Phase-sensitive amplification and squeezing in the presence of temporal gain trapping

Abstract

An optical parametric amplifier may include a waveguide with a waveguide geometry. The optical parametric amplifier may also include an optical pump optically coupled to the waveguide, the waveguide may be configured to use the optical pump and the waveguide geometry to temporally gain trap and perform phase sensitive parametric amplification of an optical signal.

Description

PHASE-SENSITIVE AMPLIFICATION AND SQUEEZING IN THE PRESENCE OFTEMPORAL GAIN TRAPPINGCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Application No. 63 / 632,818 filed on April 11, 2024, which is hereby incorporated by reference in its entirety.FIELD

[0002] The present disclosure generally relates to the field of optical amplification, and more specifically, to the phase-sensitive amplification and squeezing of light pulses with low noise and high purity in the presence of temporal gain trapping within nonlinear waveguides.BACKGROUND

[0003] Optical parametric amplification (OP A) is a technique in the field of nonlinear optics that involves the use of a high-frequency pump wave to amplify a lower-frequency signal wave, with the energy difference being carried away by a third wave, known as the idler. This process is facilitated by a nonlinear medium, which allows for the energy transfer between the waves. In many applications, the signal wave carries information that is to be amplified, such as in optical communication systems or quantum information processing. The pump wave, on the other hand, is typically a high-power laser pulse. The efficiency and effectiveness of the amplification process depend on several factors, including the properties of the pump and signal waves, the characteristics of the nonlinear medium, and the specific conditions under which the process is carried out.

[0004] Despite the advancements in OPA technology, there are still challenges associated with the amplification process, and particularly phase sensitive amplification. One of the main issues is the distortion of the signal wave during amplification. This distortion can occur due to various factors, such as the temporal walk-off between the pump and signal waves, lensing of the signal by the gain of the pump, or dispersive pulse spreading. Another challenge is the introduction of excess noise during amplification, which can degrade the quality of the amplified signal. This is particularly problematic in amplification applications with low -noise tolerance. Furthermore, the power requirements for high-gain OPA can be quite demanding, often necessitating the use of high-power laser systems. These challenges present obstacles to the widespread adoption and further development of OPA technology, particularly in applications requiring low-noise, high-fidelity amplification of weak signals.SUMMARY

[0005] In one aspect, the present disclosure relates an optical parametric amplifier. The optical parametric amplifier may also include an optical pump optically coupled to the waveguide, the waveguide may be configured to use the optical pump and the waveguide geometry to temporally gain trap and perform phase sensitive parametric amplification of an optical signal.

[0006] In embodiments of this aspect, the disclosed waveguide according to any of the embodiments above may be configured to temporally gain trap the optical signal by lowering group velocity mismatch between the optical signal and the optical pump and / or by increasing the group velocity dispersion of the optical signal.

[0007] In embodiments of this aspect, the disclosed waveguide geometry according to any of the embodiments above may include at least one of a width, a height, or a thickness of the waveguide.

[0008] In embodiments of this aspect, the disclosed waveguide geometry according to any of the embodiments above may include at least one of ridge waveguide type, multilayer cladding waveguide type, a coupled-core waveguide type, or a photonic crystal waveguide type.

[0009] In embodiments of this aspect, the disclosed waveguide geometry according to any of the embodiments above wherein the optical signal is a distorted signal and wherein the waveguide is configured to lower the distortion while performing the optical parametric amplification.

[0010] In embodiments of this aspect, the disclosed waveguide geometry according to any of the embodiments above wherein the optical signal is a continuous-wave signal and wherein the waveguide is configured to generate an ultra-fast pulse by performing the optical parametric amplification.

[0011] In embodiments of this aspect, the disclosed optical parametric amplifier according to any of the embodiments above may include a phase shifter configured to phase shift the optical pump such that the waveguide selectively performs the phase-sensitive parametric amplification of an in-phase component or a quadrature component of a the optical signal.

[0012] In embodiments of this aspect, the disclosed optical parametric amplifier according to any of the embodiments above may include a beam splitter configured to split the optical signal into an in- phase component and a quadrature component, and wherein the waveguide is configured to perform the phase-sensitive parametric amplification of the in-phase component or the quadrature component.

[0013] In embodiments of this aspect, disclosed waveguide geometry according to any of the embodiments above wherein the optical signal forms a vacuum input signal and an output after the phase-sensitive parametric amplification forms a squeezed vacuum signal.

[0014] In embodiments of this aspect, the disclosed waveguide according to any of the embodiments above may utilize quasi-phasematching structures to control the phase mismatch between the interacting waves.

[0015] In embodiments of this aspect, the disclosed waveguide geometry according to any of the embodiments above wherein the optical signal is a pulse within an optical memory cavity. In embodiments of this aspect, the disclosed waveguide geometry according to any of the embodiments above, wherein the waveguide geometry is determined in the steps of: selecting desired wavelengths for the optical signal and the optical pump, selecting the waveguide geometry to identify a range of parameters where a group velocity mismatch (GVM) between the optical signal and the optical pump is lowered and a signal group velocity dispersion (GVD) is increased, solving for a motion for the opticalsignal and the optical pump as a function of pump pulse energy using an eigenvalue solver, calculating eigenvalues, eigenvalue splitting, and mode purity as a function of pump pulse energy, and determining the waveguide geometry as being gain-trapped in response to confirming that the dominant eigenvalues are indicative of gain-trapped operation

[0016] In an aspect, the present disclosure may relate to a method of performing an optical parametric amplification. The optical parametric amplification may be performed by receiving, by waveguide with a waveguide geometry, an optical signal to be parametrically amplified and parametrically amplifying, by the waveguide using an optical pump and the waveguide geometry, by temporally gain trapping the optical signal.

[0017] In embodiments of this aspect, the disclosed method according to any of the embodiments above may include temporally gain trapping, by the waveguide, the optical signal by lowering group velocity mismatch between the optical signal and the optical pump and / or by increasing group velocity dispersion of the optical signal.

[0018] In embodiments of this aspect, the disclosed method according to any of the embodiments above may include temporally gain trapping, by the waveguide, the optical signal by increasing the group velocity dispersion of the optical signal

[0019] In embodiments of this aspect, the disclosed method according to any of the embodiments above wherein the waveguide geometry includes at least one of a width, a height, or a thickness of the waveguide.

[0020] In embodiments of this aspect, the disclosed method according to any of the embodiments above wherein the waveguide geometry includes at least one of ridge waveguide type, multilayer cladding waveguide type, a coupled-core waveguide type, or a photonic crystal waveguide type.

[0021] In embodiments of this aspect, the disclosed method according to any of the embodiments above wherein the optical signal is a distorted signal and the method may further include lowering, by the waveguide, distortion while performing the optical parametric amplification.

[0022] In embodiments of this aspect, the disclosed method according to any of the embodiments above wherein the optical signal is a continuous-wave signal and the method may further include generating, by the waveguide, ultra-fast pulse by performing the optical parametric amplification.

[0023] In embodiments of this aspect, the disclosed method according to any of the embodiments above may further include phase shifting, by a phase shifter, the optical pump; and selectively performing, by the waveguide, . the phase-sensitive parametric amplification of an in-phase component or a quadrature component of the optical signal.

[0024] In embodiments of this aspect, the disclosed method according to any of the embodiments above may further include splitting, by a beam splitter, the optical signal into in-phase component and a quadrature component; and performing, by the waveguide, the phase-sensitive parametric amplification of the in-phase component or the quadrature component.

