Vertical-cavity surface-emitting laser for physical unclonable function authentication and random number generation

Abstract

A vertical-cavity surface-emitting laser (VCSEL) (100) and an optoelectronic module are configured for hardware-based authentication and entropy generation. The VCSEL (100) may include a transversely modified multimode (TMM) cavity (111) configured to support multimode lasing. A non-circular geometry of the TMM cavity (111) and an oxidation aperture (114) may be configured to produce a unique far-field intensity pattern (402) for physical unclonable function (PUF) authentication. A broad-area emission region of the TMM cavity (111) may be configured to promote modal competition and nonlinear dynamics, such as spatial hole burning or filamentation, to produce spatiotemporal intensity fluctuations for random number generation (RNG). In some embodiments, the VCSEL (100) is biased in a sub- threshold regime to facilitate quantum random number generation (QRNG) or in a multimode regime to facilitate self-chaotic RNG. A photodetector (PD) (602) may be monolithically integrated with the VCSEL (100) to capture optical fluctuations adjacent to or vertically aligned with the TMM cavity (111).

Description

Attorney Docket No. 0338-801 -WO / 2025-034-02VERTICAL-CAVITY SURFACE-EMITTING LASER FOR PHYSICAL UNCLONABLE FUNCTION AUTHENTICATION AND RANDOM NUMBER GENERATIONCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 63 / 777,091 , filed on March 25, 2026, entitled “TRANSVERSELY MODIFIED MULTIMODE VCSELS FOR SCALABLE PUF-BASED AUTHENTICATION AND ULTRAHIGH-SPEED RANDOM NUMBER GENERATION,” the disclosure of which is incorporated herein by reference in its entirety.BACKGROUND OF THE INVENTION TECHNICAL FIELD

[0002] Embodiments of the subject matter disclosed herein generally relate to vertical-cavity surface-emitting lasers (VCSELs) and methods for generating random numbers and physical unclonable function (PUF) authentication, and more particularly, to a VCSEL that includes a transversely modified multimode cavity for entropy generation.DISCUSSION OF THE BACKGROUND

[0003] This background description is provided for the purpose of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent it is described in this background section, as well as aspects of thedescription that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present disclosure.

[0004] In the fields of digital security and device authentication, PUFs have gained prominence for their ability to generate unique challenge-response pairs based on inherent physical characteristics of a device. These hardware-based signatures are utilized for anti-counterfeiting and secure identification. However, many existing PUF technologies, such as those based on static random-access memory (SRAM) or complex nanostructures, face challenges regarding vulnerability to environmental fluctuations, sensitivity to operational conditions, and limited scalability. Furthermore, conventional optical PUFs often rely on external scattering media or fragile labels, which increases system complexity and impedes seamless integration into compact electronic platforms.

[0005] VCSELs are widely implemented in consumer electronics for applications such as optical communication and 3D sensing. Traditional circularaperture VCSELs typically support a limited number of whispering gallery modes (WGMs) due to their continuous rotational symmetry. This symmetry tends to confine the optical field near the periphery of the cavity, leaving the central gain region underutilized and limiting the total achievable output power. Additionally, broad-area circular cavities may exhibit instabilities and mode competition that are difficult to control or leverage for high-entropy generation without external optical feedback or complex modulation schemes.

[0006] Secure communication systems also require high-quality random number generation (RNG) for cryptographic key provisioning. Conventionalpseudorandom number generators (PRNGs) are based on deterministic algorithms that may become predictable if initial seeds are exposed. While quantum random number generators (QRNGs) provide high unpredictability, existing hardware implementations often depend on discrete components and precise mechanical alignment, which restricts their utility in resource-constrained or embedded environments. There is a need for a self-contained, scalable photonic platform that can provide both robust hardware-level authentication and high-speed entropy generation using established manufacturing infrastructures.SUMMARY OF THE INVENTION

[0007] Embodiments of the present disclosure relate to a VCSEL and a method for hardware authentication and random number generation. The VCSEL includes a bottom distributed Bragg reflector stack, an active region, and a top DBR stack that define a transversely modified multimode (TMM) cavity configured to support multimode lasing. An oxidation aperture is disposed within the TMM cavity and follows a non-circular geometry of the TMM cavity mesa to produce a unique far- field intensity pattern for PUF authentication. This non-circular geometry, such as a pentagonal, D-shaped, mushroom-shaped, or square geometry, is configured to produce a unique optical identifier for device-level identification.

[0008] The TMM cavity may include a broad-area emission region having an area greater than 700 pm2configured to promote spatial and spectral mode overlap. This overlap drives modal competition and nonlinear dynamics to produce spatiotemporal intensity fluctuations for producing a random bitstream. In some embodiments, the VCSEL is biased in a sub-threshold regime where an injection current is maintained below a lasing threshold level to exploit spontaneous emission noise for QRNG. In other embodiments, the VCSEL is biased in a multimode regime to exploit self-chaotic dynamics for an RNG source.

[0009] The system may further include a photodetector (PD) monolithically integrated with the VCSEL on a shared substrate. In one configuration, the PD is positioned adjacent to the TMM cavity in a co-planar integrated array to capture edge-emitted light. In another configuration, the PD is vertically stacked above theTMM cavity to capture surface-directed light in situ. A processing unit employing a convolutional neural network (CNN) may be utilized to identify unique features of the unique far-field intensity pattern for real-time authentication. The VCSEL may also include a p-metal electrode that defines an emission window configured to facilitate facial recognition scanning, allowing the device to simultaneously provide a hardware-rooted identifier and a biometric input for multi-factor authentication. Furthermore, the VCSEL may be part of a multi-key authentication system configured to produce a constellation of unique far-field responses in response to controlled challenges, such as modulated injection currents or varying operating temperatures.BRIEF DESCRIPTION OF THE DRAWINGS

[0010] For a more complete understanding of the present invention, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which:

[0011] FIG. 1 is a cross-sectional view of a VCSEL employing a TMM cavity to facilitate the production of a unique far-field intensity pattern according to an embodiment.

[0012] FIG. 2A is a graph illustrating the light-current density characteristics of a circular cavity geometry according to an embodiment.

[0013] FIG. 2B is a graph illustrating the light-current density characteristics of a square cavity geometry according to an embodiment.

[0014] FIG. 2C is a graph illustrating the light-current density characteristics of a D-shaped cavity geometry according to an embodiment.

[0015] FIG. 2D is a graph illustrating the light-current density characteristics of a mushroom-shaped cavity geometry according to an embodiment.

[0016] FIG. 2E is a graph illustrating the light-current density characteristics of a pentagonal cavity geometry according to an embodiment.

[0017] FIG. 3 is a flowchart illustrating a method for fabricating a VCSEL having a TMM cavity according to an embodiment.

[0018] FIG. 4A is a schematic view of a first unique far-field intensity pattern generated by a first VCSEL according to an embodiment.

[0019] FIG. 4B is a schematic view of a second unique far-field intensity pattern generated by a second VCSEL according to an embodiment.

[0020] FIG. 4C is a schematic view of a third unique far-field intensity pattern generated by a third VCSEL according to an embodiment.

[0021] FIG. 5A is a schematic view of a first mobile device employing a unique far-field intensity pattern for authentication according to an embodiment.

[0022] FIG. 5B is a schematic view of a second mobile device employing a unique far-field intensity pattern for authentication according to an embodiment.

[0023] FIG. 5C is a schematic view of a third mobile device employing a unique far-field intensity pattern for authentication according to an embodiment.

[0024] FIG. 6 is a system architecture diagram illustrating an anticounterfeiting authentication process using a unique far-field intensity pattern and a neural network according to an embodiment.

[0025] FIG. 7 is a schematic view illustrating a secure communication system using a unique far-field intensity pattern for device-to-device authentication according to an embodiment.

[0026] FIG. 8 is an infographic illustrating a multi-key authentication system configured to generate unique far-field responses based on varying operational challenges according to an embodiment.

[0027] FIG. 9 is a schematic view illustrating a keyless entry system configured to grant vehicle or building access based on a unique far-field intensity pattern according to an embodiment.

[0028] FIG. 10 is a flow diagram illustrating a supply chain security system using hardware-based fingerprints for product verification according to an embodiment.

[0029] FIG. 11 is a system architecture diagram illustrating a centralized authentication ecosystem for Internet of Things (loT) devices according to an embodiment.

[0030] FIG. 12 is a perspective view illustrating an array of VCSELs having pentagonal mesas on a single substrate according to an embodiment.

[0031] FIG. 13 is a top-down view illustrating a co-planar integrated array of VCSEL and PD pairs according to an embodiment.

[0032] FIG. 14 is a schematic view illustrating a secure communication system providing both hardware-based authentication and RNG according to an embodiment.

[0033] FIG. 15 is a neural network architecture diagram illustrating a CNN configured to identify features of a unique far-field intensity pattern according to an embodiment.

[0034] FIG. 16 is a cross-sectional view illustrating a monolithically integrated emitter-detector architecture having a vertically stacked PD and VCSEL according to an embodiment.

[0035] FIG. 17 is a flowchart illustrating a method for fabricating a monolithically integrated emitter-detector architecture according to an embodiment.

