GHz dynamic holographic VCSEL chip via current-addressed modes multiplexing

Domain: physics
Published: 2026-01-29
Editorial outcome: major_revision

Abstract
The intuitive wisdom in semiconductor laser engineering dictates that high-order spatial modes of vertical-cavity surface-emitting lasers (VCSELs) must be suppressed to preserve beam quality, despite their inherent potential as independent information carriers. Here, we develop current-addressed modes multiplexing holography in multimode VCSELs, where injection current-dependent dominant orbital angular momentum (OAM) components enhance information channel capacity and enable dynamic reconfigurability of holographic systems. Crucially, monolithic integration of laser-nanoprinted multiplexed holograms with VCSEL chips resolves the persistent contradiction between dynamic light-field manipulation and miniaturization of holographic optoelectronic systems. Experimental validation shows that a 2×2 chip array (unit area: ~100×100 μm2) enables dynamic 3D display with an ultra high refresh rate of ~1.93 GHz. To our knowledge, this represents the fastest holographic switching speed and most compact chip-scale system reported to date. This work establishes a platform for portable and wearable devices, ultra-high-speed short-reach interconnects, virtual and augmented reality systems with minimized latency.

Introduction
Holography provides an approach to record and reconstruct three-dimensional (3D) wavefronts of objects1, which can be implemented in various fields, including displays, imaging2, data storage3, optical communications4, information encryption5, and neuromorphic photonic computing6. To facilitate the practicality and adaptability of these applications in chip-scale, recent advancements have focused on miniaturization and dynamic switching capability of holographic systems7,8. Spatial light modulators (SLMs) and digital micromirror devices (DMDs), combined with external laser sources, have been traditionally employed for dynamic wavefront manipulation. Nonetheless, both the complex addressing circuits embedded in these digital holographic devices and the bulky size of lasers impose fundamental challenges to achieve on-chip integration. This hinders the development of emerging wearable and portable holographic information processing products.

To address this problem, incorporating integrated light sources with diffractive optical elements (DOEs) has been proven as a promising compact and versatile photonic systems9. In this context, vertical-cavity surface-emitting lasers (VCSELs) have attracted tremendous attention10–12. Such semiconductor lasers, with an epitaxial active layer and distributed Bragg reflectors (DBRs) to form the laser gain medium and resonant cavity, feature unique advantages including micron-scale size, two-dimensional (2D) array format, planar emitting surface, and high modulation speeds (above GHz). By further leveraging advanced micro- and nano-fabrication techniques (such as electron beam lithography and 3D laser nano-printing), optically digitalized holograms13 can be directly integrated onto the emitting surface of VCSELs to modulate the wavefront and the polarization states of output beams14–17, which can significantly reduce the size of holographic systems. Unfortunately, as the overall area of hologram is limited by the small emitting surface of VCSELs, the sub-micro- or nano-scale pixel resolution hinder the layout of addressing circuits to obtain an optoelectronic device for dynamic light-field control.

Other pioneering methods to dynamically manipulate the optically digitalized holograms have also been proposed, such as chemical reactions18, optical erasure and rewriting19, mechanical stretching20, twisting cascaded holograms21, and thermal regulation22. Nevertheless, additional components or steps often slow down the switching frame rate and increases system complexity, which make them inapplicable for VCSEL-integrated systems. Recently, the physical dimensions of light, such as wavelength23, polarization24, space25, time26, and modes27, have been utilized to increase the information channels of optically multiplexed holograms. To be specific, optically addressable dynamic holography can be realized by selectively controlling the properties of the input and output beams28. Therein, spatial modes multiplexing is particularly promising in boosting information channel capacity due to its theoretically infinite states. Notably, since the transverse dimension of the active region is much larger than its longitudinal length, multi-mode VCSELs usually operate in multiple transverse spatial modes, which can even be switched by adjusting the injection current29. As such, we exploit this fact to encode various holographic information channels into distinct transverse spatial modes from a multi-mode VCSEL and multiplex them into an optically digitalized hologram. Consequently, dynamic holography can be achieved by elaborately manipulating the injection current-dependent spatial modes.

Here, we develop a dynamic holographic VCSEL chip by integrating a multi-mode VCSEL with a current-addressed mode-multiplexed optically digitalized hologram. The principle to design such an ultra-compact holographic system with ultra-high switching frame rate is illustrated in Fig. 1. The lack of precise physical models of the output electrical fields from multi-mode VCSELs render it difficult to design the spatial mode-multiplexed hologram. To overcome this challenge, the orthogonal orbital angular momentum (OAM) states have been utilized to encode holographic images30 owning to the well-defined injection current-dependent OAM modes weighting coefficient spectrum (Fig. 1a). To minimize the channel crosstalk in optical multiplexed holography, the dominant OAM mode components characterized by the largest weighting coefficients (l 1, l 2, l 3 and l 4 in Fig. 1a) are selected in the design of the OAM-multiplexing hologram. In this regard, only a spatial mode state with a dominant OAM component (e.g., l 2 in Fig. 1b), given by the multi-mode VCSEL at a specific injection current, selectively reconstructs the target holographic image with a stronger Gaussian intensity profile at each pixel. Notably, the hologram can be directly integrated onto the VCSELs’ surface using 3D laser nano-printing (Fig. 1c), which further enables a holographic VCSEL chip comprising hologram arrays (Fig. 1d). As such, a dynamic holographic display can be achieved by varying the injected currents of each device over time sequences. Compared with other schemes5,25,28,31, our strategy illustrates a compact, all-in-one holographic system (including laser source and holographic devices) with only hundreds of microns. Moreover, the high-speed modulation capabilities of VCSELs allow theoretical frame rates exceeding 109 frames per second (Fig. 1e).

Results
OAM mode dynamics in multimode VCSELs
The physical mechanism of injection current-dependent OAM modes weighting coefficient spectra dynamics in multimode VCSELs is revealed in Fig. 2. Here, we explore the OAM mode components of VCSEL beams using the fiber model. Throughout this manuscript, oxidation-confined, top-emitting VCSELs emitting at ~905 nm have been employed, whose epitaxial structure mainly includes p-DBR, active region, n-DBR, and GaAs substrate (Fig. 2a). The fundamental properties of these VCSELs, including their spectral characteristics, I–V behavior, and lifetime, are presented in Supplementary Fig. 1–3 (“Methods”), respectively. In this context, the oxide aperture diameter (d) denotes the unoxidized region in the oxidized layer. The refractive index (n 2) of the oxidized region is lower than that of the unoxidized region (n 1), forming a cylindrical waveguide structure. In this model, the unoxidized central current aperture serves as the waveguide core, while the oxide confinement layer acts as the cladding. By computing the refractive indices across all epitaxial layers, an average cladding–core index difference of approximately 0.01 can be obtained32,33. As a result, using the weak-guidance approximation, a specific OAM mode state in VCSELs can be investigated by combining degenerate odd and even LPlm modes with phase differences of π/2 or 3π/2 (i.e., OAM ±l = LPlma ± i × LPlmb )34. Here, l and m denote the azimuthal (OAM order) and radial indices, while a and b indicate the degenerate odd and even LPlm modes, respectively. Notably, only the LPlm modes with m = 1 are considered owning to the degradation of higher-order LP modes in propagation. Next, represented by the LP modes with the same OAM mode order l, the OAM modes capacity of multi-mode VCSELs with different oxide aperture sizes have been analyzed in detail. For this purpose, the normalized frequency (V) determined by the oxide aperture diameter (d) in VCSELs has been calculated, which indicates the number of guided wave modes supported in such fiber model (Supplementary Note 1). Moreover, to figure out each particular guided LP modes, the longitudinal normalized propagation constant (β) representing the axial component of the light wave vector are constrained to be positive. As such, the VCSELs with larger oxide aperture sizes can support more OAM modes (Fig. 2b), laying the physical foundation for providing potential information channels in OAM multiplexing.

