Structures with three-dimensional confinement offer remarkable flexibility and superior optoelectronic properties. Fabrication methods such as molecular beam epitaxy [1, 2], chemical vapor deposition [3, 4], and lithography [5] allow precise control over size and morphology, enabling tunable properties for a wide array of applications. Beyond conventional uses in LEDs, lasers, and display technologies, such nanostructures play an increasingly critical role in quantum photonics and sensing [6–8].

A standing challenge in this domain is the ability to address individual nanostructures within an ensemble, particularly in systems with certain periodicity. While electrostatic and magnetic fields enable global tuning, they fall short when precise, site-specific control is required. Structured light [9] spatially and temporally shaped light fields engineered to have specific intensity, phase, and polarization distributions offers a compelling alternative. It enables controlled interaction with matter at the subwavelength scale, leveraging the spatial degree of freedom of light.

Of particular interest are needle beams [10] fringe-free, free-space optical Bessel-like beams that represent a specific class of truncated Bessel beams formed under specific conditions [11, 12]. Originally introduced by Durnin [13] and later extended through the development of fringes free Bessel-like configurations, these beams combine an ultra-narrow transverse profile with an extended, quasi diffraction-free propagation zone. This allows the central intensity core to remain sharply confined over millimeter- to centimeter-scale distances without the need for continuous refocusing, unlike Gaussian beams. These unique propagation-invariant characteristics have unlocked a broad spectrum of advanced applications, including optical coherence tomography, high-resolution microscopy, laser micromachining, particle manipulation [14–16], etc. Furthermore, recent developments have enabled the generation of near-field and plasmonic needle beams often referred to as photonic nanojets with sub-wavelength diameters and extreme aspect ratios (>10⁵), extending their utility in nanoscale optical probing and manipulation [17–19].

Physically, a needle beam can be viewed as the central lobe of a finite aperture Bessel-like field that arises when a conically phased wavefront interferes along the optical axis. Practical generation routes include axicons [20–22], computer-generated holograms on pixelated spatial light modulators (SLMs) [23–25], and more recently developed phase-encoded dielectric or plasmonic metasurfaces [26, 27] that shrink the platform to a sub-millimeter footprint. Because the beam diameter can be held to a few micrometers while the depth of focus exceeds hundreds of Rayleigh lengths, needle beams minimize optical cross-talk and enable layer-by-layer addressing of vertically stacked nanostructures. They also exhibit self-reconstruction [28, 29], allowing the high-intensity core to reform after partial obstruction a feature that is advantageous when propagating through scattering or inhomogeneous media. These experimentally demonstrated needle-beam implementations provide a practical and scalable route for structured excitation of individual or collective nanoscale structures, as considered in the present theoretical work.

In this work, we present a strategy to address individual nanorods in a three-dimensional periodic ensemble using an array of reconfigurable needle beams. These beams are spatially arranged to form a programmable two-dimensional pattern. Additionally, a standing-wave configuration is employed to modulate the light intensity along the propagation axis [30, 31], enabling selective excitation of vertically stacked nanorod layers. This approach enables volumetric optical addressing with minimal overlap between neighboring beams, providing a platform for high-resolution control of light-matter interactions at the ‘voxel’ scale. The programmability of the beam array allows individual needle beams to be selectively switched, modulated, or repositioned in real time, creating dynamic opportunities for controlling quantum states in complex nanostructured systems.

Moreover, the proposed control system influences the energetic spectra and wave functions of one-particle and few-particle systems confined in nanorods. By manipulating these fundamental properties, we gain control over complex phenomena such as photoluminescence (PL) and electromagnetically induced transparency (EIT). In addition, we predicted fully programmable Talbot self-imaging [32, 33] in nanorod arrays with sub-wavelength pitch. The resulting Talbot carpets provide spatially resolved feedback on which nanorods were optically excited, serving as a powerful diagnostic for validating structured-light activation schemes in dense nanostructured environments. Together, these capabilities lay the groundwork for integrated quantum photonic circuits where each nanostructure acts as a controllable nanoscale node.