[0036] FIGS. 18A to 18G illustrate a visual evolution of the integrated device through a sequence of fabrication steps including epitaxial growth, selective etchingof the photodetector and VCSEL mesas, formation of the oxidation aperture, and subsequent metallization of the independent electrodes

[0037] FIG. 19 is a flowchart illustrating a method for hardware authentication and RNG using a TMM cavity according to an embodiment.DETAILED DESCRIPTION OF THE INVENTION

[0038] The following description of the embodiments refers to the accompanying drawings. The same reference numbers in different drawings identify the same or similar elements. The following detailed description does not limit the invention. Instead, the scope of the invention is defined by the appended claims. The following embodiments are discussed, for simplicity, with regard to a VCSEL that includes a TMM cavity. In some embodiments, the TMM cavity includes a noncircular geometry, such as a pentagonal, D-shaped, or mushroom-shaped aperture, configured to produce a unique far-field emission pattern for PUF authentication. However, the embodiments to be discussed next are not limited to a certain TMM cavity geometry.

[0039] Reference throughout the specification to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with an embodiment is included in at least one embodiment of the subject matter disclosed. Thus, the appearance of the phrases “in one embodiment” or “in an embodiment” in various places throughout the specification is not necessarily referring to the same embodiment. Further, the particular features, structures or characteristics may be combined in any suitable manner in one or more embodiments.

[0040] According to an embodiment, a VCSEL configured with a TMM cavity is used to facilitate the generation of a PUF and high-speed random numbers. To enhance the complexity of the emitted light and the resulting entropy, the cavitygeometry is transversely modified into non-circular shapes, such as pentagonal, D- shaped, mushroom-shaped, or square apertures. These asymmetric geometries break the continuous rotational symmetry of the cavity, suppressing WGMs and promoting intense modal competition and nonlinear dynamics, including spatial hole burning and filamentation. The surface-directed emission from the VCSEL produces a unique far-field intensity pattern, which serves as a hardware-based optical fingerprint for device authentication. Additionally, the fast spatiotemporal intensity fluctuations generated within the TMM cavity provide a high-entropy source that may be detected and digitized to produce cryptographically secure random numbers. This integrated approach allows a single photonic device to perform both device-level identification and secure key generation.

[0041] An embodiment is illustrated in FIG. 1 , where a VCSEL 100 includes an n-GaAs substrate 102, an n-GaAs buffer 104, and an n-AIGaAs distributed Bragg reflector (DBR) stack 106, which may include an n-type AIGaAs DBR stack (e.g., 38 pairs) as a bottom mirror. An active region 108, such as a multiple quantum well (MQW) layer, is positioned atop the n-type DBR stack 106. The MQW layer is configured to emit light 112 at a specific wavelength, such as approximately 940 nm. A p-type AIGaAs DBR stack 110, for example, including 20 to 22 pairs, is disposed above the active region 108 to function as a top mirror. In some embodiments, the n- type and p-type DBR stacks 106, 110 facilitate the resonant feedback necessary for laser operation. Together, the bottom DBR stack 106, the active region 108, and the top DBR stack 110 define a TMM cavity 111 configured to support multimode lasing.

[0042] A high-aluminum content layer may be included within the p-type AIGaAs DBR stack 110 to facilitate the formation of an oxidation aperture 114 within the TMM cavity 111. The oxidation aperture 114 is configured to follow the noncircular geometry of the TMM cavity 111 mesa but typically possesses a smaller transversal footprint. For example, as described later in method 300, the oxidation aperture 114 is defined by a lateral oxidation length, such as approximately 25 pm, measured from the sidewalls of the TMM cavity 111 mesa. This unoxidized central region provides current and optical confinement while maintaining the asymmetric modal landscape defined by the cavity geometry.

[0043] Electrodes 116 and 118 are provided on n-AIGaAs DBR 106 and p- AIGaAs DBR 110, respectively. An insulation layer 120 separates the electrode 118 from the other components. In some embodiments, the electrodes 116 and 118 are configured to provide electrical biasing to the VCSEL 100. Specifically, the electrode 116 may be an n-metal electrode or n-pad formed on the n-AIGaAs DBR 106 or the n-GaAs substrate 102, while the electrode 118 may be a p-metal electrode or p-pad formed on the p-AIGaAs DBR 110.

[0044] In this configuration, the p-metal electrode 118 can be patterned to define an emission window 122 that allows the surface-directed light 112 to escape the cavity, whereas the n-metal electrode 116 provides the return path for the injection current. The term "n-metal" indicates that the electrode is in electrical contact with an n-type semiconductor layer, typically formed using a metal stack such as Ni / Ge / Au, while "p-metal" indicates contact with a p-type layer, often utilizing metals such as Ti / Au. Together, these electrodes allow for the injection of carriersinto the active region 108 to facilitate stimulated emission. In some embodiments, the electrode 118 may also function as a contact for an integrated PD, where the shared p-contact architecture allows for a compact, monolithically integrated optoelectronic module.

[0045] In contrast to a light-emitting diode (LED), which relies on spontaneous emission and typically emits incoherent light over a broad angular range and spectral width, the VCSEL 100 is a semiconductor laser that utilizes stimulated emission to produce a coherent, narrow-linewidth beam 112. Structurally, while an LED lacks a resonant cavity, the VCSEL 100 incorporates the TMM cavity 111 defined by the bottom DBR stack 106 and the top DBR stack 110, which provide the optical feedback necessary to achieve a lasing threshold. Once this threshold is surpassed, the VCSEL 100 emits light 112 vertically from the surface of the substrate 102, characterized by higher optical power density and faster modulation speeds compared to an LED. Furthermore, the inclusion of the oxidation aperture 114 within the TMM cavity 111 allows for precise control over the current confinement and the transverse mode profile. This configuration enables the VCSEL 100 to generate a unique far-field intensity pattern for PUF authentication and complex spatiotemporal intensity fluctuations for high-speed RNG, functionalities that are not attainable with the simpler, incoherent emission of a standard LED.

[0046] According to an embodiment, the microstructural variations that occur naturally during the epitaxial growth and subsequent fabrication of the DBR stacks 106, 110 and the oxidation aperture 114 contribute to a unique far-field emission profile. These physical differences, which are irreproducible across different devices,allow each VCSEL 100 to serve as a PUF for secure hardware-level identification. Additionally, the transverse modification of the cavity 111 and / or oxidation aperture 114 into asymmetric geometries (i.e., non-circular geometries such as pentagonal or D-shaped apertures), promote multimode lasing and complex nonlinear dynamics, which can be leveraged for both authentication and entropy generation.

[0047] As illustrated in FIGs. 2A to 2B, the cavity (i.e., element 111 in FIG. 1 ) geometry (which is typically circular as illustrated in FIG. 2A) may be modified into non-circular shapes, such as square (FIG. 2B), D-shaped (FIG. 2C), mushroomshaped (FIG. 2D), or pentagonal (FIG. 2E) apertures. For these cases, the DBRs 106 and 110 are also shaped accordingly, as schematically illustrated in FIGs. 2A to 2E.

[0048] These asymmetric geometries break the continuous rotational symmetry of the cavity, which effectively suppresses WGMs and promotes intense modal competition. For example, a pentagonal VCSEL may support a higher number of modes and faster mode dynamics compared to a circular counterpart. This increased modal richness contributes to a more intricate far-field intensity distribution, which improves the entropy of the resulting PUF and increases the maximum achievable optical power.

[0049] FIGs. 2A to 2E further illustrate the light-current density (L-J) characteristics for various cavity geometries. As depicted in FIG. 2A, a traditional circular VCSEL (O-VCSEL) with an aperture radius of 17 pm exhibits a power output that reaches a maximum of approximately 14 mW before undergoing thermal roll-off. This geometry has an estimated emission aperture area of approximately 907 pm2and tends to saturate at lower current levels compared to asymmetric designs. In contrast, the square VCSEL (S-VCSEL) illustrated in FIG. 2B, featuring an aperture side length of 28 pm and an estimated area of approximately 778 pm2, shows an improvement in power efficiency and peak output over the circular design. The D- shaped VCSEL (D-VCSEL) shown in FIG. 2C, configured with a curved radius of 16 pm and a flat-to-center distance of 7 pm, results in an estimated emission area of approximately 713 pm2. This D-shaped geometry demonstrates a further increase in optical power, surpassing both the circular and square geometries. The mushroomshaped VCSEL (M-VCSEL) in FIG. 2D, which integrates a semicircular top section with a narrower stem, provides an estimated emission area of approximately 907 pm2and achieves a significantly higher optical power of approximately 23.5 mW. The pentagonal VCSEL, P-VCSEL, featuring a side length of approximately 21 pm, achieves the highest optical power output at approximately 24.5 mW as illustrated in FIG. 2E.

[0050] This geometry demonstrates superior performance in delivering higher power from a single device by breaking the continuous rotational symmetry of the cavity. The P-VCSEL supports a high number of modes and promotes intense modal competition and fast mode dynamics, which makes the P-VCSEL a suitable candidate for high-speed entropy generation.

