which alters the scattered fields measured during the experiment? Also, if the authors want to stick with optically trapped nanoparticles, then why not use dielectric ones that will induce less scattering that affects their results?\n2) I'm not sure how the authors match the momentum of the incident beam with propagating SPP modes. From Fig.2, it seems that they always excite with normal incidence. I understand in Fig2A that there is a nanoring slit that allows for this momentum matching for certain part of the incident normal beam. But how do the authors manage to achieve a better momentum match in fig.2D (and future configurations in the paper)?\n3) The first sentence of the introduction is not technically correct. The propagating SPPs on metal-dielectric interfaces are eigenmodes, which means that they are always there. One does not need to illuminate the interface with light for the evanescent modes to emerge. But one needs external illumination to couple light into these modes, which is what I believe the authors were trying to communicate.\n4)Terms like \"stray signals\" or \"stray light\" are not proper scientific terminology. This light/signal comes from diffraction, and one should say this.\n5)Line 53: \"Some other properties, such as energy flow, are challenging to manipulate according to desired patterns, ...\" Why is this the case? What is stopping current methods to do this?\n6)I'm not sure what is a toroidal orbital angular momentum. It would be convenient for the reader if the authors defined what they mean by it.\n7) What is the asterix on I1* in table 1? It is never explained, or if it is I missed it completely.\n8) There are a 3-4 places that the language and grammar can be improved. For example:\nline 121 \"Fig.2E is significantly clean with higher excitation...\" should probably be: \"Fig.2E is significantly more clean with higher excitation...\"\nline 175 \"This imperfect is mainly...\", should probably be : \"These imperfections are mainly ...\"\nOverall, although the manuscript shows interesting results, they are primarily incremental so I believe that they will be of more interest to a more specialized audience than Nature Communications."}, "author_response": "Response to the Decision Letter\nResponse to reviewer #1\nComment: The manuscript demonstrates a novel and fully reconfigurable method to\nexcite arbitrary surface‐plasmon patterns on a flat metal film by encoding both\namplitude and phase at the pupil plane of a focusing objective. An inverse‐design\nalgorithm computes the required ring‐shaped holograms. The authors validate their\napproach using four target patterns (oval, arc, helix, and cycloid), quantify efficiency\nimprovements, and demonstrate dynamic particle transport along complex trajectories\nusing orbital angular momentum. We recommend this paper for publication, after the\nauthors address the following concerns.\nComment 1:The discussion beginning with “In contrast, Figs. 2 (D and E) illustrate …\nhigh modulation freedom and flexibility.” appears verbatim in both lines 116–126 and\n133–142. Please remove the redundant copy so that the explanation appears only once.\nReply 1: We thank the reviewer for the careful reading and for pointing out this\nduplication. The repeated paragraph (lines 133-142 in the original manuscript) has now\nbeen removed, and the explanation is now included only once in the revised manuscript.\nComment 2: The colorbars in Figs. 2(B), 2(E), and 4(A1) are not specified properly.\nWhat do the values 30 in Fig. 2(B), 44 in Fig. 2(E), and -60 in Fig. 4(A1) represent?\nAre these normalized quantities?\nReply 2:We appreciate the reviewer’s insightful question. In Fig. 2, the colorbar values\nrepresent the magnitude of the electric field, |E|, obtained from the FDTD simulations.\nThe incident field is normalized to a unit amplitude of 1 V·m⁻¹, providing a consistent\nreference for comparing field enhancements between our tightly focused excitation and\nconventional structured illumination. For context, achieving a stable optical trap\nrequires an optical potential depth exceeding 1k T (k is the Boltzmann constant and T\nB B\nis the temperature, which is fixed at T=300 K for normalization [28]) to ensure that the\nparticle can overcome thermal fluctuations. In Fig. 4(A1), the colorbar indicates the\ndimensionless potential depth by k T, which is a normalized quantity. Additional\nB\nclarifications regarding colorbar normalization and labeling have been added in the\nrevised manuscript to improve clarity.\nCorrespondingly,\nLine 124-126, Page 4: “For a quantitative comparison, the amplitude distributions in Fig. 2B\nand Fig. 2E are calculated from electric fields that are normalized to an incident beam with an\nelectric-field amplitude of 1 V·m⁻¹. In the absence of structure-induced stray light, the pattern in\nFig. 2E exhibits a significantly cleaner background and a higher excitation efficiency than that in\nFig. 2B. ”\nThe caption of Fig. 2, Page 5: “Fig 2 | Comparison of a holographic plasmonic helix field excited by\nstructural and structureless methods. (A) Schematic of a nanoring slit assisted plasmonic field excitation. (B)\nDistribution of the structure assisted plasmonic helix field, with the field amplitude normalized to that of an\nincident beam whose electric-field amplitude is set to 1 V·m-¹. The yellow dashed line indicates the slit’s position.\n(C) The generated chaotic plasmonic field when the nanoring slit is cleared off. (D and E). The schematic and final\nexcited plasmonic helix of our method. F. The intensity and phase of the incident beam, intensity is normalized\nalong the radius.”\nFig.4, Page 8:\nFig. 4 |The energy flux and particle transportation results of excited plasmonic slide fields. (A) The potential well\n(in units of k T), energy flux, and experimental trajectory of an Au particle in the excited Helix plasmonic field. Here\nB\nk is the Boltzmann constant and T is the temperature, which is fixed at T=300 K for normalization(B to D) The\nB\nenergy flux arrows (background is intensity) and (E to G) the corresponding experimental trajectory of the Au\nparticle in the Oval, Helix, and Cycloid shaped plasmonic fields, respectively. Different colors of the trajectories\nrepresent positions of the particle at different times, specifics see Supplementary Videos. Scalebars are 1 μm.