To further explore the injection current-dependent OAM modes competitions in multi-mode VCSELs, current density spatial distributions in the active layer and the resultant OAM modes components at various injection currents have been both studied based on the epitaxial structure and doping concentration (Supplementary Table 1). As shown in Fig. 2c, while the charge carrier distribution exhibits a Gaussian profile at a low injection current for the VCSEL with a 4 μm-diameter oxide aperture, depleting carriers can be observed at the center with the increase of the current and the aperture size, which is termed the spatial hole burning (SHB) effect35,36. The right inset of Fig. 2c illustrates a significant SHB phenomenon, which can be attributed to the preferential current flow along the annular edges of the VCSEL with a lower electrical resistance in accordance with Kirchhoff’s law. Notably, the gains of each OAM mode are determined by continuously changing current densities, giving rise to the injection current-dependent OAM modes weighting coefficient spectra (Supplementary Note 2 and Supplementary Table 2). Simulating VCSELs with large oxide apertures is challenging due to increased computational complexity and potential modeling errors. In addition, devices with different aperture sizes are equivalent in revealing the principles of mode dynamics. Thus, without losing generality, we experimentally and theoretically investigated the weighting coefficients of OAM components with l = 1 and 2 for the VCSEL with a 6 μm-diameter oxide aperture (Fig. 2d). The theoretical results (the inset is the enlarged dashed box) suggests that the dominant OAM component switches from l = 1 to l = 2 at an injection current of ~10 mA, which is consistent with the experimental result.

Current-addressed mode-multiplexed holography
Implementing such current-dependent dominant OAM components for the design of an OAM-multiplexing hologram can enable current-addressed dynamic holographic displays. The schematic to measure the OAM mode components of the output electrical field provided by the VCSEL with a 30 μm-diameter oxide aperture is illustrated in Fig. 3a, wherein different spiral phase plates (SPPs) were adopted to achieve inverse OAM mode conversion (“Methods”, Supplementary Fig. 4). As an example, the intensity distributions at the focal plane are given when the injection current is 28 mA, revealing the OAM modes weighting coefficient spectrum through the integrations of preset Gaussian profile areas (Fig. 3b). Notably, the OAM mode with l = 25 is a dominant component with the largest weighting coefficient. Next, the injection current was changed within the VCSEL’s working range (Supplementary Fig. 5), leading to diverse weighting coefficient distributions of the eight OAM modes with l = 22-29 (Fig. 3c). Supplementary Movie 1 directly visualizes the evolution of the light field under stepped current modulation, revealing the injection current–dependent spatial mode behavior of the VCSEL. To reduce the crosstalk in optical multiplexed holography, we elaborately propose an enumeration algorithm to identify distinct encoding OAM modes weighting coefficient spectra that feature a distinguishing largest weighting coefficient (Fig. 3d). The algorithm involves two main steps. First, the measured OAM weighting coefficients spectra are grouped, with each group containing four OAM mode components featuring distinct dominant OAM components. Second, the groups are evaluated to determine the one where the dominant OAM components show the greatest disparity in weighting coefficients compared to the other components within each spectrum. Hence, for the spatial modes obtained at four specific working currents (I = 101, 67, 28, and 58 mA) (Supplementary Fig. 6), the OAM modes (l = 23, 24, 25, and 26) have been regarded as the dominant OAM components in our scheme (Fig. 3c).

The design of the OAM-multiplexing hologram is illustrated in Fig. 4a (Supplementary Note 3). The Fourier holograms of four frames from a rotating windmill video are encoded by helical phase plates with OAM orders of l = −25, −26, −24, and −23, then being superposed into the final OAM-multiplexing hologram. As a result, as the four selected injection currents (I = 28, 58, 67, and 101 mA) switched at fixed time intervals, the target holographic images with an average peak signal-to-noise ratio (PSNR) exceeding 18.8 dB can be dynamically reconstructed by selectively recovering the Gaussian mode pixels (Fig. 4b). In comparison to the low-quality images reconstructed by beams generated by the same VCSEL at the other randomly selected injection currents, the improvement of the average signal-to-noise ratio (SNR) suggests the effectiveness of the enumeration algorithm mentioned above (Supplementary Fig. 7). In addition, a spatial division scheme has been adopted in the design of the OAM-multiplexing hologram of a micro-quick response (MQR) code image, which leads to a current-shared holographic encryption. To construct the hologram, the MQR code image is divided into four sections, and sampled with a comb function (Fig. 4c). Then, the Fourier holograms are encoded with the selected helical phase plates (l = −25, −26, −24, and −23), resulting in an OAM-multiplexing hologram. Therefore, after combining and binarizing the four reconstructive images obtained under the four selected injection currents, the complete MQR code image is obtained (Fig. 4d). Scanning the MQR code reveals the encrypted message “HelloWorld”.

Ultra-compact holographic VCSEL chip with ultra-high frame rate
By directly printing OAM-multiplexing holograms onto the surface of the VCSEL (Methods, Supplementary Fig. 8), we successfully demonstrate a dynamic holographic VCSEL chip using the above-mentioned current-addressed modes multiplexing holography (Fig. 5). To experimentally characterize the performances of the chips, an on-chip measurement system has been developed (Fig. 5a), wherein the VCSEL chip was powered via a metal probe that directly contacted the p-electrode (inset in bottom right). When the currents were switched, independent holographic images can be observed in the charge-coupled device (CCD) camera (inset in upper right). In our scheme, four VCSELs with oxide aperture diameters of 8 μm, 10 μm, 12 μm, and 14 μm have been selected as the light sources to construct a device array (Fig. 5b and Supplementary Fig. 9). Considering the divergence angles of the VCSELs and the printed holder height (150 μm), the hologram size was set as 100 μm × 100 μm with a pixel size of 1 μm × 1 μm to ensure optimal illumination of each hologram (inset in bottom left). Notably, 8-level transmission-type phase modulation was adopted through controlling the height of each pixel pillar (inset in bottom right).