[0051] To facilitate these various geometries and their respective performance characteristics, the TMM cavity 111 for each geometry may be configured with a broad-area emission region having an area greater than 700 pm2. This broad-areafootprint promotes spatial and spectral mode overlap to drive modal competition and nonlinear dynamics for producing spatiotemporal intensity fluctuations for RNG.

[0052] As depicted in the L-J density characteristics in FIGs. 2A to 2E, the P- VCSEL (FIG. 2E) shows more than twice the optical power density compared to the circular counterpart. This increased power and power density are closely related to the increased density of states and increased number of modes allowed by the pentagonal boundary conditions, which facilitate enhanced utilization of the gain medium across the active region.

[0053] Additionally, the P-VCSEL exhibits a more gradual decline in Q-factors beyond the initial modes, which supports efficient multimode lasing as a larger number of modes can be excited under similar injection conditions. These intricate nonlinear dynamics and spatiotemporal intensity fluctuations enable an ultrah igh- speed random number generation rate, approaching the physical limits of the measurement system. These L-J curves illustrate that by breaking the continuous rotational symmetry of the cavity, the emission aperture can facilitate enhanced gain medium utilization and higher power densities.

[0054] In addition to the power and power density improvements, the shaping of the cavity geometry significantly modifies the spectral and modal characteristics of the VCSEL. Traditional circular apertures typically favor a limited number of WGMs that tend to concentrate light near the periphery. By utilizing a pentagonal geometry as illustrated in FIG. 2E, the continuous rotational symmetry is broken, which increases the density of states and the number of supported transverse modes. Thismodal richness facilitates more intense modal competition and faster mode dynamics, which are advantageous for generating high-entropy signals.

[0055] Furthermore, the transverse modification of the cavity into asymmetric shapes such as D-shaped or pentagonal apertures allows for enhanced utilization of the gain medium. While circular designs often leave the central region underutilized, non-circular geometries promote a more uniform spatial distribution of modes across the entire active region. This improved gain utilization not only contributes to the higher peak optical power observed in asymmetric designs but also supports more efficient energy conversion above the lasing threshold, as reflected in the increased slope efficiency compared to standard circular configurations.

[0056] The shaping of the cavity also serves as an important mechanism for controlling spatial coherence and speckle formation. For applications requiring low- coherence illumination, such as speckle-free imaging, geometries like the mushroom-shaped or pentagonal apertures are particularly effective. These shapes support a large number of coexisting incoherent modes, which effectively reduces the spatial coherence of the emitted beam. This results in a significant reduction in speckle contrast, enabling clearer and more uniform illumination without the need for external moving parts or complex optical systems.

[0057] Finally, cavity geometry design provides an additional degree of freedom to stabilize or tune polarization dynamics. While circular VCSELs often exhibit unstable polarization behavior due to their high degree of symmetry, introducing straight boundaries — as seen in D-shaped or square apertures — can help define a preferred polarization axis. For instance, a D-shaped geometry canleverage the intrinsic anisotropy of the semiconductor material to enhance the orthogonal polarization suppression ratio, providing a more stable and predictable polarization state. Conversely, pentagonal designs can be used to promote polarization switching and complex interactions, which are beneficial for high-speed dynamic applications.

[0058] A method 300 for fabricating a TMM VCSEL 100 is illustrated in FIG. 3. The method 300 begins with the deposition 302 of a silicon oxide layer, for example, having a thickness of approximately 600 nm, onto a VCSEL wafer. The silicon oxide layer may serve as a hard mask and may be deposited via plasma-enhanced chemical vapor deposition (PECVD). A positive photoresist is spin-coated 304, for example, at 3,000 rpm for 30 seconds, and subjected to a soft bake. Device geometries, such as pentagonal, D-shaped, mushroom-shaped, or circular patterns, are defined 306 using a lithography system and a developer. The lithographically patterned photoresist is used to transfer 308 the device geometries into the silicon oxide mask via reactive ion etching (RIE) using CHF3gas (5 seem) under 100 W RF power, 10 mTorr chamber pressure, and a substrate temperature of 10 °C. The RIE process selectively removes the oxide.

[0059] After removing the photoresist, mesa etching is performed 310 to define a mesa structure. This etching may be performed using inductively coupled plasma reactive ion etching (ICP-RIE), reaching a depth sufficient to expose a high- aluminum content layer within the p-AIGaAs DBR stack 110. In some embodiments, the etching depth is controlled to stop at a low-aluminum content layer of the n- AIGaAs DBR stack 106. Wet thermal oxidation is then performed 312 to define theoxidation aperture 114 for current and optical confinement. The oxidation process may be conducted in an oxidation furnace, where the oxidation progress is monitored in real-time using near-infrared imaging to achieve a lateral oxidation length of approximately 25 pm from the mesa sidewalls to the oxidation aperture 114.

[0060] The method 300 continues with the deposition 314 of the insulation layer 120, such as a 300-nm-thick silicon oxide layer, via PECVD to provide sidewall electrical isolation. Contact windows are patterned 316 via photolithography and the insulation layer 120 is selectively etched using RIE to open vias for electrical contact. The n-metal electrode 116 is formed 318 on the n-AIGaAs DBR 106 or the n-GaAs substrate 102. For example, an n-type contact stack consisting of Ni / Ge / Au / Ni / Au may be deposited via electron-beam evaporation and patterned using a lift-off process. The p-metal electrode 118 is formed 320 on the p-AIGaAs DBR 110. The p- type contact stack, which may include Ti / Pt / Au, can be deposited via sputtering and patterned by lift-off to define the emission window 122. Before depositing the p- metal, the contact regions may be treated with a hydrochloric acid dip to remove native oxide from the p-GaAs surface. The method 300 concludes with an annealing step 322, such as rapid thermal annealing at 380 °C, to activate the ohmic contacts and ensure low-resistance electrical interfaces for the VCSEL 100.

[0061] In some embodiments, the light 112 escaping the VCSEL 100 generates a far-field pattern, examples of which are illustrated in FIGs. 4A to 4C. Note that far-field patterns 402 to 406 are different for the VCSEL 1 to VCSEL 3 devices. This far-field pattern is captured using an optical system (not shown) andserves as a unique identifier for devices integrated with the VCSEL 100. Due to microstructural variations occurring naturally during the epitaxial growth and fabrication of the layers 102 through 110 in the VCSEL 100, the far-field pattern is resistant to cloning, even among devices manufactured within the same batch. This surface-directed emission facilitates a PUF mechanism that provides a hardwarebased signature for security operations.

[0062] In some embodiments, the same VCSEL 100 that generates the far- field pattern is also utilized to perform facial recognition. The facial signature captured by the system provides an additional biometric layer configured to bind a physical identity of a user to the hardware-based optical fingerprint of the VCSEL 100. This dual identification protocol is configured to enhance security by requiring both a valid far-field pattern and a matching facial biometric input for successful authentication.

[0063] In some embodiments, FIGs. 5A to 5C illustrate an authentication system that leverages both the unique far-field emission patterns 402, 404, 406 and the facial biometric data of a user. Each VCSEL 100-1, 100-2, 100-3 embedded within a respective device 502, 504, 506 emits light 112 to produce a corresponding unique far-field pattern 402, 404, 406. As described in method 300, these patterns are shaped by the intrinsic microstructural variations and the specific geometry of the cavity 111, providing a signature that is resistant to cloning. Simultaneously, a camera 503, 505, 507 associated with the device may be configured to scan a facial signature of the user. This configuration establishes a multifactor authenticationprotocol that binds the hardware-based optical fingerprint of the VCSEL 100 to the physical identity of the user.

[0064] The surface-directed emission may be captured by a built-in camera or an external detection system, and the resulting image is processed using a machine learning classifier, such as a CNN, to extract unique features. These features may then be converted into a cryptographic key serving as a digital fingerprint for the device. During an authentication operation, the system compares the cryptographic key generated from the captured far-field pattern 402, 404, 406 against a reference key stored in a secure database. Access to a system or network is granted if the keys match and the biometric input is verified, whereas the device is rejected if a match is not found. In some embodiments, the authentication remains reliable even under spatial misalignment or the presence of optical noise, as the CNN is configured to identify hierarchical features from only a portion of the far-field intensity distribution.

[0065] Compared to traditional optical PUF architectures, the far-field imagebased PUF provides several technical advantages. VCSELs are produced at scale and widely utilized across various industries, allowing the far-field pattern-based PUF to leverage existing hardware infrastructure. This configuration facilitates a secure authentication paradigm that is advantageous for resource-constrained platforms, such as consumer electronics and loT devices, without adding significant size or complexity. The scalability of the fabrication process supports the economic viability of this authentication approach for mass-market applications.

[0066] As illustrated in FIGs. 5A to 5C, the authentication process utilizes a pre-trained CNN to perform real-time identification with reduced computational overhead, allowing for non-intrusive device verification. The system is resistant to physical cloning or tampering because the far-field pattern is linked to the specific microstructure of the VCSEL. Furthermore, the system demonstrates robustness against environmental perturbations, maintaining high classification accuracy in the presence of channel noise introduced by diffusers or up to 50% spatial misalignment between the light source and the acquisition system. The sensitivity of the far-field intensity distribution to operational parameters also enables the generation of multiple distinct authentication keys from a single device through controlled variations in injection current or operating temperature, providing a versatile and secure approach for large-scale deployment.