The current paper is structured as follows: in section 2, we present the methods including the proposed control architecture as well as the theoretical and numerical techniques. In section 3, we provide a comprehensive analysis of simulation results, focusing on tunable PL, EIT, and near-field diffraction behaviors under various activation scenarios. Special emphasis is placed on the programmable reshaping of optical susceptibility spectra and Talbot self-imaging patterns. Finally, section 4 concludes the work by summarizing the key outcomes.

In this work, we consider 3D array of cylindrical InAs nanorods embedded in a GaAs matrix. Each nanorod has a length of l= 105 nm and a radius of r = 35 nm. The array consists of 100 × 100 nanorods per layer, forming a laterally extended ensemble suitable for structured optical excitation. In the current model, the inter-rod center to center spacing is varied in the range of 150–400 nm, which is in the range of 15–40 μm. These values are intentionally chosen to suppress electronic tunneling and dipole–dipole interactions between neighboring nanorods, thereby allowing each nanorod to be treated as an independently excited nanoscale emitter (figure 1).

Figure 1. (a) Schematic of the proposed voxel-scale nanorod control system. A Gaussian beam is transformed by a spatial light modulator into a 2D array of needle beams that interact with the nanorod array. A back-reflecting mirror forms a standing wave, inducing axial (Z-direction) modulation. The coupling and probe fields irradiate the full volume of nanorods ensemble. Inset: intensity distribution in the YZ plane. (b)–(f) Representative configurations of nanorod excitation states based on the activation fraction. Yellow cylinders represent nanorods. Transparent cubes denote nanorods outside the control field; dark purple indicates actively illuminated nanorods. (b) Natural (inactive) state. (c) Homogeneous (fully active) state. (e), (f) Inhomogeneous configurations with selective activation of lines, planes, or custom patterns.

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Unless stated otherwise, we use electron and hole effective masses and for InAs, and band offsets and for the InAs/GaAs heterostructure. The InAs dielectric constant and refractive index are taken as 3.263 and 15.15.

At the same time, this spacing range enables a systematic investigation of the optical response as a function of nanorod separation. This geometry is motivated by recent progress in high-precision III–V nanofabrication. Highly periodic 2D GaAs nanopillar arrays have been demonstrated experimentally, for example by Ha et al [34], where directional lasing was achieved via resonant nanoantenna effects. Extension of such architectures into three dimensions can be achieved through planar stacking of lithographically aligned layers combined with chemical-mechanical polishing and epitaxial overgrowth. Template-assisted growth strategies further enable scalable and vertically ordered nanorod arrays [35–38]. Experimental feasibility of multi-layer vertical stacking in III–V systems has also been demonstrated in molecular beam epitaxy grown structures, where up to 20 vertically stacked InGaAs/GaAs quantum dot layers were realized with controlled layer spacing and alignment [39]. While the present work does not address growth optimization, these studies support the physical feasibility of the 3D nanorod geometries considered here.

To selectively control quantum states within this 3D nanorods ensemble, we propose a system based on reconfigurable needle beam arrays capable of volumetric (voxel-scale) optical addressing. Reconfigurable 2D arrays of optical needle beams can be generated experimentally by encoding axicon-type phase functions onto pixelated SLMs [24, 25]. Phase-only liquid-crystal-on-silicon SLMs allow dynamic switching, steering, and spatial reconfiguration of individual needle beams with low cross-talk, enabling selective illumination of nanoscale objects.

In reflective SLM configurations, which are commonly employed to minimize dispersion for ultrashort pulses, the oblique angle of incidence can be compensated by anisotropic scaling of the phase profile, effectively transforming circular axicons into elliptical ones. This approach has been demonstrated experimentally in proof-of-principle studies involving programmable arrays of ultrashort needle beams and spatially encoded optical patterns [24, 25]. Thus, the structured illumination conditions assumed in the present model are experimentally feasible with current SLMs.