For holographic encoding in OAM multiplexing holography, two dominant OAM states at specific injection currents have been employed for each holographic VCSEL chip, respectively. Consequently, by switching the injection currents on each VCSEL (from 9 mA, 16 mA, 23 mA, 23 mA to 19 mA, 9 mA, 27 mA, 32 mA), the dynamic holographic display (from “HOLO” to “GRAM”) can be obtained (Fig. 5c). Moreover, the current-addressed dynamic holographic display can be extended to 3D images by incorporating lens functions with varying focal lengths, thereby leveraging the depth information of the image along the light propagation direction (Supplementary Fig. 10). As such, when the holographic VCSEL chip was given as 10 mA or 18 mA, independent switchable images (Arabic number images “2, 0” or “0, 4”) can be observed at separate image planes at a propagation distance of z = 215 μm and 495 μm (Fig. 5d and Supplementary Fig. 11). Notably, the modulation response-frequency curve of the VCSEL chip illustrates that the refresh rate of the dynamic holographic display can reach up to ~1.93 GHz (Fig. 5e and Supplementary Fig. 12, “Methods”). We also conducted standard measurements of the frequency-dependent properties of the used VCSEL (Supplementary Figs. 13–15, Methods), which show that its bandwidth reaches up to 3 GHz. The gap between this bandwidth and the observed holographic refresh rate is mainly due to differences in the testing methods. These results indicate that further improvements in the packaging of the VCSEL holographic chip may support even higher refresh rates. Additionally, a diffraction grating hologram was printed onto the surface of the VCSEL to evaluate the diffraction efficiency of such an optical digitalized hologram. The diffraction efficiency is quantified by the ratio of the intensity of the +1-order diffraction spot to the total output intensity of the VCSEL. The result indicates the final average modulation efficiency of 44.68%, which is determined by the grating diffraction efficiency and the transmission efficiency of the substrate (Supplementary Fig. 16).

Methods
COMSOL multiphysics simulation
We used COMSOL Multiphysics 6.2 to calculate the current density distribution shown in Fig. 2c. First, we defined the global parameters, including both structural and material parameters, based on the epitaxial structure of the VCSELs (Supplementary Table 1). Using rotational symmetry modeling, we constructed the geometry of the VCSEL and assigned the appropriate materials to each region. The VCSEL diameter was set as the oxide aperture diameter plus 11 μm, and the inner diameter of the annular p-contact was set as the oxide aperture diameter plus 3 μm, following the device specifications. Next, we discretized the structure to enable an efficient and accurate solution of the physical field. A direct band gap spontaneous emission light transition model was applied, and the steady-state solutions were obtained through voltage sweeps and semiconductor equilibration. Finally, we analyzed the current distribution by examining a two-dimensional cross-section, located 50 nm above the active region, under different voltage conditions.

Optical setup for the measurement of OAM components weightings spectra of VCSELs and the current-addressed holographic video
To measure the OAM components weightings spectra of VCSELs and obtain the current-addressed holographic video, the conceptual illustration and the practical optical setup can be found in Fig. 3a and Supplementary Fig. 4, respectively. The VCSEL operates under continuous-wave conditions. After supplying power on the VCSEL, a ×10 objective lens was utilized to modulate the divergence angle of the light beams. Then, a half-wave plate in combination with a polarization beam splitter was employed to control the intensity of horizontal-polarized light beams continuously. After that, the beams illuminated on the spatial light modulator (SLM, model: PLUTO-NIR-010-A) and a CCD camera (model: Basler, acA2040-90uc) was put on the focal plane to capture the reconstructed holographic images. The OAM-multiplexing hologram in Fig. 4a and the helical phase plates with different OAM orders were imprinted on the SLM, respectively.

Laser nanoprinting of the holograms on the surfaces of the multimode VCSELs
A commercial photolithography system (Photonic Professional GT, Nanoscribe GmbH), equipped with a 780 nm, 80 MHz femtosecond laser, was used for printing. The process was conducted in a dip-in galvo-scan-mode configuration, utilizing the two-photon resist IP-Dip and a high numerical aperture objective lens (Plan-Apochromat 63x/1.40 Oil DIC, Zeiss). The printed structure consists of three key components: four supporting pillars (20 μm × 20 μm × 140 μm each), a supporting table (120 μm × 120 μm × 10 μm), and the holographic plates (100 μm × 100 μm).

The specific structural parameters are listed below. For the pillars, the slicing distance (step size in the longitudinal direction) was set to 0.5 μm, and the hatching distance (step size in the transverse direction) was set to 0.2 μm to optimize printing speed. For the table, the slicing distance remained at 0.5 μm, but the hatching distance was reduced to 0.05 μm to ensure a flat surface, as the laser beam must pass through it. The hologram height was 150 μm, and the slicing distance for the holograms was set to 0.226 μm, corresponding to a phase modulation of π/4 for the 905 nm VCSELs, with a hatching distance of 0.05 μm.

The detailed printing process is illustrated in Supplementary Fig. 8. The optimized printing parameters were as follows: 52 mW laser power and 20000 μm/s scanning speed for the pillars, 46 mW and 20000 μm/s for the table, and 40 mW and 10000 μm/s for the holograms. After printing, the samples were developed by immersion in propylene glycol 1-monomethyl ether 2-acetate for 30 min, followed by rinsing in isopropanol for 5 min. The devices were then air-dried through evaporation.

Characterization of the holographic VCSEL chip
As shown in Supplementary Fig. 12, the frequency response of the VCSEL holographic chip was characterized using a vector network analyzer (Rohde & Schwarz ZNLE14). Here, VCSEL_2 in Fig. 5c was selected for testing and connected to the PCB via gold wire bonding, with external linkage to the driver power supply. First, harmonic modulation signals from the network analyzer were used to cyclically switch the injection current of VCSEL_2 between 9 mA and 16 mA, inducing periodic variations in the energy of each pixel featuring a Gaussian mode in the reconstructed ‘O’ pattern. Afterwards, the optical output from one pixel was coupled into a single-mode fiber and detected by a photodetector. The single-mode fiber ensured that the photodetector collected only the energy variations of the Gaussian mode within the pixel. Finally, the photodetector output was analyzed using the network analyzer to obtain the modulation response–frequency curve.

In addition, the frequency-dependent characteristics of the used VCSELs were independently measured by a professional VCSEL manufacturer (Berxel Photonics Co., Ltd.). For these tests, the VCSELs were bonded onto a substrate, and the current signal was applied via SG probes. Modulation-response–frequency curves were acquired using the same procedure as in the holographic refresh-rate measurement, except that the photodetector directly collected the total optical output of the VCSELs. For the spectral-versus-frequency characterization, an arbitrary waveform generator (Anritsu MP1900A) replaced the vector network analyzer to provide high-speed modulation, and the resulting optical signal was coupled into an optical spectrum analyzer (YOKOGAWA AQ6370D) for spectral analysis.