\nComment 3: The authors report correlation indices larger than 0.8 between the\ndesigned and measured plasmonic fields, but it is not clear how sensitive this metric is\nto the choice of region of interest (ROI) based on equations 6 and 7. Could you please\nclarify how the spatial ROI used for the correlation calculation was defined? Was it the\nentire scanned area or only the high-intensity belt? Have you examined how the\ncorrelation index changes with different ROI bounds?\nReply 3: Thanks for raising this important point. For the designed plasmonic field\ndescribed by Eq. 1, the cross-intensity profile of the focal curve follows a Gaussian\nenvelope. In this work, without loss of generality, the threshold boundary for selecting\nthe region of interest (ROI) in the correlation calculation is defined as the area where\nthe Gaussian intensity drops to 50% of its peak value. To evaluate the robustness of this\nchoice, we further calculate the correlation coefficient across a series of ROI boundaries\ncorresponding to Gaussian attenuation levels ranging from 20% to 80%. As shown in\nFig. R1, the correlation values remain essentially unchanged over this range, indicating\nthat the metric is insensitive to the precise ROI selection. An expanded analysis of the\nROI robustness has been added to the supplementary of the revised manuscript.\nFig. R1 | Correlation Index of the plasmonic patterns under different Region-of-Interest (ROI) boundaries\nCorrespondingly,\nLine 168, 169, Page 6: “... correlation indices of both the intensity and complex amplitude\nof the plasmonic fields are calculated (see Methods section and Supplementary Note S4).”\nAdd Supplementary Note S4: Robustness of the Correlation Index against Region-of-Interest\n(ROI) Boundary Selection.\nFor the designed plasmonic field described by Eq. 1, the cross-sectional intensity profile along the\nfocal curve follows a Gaussian envelope. In the main text, the Region-of-Interest (ROI) for the\ncorrelation calculation is defined as the area where the Gaussian intensity drops to 50% of its peak\nvalue.\nTo assess the robustness of the correlation index used to compare the designed and experimental\nplasmonic fields, we evaluate its stability with respect to the choice of ROI boundary for four\nrepresentative plasmonic patterns (oval, arc, helix, and cycloid), as indicated by the different colored\ncurves. The ROI boundary is specified by the normalized Gaussian intensity threshold I/I ,\n0\nwhich is\nvaried from 0.2 to 0.8 to examine the sensitivity of the correlation metric, as shown in Fig. S3. Since\nthe primary energy remains predominantly confined within the high-intensity band, the correlation\ncoefficient exhibits almost no variation once the threshold exceeds 0.3 and remains essentially stable\nacross this range, confirming the robustness of the metric and its insensitivity to the precise ROI\nselection.\nFig. S3 | Correlation Index of the plasmonic patterns under different Region-of-Interest (ROI) boundaries.\nComment 4: The Inverse-Design Algorithm section provides a high-level description\nof the plane-wave decomposition of the target field. Please add: a)a step-by-step outline\nor flowchart detailingthe computation of the inner product over the ring aperture b) the\nnumber of sampling points/angles used, and c) an estimate of the computational cost of\nthe algorithm.\nReply 4: We thank the reviewer for this constructive suggestion. The detailed\ncomputational procedure for evaluating the inner product over the ring aperture is\nsummarized in the flowchart as shown in Fig. R2. Briefly, we begin by importing the\nnormalized target plasmonic field. Next, we define the sampling variable (sampling\npoints/angles), using a discretized angle with a step size of π/500. For each , a\n𝜃\ncorresponding plasmonic plane wave =exp[ikxsin(θ)]∙exp[ikycos(θ)] is gener\n𝜃\nated\nand subsequently normalized. The inner product shown in Eq.(3) between  and E 0 is\nthen computed to obtain the complex coefficient u. This process is repeated for all\nvalues until the complete function u( ) is obtained.\n𝜃\nIt is important to emphasize that our method does not require iterative optimization; the\n𝜃\nonly loop calculation involves traversing the sampled θ angles. Consequently, our\napproach offers a significant advantage in computational efficiency compared with\ntraditional optimization algorithms. Implemented in MATLAB and executed on a\nmachine equipped with an Intel i7-12700 CPU, the total computation time is 30.95\nseconds.\nIn the revised manuscript, we have added a detailed, step-by-step description of the\ninner-product computation in the supplementary.\nFig. R2 | Flowchart for computing the inner product over the ring aperture\nCorrespondingly,\nLine 336-337, Page 13: “where the symbol | represents the inner product of two fields,\nand the detailed simulation procedure is provided in Supplementary Note S7. From Eqs. (1 to\n⟨ ⟩\n3), the amplitude and phase distribution of initial excited plasmonic plane waves at different\nangle can be calculated, as shown in Fig. 6B. ”\nAdd s𝜃upplementary Note S7. Numerical Calculation of the Inner Product.\nTo explicitly present the numerical procedure used in the inverse-design process, Fig. S5 details the\nfull computational workflow for evaluating the angular coefficient function. Compared to the\ninverse Fourier transform in free space, the inverse design algorithm represents the target plasmonic\nfield as a linear combination of directionally separable plasmonic plane waves. Initially, the\nalgorithm introduces the normalized target field distribution E . Subsequently, a sampling variable\n0\nθ is defined, representing discrete sampling points or angles, with a specified angular step size of\nπ/500 . For each discrete θ, a corresponding plasmonic plane wave ϕ is generated and\nθ\nsubsequently normalized. This procedure effectively discretizes the continuous plasmonic modes\nwithin the angular spectrum space. The inner product between ϕ and E is then computed to\nθ 0\nobtain the complex coefficient u. By repeating this procedure for all sampled angles, the complete\nangular coefficient function u(θ) is constructed. This inner-product operation directly yields the\nprojection complex amplitude of the target field onto the plasmonic eigenmode at each angle,\nrepresenting the complex weight of its corresponding component in the angular spectrum. Therefore,\nthe algorithm enables an end-to-end mapping through complete complex-amplitude control, without\nthe need for any additional iterative optimization. Implemented in MATLAB and executed on a\nmachine equipped with an Intel i7-12700 CPU, the total computation time is 30.95 seconds.