Wavelength-Multiplexed 2D Beam Steering via a Passive Diffractive Network

We introduce a wavelength-addressable diffractive optical network that transforms illumination wavelength into a high-dimensional control parameter for arbitrarily programmable 2D beam steering. The proposed passive architecture comprises cascaded spatially optimized diffractive layers, jointly designed using deep learning, to rapidly map distinct wavelengths to predefined/desired output angles. Unlike conventional single-layer dispersive optical elements, which are physically restricted to 1D linear mapping, this framework harnesses complex wavefront transformations to utilize the illumination wavelength as an intrinsic addressing key for arbitrary 2D beam steering, eliminating the need for mechanical scanning or electronic phase control. We numerically demonstrate wavelength-controlled beam steering across 625 wavelength channels spanning 400-750 nm, realizing a 25 x 25 array of independently addressable beam positions with subwavelength positioning accuracy and high channel fidelity. Unlike conventional gratings, which constrain wavelength routing to a linear trajectory, the proposed diffractive network performs nonlocal wavefront transformations, enabling arbitrary wavelength-to-angle mappings across a 2D field of view. We further validate the proposed framework experimentally in both the terahertz and visible spectral regimes, demonstrating wavelength-multiplexed beam steering using 3D fabricated passive diffractive layers at terahertz frequencies and phase-only spatial light modulators in the visible spectrum. This wavelength-addressable diffractive architecture establishes a compact and scalable paradigm for high-speed programmable beam steering, with potential applications in optical communications, routing, imaging, sensing, and emerging photonic information-processing systems.

Wavelength-multiplexed massively parallel diffractive optical information storage and image projection

We introduce a wavelength-multiplexed massively parallel diffractive information storage platform composed of dielectric surfaces that are structurally optimized at the wavelength scale using deep learning to store and project thousands of distinct image patterns, each assigned to a unique wavelength. Through numerical simulations in the visible spectrum, we demonstrated that our wavelength-multiplexed diffractive system can store and project over 4,000 independent desired images/patterns within its output field-of-view, with high image quality and minimal crosstalk between spectral channels. Furthermore, in a proof-of-concept experiment, we demonstrated a two-layer diffractive design that stored six distinct patterns and projected them onto the same output field of view at six different wavelengths (500, 548, 596, 644, 692, and 740 nm). This diffractive architecture is scalable and can operate at various parts of the electromagnetic spectrum without the need for material dispersion engineering or redesigning its optimized diffractive layers. The demonstrated storage capacity, reconstruction image fidelity, and wavelength-encoded massively parallel read-out of our diffractive platform offer a compact and fast-access solution for large-scale optical information storage, image projection applications.

Multiplane Quantitative Phase Imaging Using a Wavelength-Multiplexed Diffractive Optical Processor

Quantitative phase imaging (QPI) is a label-free technique that provides optical path length information for transparent specimens, finding utility in biology, materials science, and engineering. Here, we present quantitative phase imaging of a 3D stack of phase-only objects using a wavelength-multiplexed diffractive optical processor. Utilizing multiple spatially engineered diffractive layers trained through deep learning, this diffractive processor can transform the phase distributions of multiple 2D objects at various axial positions into intensity patterns, each encoded at a unique wavelength channel. These wavelength-multiplexed patterns are projected onto a single field-of-view (FOV) at the output plane of the diffractive processor, enabling the capture of quantitative phase distributions of input objects located at different axial planes using an intensity-only image sensor. Based on numerical simulations, we show that our diffractive processor could simultaneously achieve all-optical quantitative phase imaging across several distinct axial planes at the input by scanning the illumination wavelength. A proof-of-concept experiment with a 3D-fabricated diffractive processor further validated our approach, showcasing successful imaging of two distinct phase objects at different axial positions by scanning the illumination wavelength in the terahertz spectrum. Diffractive network-based multiplane QPI designs can open up new avenues for compact on-chip phase imaging and sensing devices.