The fundamental DC characteristics of the VCSELs used in our experiments, including I–V curves, emission spectra, and device lifetime, were also measured at Berxel Photonics Co., Ltd. Device lifetime was evaluated using a TO-LD drawer aging resistance testing system. Specifically, 29 VCSELs with 10-µm oxide aperture diameters were tested at an injection current of 16 mA and a temperature of 85 °C for a total duration of 168 h. A typical failure criterion for VCSELs is defined as a 20% reduction in output power. All tested devices remained fully functional throughout the 168 h stress period, indicating a lifetime exceeding 168 h under accelerated conditions. Furthermore, assuming device operation at 50 °C under a drive current of 16 mA, and employing the established activation energy (Ea = –1.3 eV) reported in prior studies47, together with the standard acceleration factor (AF) calculation model48, we obtain an AF of 95.81 for the conditions of 16 mA at 85 °C (aging) versus 16 mA at 50 °C (usage). Accordingly, the estimated lifetime of the VCSELs under 50 °C and 16 mA operating conditions exceeds 16,096 h.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this article, the authors demonstrate a fast, electrically controlled, vertical-cavity surface-emitting laser (VCSEL)-based\nholographic system. By changing the current of arrays of broad-area VCSELs, the chip, which is integrated with orbital\nangular momentum (OAM)-multiplexing holograms, can produce holograms at high speeds, given the fast switching of\nVCSELs. The approach is novel, and the demonstration and implementation are impressive. I recommend the publication of\nthe article after addressing the following points:\n- Comparing this approach to spatial light modulators (SLM) in terms of speed is not a fair comparison. This is mainly\nbecause SLMs can be used to generate arbitrary waveforms, not just a fixed set of holograms.\n- How can the number of possible holograms from a single VCSEL be increased? Would a larger aperture help?\n- Is it necessary to rely on VCSELs with LP modes? Or is this the simplest technique to work with? Some recent work on\nVCSELs with chaotic cavities has shown a that these chaotic-cavity designs can significantly increase the number of modes\nwith complicated spatial profiles dynamically changing at each current. Would that be possible to use?\n- How long does it take for the spatial profile of the VCSEL to stabilize. From my experience, changing the current of broad-\narea VCSELs changes the spatial profile, but it takes some time (observable by the human eye) to stabilize. Is that the case\nhere? It would be insightful to include a video, if possible.\n- The article is concise, but it would still be great if some of the details in the supplementary information are moved to the\nmain article.\n- Why was some of the analysis done on a smaller VCSEL? Is this due to simulation limitations on the size?\n- The authors state that \"resulting in a cylindrical waveguide structure with an effective refractive index difference of about\n0.01 between the core and the cladding.\" How was this value estimated? Is it based on the literature?\n- More proofreading can improve the presentation quality of the paper.", "reviewer_2": "This study demonstrates a high performance holographic chip using multimode VCSEL. My suggestion is major revision for\nthe following reasons:\n1. The abstract is misleading. It talks “overturn paradigm” related to VCSEL, but is not; in fact, this study is not about VCSEL\ndevelopment at all. On the other hand, using multimode/high-order model is known to field, e.g., the review paper ref. 9 and\nthe references therein. The present manuscript just made it happen with high performance. It is great already. No need to\nuse uncorrelated terms to make the work sound very scientific.\n2. The basic characteristics of the VCSELs should be shown in the SI, e.g., spectral properties, I-V characteristics, estimated\nlifetime, etc. No single spectrum is shown in the current format - this is not acceptable. This is one major flaw.\n3. The authors show high refresh rate, etc., but never explains how those are achieved. This is another major flaw.\n4. More frequency dependent characterization should be provided, e.g., frequency dependent output power of VCSELs,\nbandwidth versus current density, spectral characteristics versus frequency, etc. This is also a major flaw."}, "author_response": "Response Letter to Reviewers\nWe would like to express our sincere gratitude to all reviewers for the insightful and\nconstructive comments on our manuscript. Below, we provide a point-by-point response to the\ncomments and have described the modifications made in the revision. The original comments\nare presented in italics, our responses are highlighted in blue, and the revised sections are\nmarked in red for your convenience. We believe that all the issues outlined by the Reviewers\nhave been fully addressed and trust that this revision can be considered for publication in\nNature Communications.\nReviewer #1\nIn this article, the authors demonstrate a fast, electrically controlled, vertical-cavity surface-\nemitting laser (VCSEL)-based holographic system. By changing the current of arrays of broad-\narea VCSELs, the chip, which is integrated with orbital angular momentum (OAM)-\nmultiplexing holograms, can produce holograms at high speeds, given the fast switching of\nVCSELs. The approach is novel, and the demonstration and implementation are impressive. I\nrecommend the publication of the article after addressing the following points:\nResponse:\nWe sincerely appreciate your time in reviewing our manuscript and providing positive feedback.\nWe are particularly grateful for your recognition of the novelty of our work on current-\naddressed mode-multiplexing holography based on multimode VCSELs, as well as your\nacknowledgment of the demonstrated ultrahigh refresh rate. Your comprehensive and insightful\ncomments are critically important for enhancing the quality of the manuscript. We have\naddressed each of your comments point by point in our responses below.\nComment 1.1:\nComparing this approach to spatial light modulators (SLM) in terms of speed is not a fair\ncomparison. This is mainly because SLMs can be used to generate arbitrary waveforms, not\njust a fixed set of holograms.\nResponse 1.1:\nThank you for your valuable comment regarding the speed comparison. We fully understand\nand agree with your comment. The core strength of SLMs lies in their flexibility for generating\narbitrary waveforms. In contrast, our current approach focuses specifically on high-speed\nswitching among a pre-generated set of holographic patterns. According to your suggestion,\nwe have removed the unnecessary comparison regarding refresh rate between SLMs and our\ncurrent approach to avoid misleading.\nAction:\nWe have removed the comparison of refresh rate (Main text, page 2, line 26) in Abstract section.\nMain text, page 2, line 26:\n\"Experimental validation shows...with an ultrahigh refresh rate of ~1.93 GHz. To our\nknowledge, this represents the fastest holographic switching speed …reported to date.\"\nComment 1.2:\nHow can the number of possible holograms from a single VCSEL be increased? Would a larger\naperture help?\nResponse 1.2:\nWe sincerely appreciate these professional comments regarding the enhancement of the\nmultiplexing capacity in a single holographic VCSEL device. Fundamentally, the multiple\ndegrees of freedom of light (e.g., transverse modes and polarization) can be exploited as\ninformation channels for holographic multiplexing. Thus, the number of multiplexed\nholograms can be effectively increased when the illuminating structured light field generated\nby a single VCSEL has more optical degrees of freedom.