[0025] In embodiments of this aspect, the disclosed method according to any of the embodiments above wherein the optical signal forms vacuum input and an output after the phase-sensitive parametric amplification forms a squeezed vacuum signal.BRIEF DESCRIPTION OF THE DRAWINGS

[0026] So that the way the above-recited features of the present disclosure can be understood in detail, a more particular description of the disclosure, briefly summarized above, may be made by reference to example embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only example embodiments of this disclosure and are therefore not to be considered limiting of its scope, for the disclosure may admit to other equally effective example embodiments.

[0027] FIG. 1 is a block diagram illustrating an optical system setup for phase-sensitive amplification and squeezing, according to aspects of the present disclosure.

[0028] FIG. 2A provides a composite view of a waveguide and temporal diagrams illustrating different operational states of optical parametric amplification, according to aspects of the present disclosure.

[0029] FIG. 2B depicts a collection of example waveguide types, each representing approaches that may be employed for realizing temporal gain trapping, according to aspects of the present disclosure.

[0030] FIG. 3 is an isometric view of a waveguide assembly, showing the dimensions and features of the waveguide, according to aspects of the present disclosure.

[0031] FIG. 4 is a flowchart outlining the process for designing a waveguide capable of gain-trapping, according to aspects of the present disclosure.

[0032] FIG. 5 is a flowchart outlining a method for testing a waveguide for gain-trapping, according to aspects of the present disclosure.

[0033] FIG. 6A depicts a schematic representation of an optical waveguide system designed for gaintrapping and performing amplification, according to aspects of the present disclosure.

[0034] FIG. 6B depicts a schematic representation of an optical waveguide system designed for gaintrapping and performing amplification and cleaning, according to aspects of the present disclosure.

[0035] FIG. 6C depicts a schematic representation of an optical waveguide system designed for gaintrapping and performing fast pulse conversion, according to aspects of the present disclosure.

[0036] FIG. 6D depicts a schematic representation of an optical waveguide system designed for gaintrapping and performing a process of optical parametric amplification within a memory cavity, according to aspects of the present disclosure.

[0037] FIG. 6E depicts a schematic representation of an optical waveguide system designed for gaintrapping and performing optical parametric amplification, according to aspects of the present disclosure.

[0038] FIG. 6F depicts a schematic representation of an optical waveguide system designed for gaintrapping and performing squeezing, according to aspects of the present disclosure.

[0039] FIG. 6G depicts a schematic representation of an optical waveguide system designed for gaintrapping and performing a process of optical parametric amplification within a memory cavity, according to aspects of the present disclosure.

[0040] FIG. 7 illustrates an example system diagram for designing and verifying gain-trapped waveguides, according to aspects of the present disclosure.

[0041] FIG. 8 presents a block diagram of an example computing system for the devices in FIG. 7, illustrating the interconnection of its components, according to aspects of the present disclosure.

[0042] FIG. 9 is a flowchart outlining a method of performing phase-sensitive optical parametric amplification, according to aspects of the present disclosure.DETAILED DESCRIPTION

[0043] Various example embodiments of the present disclosure will now be described in detail with reference to the drawings. It should be noted that the relative arrangement of the components and steps, the numerical expressions, and the numerical values set forth in these example embodiments do not limit the scope of the present disclosure unless it is specifically stated otherwise. The following description of at least one example embodiment is merely illustrative in nature and is in no way intended to limit the disclosure, its application, or its uses. Techniques, methods, and apparatus as known by one of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate. In all the examples illustrated and discussed herein, any specific values should be interpreted to be illustrative and non-limiting. Thus, other example embodiments may have different values. Notice that similar reference numerals and letters refer to similar items in the following figures, and thus once an item is defined in one figure, it is possible that it need not be further discussed for the following figures. Below, the example embodiments will be described with reference to the accompanying figures.

[0044] Optical parametric amplification (OP A) is a process in nonlinear optics where a shortwavelength pump provides gain to two bands of longer wavelengths, commonly referred to as the signal and idler. A conventional use of OPA may be to apply an input at the signal wavelength: the signal is then amplified in a phase-insensitive way (i.e., with gain independent of the input phase), and light at the idler wavelength is simultaneously generated in the process. However, for the special case of degenerate OPA, where the signal and idler share the same nominal wavelength, the amplification process becomes phase sensitive. In this case, the pump can either amplify or de-amplify the signal depending on the relative phase between the field associated with the pump and the signal; simply phaseshifting the signal with either a small delay line or a phase modulator may change the amplitude of the signal output from a phase-sensitive OPA.

[0045] Phase- sensitive OPA has a number of unique properties that are desirable for communications, sensing, metrology, optical computation, and quantum information processing. These may include: i) the ability to amplify weak signals while introducing a minimal amount of noise; ii) the ability togenerate squeezed light; iii) the ability to perform non-demolition measurements of quantum states; and iv) the ability to perform both linear and nonlinear operations on analog and binary information encoded in an optical field, which forms the basis for optical or analog computational circuits. At this time of writing, many proposals for optical computation, quantum computation, and optical metrology assume that high-gain OPAs develop into a compact, low -power, reliable, and easily fabricated component that can be densely integrated into photonic circuits, much like the modern transistors that are used in integrated electronic circuits.

[0046] There are several challenges to be addressed before phase-sensitive OPA can satisfy these assumptions. A challenge for OPA may be high energy consumption. Optical parametric amplification is an extremely weak process that becomes stronger when driven with a larger pump field intensify. Therefore, the large field intensities generated by high-power lasers may be needed to realize useful amounts of gain. State-of-the art commercial OPA systems have footprints that occupy square meters and consume watts of optical power. The power required for high-gain OPA can be reduced in several ways. These include the use of optical waveguides, which increase the field intensity by providing transverse confinement, the use of designs that allow for long interaction lengths (e.g., by fabricating long waveguides or optical resonators), and the use of ultrafast (femtosecond) pump pulses which compress the delivered power to a small instant in time, thereby increasing the field intensify. State-of- the-art devices have combined all of these features to realize large (> 100 decibels, or dB) parametric gains in waveguides that operate with picojoules of pump power.

[0047] Even in state-of-the-art devices, there remain several unsolved challenges. These include a complicated trade-off between pump pulse duration and interaction length, field distortions that occur during amplification by short pulses, and low device yield. Taken together, these hurdles limit the development of integrated circuits based on OPA. State-of-the-art device yields in integrated photonics are too low to fabricate large circuits, and even in small circuits the field distortions accumulated during OPA prevent high-fidelity operations.

[0048] This disclosure describes an approach to phase-sensitive optical parametric amplification (and de-amplification) that overcomes these limitations by using a dynamical process known as temporal gain trapping. In principle, gain-trapped OPAs can realize large parametric gains with low pump pulse energies, exhibit no pulse distortion (for properly chosen inputs), and may be fabricated with much higher yields than current state-of-the-art devices.

[0049] The present disclosure generally relates to the field of optical amplification, and more specifically to the phase-sensitive amplification of light pulses. In some embodiments, the present disclosure introduces a method and system designed to apply phase-sensitive gain to light signals, enabling either amplification or attenuation based on control over the pump's phase. This capability is advantageous for processing optical signals in both classical and quantum contexts, as phase-sensitive gain allows for the proportional scaling of a light signal with the least amount of noise. For instance, inthe context of a linear amplifier with positive gain, phase-sensitive amplification may reduce (e.g., minimize) the noise figure, thereby offering advantages for the manipulation and detection of faint light signals or quantum states.

[0050] In some embodiments, the disclosure describes a method for amplifying light signals that employs a technique known as temporal gain trapping. This technique involves the strategic manipulation of light within specially designed channels, known as nonlinear waveguides, to achieve a specific type of amplification. The amplification process may be designed to selectively enhance a single signal pulse, or mode, without distortion. In other words, temporal gain trapping may be achieved by engineering the waveguide's dispersion properties to match the group velocities of the pump and signal pulses and to control the group velocity dispersion (GVD) at the signal's frequency. The precise control over the optical mode allows for the temporal gain trapping effect, where the specified signal modes are preserved during amplification.