\nFig. S5 | Flowchart for computing the inner product over the ring aperture\nComment 5: Did the inverse design procedure involve an iterative solver or\noptimization loop? A brief paragraph comparing your inverse-design approach with\nother numerical techniques would help the reader to understand its novelty,\nperformance advantages, and limitations.\nReply 5: Thanks for this insightful suggestion, this is indeed a key point. A major\nadvantage of our approach is that the inverse-design procedure does not rely on iterative\nsolvers or optimization loops. Instead, it is formulated directly from the principle of\nquantum-state superposition: the target field is expressed as a linear combination of\nbasis plasmonic modes, and the complex weighting coefficients are obtained\nanalytically through inner-product evaluation. This fundamentally distinguishes our\nmethod from conventional inverse-design techniques, such as Gerchberg–Saxton–type\nphase retrieval or adjoint-based gradient optimization, which typically require\nnumerous iterations, involve convergence checks, and may be susceptible to local\nminima. In contrast, our method avoids these issues, offers higher computational\nefficiency, and retains a clear physical interpretation. A comparative discussion\nhighlighting these differences has been added to the revised manuscript (lines 348-352).\nCorrespondingly,\nLine 348-352, Page 13: “Distinct from conventional inverse-design techniques, such as\nGerchberg–Saxton–type phase retrieval or adjoint-based gradient optimization, which typically\nrequire numerous iterations, rely on convergence checks, and are prone to local minima, our method\navoids these issues, offers significantly higher computational efficiency, and retains a clear physical\ninterpretation.”\nComment 6: The manuscript reports improved “efficiency” compared to etched rings,\nbut the metric is not explicitly defined. If efficiency refers to the fraction of input optical\npower coupled into the target plasmonic mode, please specify how it is measured and\ninclude the formula used in the calculation.\nReply 6: Thank you for this helpful suggestion. To facilitate a clear and quantitative\ncomparison between the structured and unstructured configurations, we define the\ncoupling efficiency, , as the ratio of the power coupled into the excited plasmonic field\nto the total input power, calculated as:\n𝛽\n 2\n\n0\n (R1)\n 2\n E x y, dxdy\nin\nE x y, dxdy\nOur results show that the structured configuration achieves a coupling efficiency of\napproximately 12.3%, whereas our inverse-designed configuration reaches 18.5%. This\nefficiency can be further improved by generating a perfect radially polarized beam,\nwhich can enhance the trapping stiffness by compressing the energy into a thin ring that\nsatisfies the plasmonic coupling conditions [39]. In the revised manuscript, we have\nadded the definition of , its corresponding formula, and relevant references to improve\nclarity.\n𝛽\nCorrespondingly,\nLine 129-133, Page 5: “In the absence of structure-induced diffraction background, the pattern\nin Fig. 2E exhibits a significantly cleaner background and a higher excitation efficiency than that in\nFig. 2B. Quantitatively, we define the coupling efficiency β as the ratio of the power coupled into\nthe excited plasmonic field to the total input power (see Supplementary Note S2 for the formal\ndefinition). With this definition, the coupling efficiency of our inverse-designed configuration\nreaches 18.5%, exceeding that of the ring-shaped structural approach (12.3%) by 6 percentage\npoints, corresponding to a 50% relative improvement.”\nAdd supplementary Note S2.\nComparison of coupling efficiency.\nTo facilitate a clear and quantitative comparison between the ring-shaped slit and tightly focused\nreverse design configurations, we define the coupling efficiency, β, as the ratio of the power coupled\ninto the excited plasmonic field to the total input power, calculated as:\n 2\n\n0\n (S1)\n 2\n E x y, dxdy\nin\nE x y, dxdy\nwhere E x,y represents the electric field distribution within the target plasmonic field profile and\nin ( )\nthe FDTD simulations.\n( )\nTo ensure a fair comparison between the two excitation schemes, the incident field in both cases is\nnormalized to a unit amplitude, and the colorbars in Fig. S1 represent the corresponding relative\nelectric-field magnitudes. This normalization allows the field distributions shown in Fig. S1A and\nS1B to directly reflect the efficiency with which each excitation configuration couples energy into\nthe plasmonic mode. As a result, the visible enhancement in the ring-shaped slit and inverse-\ndesigned configurations provides an intuitive comparison. The ring-shaped slit configuration\nachieves a coupling efficiency of approximately 12.3%, whereas our inverse-designed configuration\nachieves an efficiency of 18.5%.This enhancement is also evident in the increased intensity of the\nexcited plasmonic field. The efficiency can be further improved by generating a perfect radially\npolarized beam, which can enhance the trapping stiffness by compressing the energy into a thin ring\nthat satisfies the plasmonic coupling conditions [39].\nFig. S1 | Efficiency Comparison of a holographic plasmonic helix field excited by (A) structural and (B)\nstructureless methods.\nAdd Reference:\n39. X. Wang, Y. Zhang, Y. Dai, et al. Enhancing plasmonic trapping with a perfect radially\npolarized beam. Photonics Research. 6, 847 (2018).\nResponse to reviewer #2\nComment: I co-reviewed this manuscript with one of the reviewers who provided\nthe listed reports. This is part of the Nature Communications initiative to facilitate\ntraining in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts.\nWe sincerely thank the reviewer and the co-reviewer for their time and efforts in\nproviding valuable feedback.\nResponse to reviewer #3\nComment: This manuscript developed a method to generate plasmonic files on a\nmetal film without using pre-fabricated nanostructures. It also demonstrated an\nenergy flow control to control particles along the plasmonic intensity profiles. This\nwork is interesting and novel by providing a versatile and flexible platform for\ncontrolling nanoscale particles, which might be interesting for the many single\nparticle based quantum applications. I would recommend this paper to be\naccepted by Nature Communications.