\nAs you correctly indicated, enlarging the oxide aperture inherently enables VCSELs to emit\nmore transverse modes, offering a viable strategy for enhancing holographic multiplexing\ncapacity. To validate this, beyond the VCSELs with oxide aperture diameters of 8 μm, 10 μm,\n12 μm, 14 μm, and 30 μm demonstarted in the main text, we conducted additional experiments\nusing VCSELs with oxide aperture diameters of 25 μm, 35 μm, and 40 μm, respectively. Based\non the measurement method for OAM modes weighting coefficient spectra shown in Figure 3,\nwe obtained 3, 4, and 6 independent current-addressed modes from these selected VCSELs,\nrespectively, as shown in Figure R1a. Correspondingly, using these three VCSELs as\nillumination sources, we designed multiplexed holograms capable of reconstructing 3 (“N”,\n“I”, “R”), 4 (“L”, “E”, “N”, “S”), and 6 (“O”, “P”, “T”, “I”, “C”, “S”) distinct holographic\nimages, respectively (Figures R1b–d). All reconstructed images exhibit average PSNR values\nexceeding 12.78 dB. Therefore, it can be expected that enlarging the oxide aperture can\nsignificantly expand the holographic capacity from a single VCSEL.\nBeyond aperture scaling, as mentioned in the Discussion section, polarization can also serve as\nan additional physical dimension to increase the number of multiplexed holograms. Previous\nstudies have demonstrated that the information channel number of meta-hologram can be\nexpanded through the synergy manipulation of polarization and OAM [1]. Therefore, utilizing\nthe transverse modes with distinct polarization states in VCSELs for holographic encoding\noffers a promising route to further increase the holographic multiplexing capacity.\nFig. R1. Impact of oxide aperture diameter of VCSELs on holographic multiplexing\ncapacity. a. Relationship between the oxide aperture diameter and the number of achievable\nencoding modes. b–d. The reconstructed holograms (lower panels) and the corresponding\ninjection currents (upper panels) for VCSELs with oxide aperture diameters of (b) 25 μm, (c)\n35 μm, and (d) 40 μm, respectively.\n[1] Yang H, et al. Angular momentum holography via a minimalist metasurface for optical\nnested encryption. Light Sci. Appl. 12, 79 (2023).\nAction:\n(1) We have added Figure R1 to the Supplementary Information as Supplementary Figure 17.\n(2) In the Discussion section, we have added an index to Supplementary Fig. 17 and revised\nthe discussion on increasing the holographic multiplexing capacity by introducing\npolarization as an additional dimension.\nMain text, page 13, line 250:\n\"Notably, VCSELs with larger oxide apertures support more spatial modes suitable for\nholographic encoding, thereby enhancing the multiplexing capacity (Supplementary Fig. S17).\nIn addition, the principle of current-addressed mode-multiplexed holography can be applied in\nthe design of metasurface holograms with subwavelength pixel resolution37,38, where\npolarization-multiplexing strategies may be incorporated to further increase the available\nholographic channel numbers39.\n…\nnested encryption. Light Sci. Appl. 12, 79 (2023).\"\nComment 1.3:\nIs it necessary to rely on VCSELs with LP modes? Or is this the simplest technique to work\nwith? Some recent work on VCSELs with chaotic cavities has shown a that these chaotic-cavity\ndesigns can significantly increase the number of modes with complicated spatial profiles\ndynamically changing at each current. Would that be possible to use?\nResponse 1.3:\nWe sincerely appreciate your insightful perspective on encoding modes selection strategies in\nmodes multiplexing holography. In our work, the selection strategies of encoding modes are\nprimarily governed by two standards. First, holographic multiplexing necessitates modes with\nsuperior orthogonality to effectively suppress channel crosstalk during information encoding\n[1]. Consequently, Laguerre–Gaussian (LG) and Hermite–Gaussian (HG) modes, have\nsuccessfully been extensively adopted as information carrier in holography multiplexing.\nSecond, from the perspective of the laser source, the lasing mode must be stable; mode\ninstability would directly degrade the reliability of holographic reconstruction. Therefore,\nwhile LP modes are not the only feasible choice, they offer a practical and effective\ninformation-encoding channel that simultaneously ensures mode orthogonality and stable\nemission characteristics.\nYour suggestion of using chaotic-cavity VCSELs to enhance holographic multiplexing capacity\nis highly insightful. The irregular cavity geometry of such devices can indeed support a\nsubstantially larger number of transverse modes [2-4], thereby enriching the potential channels\navailable for multiplexing hologram design. However, unlike the orthogonal LP modes with\ndetermined expressions, implementation other transvers modes in the design of the\nmultiplexing hologram requires accurate acquisition of the complex field distributions under\ndifferent injection currents. Notably, the inherent non-ideal orthogonality among modes\ninevitably introduces channel crosstalk, which can degrade the reconstructed image quality.\nBesides, when operating in the chaotic regime, both the output intensity and the transverse\nmodal profile fluctuate dynamically and non-periodically due to strong inter-mode competition\n[2]. This intrinsic instability poses significant challenges to maintaining reliable device\noperation in practical applications. In summary, although chaotic-cavity VCSELs offer great\npotential as illuminating source for mode-multiplexing holography, they still face notable\nchallenges in terms of holographic performance and stability.\n[1] Makey G, et al. Breaking crosstalk limits to dynamic holography using orthogonality of\nhigh-dimensional random vectors. Nat. Photonics13, 251-256 (2019).\n[2] Sciamanna M, et al. Physics and applications of laser diode chaos. Nat. Photonics 9, 151-\n162 (2015).\n[3] Lu, H., Alkhazragi, O., Lin, H. et al. Shaping the light of VCSELs through cavity geometry\ndesign. Light Sci. Appl. 14, 344 (2025).\n[4] Ma C G, et al. Chaotic microlasers caused by internal mode interaction for random number\ngeneration. Light Sci. Appl. 11, 187 (2022).\nAction:\nWe have added a discussion (Main text, page 13, line 256) to further demonstrate the outlook\non chaotic-cavity VCSELs.\nMain text, page 13, line 256:\n\"Furthermore, novel VCSEL configurations, such as chaotic-cavity VCSELs40,41,42, warrant\nfurther exploration. Their irregular geometries support a substantially larger number of\ntransverse modes, theoretically enriching the available channels for multiplexed hologram\ndesign. However, chaotic-cavity VCSELs suffer from mode complexity and instability, which\ncan degrade holographic performance and stability. Therefore, further co-design and\noptimization of the VCSEL structure and hologram algorithm may be required to address these\nchallenges.\n…\n14, 344 (2025).\ngeneration. Light Sci. Appl. 11, 187 (2022).\n162 (2015). \"\nComment 1.4:\nHow long does it take for the spatial profile of the VCSEL to stabilize. From my experience,\nchanging the current of broad-area VCSELs changes the spatial profile, but it takes some time\n(observable by the human eye) to stabilize. Is that the case here? It would be insightful to\ninclude a video, if possible.\nResponse 1.4:\nThank you for this valuable comment on the temporal stability of the light field of the VCSEL.\nAs noted, broad-area VCSELs indeed exhibit gradual evolution and stabilization delays in their\nspatial field distributions after current modulation [1,2] primarily due to transient mode\ncompetition and oscillatory field redistribution [3], as well as thermal relaxation [4].\nFollowing your suggestion, we have added one supplementary video (Video S1) showing the\nevolution of the light field for the VCSEL with oxide aperture size of 30 μm under stepped\ncurrent changes. These recordings clearly illustrate the spatial profile during current\nmodulation, providing an intuitive understanding of the current-addressed dynamic\nholographic mechanism.