[0067] In some embodiments, a TMM-VCSEL 100 utilizes a transversely modified cavity design to enhance both the peak optical power and the complexity of the far-field emission patterns. The cavity geometry may be modified into the asymmetric shapes discussed above, such as circular, square, mushroom, and pentagonal-shaped apertures. By introducing these geometric elements into the cavity structure, the TMM-VCSEL 100 facilitates enhanced gain utilization and generates intricate and dynamic far-field patterns (e.g., 402, 404, 406) suitable for secure identification.

[0068] The transversely modified cavity design creates irregularities in internal light reflection and refraction processes within the TMM-VCSEL 100, which increases the density of states and the number of supported transverse modes. Thisconfiguration promotes modal competition and nonlinear dynamics, such as spatial hole burning and filamentation, which drive fast spatiotemporal intensity fluctuations. The PUF authentication may be based on a PUF signature derived from temporal optical dynamics or spatial optical features. For example, temporal optical dynamics include variations in intensity or polarization detected over a time sequence, which are resistant to replication. In some embodiments, the far-field intensity distribution evolves over time due to mode switching and interaction, allowing video data formats to serve as high-entropy cryptographic keys. Spatial optical features include two- dimensional (2D) near-field or far-field emission patterns, such as patterns 402, 404, or 406, captured by an optical detector or imaging system. These features improve the security of the PUF as the emission profile is unique to the specific cavity configuration and the microstructural variations of each device.

[0069] The rich dynamics intrinsic to these cavity geometries also allow the TMM-VCSEL 100 to function as a high-speed RNG, which may operate in conjunction with the PUF within a secure communication architecture. For example, a pentagonal geometry supports the highest number of modes and the fastest mode dynamics, enabling an RNG rate of approximately 800 Gb / s with minimal postprocessing. Additionally, the P-VCSEL demonstrates more than twice the optical power density compared to circular designs, representing a highly efficient use of the active region 108. Mushroom-shaped geometries may be configured for high power and low spatial coherence, providing a speckle contrast as low as 0.17 for speckle- free illumination. D-shaped geometries may provide enhanced polarization stabilityand controllable multimode behavior, achieving a high orthogonal polarization suppression ratio (OPSR) of approximately 5.84.

[0070] These embodiments provide flexibility to adapt the TMM-VCSEL 100 to different security requirements and operational environments, ensuring that the PUF remains unique across diverse applications such as high-level authentication, secure communication, or anti-counterfeiting. Controlling the far-field characteristics by adjusting the cavity shape enhances the robustness of the system and facilitates the generation of multiple distinct authentication keys from a single device through challenge-response protocols.

[0071] In some embodiments, an anti-counterfeiting system 600 leverages the unique far-field emission patterns 402, 404, 406 of a VCSEL 100 as illustrated in FIG. 6. The VCSEL 100 may be integrated into a consumer electronic device 502 (e.g., a smart phone) to function as a hardware-based digital fingerprint, enabling secure identification through a centralized verification architecture. Upon activation, the VCSEL 100 emits the far-field pattern 402 that is unique to that specific device due to the intrinsic microstructural variations introduced during fabrication. A camera 602 associated with another device or a verification terminal 604 captures the far- field pattern 402 and transmits the image to a secure data center 610 for analysis.

[0072] The secure data center 610 compares the captured image against a database of reference patterns corresponding to authentic devices. Advanced machine learning classifiers, such as a CNN 612 may be utilized to perform rapid and robust pattern recognition. If the captured far-field pattern 402 matches a stored reference, the device 502 is authenticated as genuine 614, and authorizedoperations, such as secure transactions or product activation, are permitted. If a match is not identified, the system flags the device 502 as counterfeit 616 and denies access. This hardware-rooted authentication is resistant to cloning and spoofing because the emission characteristics are tied to the specific physical cavity of the VCSEL 100. Furthermore, the 2D scalability of VCSEL arrays supports the deployment of these anti-counterfeiting measures across large-scale supply chains and diverse loT ecosystems.

[0073] An embodiment describes a secure communication system 700 including devices 502 and 604 (e.g., smart phones) that use authentication based on a VCSEL 100 as illustrated in FIG. 7. In this embodiment, a first device 502 equipped with a VCSEL 100 utilizes the unique far-field pattern 402 emitted by the laser as a hardware-based optical fingerprint to authenticate itself to a second device 604. This configuration allows only trusted devices to engage in secure communication. During this process, the first device 502 initiating communication activates the VCSEL 100 to generate the unique far-field pattern 402. A camera 602 or other detection system associated with the receiving second device 604 captures the far-field image. The second device 604 is configured to compare the captured far-field pattern 402 with stored reference data associated with the trusted first device 502.

[0074] If the captured pattern 402 matches the reference data, the communication is permitted to proceed; otherwise, communication is denied. This pattern matching protocol ensures that only authenticated devices establish a communication link, which is resistant to interception by unauthorized or malicious devices. Integrating the unique far-field PUF into the hardware ensures that devicesare authenticated before initiating data exchange, protecting against unauthorized access and man-in-the-middle attacks.

[0075] A multi-key authentication system 800 utilizing the VCSEL 100 in response to varying challenges is illustrated in FIG. 8. In this embodiment, different challenges 802, such as electrical current, temperature, or polarization adjustments, are applied to the VCSEL 100 to produce multiple distinct far-field responses 402, enhancing the security of the authentication system. During an authentication operation, the VCSEL 100 may be subjected to a series of controlled challenges 802. For example, the injection current may be modulated in steps as small as 0.1 mA, such as from 49.0 mA to 49.4 mA, which alters the carrier distribution and internal spatial optical field to reshape the modal gain profile and modify transverse mode competition dynamics. Additionally, the operating temperature may be varied in increments such as 1°C, for instance from 17°C to 21 °C, to modify the refractive index of the epitaxial layers 102 through 110 and perturb the resonance conditions for the cavity modes.

[0076] Each challenge 802 alters the physical conditions within the TMM cavity 111, causing the far-field emission pattern 402 to change in response. For each applied challenge 802, a unique far-field pattern 402 is generated and captured by a detector or camera (not shown) of another device. The different emission patterns reflect the various conditions imposed on the VCSEL 100, providing a diverse set of far-field profiles.

[0077] The far-field patterns generated in response to the different challenges 802 can be processed in a data center 610 using machine learning algorithms 612(e.g., CNN) to extract unique features. These features are used to generate multiple cryptographic keys, each corresponding to a different challenge-response pair. The captured far-field patterns are compared against a pre-stored set of reference patterns in a secure database 614 or analyzed using the CNN. If the far-field profiles generated by the challenges 802 match the reference data, the device 502 associated with the VCSEL 100 is authenticated.

[0078] By using multiple challenge-response pairs to authenticate a device, the system 800 significantly enhances security through a multi-key identification protocol. This approach capitalizes on the physical modulation of the internal modal distribution under altered operating conditions, enabling a single TMM-VCSEL 100 to generate a constellation of unique, reproducible responses. The generation of multiple cryptographic keys from distinct far-field responses 402 makes the authentication process more resistant to cloning and replay attacks, as an unauthorized entity would need to replicate the entire set of challenge-response pairs across multiple physical dimensions. This multi-key capability is further scalable through the use of VCSEL arrays, where simultaneous or combinatorial readout from multiple emitters independently addressable across current and temperature dimensions exponentially increases the addressable authentication space.

[0079] Another embodiment is illustrated in FIG. 9, which describes a keyless entry system 900 utilizing the unique far-field emission patterns generated by a VCSEL 100 as a PUF. This embodiment leverages the intrinsic properties of the VCSEL 100 to provide secure, contactless access to vehicles or facilities, which mayeliminate the need for traditional keys. In this process, a VCSEL 100 embedded within a keyless entry device, such as a vehicle 902, emits a unique far-field pattern 402 when activated. This pattern is created by the inherent physical characteristics and microstructural variations of the VCSEL 100.

[0080] At an access point, such as a door 904 of a vehicle or building, a camera 602 or other detection system captures the far-field pattern 402 emitted by the VCSEL 100. The detection system is positioned to receive the surface-directed emission from the device 902 at a specific distance to facilitate accurate pattern recognition. The captured far-field pattern 402 is compared to a reference pattern stored in a secure database 614 or analyzed by a CNN 612. The database 614 and / or CNN 612 may be hosted in a server 910, which may be located next to the camera 602 (e.g., in the same building) or remotely via a secure network connection. If the far-field pattern 402 matches the stored reference, the server 910 authenticates the device 902 and grants access by unlocking the door 904.