[0051] In some embodiments, the disclosure provides a waveguide for performing temporal gaintrapping. The waveguide includes a waveguide body defining a waveguide geometry, an optical signal, and an optical pump optically coupled to the waveguide body. The waveguide geometry is determined by a process that involves selecting desired wavelengths for the optical signal and the optical pump, identifying a range of parameters where a group velocity mismatch (GVM) between the optical signal and the optical pump is sufficiently small and a signal GVD is sufficiently large, and solving for a configuration of the optical signal and the optical pump as a function of pump pulse energy using an eigenvalue solver.

[0052] In some embodiments, the disclosure provides a method for testing a waveguide for gaintrapping. The method involves choosing a wavelength for testing the waveguide, inputting an optical signal and an optical pump to the waveguide at the wavelength, correcting the PSD of the output signal, computing an overlap between the PSD difference at the wavelength and another PSD difference at another wavelength, and determining that the waveguide is gain-trapped if the overlap is greater than a predetermined threshold.

[0053] It is noted that correcting the output PSD of the signal may include removing the continuous wave (CW) background that may be present. This correction is beneficial for isolating the contribution of the optical parametric amplification process to the signal's PSD. Various methodologies can be employed to achieve this correction (e.g., filtering, subtraction of the seed spectrum from the amplified output spectrum, etc.). For example, the system may measure an output PSD with the optical pump turned off to capture a seed spectrum, measuring the output PSD with the optical pump turned on to capture an amplified output spectrum, and then compute a PSD difference between the amplified output spectrum and the seed spectrum. This process may also be automated, e.g., by modulating the pump laser and using lock-in detection to measure the generated signal. In this case, the PSD difference accurately reflects the enhancement attributable to the gain-trapping mechanism, thereby allowing foran accurate evaluation of the waveguide's performance in facilitating temporal gain trapping. This step is part of the verification process, as it ensures that the measured PSD difference is not skewed by the CW background, which could otherwise lead to erroneous conclusions regarding the waveguide's gaintrapping capabilities.

[0054] It is noted that for testing purposes, the pump pulse may be set and maintained at a constant energy level while the wavelength of a tunable signal is varied (e.g. signal is swept when characterizing eigenfunctions). The generated signal energy is measured as a function of pump pulse energy (e.g., for a few different seed wavelengths) to characterize the eigenvalue. This approach allows for the assessment of the waveguide's ability to facilitate temporal gain trapping across a spectrum of signal wavelengths. By keeping the pump pulse steady, the testing method isolates the variable of signal wavelength, ensuring that any observed effects on the amplification process are due to the waveguide's interaction with the signal rather than fluctuations in the pump energy.

[0055] These and other embodiments of the present disclosure provide a method and system for phasesensitive amplification and squeezing by gain-trapped optical parametric amplification, which can be beneficial in a variety of applications, including low-noise detection, quantum computing, quantum- enhanced metrology, optical computation, and secure quantum communication such as Quantum Key Distribution (QKD).

[0056] FIG. 1 is a block diagram illustrating an optical system setup 100, according to example embodiments. The optical system setup 100 includes an optical pump 102 and an optical signal 104, both of which are optically coupled to an interaction medium, represented here as a waveguide 106. The waveguide 106 outputs an optical output 108 based on the inputs of optical pump 102 and optical signal 104. The diagram illustrates the flow of light from the pump and signal sources through the waveguide, resulting in optical output(s) 108.

[0057] In some embodiments, the optical pump 102 may be a laser, providing the high-frequency pump wave that is beneficial to the optical parametric amplification process. In some embodiments, the optical signal 104 may be a laser, a prepared quantum state, or even a vacuum state, depending on the specific application at hand. For instance, in quantum information processing, the signal source may be a quantum state that carries information to be amplified, while in the generation of squeezed states of light, the signal source may be a vacuum that interacts with the pump wave within the waveguide 106. The versatility of the optical signal 104 allows for a wide range of applications, from classical optical communication to advanced quantum technologies.

[0058] Waveguide 106 (which may form an optical parametric amplifier based on the embodiments disclosed herein) may amplify weak signals (e.g., quantum signals) while avoiding the introduction of excess noise or distortion, thus safeguarding the integrity of the states represented by the signals. This feature is beneficial for systems where maintaining the integrity of states (e.g., quantum states) is important, such as in quantum computation, quantum sensing, quantum communication includingQuantum Key Distribution (QKD), and quantum state tomography to name a few. In these applications, any degradation of quantum states can have unwanted consequences, and in the case of QKD, it can result in an outcome of compromised security. For example, quantum error-correcting codes (QECCs) are designed to protect quantum information against errors due to decoherence and other quantum noise. A fault-tolerant threshold in QECCs refers to a point below which the error rate of quantum operations can be suppressed by the error correction process faster than it accumulates. This ensures that the computation can proceed indefinitely without a catastrophic loss of information. Therefore, the ability to perform phase-sensitive amplification and squeezing by gain-trapped optical parametric amplification is important to QECCs.

[0059] Furthermore, waveguide 106 may incorporate group-velocity matching between the pump and signal pulses. This feature extends the interaction length between the pulses without succumbing to the temporal walk-off issues that often undermine conventional OPAs, facilitating a more efficient energy transfer and yielding a higher gain.

[0060] Temporal gain-trapping may rely on four features including: 1. A means to control the phasemismatch between the pump and signal. This is typically achieved using quasi-phase matching in simple waveguides, but phase-velocity matching may become possible without quasi- phase matching in more complicated structures. 2. Group-velocity matching (or near-matching) between the pump at 2CD and the signal at CD to eliminate temporal walk-off. 3. A pump pulse with short duration. 4. A large group- velocity dispersion at the fundamental, which may cause dispersive pulse spreading in the absence of gain.

[0061] When these features are combined, the interplay between the large parametric gain localized around the peak of the pump and the dispersive pulse spreading of the signal may cause the signal pulse to propagate without changing shape. This process may be referred to as temporal gain-trapping, in analogy to other recently studied approaches to temporal trapping based on cross-phase modulation, since the parametric gain of the pump pulse confines both the shape and the location of the signal pulse. The interplay between gain and dispersion can be treated as a waveguide that confines a time-domain pulse.

[0062] By harnessing the principles of dispersion engineering and temporal gain trapping, waveguide 106 achieves large parametric gains at reduced pump power levels, which is in contrast to traditional methods. The result is a more compact, robust, and energy-efficient system for optical amplification, which is both cost-effective and environmentally friendly.

[0063] Another feature of waveguide 106 is its ability to cascade multiple OPAs, creating high-gain nonlinear circuits. This capability opens up new possibilities in the pulsed OPA community that have yet to be fully explored including but not limited to new approaches to optical computation and signal processing. It allows for not just the generation of light but also its intricate manipulation within photonic circuits, all without the risk of pulse distortion.

[0064] Waveguide 106 also plays a role in minimizing the avenues for quantum noise introduction, thereby reducing decoherence and preserving the quantum characteristics of the amplified light. This is a substantial advantage for applications that require the manipulation and detection of weak optical signals, including fragile quantum states. Waveguide 106 is well-suited for a diverse array of applications, ranging from quantum computing and quantum-enhanced metrology to optical computation and secure quantum communication, including QKD.