\nRegarding stabilization delay, because VCSELs are intrinsically GHz-bandwidth devices, this\nprocess occurs at ultrafast timescales (typically picoseconds to nanoseconds [5]), beyond the\ntemporal resolution of conventional cameras. Consequently, it is difficult to capture directly.\n[1] Bittner S, et al. Complex nonlinear dynamics of polarization and transverse modes in a\nbroad-area VCSEL. APL Photonics 7, 126108 (2022).\n[2] Degen C, et al. Transverse modes in oxide confined VCSELs: Influence of pump profile,\nspatial hole burning, and thermal effects. Opt. Express 5, 38-47 (1999).\n[3] Valle A, et al. Spatial holeburning effects on the dynamics of vertical cavity surface-\nemitting laser diodes. IEEE J. Quantum Electron 31, 1423-1431 (2002).\n[4] Chang-Hasnain C J, et al. Dynamic, polarization, and transverse mode characteristics of\nvertical cavity surface emitting lasers. IEEE J. Quantum Electron 27, 1402-1409 (2002).\n[5] Becker K, et al. Spatio-temporal emission dynamics of VCSELs: modal competition in the\nturn-on behavior. Proc. SPIE5452, 452-461 (2004).\nAction:\nWe have added Supplementary Video 1, which show the evolution of the spatial emission\nprofile with varying injection current.\nMain text, page 9, line 163:\n\"Supplementary Video 1 directly visualizes the evolution of the light field under stepped\ncurrent modulation, revealing the injection current–dependent spatial mode behavior of the\nVCSEL.\"\nComment 1.5:\nThe article is concise, but it would still be great if some of the details in the supplementary\ninformation are moved to the main article.\nResponse 1.5:\nWe sincerely appreciate your positive feedback and valuable suggestion. We fully agree that\nincorporating key details from the Supplementary Information into the main text can enhance\nthe completeness and readability of the manuscript.\nAction:\nAccordingly, we have moved several essential figures and their corresponding explanations\ninto the main text:\n(1) Supplementary Figure 3 (Flowchart of the enumeration algorithm for current-addressed\nmode-multiplexed holographic encoding) has been moved to the main text. It is now integrated\nwith the original Figure 3a–c to form a new Figure 3, which systematically illustrates the\nprinciple of current-addressed mode-multiplexed holographic encoding.\n(2) Supplementary Figure 6 (Current-shared holographic encryption scheme) has also been\nmoved to the main text. Together with panels d and e of the original Figure 3, it now forms a\nnew Figure 4, which presents the implementation of different holographic functions, including\ncurrent-addressed holographic video and holographic encryption.\nThe original Figure 4 is now renumbered as Figure 5. Corresponding text in the main\nmanuscript has been updated to ensure consistency with these changes.\nFig. 3\nPrinciple of current-addressed mode-multiplexed holographic encoding. a. Conceptual\nillustration of optical setup. SPP: spiral phase plate. b. The intensity distributions at the focal\nplane when VCSEL beams at an injection current of 28 mA illuminated on SPP with distinct\nOAM orders (left panel), the resultant OAM modes weighting coefficient spectra reveals that\nthe OAM modes with l=25 is a dominant component (right panel). c. The OAM weighting\ncoefficient distributions for various injection currents within working range (left panel). Here,\nthe pseudo-colors represent eight OAM modes with l=22-29. After he enumeration algorithm,\nfour encoding OAM modes that feature a distinguishing largest weighting coefficient have been\nselected (right panel). d. The detailed illustration of the enumeration algorithm for the four\ncurrent-addressed modes. First, the measured OAM weighting coefficients spectra are grouped,\nwith each group containing four OAM mode components featuring distinct dominant OAM\ncomponents. Second, the groups are evaluated to determine the one where the dominant OAM\ncomponents show the greatest disparity in weighting coefficients compared to the other\ncomponents within each spectrum. As a result, the four dominant OAM components from the\nselected group can be utilized to design the OAM-multiplexing hologram.\nFig. 4\nCurrent-addressed holographic video and current-shared holographic encryption\nscheme. a. The design process of the OAM-multiplexing hologram for the target video\ncomprising four image frames. b. The reconstructive video images (bottom row) when\nswitching the appropriate injection currents (middle row) at a time sequence of 250 ms (upper\nrow). c. Design process of the OAM-multiplexing hologram of a MQR code image for current-\nshared holographic encryption. d. Experimental reconstruction of the OAM-multiplexing\nhologram. After combining and binarizing the four reconstructive images, the complete MQR\ncode image can be obtained. Scanning the MQR code reveals the encrypted message \"Hello\nWorld\".\nWe have added descriptions regarding the updated Figure 3 (Main text, page 9, line 165).\nMain text, page 9, line 165:\n\"To reduce ... coefficient (Fig. 3d). Here, the enumeration algorithm involves two main steps.\nFirst, the measured OAM weighting coefficients spectra are grouped, with each group\ncontaining four OAM mode components featuring distinct dominant OAM components.\nSecond, the groups are evaluated to determine the one where the dominant OAM components\nshow the greatest disparity in weighting coefficients compared to the other components within\neach spectrum.\"\nWe have added descriptions regarding the updated Figure 4 (Main text, page 10, line 190).\nMain text, page 10, line 190:\n\" To construct the hologram, the MQR code image is divided into four sections, and sampled\nwith a comb function (Fig. 4c). Then, the Fourier holograms are encoded with the selected\nhelical phase plates (l=-25, -26, -24, and -23), resulting in an OAM-multiplexing hologram.\nTherefore, after combining and binarizing the four reconstructive images obtained under the\nfour selected injection currents, the complete MQR code image is obtained (Fig. 4d). Scanning\nthe MQR code reveals the encrypted message \"Hello World\".\"\nComment 1.6:\nWhy was some of the analysis done on a smaller VCSEL? Is this due to simulation limitations\non the size?\nResponse 1.6:\nWe appreciate your professional question regarding the VCSEL device size in simulation. The\nuse of smaller oxide apertures for specific analyses was primarily driven by the need to balance\nsimulation complexity and accuracy, which indeed relate to inherent limitations in the modeling\nprocess.\nFirst, simulating the spatial current distribution and mode competition dynamics in VCSELs\nbecomes more complex as the oxide aperturediameter increases, as detailed in Supplementary\nNote 2 (\"Mode Competition Analysis in Multimode VCSELs\"). Specifically, the computational\nload for mode competition escalates rapidly with the number of supported transverse modes.\nSince the VCSELs with larger oxide apertures support more transverse modes, both\ncomputation and solution convergence become significantly more demanding.\nSecond, simulation accuracy degrades for the VCSELs with larger oxide apertures due to\nincreasingly non-uniform current injection. In practice, factors such as electrode geometry,\netching profile, and oxidation conditions during fabrication strongly influence the spatial\ncurrent distribution. These effects are challenging to model comprehensively, leading to larger\ndiscrepancies between simulations and experimental measurements.\nSince VCSELs with small or large oxide apertures exhibit equivalence in elucidating mode\ndynamics, we selected VCSELs with small oxide apertures sizes for simulations to enhance\ncomputational efficiency and accuracy.\nAction:\nWe have added an explanation (Main text, page 8, line 143) for the analysis focused on\nVCSELs with smaller oxide apertures.