\nComment 1: In figure2, the comparison between the structureless method and the\nconventional methods is clearly shown. However, it would be better to have a\nquantitative comparison. For example, the author can define a FoM of the generated\npattern. How much do they differ? Or for some other particle trapping profile, to\nachieve similar trapping depth, how much input energy differs? A quantitative\ncomparison here might be interesting to see.\nReply 1: Thank you for this valuable suggestion. To provide a quantitative comparison\nbetween the structured and unstructured configurations, we define the coupling\nefficiency, , as the ratio of the optical power delivered into the target plasmonic mode\nto the total input laser power. The calculation is as follows:\n𝛽\n 2\n\n 0 (R1)\n 2\n E x y, dxdy\nin\nE x y, dxdy\nOur results show that the structured configuration achieves a focusing efficiency of\napproximately 12.3%, while the inverse-designed configuration attains 18.5%. The\nefficiency can be further improved by generating a near-ideal radially polarized beam,\nwhich enhances the longitudinal field at the focus and increases the plasmonic trapping\nstiffness [39]. In the revised manuscript, we have added the definition of , its\ncorresponding formula, and relevant references for clarity.\n𝛽\nCorrespondingly,\nLine 129-133, Page 5: “In the absence of structure-induced diffraction background, the pattern\nin Fig. 2E exhibits a significantly cleaner background and a higher excitation efficiency than that in\nFig. 2B. Quantitatively, we define the coupling efficiency β as the ratio of the power coupled into\nthe excited plasmonic field to the total input power (see Supplementary Note S2 for the formal\ndefinition). With this definition, the coupling efficiency of our inverse-designed configuration\nreaches 18.5%, exceeding that of the ring-shaped structural approach (12.3%) by 6 percentage\npoints, corresponding to a 50% relative improvement.”\nAdd supplementary Note S2.\nComparison of coupling efficiency.\nTo facilitate a clear and quantitative comparison between the ring-shaped slit and tightly focused\nreverse design configurations, we define the coupling efficiency, β, as the ratio of the power coupled\ninto the excited plasmonic field to the total input power, calculated as:\n 2\n\n0\n (S1)\n 2\n E x y, dxdy\nin\nE x y, dxdy\nWhere E x,y represents the electric field distribution within the target plasmonic field profile\n0\n( )\nand E x,y represents incident electric Field on the front surface of the gold film, both obtained\nin\nfrom the FDTD simulations. To ensure a fair comparison between the two excitation schemes, the\n( )\nincident field in both cases is normalized to a unit amplitude, and the colorbars in Fig. S1 represent\nthe corresponding relative electric-field magnitudes. This normalization allows the field\ndistributions shown in Fig. S1A and S1B to directly reflect the efficiency with which each excitation\nconfiguration couples energy into the plasmonic mode. As a result, the visible enhancement in the\nring-shaped slit and inverse-designed configurations provides an intuitive comparison. The ring-\nshaped slit configuration achieves a coupling efficiency of approximately 12.3%, whereas our\ninverse-designed configuration reaches 18.5%. This enhancement is also evident in the increased\nintensity of the excited plasmonic field. The efficiency can be further improved by generating a\nperfect radially polarized beam, which can enhance the trapping stiffness by compressing the energy\ninto a thin ring that satisfies the plasmonic coupling conditions [39].\nFig. S1 | Efficiency Comparison of a holographic plasmonic helix field excited by (A) structural and (B)\nstructureless methods.\nComment 2: In figure3, it was not clear to me why the simulation looks worse then the\ntheory, especially for the high-spatial-frequency patterns. Also, why does the\nexperimental results look worse than the simulation result? Is it due to misalignment of\nthe lenses?\nReply 2: Thank you for your thoughtful comment. In our method, the theoretical target\nplasmonic field is constructed as a superposition of plane waves, with the corresponding\ncomplex amplitude weights determined through an inverse-design procedure. During\nthe actual propagation of the plasmonic field, however, the Joule losses and other\ndissipative mechanisms inevitably distort these complex weights, resulting in\ndeviations between the simulated fields and the ideal theoretical patterns, especially for\nhigh-spatial-frequency components. To quantify these differences, we performed\nFDTD simulations of the designed fields and evaluate their consistency with the\ntheoretical targets using correlation coefficients.\nFor the experimental results, as you mentioned, misalignment of the optical elements\nis indeed one factor that affects the accuracy of the generated field. Although such\nerrors can be reduced by improving the positional accuracy of the optical components,\nthey remain a practical limitation. Additionally, the experimental optical system\ninherently behaves as a low-pass filter, suppressing high-frequency components and\nmaking it challenging to reproduce sharp features in the target field. This filtering effect\nfurther contributes to the discrepancies observed between the experimentally measured\nfields and simulated patterns.\nWe have added these discussions in the revised manuscript, correspondingly,\nLine 184-190, Page 7: “Furthermore, Table 1 shows that the FDTD results are slightly\ndegraded compared with the ideal theoretical values. This discrepancy mainly arises because\nthe plasmonic field in theory is constructed as a superposition of plane waves, whose complex\namplitude weights are prescribed by the inverse-design procedure. During the actual\npropagation of the plasmonic field, however, Joule losses and other dissipative mechanisms\ninevitably reshape these complex weights, leading to deviations between the simulated fields\nand the ideal target pattern, particularly in the high–spatial-frequency components.”\nComment 3: In the experiment, a gold particle was used. May I ask why using gold\nparticles? Is it because gold has a very strong plasmonic response? How does this\ntechnique apply for other particles with weaker plasmonic responses?