[0065] In specific examples, waveguide 106 may be tailored to restrict the amplification process to a singular temporal mode. This is a marked improvement over traditional OPAs, which often indiscriminately distribute gain across various pulse shapes, leading to signal distortion and excess noise. Waveguide 106 utilizes temporal gain trapping to circumvent signal pulse distortion during amplification. This is accomplished by fine-tuning the pump pulse energy (or equivalently, the peak gain coefficient) of the waveguide, the waveguide dispersion, and the pump pulse duration to ensure that the gain extracted by one gain-trapped mode dominates over all other modes. Under these conditions, any signal pulse input to the waveguide is output as the gain-trapped mode, and subsequent amplification stages (by further gain-trapped OPAs) amplify this signal pulse cleanly with its temporal shape intact.

[0066] Waveguide 106 design capitalizes on dispersion engineering within nonlinear waveguides to achieve temporal gain trapping, a technique that strategically manipulates light to realize a distinct amplification type. This approach is particularly advantageous for amplifying short light pulses without altering their temporal profile, which is beneficial for maintaining the fidelity of quantum states throughout the amplification process.

[0067] While FIG. 1 illustrates one example configuration of an optical system setup utilizing waveguide 106, it is to be understood that waveguide 106 may be employed in a multitude of other configurations and systems beyond what is depicted. The flexibility in the design of waveguide 106 allows it to be integrated into various optical architectures, catering to a broad spectrum of applications that demand phase-sensitive amplification. For instance, waveguide 106 can be adapted for use in systems where multiple waveguides are arranged in parallel or series to achieve specific amplification goals, or in configurations where waveguide 106 serves as a core component in more complex optical circuits. Additionally, waveguide 106 can be utilized in conjunction with other optical elements such as filters, modulators, and detectors to construct sophisticated systems tailored for advanced optical processing tasks. This versatility underscores the broad applicability of waveguide 106 across different domains of optical technology, ranging from basic research to industrial applications.

[0068] Referring now to FIG. 2A, a composite view 200 of a waveguide 202 (forming an OPA) and temporal diagrams illustrating different operational states of OPA is depicted. The waveguide 202 includes a base 202B and a channel 202A having quasi-phasematching sections 202C and 202D. The temporal diagrams depict a conventional OPA temporal diagram 204, a group-velocity matched OPAtemporal diagram 206, and a gain-trapped OPA temporal diagram 208. The diagrams demonstrate the evolution of the signal pulse under different amplification conditions over time instances Tl, T2, T3, T4, and T5.

[0069] In the conventional OPA temporal diagram 204, the signal pulse results in an unaligned (temporal walk-off) and unamplified signal at time instance T5. This is due to the group-velocity mismatch between the pump and signal pulses, which limits the interaction length and thus the total gain that can be extracted by the signal.

[0070] In contrast, the group-velocity matched OPA temporal diagram 206 is aligned but produces a distorted signal pulse at time instance T5. This distortion is caused by gain lensing - a phenomenon where the large parametric gain localized around the peak of the pump amplifies the peak of the signal pulse more than the tails, causing the duration of the signal pulse to shrink.

[0071] In contrast, the gain-trapped OPA temporal diagram 208, results in gain without distortion or misalignment due to the benefits of gain-trapping. In this case, the GVD of the signal pulse is engineered to cancel gain lensing. This allows a signal pulse to extract gain without undergoing distortion, a feature that is particularly beneficial for constructing optical circuits comprising many components.

[0072] In some embodiments, the waveguide 202 may incorporate quasi-phase matching structures within the waveguide body, as represented by quasi-phasematching sections 202C and 202D. These structures may be characterized by a periodic variation in the refractive index or material composition along the length of the waveguide body. This periodic variation enables phase-matched OPA and allows for control over the waveguide dispersion using the geometry of the waveguide cross-section.

[0073] In some embodiments, the waveguide 202 may be designed to achieve temporal gain trapping by combining both phase-matched (or quasi-phasematched) OPA and dispersion engineering. This may involve a combination of a short pump pulse, group-velocity matching between the interacting waves, and a large group-velocity dispersion at the signal's frequency. When these conditions are satisfied, the pump provides gain to a single signal pulse, which undergoes amplification without distortion.

[0074] In some examples, the waveguide 202 may be designed to operate at arbitrary wavelengths, thereby expanding its potential applications. In some examples, the waveguide 202 may be designed to operate with relatively small amounts of optical power, thereby reducing the energy requirements for amplification.

[0075] In some embodiments, the waveguide 202 may be designed to amplify weak signals, generate squeezed light, manipulate quantum states, perform optical computation, and / or enhance detection sensitivity. In some embodiments, the waveguide 202 may be designed to operate in a variety of environments, including but not limited to quantum computing systems, quantum-enhanced metrology systems, optical computation systems, and / or secure quantum communication systems such as QKD.

[0076] Referring now to FIG. 2B, a collection 240 of example waveguide types, each designed for specific optical properties and applications, is depicted. The waveguide types include a ridge waveguidetype 242, a multilayer cladding waveguide type 246, a coupled-core waveguide type 248, and a photonic crystal waveguide type 250 to name a few. Each of these waveguide types is engineered to achieve desired effects such as phase-matching, group velocity matching, and dispersion control for applications like optical parametric amplification. It is to be noted that the waveguide types depicted in FIG. 2B, are illustrative examples of some forms that a waveguide can take. The selection and design of a waveguide are contingent upon the specific use context and the requirements of the application at hand. The form of the waveguide including waveguide geometry, material composition, and dispersion properties are all variables that can be tailored to optimize the performance of the optical parametric amplification system for the intended application. This flexibility in waveguide design is a testament to the adaptability of the disclosed technology, allowing for customized solutions that address the diverse challenges and demands of different optical systems. Whether the application involves quantum computing, quantum-enhanced metrology, or secure quantum communication, the waveguide can be engineered to facilitate temporal gain trapping and phase- sensitive amplification, ensuring the fidelity and integrity of the amplified signals.

[0077] In some embodiments, the ridge waveguide type 242 may be designed with a raised central region to guide light. The multilayer cladding waveguide type 246 may include multiple layers to control light propagation. This design can provide enhanced control over the optical properties of the waveguide, such as its refractive index profile and dispersion characteristics. The coupled-core waveguide type 248 may have multiple cores that interact to manage light signals. The photonic crystal waveguide type 250 may incorporate a periodic structure to manipulate light at the nanoscale. This design can provide a high degree of control over the propagation of light within the waveguide, enabling the creation of waveguides with tailored dispersion properties and phase -matching conditions. The designs mentioned above may provide a high degree of control over the propagation of light within the waveguide making them suitable for a variety of applications, including but not limited to optical communication systems, optical sensors, and optical computing devices to name a few.

[0078] It is noted that selection of waveguide designs, such as the ridge waveguide type 242, the multilayer cladding waveguide type 246, the coupled-core waveguide type 248, and the photonic crystal waveguide type 250, may be influenced by their ability to robustly access different wavelength ranges. This robust access to a spectrum of wavelengths may be a determining factor for their use in various applications, rather than being confined to specific use cases.

[0079] The waveguide types depicted in the waveguide collection 240 may be used individually or in combination (e.g. cascade) to realize a variety of optical systems and devices. The selection of a specific type of waveguide, such as a multilayer cladding waveguide or a photonic crystal waveguide, may be driven by the specific operational requirements of the application at hand, rather than a broad categorization of their function. For instance, a multilayer cladding waveguide, which is characterized by multiple layers of different materials, can offer precise control over light propagation. This may makeit suitable for applications operating at short wavelengths, where the ability to manage light propagation with high precision is beneficial. On the other hand, a photonic crystal waveguide, which is a type of waveguide that manipulates light at the nanoscale by creating a periodic variation in the refractive index, might be selected for its efficacy in handling long pulses. It's worth noting that the choice of waveguide type is not a one-size-fits-all decision, but rather a strategic choice that depends on the specific requirements of the application. Factors such as the desired operational wavelength, the nature of the input signal (e.g., its pulse duration and intensity), and the specific performance requirements (e.g., the level of gain, noise figure, and distortion tolerance) all play a role in determining the appropriate waveguide type. Therefore, the design and selection of the waveguide is an aspect of the overall system design, and can greatly influence the performance and efficiency of the phase-sensitive amplification process.