\nMain text, page 8, line 143:\n\"Simulating VCSELs with large oxide apertures is challenging due to increased computational\ncomplexity and potential modeling errors. In addition, devices with different aperture sizes are\nequivalent in revealing the principles of mode dynamics. Thus, without losing generality, we\nexperimentally and theoretically investigated the weighting coefficients of OAM components\nwith l=1 and 2 for the VCSEL with a 6 μm-diameter oxide aperture (Fig. 2d). \"\nComment 1.7:\nThe authors state that \"resulting in a cylindrical waveguide structure with an effective\nrefractive index difference of about 0.01 between the core and the cladding.\" How was this\nvalue estimated? Is it based on the literature?\nResponse 1.7:\nWe appreciate your professional question regarding the method for constructing the waveguide\nstructure. The value of approximately 0.01 between the core and cladding in oxide-confined\nVCSELs is based on the reported literature [1, 2]. To be specific, this value is typically\nestablished using the waveguide approximation method. In this established modeling approach,\nthe unoxidized central current aperture region is regarded as the waveguide core, while the\noxide confinement layer acts as the cladding. As such, the transverse refractive index profile is\nmodeled as a weakly guiding cylindrical waveguide. By computing the refractive indices across\nall epitaxial layers in the model, an average cladding-core index difference of approximately\n0.01 can thus be obtained [1, 2].\n[1] Hadley G R. Effective index model for vertical-cavity surface-emitting lasers. Opt. Lett.20,\n1483-1485 (1995).\n[2] Larsson A. Advances in VCSELs for communication and sensing. IEEE J. Sel. Top.\nQuantum Electron.17, 1552-1567 (2011).\nAction:\nWe have revised the relevant content in OAM mode dynamics in multimode VCSELs section\nwithin the manuscript.\nMain text, page 6, line 109:\n\"The refractive index (n ) of the oxidized region is lower than that of the unoxidized region\n2\n(n ), forming a cylindrical waveguide structure. In this model, the unoxidized central current\n1\naperture serves as the waveguide core, while the oxide confinement layer acts as the cladding.\nBy computing the refractive indices across all epitaxial layers, an average cladding–core index\ndifference of approximately 0.01 can be obtained32,33.\n…\n1483-1485 (1995).\nQuantum Electron.17, 1552-1567 (2011).\n\"\nComment 1.8:\nMore proofreading can improve the presentation quality of the paper.\nResponse 1.8:\nWe sincerely thank you for your valuable suggestion. We have conducted a thorough review of\nthe entire manuscript and have addressed improvements in language fluency, sentence structure,\nand terminology consistency in the revised version.\nAction:\nWe have corrected errors in grammar (singular/plural noun, adjective, verb and so on)\nthroughout the manuscript, including the following:\nMain text, page 3, line 33: \"wavefront\" to \"wavefronts\".\nMain text, page 3, line 38: \"SLM\" to \"SLMs\".\nMain text, page 3, line 41: \"a fundamental challenge\" to \"fundamental challenges\".\nMain text, page 3, line 47: \"attentions\" to \"attention\".\nMain text, page 4, line 71: \"operates\" to \"operate\".\nMain text, page 5, line 73: \"distinctive\" to \"distinct\".\nMain text, page 5, line 78; page 5, line 82: \"modes-multiplexed\" to \"mode-multiplexed\".\nMain text, page 5, line 86; page 5, line 88; page 9, line 175; page 11, line 215; page 26, line\n494; page 28, line 512: \"dominate\" to \"dominant\".\nMain text, page 5, line 93: \"array\" to \"arrays\".\nMain text, page 6, line 101; page 8, line 142: \"spectrum\" to \"spectra\".\nMain text, page 8, line 140: \"modes\" to \"mode\".\nMain text, page 8, line 141: \"continuous\" to \"continuously\".\nMain text, page 8, line 153: \"display\" to \"displays\".\nMain text, page 9, line 157; page 11, line 198: \"Method\" to \"Methods\".\nMain text, page 10, line 181: \"current\" to \"currents\".\nMain text, page 10, line 181: \"interval\" to \"intervals\".\nMain text, page 10, line 183: \"exceed\" to \"exceeding\".\nMain text, page 10, line 185: \"random\" to \"randomly\".\nMain text, page 11, line 206; page 19, line 381; page 19, line 382: \"oxidation\" to \"oxide\".\nWe have corrected errors in expression throughout the manuscript, including the following:\nMain text, page 3, line 38: \"digital micromirrors\" to \"digital micromirror devices (DMDs)\".\nMain text, page 4, line 52: \"electron beam lithography, 3D laser nano-printing, et al.\" to \"such\nas electron beam lithography and 3D laser nano-printing\".\nMain text, page 4, line 63: \"not applicable\" to \"inapplicable\".\nMain text, page 5, line 81: \"it's\" to \"it\".\nMain text, page 6, line 95: \"at time sequences\" to \"over time sequences\".\nMain text, page 8, line 137: \"termed as\" to \"termed\".\nMain text, page 11, line 207: \"construct devices array\" to \"construct a device array\".\nMain text, page 11, line 211; page 11, line 213: \"is\" to \"was\".\nMain text, page 21, line 418: \"1/4π\" to \"π/4\".\nReviewer #2\nThis study demonstrates a high performance holographic chip using multimode VCSEL. My\nsuggestion is major revision for the following reasons:\nResponse:\nWe sincerely thank you for the thoughtful evaluation and professional suggestions. We have\ncarefully addressed the key concerns you raised. Your comments are valuable for improving\nthe quality of our manuscript. Our detailed responses to each point are provided below.\nComment 2.1:\nThe abstract is misleading. It talks \"overturn paradigm\" related to VCSEL, but is not; in fact,\nthis study is not about VCSEL development at all. On the other hand, using multimode/high-\norder model is known to field, e.g., the review paper ref. 9 and the references therein. The\npresent manuscript just made it happen with high performance. It is great already. No need to\nuse uncorrelated terms to make the work sound very scientific.\nResponse 2.1:\nWe sincerely thank your positive evaluation that this work is \"great\" . And we also appreciate\nyour constructive comment regarding the need to improve the exaggerated claim about\nparadigm overturning in the abstract. We fully agree that the core contribution of this work lies\nnot in overturning the fundamental VCSEL paradigm, but in establishing a novel conceptual\nframework for ultra-high frame rate dynamic holographic chips based on current-addressed\nmodes multiplexing holography in multimode VCSELs. This approach leverages intrinsic\nmode-switching characteristics to achieve micrometer-scale dynamic holographic VCSEL\ndevices at high speeds. In accordance with your guidance, we have revised the abstract and\nremoved the phrase ‘overturn paradigm’.\nAction:\nWe have removed the corresponding exaggerated claim about paradigm overturning (Main text,\npage 1, line 17) from the manuscript abstract.\nMain text, page 1, line 17:\n\"Here, we develop current-addressed modes multiplexing holography in multimode\nVCSELs...\"\nComment 2.2:\nThe basic characteristics of the VCSELs should be shown in the SI, e.g., spectral properties, I-\nV characteristics, estimated lifetime, etc. No single spectrum is shown in the current format -\nthis is not acceptable. This is one major flaw.\nResponse 2.2:\nWe sincerely appreciate your valuable feedback highlighting the omission of the basic VCSEL\ncharacteristics in our manuscript. Following your suggestion, we have supplemented the\nmeasurements to include the VCSEL’s emission spectrum, I–V characteristics, and estimated\nlifetime. These data have been added to the Supplementary Materials, and the corresponding\ntesting methods have been described in the Methods section.\nAction:\nWe have added Supplementary Figures S1–S3 to present the VCSEL’s emission spectrum, I–\nV characteristics, and estimated lifetime.\nSupplementary Figure 1. Emission spectra of VCSELs with different oxide aperture\ndiameters at various operating currents. a. Oxide aperture diameter: 10 μm. b. Oxide\naperture diameter: 30 μm.