[0081] The far-field pattern 402 generated by the VCSEL 100 serves as a hardware-based optical fingerprint that is resistant to duplication or spoofing. Even if an unauthorized entity obtains a physical copy of the keyless entry device, the far- field emission pattern remains unique to the original VCSEL microstructure. The system 900 also provides secure access without physical contact, allowing for fast and seamless entry. The far-field pattern can be captured and authenticated in realtime with the CNN 612, which ensures low latency in the entry process. Furthermore, the security of the system 900 may be enhanced by applying a multi-key identification protocol, where the device 902 must provide a constellation of far-fieldresponses in response to varying challenges 802, such as modulated injection currents or temperatures (as discussed above with regard to the system 800), to grant access to the door 904.

[0082] An embodiment illustrated in FIG. 10 describes a system 1000 for securing a supply chain by integrating VCSEL-based RUF technology into various products 1002 or components. In this embodiment, products 1002 moving through the supply chain are embedded with one or more VCSELs 100, which may include TMM cavities such as the pentagonal or D-shaped apertures previously described. These VCSELs 100 generate unique far-field patterns 402 that serve as hardwarebased optical fingerprints, ensuring the authenticity and integrity of the product 1002 as it moves through various stages of the supply chain. At a manufacturing stage 1004, each product 1002 is embedded with a VCSEL 100 that generates a unique far-field emission pattern 402. This pattern, derived from the intrinsic microstructural variations and the specific geometry of the cavity 111, acts as a RUF that is resistant to cloning or replication, providing a secure identifier for the product 1002.

[0083] As the product 1002 moves through the supply chain — from manufacturing 1004 to shipping 1006, distribution 1008, and retail 1010 — its far-field pattern 402 is captured at designated checkpoints 1020 (only one shown for simplicity). Each checkpoint 1020 is equipped with a camera or detector 602 configured to record the far-field pattern 402 and transmit the image to a centralized verification system 910, such as a data center 610. The system 1000 may utilize a CNN 612 to perform real-time authentication by comparing captured features against a reference database. Because the TMM-VCSEL 100 is highly sensitive tooperational parameters, the system 1000 may implement a multi-key identification protocol where the product 1002 is authenticated based on a constellation of responses generated under varying challenges 802, such as specific injection currents or operating temperatures.

[0084] Furthermore, as illustrated in FIG. 10, the VCSEL 100 may simultaneously function as a high-entropy source for RNG. While the surface- directed emission is used for PUF-based tracking and authentication at each checkpoint 1020, the fast spatiotemporal intensity fluctuations resulting from nonlinear modal interactions, such as spatial hole burning and filamentation, allow for the generation of cryptographic keys. These keys can be used to establish a secure communication channel between the product 1002 and the centralized verification system 910, ensuring that the tracking data remains encrypted and protected from tampering throughout the entire life cycle of the product 1002. From manufacturing 1004 to the final point of sale at retail 1010, the dual functionality of the TMM-VCSEL 100 ensures that the product 1002 has not been altered, replaced, or counterfeited.

[0085] In some embodiments, a system 1100 for authenticating loT devices utilizing VCSEL based PUF technology is illustrated in FIG. 11. In this embodiment, various loT devices, such as sensors 1102, smartphones 502, televisions 1104, and computers 1106, are embedded with TMM VCSELs. Each TMM-VCSEL generates a unique far-field pattern 402 that serves as a distinct, hardware-based identifier for the device. The far-field pattern 402 is shaped by intrinsic microstructural variations and the specific geometry of a transversely modified cavity, such as the pentagonalor D-shaped apertures previously described, which ensure that each device is securely identified.

[0086] Before an loT device is permitted to join a network, a camera or other detection system captures its far-field pattern 402 and compares the image to a stored reference in a centralized database 610. A processing unit may utilize machine learning algorithms, such as a CNN 612, to extract unique features from the far-field intensity distribution and generate a cryptographic key for authentication. Once the far-field pattern 402 has been verified, the loT device is authenticated and granted access to the network. If the far-field pattern 402 does not match the stored reference, access is denied, protecting the network from unauthorized or counterfeit devices.

[0087] Following authentication, the loT device utilizes a generated cryptographic key to establish secure communication within the network. The hardware-rooted PUF ensures that only authenticated devices engage in data exchange, mitigating risks associated with unauthorized access, data breaches, or tampering. Additionally, the fast dynamics of the TMM-VCSEL allow it to function as a high-entropy source for RNG. While the surface-directed emission facilitates PUF- based identity verification, the intrinsic spatiotemporal intensity fluctuations, driven by nonlinear effects such as spatial hole burning and filamentation, allow for the generation of random bitstreams. These random sequences may be used to periodically refresh encryption keys during a communication session, ensuring both identity verification and encrypted transmission for loT devices. The integration ofPUF and RNG functionalities within a single TMM-VCSEL provides a scalable and cost-effective security solution for edge-facing loT infrastructure.

[0088] An embodiment illustrated in FIG. 12 illustrates an array configuration of the VCSEL 100 on a single substrate 502. The array may be configured as a two- dimensional (2D) arrangement including a plurality of pentagonal mesas. In some embodiments, the spatial arrangement includes N (e.g., 4) outer pentagonal mesas 100-1 positioned in a square or rectangular pattern around M (e.g., a central) pentagonal mesa(s) 100-2. This distributed geometry facilitates improved thermal dissipation and allows for the simultaneous operation of multiple independent entropy sources. Each pentagonal mesa 100-1 , 100-2 within the array is configured to produce a unique far-field pattern 402 for PUF authentication. Furthermore, the 2D scalability of the array allows for parallel RNG, where the aggregate bit rate is increased by the number of active channels in the array.

[0089] In some embodiments, the RNG capability of the VCSEL 100 is used to periodically refresh encryption keys during a communication session, which further enhances security. The system 1200 dynamically generates new cryptographic keys, which is configured to mitigate risks associated with key interception. By integrating both PUF and RNG functionalities within a single TMM-VCSEL 100, the system 1200 reduces the need for additional hardware components while providing robust, hardware-rooted security. This integrated platform is scalable for various applications, including secure communication between loT devices 1102, 1104, 1106, smart home systems, and other environments requiring both device authentication and encrypted data transmission. Furthermore, the 2D scalability ofVCSEL arrays supports massively parallel high-speed RNG, where each channel may achieve rates of hundreds of Gb / s, and a monolithic stack integrating a photodetector directly atop the VCSEL 100 may be used to achieve a tamperresistant, alignment-free entropy source.

[0090] To generate random bitstreams, the optical output 112 from the P- VCSEL 100 is detected by a PD, which converts the spatiotemporal fluctuations into an electrical signal. This signal is then digitized through an analog-to-digital converter (ADC) and subjected to lightweight post-processing. Due to the high- frequency content and low temporal correlation of the pentagonal cavity's emission, the system is configured to deliver a random number generation rate of approximately 800 Gb / s from a single channel using minimal post-processing, such as a self-delayed exclusive OR, XOR, operation. This configuration allows the P- VCSEL 100 to function as an efficient, chip-scale entropy engine suitable for high- throughput cryptographic applications without the need for external optical feedback or complex modulation.

[0091] In some embodiments, a monolithically integrated optoelectronic module 1302 includes a VCSEL 100 and a PD 602 fabricated on a single chip 1304 to facilitate a compact and tamper-resistant optical entropy source. As illustrated in the co-planar architecture of FIG. 13, the VCSEL 100 and the PD 602 are integrated on a shared substrate 1302. This configuration allows the PD 602 to serve as a hardware-rooted identifier by exploiting intrinsic physical characteristics such as dark current variability, responsivity differences, specific noise characteristics, and spectral response diversity. These inherent variances arise from microscopicdifferences in material properties and fabrication processes, such as material defects and surface roughness, which produce unique electrical responses for identical optical inputs. By applying controlled optical challenges from the VCSEL 100 — such as modulated light intensity, varying wavelengths, or polarization states — the resulting electrical outputs from the PD 602 form unique challenge-response pairs (CRPs). These CRPs may be analyzed by a processing unit and compared against a secure database 614 for multi-factor authentication and secure hardware identification.

[0092] The monolithically integrated VCSEL 100 and PD 602 are configured to operate in at least two entropy-generation modes determined by an injection current relative to a lasing threshold. In a sub-threshold mode, the injection current is maintained below the lasing threshold level. Because optical gain is lower than cavity losses, stimulated emission is not dominant. Light 112 emitted in this regime is primarily a result of spontaneous emission. This operational state allows the VCSEL 100 to function as a quantum entropy source by leveraging fundamental quantum fluctuations, which produce an inherently stochastic and unpredictable optical signal. In some embodiments, the integrated PD 602 captures these quantum-driven intensity fluctuations to facilitate QRNG.

[0093] In an above-threshold mode, the injection current exceeds the lasing threshold such that stimulated emission produces multimode optical dynamics. In this multimode regime, the TMM cavity 111 promotes modal competition and nonlinear interactions, such as spatial hole burning or filamentation, which generate high-speed spatiotemporal intensity fluctuations. These fluctuations are utilized togenerate physical random numbers. The integrated PD 602 captures the optical signals in situ for both modes, enabling a reconfigurable and tamper-resistant entropy engine, and a processing unit digitizes the signal to produce random bitstreams.