\nReply 3:Thanks for this question. In this work, gold nanoparticles are chosen primarily\ndue to their strong absorption and scattering properties, which pose significant\nchallenges for trapping in conventional optical tweezers. Consequently, our results\nunderscore the advantages of the plasmonic approach we have developed. Importantly,\nour approach is not limited to metallic particles; it also holds for dielectric particles\nexhibiting considerably weaker plasmonic responses.\nAs illustrated in Figure R3, we add validation experiments using SiO₂ particles, which\ndemonstrate stable trapping and guided transport along the designed holographic\nplasmonic trajectory. These results confirm the generality and robustness of our\ntechnique across different particle types. These new experimental data have been\nincorporated into the revised manuscript and Supplementary Materials.\nFig. R3 |The corresponding experimental trajectory of the SiO₂ particles in the (A) Arc, and (B)Oval shaped\nplasmonic fields. Scalebars are 3 μm.\nCorrespondingly,\nLine 277-282, Page 11: “In addition to trapping metallic nanoparticles, our method is\nalso applicable to the micromanipulation of dielectric particles (see Supplementary\nNote S6). To demonstrate its generality, we further perform trapping experiments with\nSiO₂ microspheres, showing that these dielectric particles can likewise be guided along\ntrajectories prescribed by the holographic plasmonic fields. These results confirm the\nuniversality of our approach for microparticle trapping and transport.”\nAdd supplementary Note S6.\nExperimental Transport of Dielectric particles (SiO₂)\nBenefiting from the fine control of plasmonic energy flow, the holographic plasmonic tweezer\nsystem is not limited to metallic particles but is equally effective for dielectric particles. We\nadditionally performed trapping experiments on dielectric particles, which exhibit relatively weak\nplasmonic responses. In experiment, a diluted suspension of SiO₂ microspheres was dropped onto\nthe gold film. SiO₂ particles located near the potential wells were stably captured at the deepest\nvalley under the axial gradient forces, and then continuously transported along the designed\ntrajectories under the drive of the plasmonic energy flow, as shown in Fig. S4. It should be\nemphasized that the trapping power is also crucial for ensuring stable transportation. Considering\ndifferent trajectory lengths lead to variations in the locally distributed energy, the incident power\nwas set to 5 mW to balance trapping stability and transportation efficiency. Compared with metallic\nparticles, dielectric particles exhibit weaker scattering, which contributes to their higher stability\nduring transportation. These results confirm the generality and robustness of our technique across\ndifferent particle types.\nFig. S4 | The experimental trajectory of the SiO₂ particles in the (A) Arc, and (B)Oval shaped\nplasmonic fields. Scalebars are 3 μm.\nResponse to reviewer #4\nComment: The authors of the manuscript \"Structureless Excitation and\nManipulation of Dynamic Holographic Plasmonic Slides\" present a way to\nmanipulate the phase, intensity and properties of plasmon excited on a flat metal-\ndielectric interface, to produce a holographic image. I found the paper interesting\nand engaging, with the experimental results showing improvement on current\nmethods used. However, I'm unsure if the progress on the method is significant\nenough for publication in Nature Communications. I believe that this work will be\nmore suited in a more specialised journal, such as Nanophotonics.\nReply: We sincerely thank the reviewer for the time and effort dedicated to evaluating\nour manuscript and for acknowledging that the work is interesting, engaging, and\nexperimentally improves upon existing approaches. We appreciate the opportunity to\nclarify the broader impact and fundamental importance of our contribution.\nThe conventional plasmonic manipulation approaches rely on nanostructures, which\ninherently suffer from structural scattering, limited reconfigurability, and the inability\nto control key properties such as energy flow. These limitations have long restricted the\nfidelity and adaptability of plasmonic field engineering. In contrast, the present work\nfundamentally addresses these challenges by introducing an unstructured, reverse-\nengineered holographic excitation framework that enables an all-optical methodology.\nThis approach enables:\n1. the generation of high-fidelity plasmonic fields devoid of structural scattering and\nmode distortion;\n2. real-time reconfigurability of plasmonic profiles integrated with optomechanical\nfunctionality, representing a significant advancement toward scalable, and adaptive\nplasmonic systems;\n3.controllable energy flow driven by orbital angular momentum (OAM), capable of\ntransporting microparticles, thereby effectively realizing a structureless plasmonic\noptical tweezers.\nThis nanofabrication-free and reprogrammable platform transcends the limitations of\nstatic plasmonic configurations. To the best of our knowledge, this is the first\ndemonstration of dynamically reconfigurable, structure-free holographic plasmonic\nfields that support functional energy-flow manipulation. We believe that these\ndevelopments hold substantial potential for applications in precision manipulation, on-\nchip sensing, and reconfigurable photonics.\nNevertheless, I have a couple of points that the authors can improve on, before\nsubmitting the paper in a more specialized journal:\nComment 1: I'm a bit puzzled why the authors chose to do their experiments by\noptically trapping nanoparticles. Would a probe-tip not be a better choice, since it won't\nsuffer from Brownian motion which alters the scattered fields measured during the\nexperiment? Also, if the authors want to stick with optically trapped nanoparticles, then\nwhy not use dielectric ones that will induce less scattering that affects their results?\nReply 1: Thank you for your thoughtful and constructive comments. We address your\nquestions point by point below.\n(1) Why conduct experiments using optically trapped nanoparticles, instead of using a\nprobe tip for field mapping?\nOptical manipulation at the nanoscale has become increasingly important as advanced\nmanufacturing, chip-level processing, and life sciences continue to progress toward\nsmaller length scales. Plasmonic optical tweezers are particularly attractive in this\ncontext because the near-field confinement of surface plasmon polaritons enables\nsignificantly stronger gradient forces and weaker scattering forces compared with\nconventional free-space tweezers. However, this very advantage of plasmonic near\nfields also imposes a fundamental limitation: their confinement to the metal surface\nmakes flexible modulation extremely challenging. Consequently, previous plasmonic\ntweezers have only demonstrated relatively simple trapping and translation operations.