\nSupplementary Figure 2. Voltage-current curves for the four VCSEL units with different\noxide aperture diameters in the holographic VCSEL chip. a. Oxide aperture diameter: 8\nμm. b. Oxide aperture diameter: 10 μm. c. Oxide aperture diameter: 12 μm. d. Oxide aperture\ndiameter: 14 μm. e. Oxide aperture diameter: 30 μm.\nSupplementary Figure 3. Output power versus aging time for the VCSELs with a 10-µm\noxide aperture diameter, obtained from the accelerated aging test.\nWe have added a subsection in the Methods section detailing the measurement procedures.\nMain text, page 23, line 450:\n\"The fundamental DC characteristics of the VCSELs used in our experiments, including I–V\ncurves, emission spectra, and device lifetime, were also measured at Berxel Photonics Co., Ltd.\nDevice lifetime was evaluated using a TO-LD drawer aging resistance testing system.\nSpecifically, 29 VCSELs with 10-µm oxide aperture diameters were tested at an injection\ncurrent of 16 mA and a temperature of 85 °C for a total duration of 168 hours. A typical failure\ncriterion for VCSELs is defined as a 20% reduction in output power. All tested devices\nremained fully functional throughout the 168-hour stress period, indicating a lifetime\nexceeding 168 hours under accelerated conditions.Furthermore, assuming device operation at\n50 °C under a drive current of 16 mA, and employing the established activation energy (Ea =\n–1.3 eV) reported in prior studies47, together with the standard acceleration factor (AF)\ncalculation model48, we obtain an AF of 95.81 for the conditions of 16 mA at 85 °C (aging)\nversus 16 mA at 50 °C (usage). Accordingly, the estimated lifetime of the VCSELs under 50\n°C and 16 mA operating conditions exceeds 16,096 hours.\"\nover Multi-Mode and Single-Mode Fibers. Photonics 12, 1037 (2025).\n11PC01 (2012).\nComment 2.3:\nThe authors show high refresh rate, etc., but never explains how those are achieved. This is\nanother major flaw.\nResponse 2.3:\nWe sincerely thank you for this professional comment. Specifically, the refresh rate ofVCSEL\nholographic chip was characterized via small-signal modulation measurements. As shown in\nSupplementary Figure 12, the refresh rate of VCSEL_2 (Fig. 5c), which generates the letter\nimages \"O\" and \"R\", was measured using a Vector Network Analyzer (Rohde & Schwarz,\nZNLE14).\nIn our current-addressed mode-multiplexed holographic scheme, when the injection current of\nVCSEL_2 is switched from 9 mA to 16 mA, the dominant OAM mode changes. This leads to\na pronounced decrease in the energy of each pixel featuring Gaussian mode in the reconstructed\n“O” pattern and a corresponding increase in that of the “R” pattern, thereby realizing\nholographic image switching.\nTo quantify the refresh rate, the optical signal from a single pixel was coupled into a single-\nmode fiber and detected by a photodetector. The single-mode fiber ensured that the\nphotodetector collected only the energy variations of the Gaussian mode within the pixel.\nSubsequently, a frequency-swept signal generated by the network analyzer was applied to\nrapidly modulate the VCSEL bias current, cyclically switching it between 9 mA and 16 mA.\nBy analyzing the photodetector output, a modulation bandwidth of 1.93 GHz was obtained for\nthe holographic VCSEL chip.\nAction:\nWe have revised description (Main text, page 22, line 428) in Bandwidth measurement for the\nVCSEL chip section within the manuscript.\nMain text, page 22, line 428:\n\"As shown in Supplementary Fig. 12, the frequency response of the VCSEL holographic chip\nwas characterized using a vector network analyzer (Rohde & Schwarz ZNLE14). Here,\nVCSEL_2 in Fig. 5c was selected for testing and connected to the PCB via gold wire bonding,\nwith external linkage to the driver power supply. First, harmonic modulation signals from the\nnetwork analyzer were used to cyclically switch the injection current of VCSEL_2 between 9\nmA and 16 mA, inducing periodic variations in the energy of each pixel featuring Gaussian\nmode in the reconstructed ‘O’ pattern. Afterwards, the optical output from one pixel was\ncoupled into a single-mode fiber and detected by a photodetector. The single-mode fiber\nensured that the photodetector collected only the energy variations of the Gaussian mode within\nthe pixel. Finally, the photodetector output was analyzed using the network analyzer to obtain\nthe modulation response–frequency curve.\"\nWe have revised one supplementary figure (Supplementary Materials, fig. S12) to further\nclarify VCSEL high refresh rate.\nSupplementary Materials, fig. S12:\nSupplementary Figure 12. Bandwidth measurement for the holographic VCSEL chip. a.\nFlowchart of testing method. b. Schematic illustration of the experimental setup for bandwidth\ncharacterization.\nComment 2.4:\nMore frequency dependent characterization should be provided, e.g., frequency dependent\noutput power of VCSELs, bandwidth versus current density, spectral characteristics versus\nfrequency, etc. This is also a major flaw.\nResponse 2.4:\nWe sincerely thank the reviewer for this valuable suggestion regarding the frequency-\ndependent characterization of the VCSELs. Following your advice, we have conducted\nadditional measurements to characterize the frequency response of the VCSELs, including\nfrequency-dependent output power, bandwidth versus current density, and spectral\ncharacteristics versus frequency.\nAction:\nWe have added Supplementary Figures S13–S15 to present the frequency-dependent output\npower, bandwidth versus current density, and spectral characteristics versus frequency of the\nVCSELs.\nMain text, page 12, line 230:\n\"(Supplementary Figure 13-15, Methods)\"\nSupplementary Materials, fig. S13:\nSupplementary Figure 13. Modulation response–frequency curves of VCSELs with\ndifferent oxide aperture diameters. a. Oxide aperture diameter: 10 μm; current: 9 mA. b.\nOxide aperture diameter: 30 μm; current: 28 mA.\nSupplementary Materials, fig. S14:\nSupplementary Figure 14. Modulation response–frequency curves of VCSELs with\ndifferent oxide aperture diameters at various injection current.a. Oxide aperture diameter:\n10 μm. b. Oxide aperture diameter: 30 μm. The values in parentheses indicate the current\ndensities of the active layer under the corresponding currents.\nSupplementary Materials, fig. S15:\nSupplementary Figure 15. Emission spectra of VCSELs with different oxide aperture\ndiameters at various operating frequencies. a. Oxide aperture diameter: 10 μm (I = 9mA).\nb. Oxide aperture diameter: 30 μm (I = 28mA).\nWe have added a subsection in the Methods section detailing the measurement procedures.\nMain text, page 22, line 440:\n\"In addition, the frequency-dependent characteristics of the VCSELs were independently\nmeasured by a professional VCSEL manufacturer (Berxel Photonics Co., Ltd.). For these tests,\nthe VCSELs were bonded onto a substrate, and the current signal was applied via SG probes.\nModulation-response–frequency curves were acquired using the same procedure as in the\nholographic refresh-rate measurement, except that the photodetector directly collected the total\noptical output of the VCSELs. For the spectral-versus-frequency characterization, an arbitrary\nwaveform generator (Anritsu MP1900A) replaced the vector network analyzer to provide high-\nspeed modulation, and the resulting optical signal was coupled into an optical spectrum\nanalyzer (YOKOGAWA AQ6370D) for spectral analysis.\""}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed the reviewer's comments. I recommend publication."}, "author_response": "Response:\nWe sincerely thank you for the constructive suggestions provided throughout the review\nprocess. These comments were invaluable and significantly helped us improve the clarity and\noverall quality of the manuscript."}]

Decision letter