[0094] For an embodiment utilizing a pentagonal cavity 111 , the system is configured to deliver an RNG rate of approximately 800 Gb / s per channel.Furthermore, the processing unit may utilize a CNN 612 to authenticate the device using unique far-field patterns 402. The system is configured to maintain a classification accuracy of approximately 98.7% even when subjected to a 50% spatial misalignment between the VCSEL 100 and the acquisition system.

[0095] The monolithic integration of the VCSEL 100 and the PD 602 further supports high-throughput, multi-channel RNG. In some embodiments, the PD 602 is positioned to capture intensity fluctuations from the VCSEL 100 in situ without the use of external optics. For example, the PD 602 may be paired with a TMM cavity configured to produce fast spatiotemporal intensity fluctuations through nonlinear modal interactions. The PD 602 detects these high-entropy fluctuations, which are then digitized and post-processed to generate cryptographically secure random bits. To ensure high signal integrity, the VCSEL 100 and the PD 602 may be electrically isolated using air trenches formed through selective etching or via ion implantation to suppress carrier diffusion and crosstalk. This integrated architecture provides an alignment-free and scalable entropy source where the RNG capability may be used to periodically refresh encryption keys during a communication session. Such a system is suitable for diverse applications, including secure loT device interaction,smart home systems, and secure data transmission in embedded hardware environments.

[0096] According to an embodiment illustrated in FIG. 14, a secure communication system 1400 leverages the dual functionality of a plurality of VCSELs 100 to provide integrated hardware-based identity verification and encrypted data transmission. In this configuration, a first device 502, such as a laptop, is equipped with a VCSEL array 1402 configured to emit a set of unique far-field patterns 402 serving as a PUF. Each far-field pattern 402, which results from intrinsic microstructural variations and a specific transversely modified cavity geometry of each VCSEL 100, is captured by a sensor 602 associated with a second device 604.

[0097] The secure communication protocol between the first device 502 and the second device 604 involves a dual-step process. In step 1404, the second device 604 is configured to perform device authentication with the PUF to verify the identity of the first device 502 by comparing unique features extracted from the captured far- field patterns 402 with reference patterns. In step 1406, once mutual authentication is established, the inherent spatiotemporal intensity fluctuations of the VCSEL array 100 are utilized as a random number generator for cryptographic key generation and information encryption. This multi-functional architecture ensures that the communication channel between the first device 502 and the second device 604 is both authenticated and encrypted using high-entropy keys derived from the same photonic hardware.

[0098] Beyond providing a hardware-based identifier that is resistant to cloning, the VCSEL 100 functions as a source of high-entropy random numbersdriven by its fast spatiotemporal dynamics. The intrinsic intensity fluctuations within a TMM cavity — driven by nonlinear modal interactions such as spatial hole burning and filamentation — produce unpredictable optical signals. These signals are detected, digitized, and processed to generate cryptographically secure random numbers. These random numbers are utilized to generate one or more cryptographic keys for encrypting the communication between the first device 502 and the second device 604, ensuring that the data exchanged remains confidential.

[0099] The secure communication system 1400 is configured to establish a protected communication channel where only trusted devices verified through the hardware-rooted PUF can participate. In some embodiments, the RNG capability of the VCSEL 100 is configured to periodically refresh the cryptographic keys during an active communication session, which further mitigates risks associated with signal interception or side-channel attacks. This integrated approach, which combines PUF-based authentication and laser-driven RNG within a unified photonic platform, reduces the need for additional hardware components and provides a scalable solution for secure data operations in loT networks, smart home systems, and cloud infrastructure. Furthermore, the system may incorporate a monolithic architecture where a photodetector is integrated alongside or atop the VCSEL 100 to capture fluctuations in situ, enhancing the tamper-resistance and compactness of the secure communication system.

[0100] In some of the embodiments discussed above, an authentication system utilizes machine learning to perform real-time identification and verification of a device. Specifically, a machine learning classifier, such as a CNN 612, isconfigured to automate feature extraction and enable authentication without a reliance on extensive pre-stored reference datasets. As illustrated in FIG. 15, a CNN 612 includes an input layer 1502 configured to receive a far-field pattern 402, such as a 100 x 100 pixel intensity image. The input layer 1502 is followed by a plurality of convolutional layers 1504, 1508, and 1512. For example, a first convolutional layer 1504 may be configured with 64 filters to produce a 96 x 96 feature map. A first max pooling layer 1506, such as a 2 x 2 pooling window, follows the first convolutional layer 1504 to reduce spatial dimensions. A second convolutional layer 1508 may be configured with 64 filters to produce a 44 x 44 feature map, followed by a second max pooling layer 1510. A third convolutional layer 1512 may be configured with 64 filters to produce a 20 x 20 feature map, which is subsequently processed by a third max pooling layer 1514.

[0101] The hierarchical features extracted by the convolutional layers are then flattened in a flattening layer 1516 to form a 1 x 6400 vector. This vector is passed to a fully connected dense layer 1518, which may include 100 neurons. Finally, an output layer 1520, utilizing a Softmax activation function, is configured to perform multi-label classification to identify a specific device or operational state. The CNN 612 is configured to identify unique features of the far-field pattern 402 even under spatial misalignment or the presence of optical noise, as the network extracts hierarchical features from only a portion of the far-field intensity distribution. In some embodiments, the system achieves 100% accuracy in individual VCSEL identification and maintains high reliability with up to 50% optical misalignment tolerance.

[0102] The authentication system is further configured to implement a multikey identification protocol by exploiting the sensitivity of the far-field emission patterns to controlled variations in injection current and operating temperature. The inventors found that the far-field pattern 402 of a VCSEL 100 evolves in response to challenges 802. For example, when the injection current is modulated in steps as small as 0.1 mA, such as from 49.0 mA to 49.4 mA, the carrier distribution and internal spatial optical field are altered, which reshapes the modal gain profile and modifies transverse mode competition dynamics. This results in distinct, reproducible far-field responses that can be resolved by the CNN 612 to generate additional authentication keys. Similarly, varying the operating temperature in increments such as 1°C, for instance from 17°C to 21 °C, modifies the refractive index of the epitaxial layers 102 through 110 and perturbs the resonance conditions for the cavity modes, further diversifying the available authentication responses. This multi-key capability allows a single hardware device to support a large constellation of unique cryptographic keys across multiple tunable physical dimensions.

[0103] According to an embodiment, the authentication systems discussed above are configured to maintain high classification accuracy even in the presence of spatial misalignment between the TMM-VCSEL 100 and the acquisition system. In practical deployment scenarios, achieving perfect alignment between the imaging system and the light-emitting device is often infeasible due to mechanical tolerances, user handling, or environmental disturbances. To evaluate the robustness of the authentication system under such conditions, spatial misalignments were simulated by randomly cropping far-field intensity images acquired from the TMM-VCSEL 100.Each image was cropped using a window covering only 25% of the total image area, which corresponds to a 50% spatial offset between the source and the acquisition system. Under these conditions, the spatial information available for classification is significantly reduced.

[0104] To further evaluate the system, the test was repeated with a diffuser inserted into the optical path, producing speckle-like patterns where the spatial localization of device-specific features is reduced. Under this condition, the cropping window was enlarged to cover 70% of the original image area, representing a 30% misalignment, ensuring that a sufficient portion of the redistributed optical features was retained. Despite the severe degradation in spatial information, the CNN 612 demonstrated strong adaptability. It was found that the training and validation accuracy under these conditions remained high. For the non-diffused case, the network converged rapidly, while the diffuse case required a longer training duration due to the increased classification difficulty.

[0105] The authentication system achieves a classification accuracy of approximately 98.7% without a diffuser and 96.7% with a diffuser. These results confirm that the far-field patterns 402 preserve sufficient entropy for accurate identification even under partial occlusion and optical perturbation. This resilience to spatial misalignment makes the TMM-VCSEL 100 particularly suitable for mobile, handheld, or embedded systems where precise optical alignment cannot be guaranteed. The robustness of the far-field patterns 402 arises from the rich spatial modes inherent to the asymmetric cavity geometries, which ensures that identifyingfeatures are distributed across the entire far-field intensity distribution rather than being confined to a single region.

[0106] According to an embodiment illustrated in FIG. 16, a monolithically integrated emitter-detector architecture is configured to facilitate high-throughput entropy extraction and hardware authentication within a single photonic platform. This integrated stack 1600 is fabricated on an n-GaAs substrate 102 followed by an n-GaAs buffer 104. The VCSEL 100 section includes an n-AIGaAs DBR stack 106 having, for example, 38 pairs of n-type AIGaAs layers as a bottom mirror. An active region 108, which may include MQWs, such as InGaAs / GaAsP MQWs, is positioned atop the n-DBR stack 106 and configured for light emission at a specific wavelength such as 940 nm. A p-AIGaAs DBR stack 110, for example, including 22 pairs of p- type AIGaAs layers, is disposed above the active region 108 to function as a top mirror. A high-aluminum content layer, such as AI0.93Ga0.02As, is included within the p-AIGaAs DBR stack 110 to facilitate the formation of an oxidation aperture 114 for current and optical confinement.