\nThe central contribution of our work lies not only in the creation of a structureless\nholographic plasmonic field, but also in demonstrating that such engineered fields can\nsubstantially expand the manipulation capabilities of nanoparticles, enabling functions\nthat were previously inaccessible in plasmonic-field-based optical manipulation. The\nuse of gold nanoparticles highlights the capability of our method to achieve complex\nand dynamic trapping in a highly challenging regime.\nIt is important to clarify that the field-mapping experiment is conceptually distinct from\nthe optical-tweezing experiment, and is specifically designed to verify that we indeed\ngenerate the desired holographic plasmonic field. In the field-mapping measurements,\nthe gold nanoparticle is immobilized on the substrate and therefore does not undergo\nBrownian motion. By analyzing the scattered field from this stationary nanoparticle,\nwe reconstruct the spatial distribution of the holographic plasmonic field, following the\nprocedure described in Ref. [25]. In contrast, in the optical-tweezing experiments, the\nnanoparticles are freely trapped and transported by the engineered plasmonic field in a\nliquid environment.\nWe fully agree that a probe-tip-based near-field method could also be used to measure\nholographic plasmonic fields. Here, we chose not to adopt this approach primarily for\nreasons of system compatibility and experimental simplicity. The stationary-\nnanoparticle field-mapping method can be implemented within the same optical\nplatform as the plasmonic tweezers, without adding a separate near-field probe system.\nThis integration allows us to characterize and manipulate the holographic plasmonic\nfield in a unified setup, which is more practical and robust for the purposes of this work.\n(2) Why not use dielectric particles for trapping?\nGold nanoparticles exhibit strong absorption and scattering, resulting in significant\nscattering forces that make them difficult to trap using traditional free-space optical\ntweezers. Therefore, demonstrating stable trapping of these challenging particles\nprovides clear validation of the enhanced capabilities offered by our holographic\nplasmonic platform.\nThat said, our method is equally applicable to dielectric particles. To demonstrate this\ngenerality, we have included experimental results using SiO₂ microspheres, which\nexhibit stable trapping and guided transport along the designed holographic plasmonic\ntrajectory (see Fig. R4 and Supplementary Video). These results confirm that the\ntechnique is robust for both metallic and dielectric particles.\nFig. S4 | The corresponding experimental trajectory of the SiO₂ particles in the (A) Arc, and (B)Oval shaped\nplasmonic fields. Scalebars are 3 μm.\nWe appreciate this comment for highlighting aspects that were not sufficiently\nemphasized in the original manuscript, particularly the significance of optical trapping.\nIn the revised version, we have updated the title, abstract, and introduction to clarify\nthe role and importance of plasmonic-field-based optical manipulation. Additionally,\nwe have included the SiO₂ trapping experiments in the supplementary materials.\nCorrespondingly,\nLine 277-282, Page 4: “In addition to trapping metallic nanoparticles, our method is also\napplicable to the micromanipulation of dielectric particles (see Supplementary Note S6). To\ndemonstrate its generality, we further perform trapping experiments with SiO₂ microspheres,\nshowing that these dielectric particles can likewise be guided along trajectories prescribed by\nthe holographic plasmonic fields. These results confirm the universality of our approach for\nmicroparticle trapping and transport.”\nLine 407-414, Page 16: “In this work, we perform two types of experiments: a field-\nmapping measurement to verify the generation of the holographic plasmonic field, and an\noptical-tweezing experiment to demonstrate its applicability to nanoparticle manipulation.\nBoth experiments share the same optical setup; the main difference lies in the role of the\nnanoparticle. In the field-mapping experiment, the particle is immobilized on the metal film\nand used as a nanoscale probe that scatters the holographic plasmonic field for reconstructing\nits spatial distribution25. In the optical-tweezing experiment, the particle initially undergoes\nunrestricted motion within a liquid medium before being confined and manipulated by the\nholographic plasmonic field.”\nAdd supplementary Note S6.\nExperimental Transport of Dielectric (SiO₂) Microparticles in Holographic Plasmonic Fields\nBenefiting from the fine control of plasmonic energy flow, the holographic plasmonic tweezer\nsystem is not limited to metallic particles but is equally effective for dielectric particles. We\nadditionally performed trapping experiments on dielectric particles, which exhibit relatively weak\nplasmonic responses. In experiment, a diluted suspension of SiO₂ microspheres was dropped onto\nthe gold film. SiO₂ particles located near the potential wells were stably captured at the deepest\nvalley under the axial gradient forces, and then continuously transported along the designed\ntrajectories under the drive of the plasmonic energy flow, as shown in Fig. S4. It should be\nemphasized that the trapping power is also crucial for ensuring stable transportation. Considering\ndifferent trajectory lengths lead to variations in the locally distributed energy, the incident power\nwas set to 5 mW to balance trapping stability and transportation efficiency. Compared with metallic\nparticles, dielectric particles exhibit weaker scattering, which contributes to their higher stability\nduring transportation. These results confirm the generality and robustness of our technique across\ndifferent particle types.\nFig. S4 | The corresponding experimental trajectory of the SiO₂ particles in the (A) Arc, and (B)Oval shaped\nplasmonic fields. Scalebars are 3 μm.\nComment 2: I'm not sure how the authors match the momentum of the incident beam\nwith propagating SPP modes. From Fig.2, it seems that they always excite with normal\nincidence. I understand in Fig2A that there is a nanoring slit that allows for this\nmomentum matching for certain part of the incident normal beam. But how do the\nauthors manage to achieve a better momentum match in fig.2D (and future\nconfigurations in the paper)?