As illustrated in figures 1(a), a non-resonant Gaussian laser is expanded and passed through SLM, generating a programmable 2D array of needle beams. These beams propagate through the nanorod array and reflect off a back mirror, forming a standing wave that modulates the optical field along the propagation (Z) axis. The mirror’s position can be tuned along the Z-axis, allowing dynamic control over excitation planes within the volume. Additionally, probe and coupling beams are aligned via a polarizing beam splitter and uniformly illuminate the array.

This configuration provides full 3D spatial control over the optical excitation profile. Various excitation patterns are illustrated in figures 1(b)–(f), where transparent cubes denote unexcited nanorods and darker purple cubes represent those illuminated by the needle beams. Two limiting cases are shown: the natural state (figure 1(b)), where no nanorods are illuminated, and the homogeneous state (figure 1(c)), where all nanorods are exposed to needle beams.

Between these limits lies a tunable regime of inhomogeneous activation (figures 1(c)–(e)), where specific lines, planes, or arbitrary patterns of nanorods are selectively addressed by switching individual needle beams on or off. In the present scheme, the term activation refers exclusively to non-resonant intense-laser-field (ILF) dressing of nanorod electronic states by the needle-beam field. The needle beams act as a spatially structured, non-resonant dressing field that modifies the effective confinement potential via the Kramers–Henneberger mechanism [40], leading to a renormalization of single-particle, excitonic, and biexcitonic energy levels. The resulting spectral shifts therefore originate from field dressing induced energy renormalization.

To quantify this configurational flexibility, we define the activation fraction where is the number of nanorods illuminated by active needle beams and is the total number of nanorods in the ensemble. In simulations, is a control parameter set by the programmed on/off configuration of the reconfigurable needle-beam array.

Given the non-interacting nature of the nanorods and minimal cross-talk due to the needle beams’ confinement, this parameter is sufficient to characterize the optical control regime. Beyond localized excitation and energy-level modulation, our control method enables manipulation of the collective optical response of nanorod ensembles. In particular, we examine how a single layer (2D plane) of nanorods behaves as a diffraction grating for the probe laser field, and how this response varies under different spatial configurations and activation regimes.

Assuming that the probe field is a uniform plane wave incident perpendicular to the vertical cross-sections of the nanorods, each nanorod can be approximated as a rectangular aperture. This allows us to treat the entire nanorod layer as a rectangular-aperture-based amplitude grating. The modulation of the probe field is governed by the local optical susceptibility of each nanorod, which is dynamically altered through EIT when the coupling field is strong. Thus, the activation pattern indirectly controls the transmission amplitude and phase, forming a programmable diffraction grating.

To model the optical response of individual and ensemble InAs nanorods under needle beams control, we adopted a multiscale computational approach combining analytical transformations, numerical eigenstate calculations, variational quantum methods, and open quantum system dynamics. First, the single-particle electron and hole eigenstates were computed within the framework of the envelope function approximation and single-band effective mass theory, incorporating the Kramers–Henneberger transformation to account for ILF dressing [39]. A Woods–Saxon potential [40] was used to model the gradual material transition between the InAs nanorods and the GaAs matrix, including a tunable diffusion parameter. These eigenstates were computed using the finite element method implemented in Wolfram Mathematica [41].

Using the obtained wave functions and energies, we constructed exciton and biexciton states via the Variational Quantum Monte Carlo Method [42]. A screened Coulomb potential was modified by ILF dressing to derive the interaction terms. We employed correlated Gaussian–Jastrow trial wavefunctions for the exciton case [43] and a minimal-parameter biexciton trial function derived from Takagahara’s approach [44]. Ground state energies were estimated using adaptive quasi-Monte Carlo integration with parameter optimization by energy minimization.

The optical response, including PL and EIT, was modeled by solving a Lindblad master equation [45] for a three-level quantum system representing the ground, exciton, and biexciton states. Optical susceptibility spectra were obtained under steady-state conditions and used to compute absorption and emission via the Roosbroeck–Shockley relation.