[0107] To enable the monolithic integration of a PD 602 directly above the VCSEL 100, a contact layer 1602 such as a p-n-GaAs layer is formed on the p- AIGaAs DBR stack 110, which may function as a shared p-contact for both active elements. An etch-stop layer 1604, such as a p-doped Alo.5Gao.5As layer having a thickness of approximately 100 nm, is positioned above the contact layer 1602 to facilitate selective removal during device fabrication.

[0108] The PD 602 follows a vertical P-l-N configuration grown atop the etchstop layer, including a p-GaAs layer 1606, an absorption region 1608, and an n-GaAs layer 1610. The absorption region 1608 may include 25 pairs of InGaAs / GaAsP layers engineered for efficient absorption at the VCSEL 100 emission wavelength. The top n-GaAs layer 1610 may have a thickness of approximately 200 nm to provide a stable electrical interface. This monolithic architecture 1600 allows the PD 602 to capture intensity fluctuations or far-field patterns directly from the VCSEL 100 in situ, providing a compact and tamperresistant optoelectronic module for secure hardware applications.

[0109] According to an embodiment illustrated in FIG. 17, a method 1700 for fabricating a monolithically integrated emitter-detector architecture is configured to achieve a compact, tamper-resistant optoelectronic module 1600. The method 1700 begins with the epitaxial growth 1702 of a VCSEL 100 on an n-GaAs substrate 102. This growth includes forming an n-GaAs buffer 104, an n-AIGaAs DBR stack 106, an active region 108, and a p-AIGaAs DBR stack 110 as discussed with regard to FIG.3. A high-aluminum content layer is included within the p-AIGaAs DBR stack 110 for later formation of an oxidation aperture 114. A contact layer 1602, such as a p++- GaAs layer, is formed 1704 atop the p-AIGaAs DBR stack 110 to serve as a shared p-contact. Above this, an etch-stop layer 1604, such as a p-doped Alo.5Gao.5As layer, is deposited 1706, followed by the growth of the PD 602 section. The PD 602 growth includes a p-GaAs layer 1606, an absorption region 1608, and an n-GaAs layer 1610. The VCSEL mesa and PD section are illustrated in FIG. 18A.

[0110] The fabrication process continues with a PD mesa etch 1708 to define the detector structure. This etching process is configured to terminate at the etchstop layer 1604. A hydrochloric acid (HCI) treatment is then performed to selectivelyremove 1710 the residual etch-stop layer 1604, exposing the contact layer 1602, as illustrated in FIG. 18B. Next, a VCSEL mesa etch 1712 is performed to define the laser structure (see FIG. 18C), typically reaching a depth that exposes the high- aluminum content layer within the p-AIGaAs DBR stack 110. Wet thermal oxidation 1714 is then conducted to form the oxidation aperture 114 (see FIG. 18D), providing current and optical confinement. An insulation layer 120 is deposited and patterned 1716 to provide p-metal isolation, as shown in FIG. 18E. Metallization steps 1718 follow to form electrodes, including a p-metal electrode 118 on the contact layer 1602 (see FIG. 18F), which is shared by the VCSEL 100 and the PD 602, an n-metal electrode 1802 for the top of the PD 602 only, and an independent n-metal electrode 116 for the VCSEL 100 only (see FIG. 18G).

[0111] As illustrated in FIG. 18G, the resulting device 1600 corresponds to a monolithically integrated version of the VCSEL 100 and PD 602 architecture. In this embodiment, the PD 602 is positioned directly above the VCSEL 100, where the PD 602 mesa fully covers the emission aperture defined by the oxidation aperture 114. This configuration allows the PD 602 to capture intensity fluctuations and far-field patterns directly from the VCSEL 100 in situ without external optics. The top electrode 1802 of the PD 602 may be configured as a blocked electrode to suppress light leakage and reinforce the security of the entropy source by reducing optical side-channel vulnerabilities. The shared contact layer 1602 facilitates a compact stacked architecture, while the independent n-metal electrodes 116 allow the VCSEL 100 to be driven in a sub-threshold regime to exploit spontaneous emission noise for quantum random number generation, or in a multimode regime to exploit self-chaoticintensity fluctuations for high-speed random number generation. The shared electrode 118 provides a common return path for the integrated components. The integrated device 1600 is configured to generate random bitstreams at an aggregate rate exceeding 10 Gb / s per channel, supported by the intense modal competition inherent in the transversely modified cavity of the VCSEL 100.

[0112] The monolithically integrated emitter-detector architecture 1600 is configured to operate as an entropy source for secure device identification and random number generation. This integrated stack facilitates a self-contained security module where the PUF and RNG are performed within a single photonic platform. The monolithically integrated architecture leverages the intrinsic spatiotemporal intensity fluctuations and microstructural variations of the cavity to provide high- entropy cryptographic keys.

[0113] The integrated device 1600 exhibits distinct electrical and optical performance characteristics. The current-voltage (l-V) curve (not shown) for the VCSEL section indicates a turn-on voltage of approximately 2.3 V. While this is slightly higher than conventional 940 nm designs, the increase is attributed to the additional series resistance and fabrication complexities associated with the vertically stacked PD. Furthermore, the integration of a blocked top electrode is configured to suppress light leakage and reinforce the security of the entropy engine by mitigating optical side-channel vulnerabilities.

[0114] In terms of device characterization, the photocurrent response of the integrated PD provides an effective proxy for the internal optical output power of the VCSEL, which is fully encapsulated within the stack. The photocurrent versusVCSEL current shows a nonlinear increase at approximately 30 mA, corresponding to the lasing threshold. Below this threshold, the emission is dominated by spontaneous emission originating from quantum fluctuations. This sub-threshold regime is particularly advantageous for RNG, as it provides a high-quality entropy source that is captured in situ by the PD without the need for external optics. The PD current-voltage response shows that the integrated architecture remains operational even under zero-bias conditions, with the dark current maintained at approximately 10 pA. The normalized emission spectra (not shown) further demonstrate the transition from broad spontaneous emission at 20 mA to sharp lasing peaks at 40 mA.

[0115] The RNG performance of the integrated emitter-detector architecture 1600 is further characterized by the radio-frequency (RF) spectra and autocorrelation functions (ACF). The RF spectra for the VCSEL biased at 20 mA and 30 mA reveal broadband noise extending up to approximately 1 GHz, which is suitable for entropy extraction. The temporal signal captured by the integrated PD exhibits a nearGaussian distribution. Following post-processing through least significant bit (LSB) extraction, the distribution becomes nearly uniform, ensuring an equal probability for each bit. Additionally, the ACF results demonstrate that while the raw signal contains temporal correlations, the processed bitstream exhibits a sharp delta-like peak at zero lag. This statistical independence allows the monolithically integrated architecture 1600 to deliver an RNG rate of 10 Gb / s per channel. The generated bitstream successfully passes the full NIST SP 800-22 statistical test suite, confirming its suitability for cryptographic-grade applications.

[0116] In one embodiment, a method 1900 for hardware authentication and RNG includes several operational steps as illustrated in FIG. 19. The method 1900 begins by activating 1902 a TMM cavity 111 of a VCSEL 100 to produce multimode lasing. In step 1904, the system captures a unique far-field intensity pattern 402 defined by a non-circular geometry of the cavity 111 to perform RUF authentication. Finally, in step 1906, the method involves detecting spatiotemporal intensity fluctuations from a broad-area emission region of the TMM cavity 111 having an area greater than 700 pm2to generate a random bitstream.

[0117] In some embodiments, the method 1900 further includes configuring the entropy source by biasing the VCSEL 100 in a sub-threshold regime including an injection current maintained below a lasing threshold level to exploit spontaneous emission noise for QRNG. Alternatively, the method may include biasing the VCSEL 100 in a multimode regime to exploit self-chaotic dynamics driven by nonlinear dynamics, such as spatial hole burning and filamentation, for a conventional RNG source.

[0118] To facilitate different detection architectures, the method 1900 may include capturing edge-emitted light from the TMM cavity 111 using a RD 602 monolithically integrated adjacent to the TMM cavity 111 in a co-planar integrated array 1302. In another embodiment, the method includes capturing surface-directed light from the TMM cavity 111 in situ using a RD 602 vertically stacked above the TMM cavity 111.

[0119] Furthermore, the method 1900 may implement a multi-key authentication protocol by subjecting the VCSEL 100 to a series of controlledchallenges 802. These challenges 802 include at least one of modulated injection currents or varying operating temperatures to produce a constellation of unique far- field responses for multi-key authentication. This variability allows the VCSEL 100 to serve as a reconfigurable hardware-based identifier for secure communication and device verification.

[0120] In some embodiments, the method for generating random bitstreams and performing authentication includes the use of a VCSEL configured with a TMM cavity 111.

[0121] The method may involve configuring the TMM cavity 111 with a noncircular geometry including at least one of a pentagonal, D-shaped, mushroomshaped, or square geometry to facilitate the production of a unique far-field intensity pattern 402 for PUF authentication. In certain embodiments, the method includes configuring the non-circular geometry of the cavity 111 as a pentagonal geometry to promote fast mode dynamics, enabling an RNG rate of at least 800 Gb / s.