\nReply 2: Thank you for raising this important question. It is well known that the in-\nplane momentum of an SPP exceeds that of light in free space, and therefore additional\nmomentum compensation is required for efficient excitation. Several common\nwavevector-matching mechanism as follows.\nThe first configurations is prism-based coupling. The classical Otto and Kretschmann\nconfigurations, introduced in 1968, compensate the in-plane momentum by tuning the\nincidence angle(Fig. R5a-b) [Zeitschrift für Naturforschung A. 23, 2135-2136 (1968);\nZeitschrift für Physik A Hadrons and nuclei. 216, 398-410 (1968)]. This scheme is\nsimple and efficient, However, the propagating SPP diverge along the metal surface\nand do not generate sufficiently strong optical gradient force, this approach has long\nbeen considered unsuitable for optical trapping.\nSecond, surface plasmons can also be excited by near field scattering by a tip near a\nmetal surface (Fig. R5d), such as by particles or nanometre-sized scatters on a surface\n(Fig. R5e). Since near-field scatterers have a wide spatial frequency spectrum, there are\ncomponents that will satisfy the matching conditions required to excite the SPP. This\napproach is simple but often inefficient because only a small fraction of the scattered\nlight contributes to excitation. To enhance efficiency, periodic gratings are often\nintroduced. They supply defined spatial frequency components that mix with the\nincident light and create strong momentum components matching the SPP wavevector\n(Fig. R5f). The fixed nature of nanostructures greatly limits the dynamic modulation of\nthe excited plasmonic field. In addition, imperfections in the structures can introduce\nextra scattering, leading to a reduction in the intensity of the desired optical field.\nIn our system, a high-NA objective produces a continuum of incident wavevectors\naround the nominal optical axis (Fig. R5c). When the metal film is positioned\nbefore the focal plane, only the annular portion of the illumination that meets the\nsurface-plasmon resonance (SPR) angle contributes to coupling. This annular\nband functions similarly to the ring illumination used in prism-based schemes: it\nselectively concentrates optical power near the required in-plane momentum while\nsuppressing direct transmission through the metal. The excited SPP then act as\nsecondary circular wave sources that propagate inward and coherently interfere to form\na strong central convergence point Ref. [5] & [Optics letters. 37,4627-4629 (2012)].\nThis coupling mechanism is directly responsible for the improved momentum matching\nobserved in Fig. 2D and subsequent configurations. The designed holographic\nstructures reshape the spatial phase of the incident field so that the high-NA objective\npreferentially redistributes energy into the angular components that most efficiently\nsatisfy the SPP dispersion relation. As a result, this configuration inherently provides\nthe in-plane momentum required for efficient excitation of surface plasmons, while\neliminating fabrication-related constraints and maintaining high excitation efficiency.\n[Plasmonics. 13, 991-996 (2018)]. Furthermore, this efficiency can be improved by\nemploying perfect radially polarized beams, by compressing the energy into a thin ring\nthat satisfies the plasmonic coupling conditions.[Photonics Research. 6, 847-852\n(2018)].\n[editorial note: figure redacted]\nFig. R5 |Configurations for SPP wavevector matching. [Light-Sci. Appl. 10, 59 (2021)]\nCorrespondingly,\nLine 75-77, Page 3: “Principles. To generate a holographic plasmonic field, as illustrated\nin Fig. 1A, a specifically designed incident light field is utilized in a tight focusing system to\nilluminate a smooth metallic thin film. The high-NA focusing system provides large incident\nangles, so that the in-plane wave-vector components satisfy the required wave-vector\nmatching condition for plasmon excitation5. In our approach, the incident light field is\nproduced with a reversal design algorithm, which enables the precise control of the formed\nplasmonic field as desired. ...”\nComment 3: The first sentence of the introduction is not technically correct. The\npropagating SPPs on metal-dielectric interfaces are eigenmodes, which means that they\nare always there. One does not need to illuminate the interface with light for the\nevanescent modes to emerge. But one needs external illumination to couple light into\nthese modes, which is what I believe the authors were trying to communicate?\nReply 3: Thank you for the clarification. We agree with the reviewer’s statement that\nSPP at a metal–dielectric interface are eigenmodes that inherently exist without external\nillumination. In the revised manuscript, we have corrected the introductory sentence\naccordingly to accurately reflect this physical concept.\nCorrespondingly,\nLine 27-31, Page 1: “Surface plasmons are electromagnetic eigenmodes bound to\nmetal–dielectric interfaces, with evanescent fields that decay away from the surface¹.\nBy coupling incident light into these surface modes under appropriate wave-vector\nmatching conditions, one obtains a propagating plasmonic wave that runs along the\ninterface and remains tightly confined near it, effectively forming a near-field optical\n“belt”²-⁴. ”\nComment 4: Terms like \"stray signals\" or \"stray light\" are not proper scientific\nterminology. This light/signal comes from diffraction, and one should say this.\nReply 4: Thank you for your comment. To improve scientific accuracy, we have used\nthe “diffraction components” in the revised manuscript.\nCorrespondingly,\nLine 14-16, Page 2: “However, holographic plasmonic fields are usually realized with\ncomplex nanostructures, introducing diffraction background and limiting flexibility and\ndynamic reconfigurability.”\nLine 48-50, Page 2: “Primarily, the metallic nanostructures introduce unavoidable\ndiffraction components and significant energy losses, which detract from the fidelity of the\ngenerated plasmonic field20.”\nLine 116-118, Page 4: “Furthermore, the diffraction background induced by the structure\nsignificantly degrades the signal-to-noise ratio and accuracy of the generated plasmonic field.”