Multiplexed all-optical permutation operations using a reconfigurable diffractive optical network

Large-scale and high-dimensional permutation operations are important for various applications in e.g., telecommunications and encryption. Here, we demonstrate the use of all-optical diffractive computing to execute a set of high-dimensional permutation operations between an input and output field-of-view through layer rotations in a diffractive optical network. In this reconfigurable multiplexed material designed by deep learning, every diffractive layer has four orientations: 0, 90, 180, and 270 degrees. Each unique combination of these rotatable layers represents a distinct rotation state of the diffractive design tailored for a specific permutation operation. Therefore, a K-layer rotatable diffractive material is capable of all-optically performing up to 4^K independent permutation operations. The original input information can be decrypted by applying the specific inverse permutation matrix to output patterns, while applying other inverse operations will lead to loss of information. We demonstrated the feasibility of this reconfigurable multiplexed diffractive design by approximating 256 randomly selected permutation matrices using K=4 rotatable diffractive layers. We also experimentally validated this reconfigurable diffractive network using terahertz radiation and 3D-printed diffractive layers, providing a decent match to our numerical results. The presented rotation-multiplexed diffractive processor design is particularly useful due to its mechanical reconfigurability, offering multifunctional representation through a single fabrication process.

All-optical complex field imaging using diffractive processors

Complex field imaging, which captures both the amplitude and phase information of input optical fields or objects, can offer rich structural insights into samples, such as their absorption and refractive index distributions. However, conventional image sensors are intensity-based and inherently lack the capability to directly measure the phase distribution of a field. This limitation can be overcome using interferometric or holographic methods, often supplemented by iterative phase retrieval algorithms, leading to a considerable increase in hardware complexity and computational demand. Here, we present a complex field imager design that enables snapshot imaging of both the amplitude and quantitative phase information of input fields using an intensity-based sensor array without any digital processing. Our design utilizes successive deep learning-optimized diffractive surfaces that are structured to collectively modulate the input complex field, forming two independent imaging channels that perform amplitude-to-amplitude and phase-to-intensity transformations between the input and output planes within a compact optical design, axially spanning ~100 wavelengths. The intensity distributions of the output fields at these two channels on the sensor plane directly correspond to the amplitude and quantitative phase profiles of the input complex field, eliminating the need for any digital image reconstruction algorithms. We experimentally validated the efficacy of our complex field diffractive imager designs through 3D-printed prototypes operating at the terahertz spectrum, with the output amplitude and phase channel images closely aligning with our numerical simulations. We envision that this complex field imager will have various applications in security, biomedical imaging, sensing and material science, among others.

Subwavelength Imaging using a Solid-Immersion Diffractive Optical Processor

Phase imaging is widely used in biomedical imaging, sensing, and material characterization, among other fields. However, direct imaging of phase objects with subwavelength resolution remains a challenge. Here, we demonstrate subwavelength imaging of phase and amplitude objects based on all-optical diffractive encoding and decoding. To resolve subwavelength features of an object, the diffractive imager uses a thin, high-index solid-immersion layer to transmit high-frequency information of the object to a spatially-optimized diffractive encoder, which converts/encodes high-frequency information of the input into low-frequency spatial modes for transmission through air. The subsequent diffractive decoder layers (in air) are jointly designed with the encoder using deep-learning-based optimization, and communicate with the encoder layer to create magnified images of input objects at its output, revealing subwavelength features that would otherwise be washed away due to diffraction limit. We demonstrate that this all-optical collaboration between a diffractive solid-immersion encoder and the following decoder layers in air can resolve subwavelength phase and amplitude features of input objects in a highly compact design. To experimentally demonstrate its proof-of-concept, we used terahertz radiation and developed a fabrication method for creating monolithic multi-layer diffractive processors. Through these monolithically fabricated diffractive encoder-decoder pairs, we demonstrated phase-to-intensity transformations and all-optically reconstructed subwavelength phase features of input objects by directly transforming them into magnified intensity features at the output. This solid-immersion-based diffractive imager, with its compact and cost-effective design, can find wide-ranging applications in bioimaging, endoscopy, sensing and materials characterization.

Information hiding cameras: optical concealment of object information into ordinary images

Data protection methods like cryptography, despite being effective, inadvertently signal the presence of secret communication, thereby drawing undue attention. Here, we introduce an optical information hiding camera integrated with an electronic decoder, optimized jointly through deep learning. This information hiding-decoding system employs a diffractive optical processor as its front-end, which transforms and hides input images in the form of ordinary-looking patterns that deceive/mislead human observers. This information hiding transformation is valid for infinitely many combinations of secret messages, all of which are transformed into ordinary-looking output patterns, achieved all-optically through passive light-matter interactions within the optical processor. By processing these ordinary-looking output images, a jointly-trained electronic decoder neural network accurately reconstructs the original information hidden within the deceptive output pattern. We numerically demonstrated our approach by designing an information hiding diffractive camera along with a jointly-optimized convolutional decoder neural network. The efficacy of this system was demonstrated under various lighting conditions and noise levels, showing its robustness. We further extended this information hiding camera to multi-spectral operation, allowing the concealment and decoding of multiple images at different wavelengths, all performed simultaneously in a single feed-forward operation. The feasibility of our framework was also demonstrated experimentally using THz radiation. This optical encoder-electronic decoder-based co-design provides a novel information hiding camera interface that is both high-speed and energy-efficient, offering an intriguing solution for visual information security.