[0080] The waveguide types depicted in the waveguide collection 240 may be fabricated using a variety of materials and fabrication techniques. For example, the waveguides may be fabricated from materials such as silicon, silica, lithium niobate, or any other suitable material. The fabrication techniques may include lithography, etching, deposition, or any other suitable technique.

[0081] The waveguide types depicted in the waveguide collection 240 may also be designed to operate over a wide range of wavelengths. This can enable the waveguides to be used in a variety of applications, including but not limited to telecommunications, sensing, imaging, and quantum information processing.

[0082] Referring now to FIG. 3, an isometric view of a waveguide assembly 300 (e.g., ridge waveguide) is depicted, according to example embodiments. The waveguide assembly 300 includes a modified top section 302 situated atop a waveguide base 304. The modified top section 302 incorporates phase matching features 302A and 302B. The waveguide assembly 300 is defined by length dimensions LI and L2, which indicate the lengths of the phase matching features, a total waveguide length L3, waveguide width dimensions W1 and W2 indicating the top section width and base section width, and waveguide height dimensions Hl and H2 indicating the top section height and base section height. It is noted that in the pursuit of achieving gain-trapped operation within a waveguide, the design parameters extend beyond geometric considerations. The waveguide's ability to facilitate temporal gain trapping may be contingent upon a confluence of factors that are engineered to create the desired amplification characteristics. These parameters may include, but are not limited to, the thickness of cladding layers, which can influence the confinement and dispersion of light within the waveguide. Other parameters such as the waveguide's cross-sectional dimensions, material composition, and the incorporation of quasi-phase matching structures are also tailored to optimize the nonlinear interactions between the pump and signal pulses. Collectively, these design elements are orchestrated to ensure that the waveguide operates within the parameter range that enables temporal gain trapping, ultimately leading to high-fidelity, low -noise amplification of the signal pulse.

[0083] In some aspects, the waveguide assembly 300 may be designed to facilitate gain-trapping by adjusting one or more of the dimensions (e.g. cross-sectional dimensions) of the waveguide. These dimensions may include the width (waveguide width dimensions W1 and W2), the height (waveguide heights Hl and H2), or the thickness of the waveguide assembly 300. By adjusting these dimensions, the waveguide geometry can be optimized to achieve temporal gain trapping.

[0084] In some embodiments, the phase matching features 302A and 302B integrated into the modified top section 302 of the waveguide assembly 300 may be designed to facilitate phase-matching. Phasematching is a condition in which the phase velocities of the interacting waves are equal, allowing for efficient energy transfer between the waves. By incorporating phase matching features 302A and 302B into the waveguide assembly 300, the waveguide can be designed to achieve efficient optical parametric amplification.

[0085] In some examples, the waveguide design algorithm may select the waveguide geometry to identify a range of parameters where a GVM between the optical signal and the optical pump is made sufficiently small and a signal GVD is made sufficiently large. By optimizing the waveguide geometry in this manner, the waveguide assembly 300 can be designed to achieve efficient and distortion-free amplification of light signals.

[0086] For example, to achieve temporal gain trapping in the waveguide assembly 300, the width dimensions W 1 and W2 may be fine-tuned to alter the mode field diameter, thereby affecting the overlap between the pump and signal modes. A narrower width may be chosen to increase the intensity of the light within the waveguide, enhancing the nonlinear interaction responsible for the amplification. The dimensions (e.g., width dimensions W1 and W2, height dimensions Hl and H2, etc.) may be adjusted to control the confinement in the waveguide and dispersion relations of the confined modes, which can be used to engineer the GVMs, GVDs and other dispersive effects. By carefully selecting the thickness of the waveguide, the dispersion properties can be tailored to ensure that the GVD at the signal's frequency is optimized, allowing the signal pulse to maintain its shape throughout the amplification process. These adjustments to the cross-sectional dimensions of the waveguide are made in conjunction with the selection of appropriate materials and quasi-phase matching structures to ensure that the waveguide operates within the desired parameter range for gain-trapping, ultimately leading to high- fidelity, low-noise amplification of the signal pulse.

[0087] It is also noted that waveguide assembly 300 may be designed to operate over a wide range of wavelengths. This can enable the waveguide assembly 300 to be used in a variety of applications, including but not limited to telecommunications, sensing, imaging, and quantum information processing.

[0088] Prior to discussing algorithms for designing a gain-trapped waveguide and verifying that a waveguide is gain-trapped, it may be beneficial to discuss computer hardware devices that act as a platform for performing the designing and verifying algorithms. Examples of these devices are shownin FIG. 7 as a system 700 for designing and verifying gain-trapped waveguides. The system 700 may include various devices interconnected via a network 708, which serves as a communication hub. In some examples, the system 700 includes a user device 702, database 704 and design / verification server 706.

[0089] The system 700 is a comprehensive platform that facilitates the design, simulation, and verification of gain-trapped waveguides, enabling researchers and engineers to optimize these devices for various applications. The system 700 includes various devices interconnected via a network 708, which serves as a communication hub. This network 708 allows for seamless data exchange and coordination among the different components of the system, ensuring efficient and accurate design and verification processes.

[0090] In some examples, the system 700 includes a user device 702, a database 704, and a design / verification server 706. The user device 702 could be a computer or a workstation equipped with the appropriate software tools for designing and simulating gain-trapped waveguides. It provides an interface for users to input design parameters, run simulations, and analyze results.

[0091] The database 704 stores information that can aid in the design and verification process. This could include data on different waveguide materials and their properties, previous design iterations and their performance metrics, and computational models for simulating waveguide behavior. The database 704 can be accessed by the user device 702 and the design / verification server 706 for retrieving and storing data.

[0092] The design / verification server 706 is a computing resource that performs the computational tasks involved in the design and verification process. It can run complex simulations based on the design parameters inputted through the user device 702 and verify the performance of the designed waveguides against predefined criteria. The results of these simulations and verifications are then sent back to the user device 702 for analysis.

[0093] Together, these components form a robust system for designing and verifying gain-trapped waveguides, accelerating the development of these devices and enhancing their performance in various applications.

[0094] Now that the hardware has been introduced, example algorithms for designing a gain-trapped waveguide and verifying that a waveguide is gain-trapped are now described with respect to FIG. 4 and FIG. 5.

[0095] FIG. 4 is a flow diagram illustrating a method 400 for designing a waveguide capable of gaintrapping, according to example embodiments.

[0096] At step 402, the desired wavelengths for the pump laser and signal laser are chosen, for example, by the designer via user device 702. This selection may be based on the specific requirements of the application, such as the desired optical properties, the available optical power, or the complexity of theoptical system. In some cases, the wavelengths may be selected to optimize the performance of the waveguide in terms of efficiency, bandwidth, or noise performance.

[0097] At step 404, the waveguide geometry is swept or varied, for example, by the design algorithm executed on server 706, to determine a range of parameters where a GVM between the optical signal and the optical pump is made sufficiently small and a signal GVD is made sufficiently large. This optimization may involve adjusting the cross-sectional dimensions of the waveguide, such as the width, height, or thickness, or modifying the material composition or refractive index profile of the waveguide. In some cases, a computational model may be used to simulate the optical properties of the waveguide and guide the optimization process.