[0122] Additionally, the method may facilitate simultaneous identification and biometric capture. This can be achieved by patterning a p-metal electrode 118 to define an emission window 122 configured to facilitate facial recognition scanning. The method then involves simultaneously providing a hardware-based optical fingerprint via the unique far-field intensity pattern 402 and a biometric input via the facial recognition scanning.

[0123] To support monolithically integrated detection architectures, the method may include capturing light from the TMM cavity 111 using a PD 602 monolithically integrated with the VCSEL 100 on a shared substrate 102. In oneimplementation, the PD 602 is positioned adjacent to the TMM cavity 111 in a coplanar integrated array 1302 to capture edge-emitted light from the VCSEL 100. Alternatively, the method may include capturing surface-directed light in situ using a PD 602 vertically stacked above the TMM cavity 108.

[0124] The method may also be scaled for parallel operations by utilizing a two-dimensional array 1402 on a substrate 502 including a plurality of pentagonal mesas 100-1 , 100-2 configured for parallel high-speed RNG. For real-time processing, the method includes employing a processing unit 610 with a CNN 612 configured to identify unique features of the unique far-field intensity pattern 402 for real-time device authentication.

[0125] In some embodiments, the method is deployed within specific secure environments. For example, the unique far-field intensity pattern 402 may be utilized as a hardware-based identifier for network access authentication when the VCSEL 100 is embedded within an loT device. Similarly, the unique far-field intensity pattern 402 can serve as an optical fingerprint for a keyless entry system 900 to grant contactless access to a vehicle 902 or a building 904.

[0126] The terms “about” and “substantially” when used in this application mean a variation of up to 20% of the parameter characterized by these terms.

[0127] It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first object or step could be termed a second object or step, and, similarly, a second object or step could be termed a first object or step, withoutdeparting from the scope of the present disclosure. The first object or step, and the second object or step, are both, objects or steps, respectively, but they are not to be considered the same object or step.

[0128] The terminology used in the description herein is for the purpose of describing particular embodiments and is not intended to be limiting. As used in this description and the appended claims, the singular forms "a," "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term "and / or" as used herein refers to and encompasses any possible combinations of one or more of the associated listed items. It will be further understood that the terms "includes," "including," "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. Further, as used herein, the term "if" may be construed to mean "when" or "upon" or "in response to determining" or "in response to detecting," depending on the context.

[0129] The disclosed embodiments provide an optoelectronic platform and a VCSEL having a TMM cavity configured for hardware-level security. It should be understood that this description is not intended to be limiting. On the contrary, the embodiments are intended to cover alternatives, modifications, and equivalents, which are included in the spirit and scope of the disclosure as defined by the appended claims. Further, in the detailed description of the embodiments, numerous specific details are set forth in order to provide a comprehensive understanding ofthe claimed subject matter. However, one skilled in the art would understand that various embodiments may be practiced without these specific details.

[0130] Although the features and elements of the present embodiments are described in the embodiments in particular combinations, each feature or element can be used alone without the other features and elements of the embodiments or in various combinations with or without other features and elements disclosed herein.

[0131] This written description uses examples of the subject matter disclosed to enable any person skilled in the art to practice the same, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the subject matter is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims.

[0132] The entire content of all the publications listed herein is incorporated by reference in this patent application.[1] Alkhazragi, O. et al. Modifying the coherence of vertical-cavity surface-emitting lasers using chaotic cavities. Optica 10, 191 (2023).[2] Lu, H. et al. Parallel on-chip physical random number generator based on self- chaotic dynamics of free-running broad-area VCSEL array. IEEE J. SeL Top.Quantum Electron. 31, 1700511 (2025).[3] Lu, H. et al. Ultrafast dynamics in tailored VCSEL cavity geometry toward high- efficiency physical random number generation. APL Photonics 10, 046105, (2025).

Claims

WHAT IS CLAIMED IS:

1. A vertical-cavity surface-emitting laser (VCSEL) (100) comprising:a bottom distributed Bragg reflector (DBR) stack (106);an active region (108);a top DBR stack (110), wherein the bottom DBR stack (106), the active region (108), and the top DBR stack (110) define a transversely modified multimode (TMM) cavity (111) configured to support multimode lasing; andan oxidation aperture (114) located within the TMM cavity (111), wherein a transversal non-circular geometry of the TMM cavity and the oxidation aperture (114) is configured to produce a unique far-field intensity pattern (402) for physical unclonable function (RUF) authentication.

2. The VCSEL of claim 1 , wherein the transversal non-circular geometry of the TMM cavity and the oxidation aperture includes at least one of a pentagonal, D- shaped, mushroom-shaped, or square geometry.

3. The VCSEL of claim 1 , wherein the TMM cavity comprises a broad-area emission region having an area greater than 700 pm2configured to promote spatial and spectral mode overlap to drive modal competition and nonlinear dynamics for producing spatiotemporal intensity fluctuations for random number generation (RNG).

4. The VCSEL of claim 3, configured to operate in at least two entropygeneration modes determined by an injection current relative to a lasing threshold, comprising:a sub-threshold mode, in which the injection current is maintained below the lasing threshold such that emission is dominated by spontaneous emission noise to generate quantum random numbers; andan above-threshold mode, in which the injection current exceeds the lasing threshold such that stimulated emission produces multimode optical dynamics configured to generate physical random numbers.

5. The VCSEL of claim 1 , wherein the PUF authentication is based on a PUF signature derived from at least one of:temporal optical dynamics of the VCSEL including variations in intensity or polarization detected over a time sequence; orspatial optical features including a two-dimensional near-field or far-field emission pattern captured by an optical detector or imaging system.

6. The VCSEL of claim 3, wherein the transversal non-circular geometry of the TMM cavity and the oxidation aperture includes a pentagonal geometry configured to promote mode dynamics for an RNG rate of at least 800 Gb / s.

7. The VCSEL of claim 1 , further comprising:a p-metal electrode (118) that defines an emission window (122) configured to facilitate facial recognition scanning.

8. The VCSEL of claim 7, wherein the VCSEL is configured to simultaneously provide a hardware-rooted identifier via the unique far-field intensity pattern and a biometric input via the facial recognition scanning.

9. The VCSEL of claim 1 , further comprising:a photodetector (PD) monolithically integrated with the VCSEL on a shared substrate.

10. The VCSEL of claim 9, wherein the PD is positioned adjacent to the TMM cavity in a co-planar integrated array configured to capture edge-emitted light from the VCSEL.

11. The VCSEL of claim 9, wherein the PD is vertically stacked above the TMM cavity to capture surface-directed light from the VCSEL, in situ.

12. The VCSEL of claim 1 , wherein the VCSEL is part of a two-dimensional array on a substrate including a plurality of pentagonal mesas configured for parallel RNG.

13. The VCSEL of claim 1 , wherein the VCSEL is part of a multi-key authentication system configured to produce a constellation of unique far-field responses in response to a series of controlled challenges including at least one of modulated injection currents or varying operating temperatures.

14. The VCSEL of claim 1 , further comprising:a processing unit employing a convolutional neural network (CNN) configured to identify unique features of the unique far-field intensity pattern for real-time device authentication.

15. The VCSEL of claim 1 , wherein the VCSEL is embedded within an Internet of Things (loT) device configured to utilize the unique far-field intensity pattern as a hardware-rooted identifier for network access authentication.

16. The VCSEL of claim 1 , wherein the unique far-field intensity pattern is configured to serve as a hardware-rooted identifier for a keyless entry system to grant contactless access to a vehicle or a building.

17. A method (1900) for hardware authentication and random number generation (RNG) comprising:activating (1902) a transversely modified multimode (TMM) cavity of a vertical-cavity surface-emitting laser (VCSEL) to produce multimode lasing, whereinthe TMM cavity is defined by a stack comprising a bottom distributed Bragg reflector (DBR) stack (106), an active region (108), and a top DBR stack (110);capturing (1904) a unique far-field intensity pattern (402) defined by a noncircular geometry of the TMM cavity and an oxidation aperture (114) to perform physical unclonable function (RUF) authentication; anddetecting (1906) spatiotemporal intensity fluctuations from a broad-area emission region of the TMM cavity having an area greater than 700 pm2to generate a random bitstream.

18. The method of claim 17, wherein activating the TMM cavity further comprises operating the VCSEL in at least two entropy-generation modes determined by an injection current relative to a lasing threshold, the modes comprising:a sub-threshold mode, in which the injection current is maintained below the lasing threshold such that emission is dominated by spontaneous emission noise to generate quantum random numbers; andan above-threshold mode, in which the injection current exceeds the lasing threshold such that stimulated emission produces multimode optical dynamics configured to generate physical random numbers.

19. The method of claim 17, further comprising:capturing edge-emitted light from the TMM cavity using a photodetector (PD) (602) monolithically integrated adjacent to the TMM cavity in a co-planar integrated array; orcapturing surface-directed light from the TMM cavity in situ using a PD vertically stacked above the TMM cavity.

20. The method of claim 17, further comprising:subjecting the VCSEL to a series of controlled challenges including at least one of modulated injection currents or varying operating temperatures to produce a constellation of unique far-field responses for multi-key authentication.

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