\nLine 127-128, Page 4: “In the absence of structure-induced diffraction background, the\npattern in Fig. 2E exhibits a significantly cleaner background and a higher excitation efficiency\nthan that in Fig. 2B. ”\nComment 5: Line 53: \"Some other properties, such as energy flow, are challenging to\nmanipulate according to desired patterns, ...\" Why is this the case? What is stopping\ncurrent methods to do this?\nReply 5: Thank you for your comment. Controlling the energy flow distribution is\ninherently more challenging because it requires precise manipulation of both amplitude\nand phase. Current limitations in micro- and nano-fabrications introduce unavoidable\nstructural deviations that generate diffraction and background crosstalk, making it\ndifficult to accurately reproduce the target phase distribution. Moreover, most current\nSPP modulation schemes rely solely on phase control[Nano Letters, 17, 7920(2017);\nSci. Adv. 4, eaao0533 (2018); Nat. Commun. 6, 8360 (2015), whereas our inverse-\ndesign approach enables full complex-amplitude modulation. To the best of our\nknowledge, this work is the first experimental demonstration of controlled trajectory\ntransport of small structures using plasmonic tweezers.\nCorrespondingly,\nLine 53-56, Page 2: “Some other properties, such as energy flow, are challenging to\nmanipulate according to desired patterns because the diffraction background perturbs the\nphase of the plasmonic field12,19-21. These properties are particularly important for the\nmodulation of on-chip optical energy and particle transmission.”\nAdd Reference:\n21. P. R. Huft, J. D. Kolbow, J. T. Thweatt, N.C. Lindquist, Holographic plasmonic nanotweezers\nfor dynamic trapping and manipulation. Nano Letter. 17, 7920(2017).\nComment 6: I'm not sure what is a toroidal orbital angular momentum. It would be\nconvenient for the reader if the authors defined what they mean by it.?\nReply 6: Thank you for your insightful comment. We apologize for any possible\nconfusion caused by the use of the term “toroidal orbital angular momentum (OAM)”\nin the original manuscript, as it may be mistaken for toroidal vortices or toroidal dipoles\nin other contexts. In our work, the inverse-design approach reshapes the OAM\ndistribution into a ring-shaped pattern, generating a circular in-plane energy flow on the\nplasmonic surface. To avoid confusion, we have replaced “toroidal OAM” with “ring-\nshaped OAM” throughout the revised manuscript.\nCorrespondingly,\nLine 62-63, Page 2: “ Furthermore, it is demonstrated that by loading the ring-shaped\norbital angular momentum (OAM) onto the incident light,...”\nComment 7: What is the asterix on I1* in table 1? It is never explained, or if it is I\nmissed it completely.?\nReply 7: Thank you for pointing out this issue. The asterisk (“*”) appearing after I₁ in\nTable 1 was an inadvertent typographical error and does not indicate any special\ncondition or footnote. There is no corresponding explanation in the text. In the revised\nmanuscript, we have removed the asterisk to avoid confusion and ensure consistency.\nCorrespondingly,\nLine 191, Page 7:\nTable 1 | Quantitative analysis of the holographic plasmonic OAM belts\nCorrelation index I / I I /I I /I\n1 0 2 1 3 1\nγ 0.9390 0.9874 0.8445\nOval\nη 0.8255 0.8276 /\nγ 0.9243 0.9438 0.8873\nArc\nη 0.8493 0.8108 /\nγ 0.9335 0.9406 0.7747\nHelix\nη 0.8191 0.7573 /\nCycloid γ 0.8011 0.7804 0.5831\nη 0.6578 0.5649 /\nComment 8: There are a 3-4 places that the language and grammar can be improved.\nFor example:\nline 121 \"Fig.2E is significantly clean with higher excitation...\" should probably be:\n\"Fig.2E is significantly more clean with higher excitation...\"\nline 175 \"This imperfect is mainly...\", should probably be : \"These imperfections are\nmainly ...\"\n.?\nReply 8: Thank you for pointing out these language issues. The highlighted phrases\nhave been corrected in the revised manuscript. In addition, we have also carefully\nreviewed the manuscript for comparable grammatical and stylistic concerns, and the\nwording has been refined in multiple sections to enhance clarity and readability. All\nmodifications are highlighted in the revised version.\nResponse to the Decision Letter\nREVIEWERS' COMMENTS\nReviewer #1 (Remarks to the Author):\nThe authors have satisfactorily addressed all of our comments. We recommend\naccepting the revised manuscript in its current form.\nResponse: We thank the reviewer for the positive assessment and recommendation.\nWe appreciate your careful review and are pleased that our revisions have fully\naddressed your comments.\nReviewer #2 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed\nreports. This is part of the Nature Communications initiative to facilitate training\nin peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts.\nResponse: We sincerely thank the reviewer for their contribution and for\nparticipating in this peer-review training initiative. We appreciate the effort and\nthoughtful evaluation of our work, and we are grateful for the support of this\ninitiative.\nReviewer #3 (Remarks to the Author):\nI appreciate the authors' responses and revisions. All of my previous questions and\ncomments haven been addressed, and the manuscript is now complete and clear. I\nwould recommend the paper for publication.\nResponse: We sincerely thank the reviewer for the encouraging feedback. We are\nglad that the revisions addressed all of your previous questions and comments, and\nwe appreciate your recommendation for publication.\nReviewer #4 (Remarks to the Author):\nThe authors improved the manuscript significantly and answered my questions\nwell. I'm happy to accept now the paper for publication in Nature\nCommunications.\nResponse: We thank the reviewer for the positive evaluation. We appreciate your\nrecognition of the improvements and are grateful for your support of publication."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have satisfactorily addressed all of our comments. We recommend accepting the revised manuscript in its current form.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "I appreciate the authors' responses and revisions. All of my previous questions and comments haven been addressed, and the manuscript is now complete and clear. I would recommend the paper for publication.", "reviewer_4": "The authors improved the manuscript significantly and answered my questions well. I'm happy to accept now the paper for publication in Nature Communications."}, "author_response": ""}]

Decision letter