[0098] At step 406, equations of motion for the optical signal and the optical pump are solved, for example, by the server 706, as a function of device parameters (e.g. pump pulse energy, pump pulse shape, phase mismatch, group velocity mismatch, and group velocity dispersion). This step may involve numerical methods or analytical techniques to solve the equations of motion (such as split-step Fourier methods, or an eigenvalue solver), which describe the evolution of the optical fields within the waveguide.where amand am* are complex flux amplitudes associated with the mthFourier component of the signal wave; ymn is the gain coefficient for each pair of signal modes, as provided by the Fourier components of the pump; and Akncontains contributions to the phase-mismatch by the dispersion relations of the waveguide, evaluated for the nth Fourier component.

[0099] For example, given a known pump field and the nominal value of the nonlinearity, K, and therefore the matrix ymn; the dispersion relations of the waveguide and quasi-phase-matching structure (and therefore Akn); and the waveguide length, solve the above equations of motion (Eqn. 1) to obtain the Green’s function (G(z)).where Ain and Aout are unitary matrices that project the input and output of the OP A into a basis of supermodes. The columns of Ajnand Aout correspond to waveforms that describe the input and outputsupermodes of the OPA, respectively; r](z) is a diagonal matrix that describes the gain accumulated by each supermode.

[0100] In some embodiments, other treatments may be used. That is, there may be an equivalent representation of the system dynamics in the quadrature (x-p) basis. One could also forgo the undepleted-pump approximation and integrate the coupled-wave equations directly.

[0101] At step 408, perform a Bloch-Messiah decomposition of the Green’s function (Eqn. 2) may be performed (for example by the server 706) to obtain the input and output modes of the OPA as a function of device length, as well as the singular values that describe the gain accumulated by each mode. These calculations may provide insight into the behavior of the optical fields within the waveguide and can be used to assess the performance of the waveguide in terms of gain, noise, and purity. The purity of the OPA may be calculated using the Schmidt number (Eqn. 3).(Eqn. 3)The purity of the amplifier, as a function of propagation coordinate z, where the parameters r|(z) may be obtained by performing a singular value decomposition on the S(z) block of the Green’s function.

[0102] It is noted that a gain-trapped OPA may be mathematically defined as a condition that a subset of the OPA modes (i.e. pairs of input and output modes) no longer change shape for sufficiently large z or sufficiently large nonlinearity. For OP As where the system matrix is well described as being z- invariant, the input modes Ain(z) associated with gain-trapped modes asymptote to the corresponding left eigenvectors of the system matrix M, and the output modes associated with gain-trapped modes asymptote to the corresponding right eigenvectors of the system matrix M. In many cases, the gaintrapped modes may be the eigenvectors that accumulate the most gain.

[0103] It is noted that for OP As where the system matrix, is well described as being z-invariant, (M(z) = M(0)), gain-trapped OPA may also be mathematically defined as the condition that there exists a subspace of bound modes, corresponding to discrete pairs of eigenvectors and eigenvalues of the system matrix M that are distinct from the continuum modes (i.e. discrete eigenvectors with corresponding eigenvalues that are separated from the continuum modes by a gap in the complex plane).

[0104] For OPAs with system matrices that evolve along the propagation coordinate, z, the above eigenfunction analysis can be performed locally (i.e. at any value of z) to determine if portions of the OPA locally exhibit gain-trapped operation.

[0105] For OPAs with system matrices that evolve along the propagation coordinate, z, the above eigenfunction analysis can be performed locally (i.e. at any value of z) to determine if portions of the OPA locally exhibit gain-trapped operation.

[0106] In some aspects, method 400 may be iterated, for example, by the server 706 in conjunction with database 704, or repeated multiple times to refine the design of the waveguide. For example, at step 410, it may be determined whether the gain trapped design is achieved. If not achieved, the waveguide geometry optimization step 404, the equations of motion solving step 406, and the decomposition step may be repeated with different parameters or constraints to explore a wider range of possible waveguide designs under different operating conditions. That is, if the waveguide fails to achieve gain-trapped operation, the method 400 return to the start and try other waveguide designs that better satisfy the gaintrapped conditions (low GVM, large signal GVD, small pump pulse duration), before repeating the above steps 402-410.

[0107] In some embodiments, method 400 may be supplemented with additional steps or considerations. For example, the process may include steps for fabricating the waveguide, testing the waveguide, or integrating the waveguide into a larger optical system. The process may also consider factors such as the cost, manufacturability, or reliability of the waveguide.

[0108] Method 400 may be used to design waveguides for a variety of applications, including but not limited to telecommunications, sensing, imaging, and quantum information processing. Method 400 may be adapted or customized based on the specific requirements of the application, such as the desired optical properties, the available optical power, or the complexity of the optical system.

[0109] Subsequently, the waveguide geometry optimization step 404 is undertaken to achieve temporal gain trapping. This step is germane to lowering GVM and increasing signal GVD at the selected wavelengths. It involves meticulous adjustments to the cross-sectional dimensions of the waveguide, such as the width and the height, to enhance nonlinear interactions and control mode confinement, respectively.

[0110] For example, at step 412 after verifying that an OPA exhibits gain-trapped operation, the gain of the dominant mode (given by the largest value of exp(r](z))), the purity of the OPA (given by Eqn (3)), and the cascadability of the OPA (given by the overlap, or inner product, of the input and output modes) may be optimized by varying parameters such as the pump power, device length, and phase-mismatch. In some embodiments, the phase-mismatch may be varied along the device length to take advantage of the properties of different gain-trapped modes along different segments of the OPA.[oni] FIG. 5 is a flow diagram illustrating a method 500 for testing a waveguide for gain-trapping, according to example embodiments. Gain-trapped operation may be determined by measuring the eigenvalues of the OPA modes, or the eigenvectors, as a function of input conditions. Pump-probe measurements (also referred to as stimulated emission tomography) can be used to determine if an OPA achieves temporal gain trapping. This measurement can be performed by driving the OPA with a short pump pulse centered around the nominal pump frequency (2co), and seeding the OPA with a continuous- wave tunable signal near the nominal operating wavelength (CD). For a gain-trapped OPA operating withone dominant eigenmode, both the eigenvalue and eigenvector of the OPA will be a weak function of the input wavelength, aside from a peak localized near the seed wavelength.

[0112] At step 502, a wavelength is chosen for testing the waveguide. The wavelength may be chosen, for example, by the test engineer via user device 702, based on the specific requirements of the application, such as the desired optical properties, the available optical power, or the complexity of the optical system. In some cases, multiple discrete wavelengths across a predetermined spectral range may be chosen for testing, providing a comprehensive assessment of the waveguide's performance across a broad range of operating conditions.

[0113] At step 504, an optical signal and an optical pump are input, for example, by the test engineer, to the waveguide at the chosen wavelength, and the output PSD is measured with the optical pump turned on. This measurement captures the amplified output spectrum, which includes both the PSD (PSDseed) of the input seed and the PSD (PSD0Ut) of the light generated by the OPA process within the waveguide. In some cases, the output PSD may be measured using a spectrometer with a resolution finer than the smallest expected spectral feature of the seed spectrum, ensuring a high level of accuracy in the measurement.

[0114] At step 506, the output spectrum may be corrected, for example, by the server 706, to remove the seed spectrum (i.e., correct the measured PSD to suppress the continuous wave (CW) background). This may be obtained either by subtracting the seed spectrum from the output spectrum to obtain PSDOPA, or by removing the region around the seed wavelength, interpolating the power spectrum in this region using neighboring values. For example, to correct the output spectrum to remove the seed spectrum, the method computes (see Eqn. 4) PSD difference. For example, the difference between the amplified output spectrum and the seed spectrum is calculated. This difference represents the PSD (PSDOPA) of the light generated by the OPA process within the waveguide.PSDOPA ~ PSD0Ut- PSDseed (Eqn. 4)

[0115] In some cases, the PSD difference may be computed by normalizing the PSD with the optical pump turned ON to the PSD with the optical pump turned OFF, providing a measure of the amplification achieved by the waveguide. It is noted that rather than subtracting the seed spectrum from the amplified output spectrum the signal can be detected using a lock-in amplifier. This technique may involve modulating the intensity or frequency of the pump at a known reference frequency and then using the lock-in amplifier to measure the signal at the same frequency. By correlating the detected signal with the reference modulation of the pump, the lock-in amplifier can isolate the contribution of the OPA process to the signal's PSD. This method provides a means to accurately characterize the gain-trapping behavior of the waveguide without the influence of the CW background.