All-Optical Phase Conjugation Using Diffractive Wavefront Processing

Optical phase conjugation (OPC) is a nonlinear technique used for counteracting wavefront distortions, with various applications ranging from imaging to beam focusing. Here, we present the design of a diffractive wavefront processor to approximate all-optical phase conjugation operation for input fields with phase aberrations. Leveraging deep learning, a set of passive diffractive layers was optimized to all-optically process an arbitrary phase-aberrated coherent field from an input aperture, producing an output field with a phase distribution that is the conjugate of the input wave. We experimentally validated the efficacy of this wavefront processor by 3D fabricating diffractive layers trained using deep learning and performing OPC on phase distortions never seen by the diffractive processor during its training. Employing terahertz radiation, our physical diffractive processor successfully performed the OPC task through a shallow spatially-engineered volume that axially spans tens of wavelengths. In addition to this transmissive OPC configuration, we also created a diffractive phase-conjugate mirror by combining deep learning-optimized diffractive layers with a standard mirror. Given its compact, passive and scalable nature, our diffractive wavefront processor can be used for diverse OPC-related applications, e.g., turbidity suppression and aberration correction, and is also adaptable to different parts of the electromagnetic spectrum, especially those where cost-effective wavefront engineering solutions do not exist.

All-optical image denoising using a diffractive visual processor

Image denoising, one of the essential inverse problems, targets to remove noise/artifacts from input images. In general, digital image denoising algorithms, executed on computers, present latency due to several iterations implemented in, e.g., graphics processing units (GPUs). While deep learning-enabled methods can operate non-iteratively, they also introduce latency and impose a significant computational burden, leading to increased power consumption. Here, we introduce an analog diffractive image denoiser to all-optically and non-iteratively clean various forms of noise and artifacts from input images - implemented at the speed of light propagation within a thin diffractive visual processor. This all-optical image denoiser comprises passive transmissive layers optimized using deep learning to physically scatter the optical modes that represent various noise features, causing them to miss the output image Field-of-View (FoV) while retaining the object features of interest. Our results show that these diffractive denoisers can efficiently remove salt and pepper noise and image rendering-related spatial artifacts from input phase or intensity images while achieving an output power efficiency of ~30-40%. We experimentally demonstrated the effectiveness of this analog denoiser architecture using a 3D-printed diffractive visual processor operating at the terahertz spectrum. Owing to their speed, power-efficiency, and minimal computational overhead, all-optical diffractive denoisers can be transformative for various image display and projection systems, including, e.g., holographic displays.

Pyramid diffractive optical networks for unidirectional magnification and demagnification

Diffractive deep neural networks (D2NNs) are composed of successive transmissive layers optimized using supervised deep learning to all-optically implement various computational tasks between an input and output field-of-view (FOV). Here, we present a pyramid-structured diffractive optical network design (which we term P-D2NN), optimized specifically for unidirectional image magnification and demagnification. In this P-D2NN design, the diffractive layers are pyramidally scaled in alignment with the direction of the image magnification or demagnification. Our analyses revealed the efficacy of this P-D2NN design in unidirectional image magnification and demagnification tasks, producing high-fidelity magnified or demagnified images in only one direction, while inhibiting the image formation in the opposite direction - confirming the desired unidirectional imaging operation. Compared to the conventional D2NN designs with uniform-sized successive diffractive layers, P-D2NN design achieves similar performance in unidirectional magnification tasks using only half of the diffractive degrees of freedom within the optical processor volume. Furthermore, it maintains its unidirectional image magnification/demagnification functionality across a large band of illumination wavelengths despite being trained with a single illumination wavelength. With this pyramidal architecture, we also designed a wavelength-multiplexed diffractive network, where a unidirectional magnifier and a unidirectional demagnifier operate simultaneously in opposite directions, at two distinct illumination wavelengths. The efficacy of the P-D2NN architecture was also validated experimentally using monochromatic terahertz illumination, successfully matching our numerical simulations. P-D2NN offers a physics-inspired strategy for designing task-specific visual processors.