Lastly, to analyze near-field diffraction and Talbot self-imaging, the structured nanorod arrays were modeled as programmable amplitude and phase gratings, defined by the activation patterns of the needle beams. Fresnel diffraction was computed using Fourier-based propagation methods [46] under the paraxial approximation, with structured gratings represented in both real and spatial frequency domains. This allowed us to efficiently simulate the evolution of structured diffraction carpets across various control states. All numerical simulations were validated through convergence tests and were repeated for multiple beam configurations and activation fractions to ensure reproducibility and robustness.

Thus, the multiscale simulation workflow proceeds from finite-element calculations of laser-dressed single-particle states, to variational quantum Monte Carlo evaluation of exciton and biexciton energies and dipole matrix elements, and finally to Lindblad master-equation modeling of the quantum-optical response, from which the steady-state optical susceptibility is analytically extracted using numerically determined parameters.

We begin our analysis by examining the optical susceptibility χ of the three-level nanorod system under various excitation and control configurations (figure 2).

Figure 2. Schematic illustration of the three-level ladder system used to describe the optical response of the nanorod ensemble.

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The three-level ladder system corresponds to the many-body excitonic states supported by an individual InAs nanorod: the ground state (no exciton), the single-exciton state , and the biexciton state . The right panel of figure 2 shows the resulting ladder configuration, where the transitions and are energetically ordered. In our model, the probe field drives the lower transition , while an independent coupling (control) field resonantly or near-resonantly addresses the upper transition .

Within this framework, the system’s optical response to the probe field is naturally characterized through the optical susceptibility, which serves as a key indicator of the strength and nature of the light-matter interaction. In particular, the imaginary part of the susceptibility corresponds to absorption of the probe field, while the real part governs the associated modulation of the refractive index.

These two components collectively determine the optical transparency and dispersion characteristics of the NR ensemble, especially under conditions of coherent excitation including EIT. For the specific system under consideration modeled as a ladder-type three-level quantum system analytical expressions for χ were derived under steady-state conditions by solving the Lindblad master equation. These expressions form the basis for simulating the system’s absorption and dispersion responses as functions of the probe energy, coupling strength, and nanorod activation pattern, which we now explore in detail.

where is the number of illuminated nanorods, - the dipole matrix element between the exciton and ground states, - are the decay rates for the exciton to ground and biexciton to exciton transitions, respectively. are the Rabi frequencies of the corresponding transitions. The detuning parameters and correspond to the frequency offsets of the probe and coupling fields from their respective resonant transitions.

The specific value chosen as a representative magnitude consistent with reported dephasing rates in semiconductor nanostructures at room temperature. We emphasize, however, that the exact dephasing rates depend sensitively on temperature, nanorod geometry, material composition, and fabrication quality. As our study is theoretical and aims to propose an experimentally realizable scheme, the precise values of must ultimately be determined experimentally for each specific implementation.

In figures 3(a) and (c) the density plots for the imaginary part of the optical susceptibility χ are presented for the natural state, where no nanorods are illuminated by the control (needle beam) system (figure 1(b)).

Figure 3. Density plots of the imaginary part of the optical susceptibility χ, proportional to the absorption coefficient of the probe field. In all plots, the X-axis denotes the energy of the probe laser . (a) and (c) Y-axis represents the coupling Rabi frequency at fixed near-resonant . (b) and (d) Y-axis shows the coupling Rabi frequency, and the coupling laser energy is fixed at . (a) and (b) correspond to the natural state where no nanorods are illuminated. (c) and (d) correspond to the case where 80% of the nanorods are activated using structured needle beams with intensity .

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Figure 3(a) maps the imaginary part of the optical susceptibility χ which is related to the absorption response as a function of the probe laser energy (X-axis) and the coupling field Rabi frequency (Y-axis), with the coupling laser energy fixed at its resonant value . At low values of , the absorption spectrum displays a single broad peak centered at the exciton resonance, indicating negligible quantum interference between states. As the Rabi frequency increases, starting from ~35 meV we observe the emergence of a narrow transparency window flanked by two absorption peaks which is a characteristic signature of EIT. This transparency window arises from destructive interference between the excitation pathways involving the probe and coupling fields. Notably, the width of the EIT window expands with increasing , illustrating the enhanced coherence and stronger coupling between quantum states under more intense coupling fields.