[0116] In either case, at step 508, the overlap between each pair of these measured power spectra may be calculated, for example, by the server 706, ignoring the phase of the eigenmodes, and normalizing each power spectrum to contain unity power. For example, the overlap between the corrected PSD at achosen wavelength and another PSD at another chosen wavelength is computed. This overlap provides a measure of the consistency of the waveguide's performance across different wavelengths. In some cases, the overlap may be computed using an integral computed using a pair of normalized (background corrected) PSD, providing a robust measure of the waveguide's performance.

[0117] At step 510, it is determined, for example, by the server 706, whether more wavelength measurements may be needed. If no further measurements are deemed to be warranted, the method proceeds (see Eqn. 5) to step 512.

[0118] At step 512, it is determined, for example, by the server 706, whether the overlap is greater than a predetermined threshold (e.g., 90% overlap for all seed wavelengths). If the overlap is greater than the threshold, indicating that the waveguide's performance is consistent across different wavelengths, the method 500 may proceed to step 516 and a gain-trapped outcome is achieved, confirming that the waveguide is capable of gain-trapping. If, however, the overlap is not greater than the threshold, the method 500 leads to step 514 and the non gain-trapped outcome is achieved, indicating that the waveguide is not capable of gain-trapping.

[0119] In some aspects, the method 500 may include additional steps or considerations. For example, the method may include the step of adjusting the optical pump power and repeating the measurements to determine the effect of pump power on gain-trapping efficiency. Similarly, the method may include the step of adjusting the optical signal power and repeating the measurements to determine the effect of signal power on gain-trapping efficiency. In some embodiments, the method 500 may include the step of using a tunable filter to isolate specific spectral components before measuring the output PSD, providing a more detailed assessment of the waveguide's performance. In some examples, the predetermined threshold for determining gain-trapping may be based on a comparison with a theoretical model of expected gain-trapping performance, providing a rigorous benchmark for the waveguide's performance. In other examples, the method may include the step of performing a time-resolved measurement of the amplified output spectrum to assess temporal characteristics of the gain-trapping, providing additional insights into the waveguide's performance.

[0120] Consider a specific example for evaluating the performance of a waveguide designed for use in a high-precision optical sensing system. In this scenario, the waveguide is intended to amplify weak optical signals from a sensor without introducing noise that could compromise the sensitivity and accuracy of the measurements. The testing process, as outlined in FIG. 5, begins with the initial measurement step 502, where a wavelength is chosen that matches the operational wavelength of thesensor system. This wavelength is selected to ensure that the waveguide's performance is assessed under conditions that closely mimic its intended use.

[0121] The testing continues with the pump on measurement step 504, where an optical signal, representative of the sensor's output, and an optical pump are input into the waveguide. The output PSD is measured with the pump activated, capturing the amplified output spectrum. This spectrum is expected to show an increase in the signal's intensity, indicative of successful amplification by the waveguide. The spectrometer used for this measurement is chosen for its high resolution, capable of detecting subtle features in the spectrum that are indicative of the waveguide's amplification characteristics.

[0122] Upon reaching the additional measurements decision 508, the testing protocol evaluates whether the initial wavelength measurements are sufficient or if additional wavelengths are to be tested to ensure a comprehensive evaluation of the waveguide's performance. If the initial tests are satisfactory, the method advances to the compute overlap step 510, where the consistency of the waveguide's gaintrapping capability across the tested wavelengths is assessed. A certain degree of overlap between the PSD differences at various wavelengths would suggest that the waveguide maintains consistent amplification characteristics, a desirable trait for precision sensing applications.

[0123] The final step in the testing process is the overlap threshold decision 512, which determines if the computed overlap meets or exceeds a predetermined threshold. If the threshold is met or exceeded, the gain-trapped outcome 516 is achieved, confirming the waveguide's suitability for the high-precision optical sensing system. Conversely, if the overlap falls short of the threshold, the non gain-trapped outcome 514 is reached, indicating that further refinement of the waveguide design may be beneficial to meet the stringent requirements of the sensing application.

[0124] Throughout the testing process, additional considerations, such as adjusting the pump and signal powers or employing a tunable filter, may be implemented to fine-tune the testing conditions and gain deeper insights into the waveguide's performance. The predetermined threshold for gain-trapping is carefully chosen based on theoretical models and the specific demands of the sensing system, ensuring that the waveguide meets the high standards expected for such sensitive applications. Time-resolved measurements may also be conducted to evaluate the temporal dynamics of the gain-trapping process, providing a complete characterization of the waveguide's capabilities.

[0125] FIGS. 6A-6G illustrate operations of an OPA that includes a gain-trapped waveguide, according to example embodiments. However, it is to be understood that these example operations are not exhaustive. The versatility of gain-trapped waveguides — and therefore OPAS-extends beyond the depicted scenarios, enabling a wide array of additional applications. These waveguides can be tailored to suit specific operational and parametric amplification requirements in diverse fields, ranging from advanced scientific research to practical industrial uses. The underlying principle of gain-trapping can be adapted to enhance the performance of systems where precise control of light amplification is desired,or where the preservation of the quantum characteristics of light may be of concern. Thus, the potential use cases for OPAs with gain-trapped waveguides are as varied as the challenges and opportunities present in the ever-evolving landscape of optical technologies.

[0126] Referring now to FIG. 6A, a schematic representation 600 of the gain-trapping process in a waveguide in an OPA is depicted. An input pump pulse 602A and an input signal pulse 602B enter the waveguide 604. The configuration illustrates the basic setup where the pump and signal pulses are introduced into the gain-trapped waveguide, which is designed to facilitate the amplification of the signal pulse with minimal distortion.

[0127] As the pulses travel through the gain-trapped waveguide 604, the input signal pulse 602B is amplified, resulting in an output pump pulse 606A and an output amplified signal 606B, which may exit the gain-trapped waveguide 604. The gain-trapping process may cause the signal pulse 602B to be amplified with high fidelity, preserving its phase and temporal shape, which is particularly beneficial for applications requiring low-noise amplification.

[0128] Possible modifications to the setup shown in FIG. 6A could include varying the input pulse energies, adjusting the waveguide geometry for different amplification regimes, or incorporating additional optical elements such as filters or modulators to tailor the output for specific applications. Alternatives might involve integrating the waveguide into more complex optical circuits for advanced signal processing tasks.

[0129] Referring now to FIG. 6B, a schematic representation 610 of an optical waveguide system that employs gain- trapping to eliminate pulse distortion is presented. A pump input waveform 612A and a distorted signal input 612B are introduced into a gain-trapped waveguide 614. This figure illustrates the basic components of the system, where the pump and distorted signal are fed into the waveguide optimized for gain-trapping. In this example, Fig. 6B the input signal is not an eigenmode (i.e. a distorted pulse). Rather, the OPA reshapes the signal into an output mode equal to the gain-trapped mode. This example is effectively a "mode cleaner", where any input is mapped into a well-defined output.

[0130] The gain-trapped waveguide 614 processes the input waveforms, with the pump output waveform 616A emerging unchanged, while the distorted signal input 612B is transformed into a cleaned signal output 616B. The gain-trapping mechanism within the waveguide corrects the signal distortions, such as chirp or high-order dispersion, resulting in a clarified and amplified signal that retains the desired characteristics of the original input.