Let us move on to analyzing the case of figure 3(b), here the is fixed at mark, however, the Y-axis denotes the coupling laser energy . Unlike the previous case where the absorption exhibited a V-shape here, it exhibits an N-shaped spectrum. Here we can see clearly that the case where two peaks in the probe absorption are only equal around the coupling resonance. At maximum quantum coherence is achieved leading to effective destructive interference. When the detuning is different from zero, we can see that one of the absorption peaks begins to dominate the other, moreover, as the detuning increases, we see an additional increase in the transparency window.

We now turn to the case in figures 3(c) and (d), where the control system is activated, with 80% of the nanorods illuminated by structured needle beams at intensity . This specific activation level was chosen because it clearly reveals the effects of localized field-induced modulation. For this case, the coupling laser energy is taken as an intermediate value , averaging the coupling resonances of the inactive (natural) and active (controlled) nanorod populations. This results in significant spectral modifications. Unless stated otherwise, the coupling laser energy is chosen at the spectral midpoint between the resonances of the inactive and ILF-dressed nanorod sub-ensembles, ensuring that both populations contribute comparably to the ensemble-averaged coherent response.

First, the resonance energies shift, reflecting the influence of intense laser field dressing on the energy levels, , . Moreover, we observe new spectral features emerging: for low than Rabi frequencies, a bright triangular central peak appears, accompanied by two weaker satellite peaks on either side. As the coupling Rabi frequency increases, a second set of satellites becomes visible, and the central peak begins to diminish a signature of the emergence of a transparency window between the two absorption doublets. Each doublet exhibits a local minimum, indicating partial suppression of absorption, though these regions are not fully transparent, as will become more evident in figure 3. This second set of satellites originates from the coexistence of nanorod sub-ensembles experiencing different local dressing conditions under structured illumination, which satisfy the EIT resonance at distinct probe energies.

In the final plot of figure 3(d) we can see that analogously to the case discussed previously we have an emergence of the second set of peaks in the absorption and sure enough the spot where these peaks are all relative is around .

To further explore the EIT phenomenon in the nanorod ensemble, figure 4 presents the dependence of the imaginary and real parts of the optical susceptibility χ on the probe laser energy for varying coupling Rabi frequencies . Each row in the figure represents a different activation scenario: the natural state with no needle beam illumination (figures 4(a) and (b)); full homogeneous activation of the nanorod ensemble by needle beams with intensity values (figures 4(c) and (d)) and (figures 4(e) and (f)).

Figure 4. Dependence of the imaginary (left column) and real (right column) parts of the optical susceptibility χ on the probe laser energy for different values of the coupling Rabi frequency , under varying nanorod activation conditions. (a), (b) Natural state with no nanorods illuminated . (c), (d) Homogeneous activation of the nanorod ensemble (100% of nanorods are illuminated ). (e), (f) Homogeneous activation using structured needle beams at an intensity of . Each row corresponds to a different control configuration, while the coupling strength is varied within each subplot to highlight the evolution of absorption and refractive index modulation across regimes.

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In the unperturbed, or natural, configuration (figures 4(a) and (b)), the nanorods are not illuminated by any control field. At = 0, the coupling field is off, the coupling laser is turned off, and the system exhibits a single absorption peak centered at , corresponding to the probe resonance energy of 502 meV. This peak results from direct transitions between the ground and exciton states, without quantum interference. The real part of the susceptibility shows a sharp normal-to-anomalous dispersion transition near resonance, with the refractive index decreasing as the probe energy increases. As the coupling Rabi frequency increases, a clear transparency window emerges between two absorption peaks a typical signature of EIT. This spectral splitting arises from destructive interference between two excitation pathways in the ladder-type three-level system. In the corresponding profile (figure 4(b)), we observe the development of a structured dispersion curve with triple zero-crossings, indicative of sharp refractive index modulation near the transparency window.

When the nanorod array is homogeneously illuminated with moderate intensity