[0131] Modifications to the system in FIG. 6B could include the use of different waveguide materials to optimize for various signal properties or the implementation of dynamic control systems to adjust the gain-trapping parameters in real-time. Alternative configurations may employ multiple gain-trapped waveguides in series or parallel to handle a range of signal distortions or to amplify multiple signal channels simultaneously.

[0132] Referring now to FIG. 6C, a schematic representation 620 of an optical waveguide designed for gain-trapping is shown. A pump input 622A and a continuous-wave signal input 622B are input to gaintrapped waveguide 624. The figure outlines the basic setup where a continuous-wave signal is combined with a pulsed pump in the gain-trapped waveguide.

[0133] The gain-trapped waveguide 624 amplifies the continuous-wave signal input 622B using the pump input 622A, resulting in an output pump 626A and an ultra-fast pulse output 626B. The gaintrapping process enables the generation of ultra-fast pulses by amplifying the overlap between the continuous-wave signal and the gain-trapped mode, providing a source of ultra-fast pulses for various applications.

[0134] Potential modifications to the configuration in FIG. 6C include altering the duration and shape of the pump pulse to control the characteristics of the ultra-fast output pulse or using waveguides with different dispersion properties to tailor the pulse width and spectrum. Alternative approaches might involve using this setup for frequency comb generation or for the synchronization of ultra-fast pulses in complex optical systems.

[0135] Referring now to FIG. 6D, a schematic diagram 630 illustrates an optical system employing gain-trapped waveguides as in-line amplifiers. An input pulse 632 is fed into an optical fiber 634, producing a signal pulse 636B, which, along with a pump pulse 636A, is input into a gain-trapped waveguide 638. The basic configuration shows how the gain-trapped waveguide is used to amplify signals within an optical transmission line.

[0136] The gain-trapped waveguide 638 amplifies the signal pulse 636B, outputting pump pulse 640A and signal pulse 640B, which are then fed into another optical fiber 642. This process is repeated with a second pump pulse 644A and the signal pulse 644B which are input to second gain-trapped waveguide 646, resulting in further amplified pump pulse 648A and signal pulse 648B. The use of gain-trapped waveguides as in-line amplifiers ensures low noise-figure amplification and the elimination of pulse distortions accumulated during propagation.

[0137] Modifications to the system in FIG. 6D could involve integrating additional optical components such as isolators or circulators to enhance signal stability or employing adaptive control mechanisms to optimize the amplification process dynamically. Alternative configurations may use different types of fibers or waveguides to accommodate various signal formats or to enable wavelength-division multiplexing in telecommunications systems.

[0138] Referring now to FIG. 6E, a schematic representation 650 of an optical hybrid using gain-trapped optical parametric amplification is depicted. Signal pulses 652A and vacuum 652B are input to a signal splitting element 654, which divides the signal equally. The split signals 656B and 656D are then amplified by two gain-trapped waveguides 658A and 658B, with pump pulses 656A and 656C. The figure shows the basic components of an optical hybrid, where the signal is split and amplified in two separate paths.

[0139] The gain-trapped waveguides 658A and 658B amplify the in-phase and quadrature components of the signal, respectively, resulting in output pump pulses 660A and 660C, and amplified in-phase and quadrature signal components 660B and 660D respectively. This configuration allows for the simultaneous generation of amplified in-phase and quadrature components, which are useful for phasesensitive detection or processing.

[0140] Possible modifications to the optical hybrid in FIG. 6E include but are not limited to incorporating phase shifters to control the phase relationship between the two paths. Alternatives might involve using this setup for coherent communications systems or for measuring continuous-variable quantum states that may be used in quantum sensing or information applications.

[0141] Referring now to FIG. 6F, an optical parametric amplification schematic 670 is shown. An input pump signal waveform 672A and an input vacuum state 672B are introduced into a gain-trapped waveguide 674, leading to an output pump signal waveform 676A and an output squeezed vacuum state 676B. The figure illustrates the basic setup for generating squeezed light, a quantum resource, through phase-sensitive amplification of a vacuum state. The transformation of the input signal Wigner distribution 672C through the gain-trapped waveguide 674 results in the output signal Wigner distribution 676C, demonstrating the squeezing and amplification process.

[0142] Modifications to the schematic in FIG. 6F could include changing the pump waveform or waveguide design to modify the signal mode to be squeezed, adjusting the phase of the pump to change the phase of the squeezing, inputting different signals to undergo squeezing, or adjusting the length of the waveguide to vary the degree of squeezing. Alternative approaches might involve integrating the gain-trapped waveguide into larger quantum circuits for tasks such as quantum error correction or entanglement distribution.

[0143] Referring now to FIG. 6G, a diagram 680 illustrates the process of optical parametric amplification within a memory cavity. A pump pulse 682A and a signal pulse 682B enter the gaintrapped waveguide 684, which produces an output pump pulse 686A and an amplified signal pulse 686B. The figure represents the basic configuration of a coherent Ising machine, where a memory cavity encloses an optical nonlinearity to form an optical parametric oscillator (OPO).

[0144] Pulses 688 represent the intracavity pulses which act as spins or bits that encode the solution to an Ising problem. The combination of amplification and feedback cause the pulse amplitudes to evolve from an initial state (vacuum) into a final state that solves an Ising problem. Feedback pulse 690 is generated either using an optical circuit or the combination of an optical source and an electronic machine. For the case of a simple Coherent Ising Machine (CIM), the feedback pulses may be given by a linear combination of the intracavify fields, and the injection of the feedback pulses into the memory cavity can be interpreted as a form of mutual coupling between the intracavify pulses. The structure of this mutual coupling encodes the Ising problem to be solved. The coherent Ising machine encodes the solution to an NP-hard combinatorial optimization problem in the out-coupled OPO pulses 692. Possiblemodifications to the system in FIG. 6G include altering the cavity design to control the feedback dynamics or incorporating additional nonlinear elements to enhance the computational capabilities. Alternative configurations may use the coherent Ising machine for simulating physical systems or for implementing quantum annealing protocols to name a few. Any variant of CIM can use gain-trapped OPAs as the intracavity element, and to, for example, process the outputs, inputs, bias the cavity, or compute the feedback.

[0145] Beyond the aforementioned applications, the gain- trapped waveguide presents a versatile platform for a variety of innovative use cases. One such application is a variant on an optical homodyne by combining the pump with a phase-shifter to selectively amplify the in-phase or quadrature component of the signal. This approach offers a clean method for combining or splitting optical signals, which is particularly advantageous in systems where signal integrity is paramount. Another application is as an optical multiplier, which can be utilized for advanced signal processing tasks. By leveraging the gaintrapping mechanism, the waveguide can multiply optical signals, potentially enhancing the capabilities of optical computing systems.

[0146] Additionally, the gain-trapped waveguide can serve as an optical sensor, where one gain-trapped OPA is used to generate a pulse that probes the environment, and another gain-trapped OPA is employed to amplify the returned signal. This dual-OPA setup could lead to improvements in the sensitivity and accuracy of optical sensing technologies. Furthermore, the waveguide can be used as an optical sampler, where a gain-trapped OPA is utilized to isolate specific parts of an optical waveform. This capability could be particularly useful in applications such as optical coherence tomography (OCT) or in the analysis of complex optical signals, where isolating and examining particular temporal segments of a waveform is desired. Each of these use cases demonstrates the broad applicability and potential of the gain-trapped waveguide to revolutionize various domains within optical technology.

[0147] It should be noted that just as transistors are building blocks for electronic signal processing, gain trapped OPAs can serve a similar function in the realm of optical signal processing. By harnessing the capabilities of gain trapped OPAs, optical signals can be processed with a level of precision and efficiency that parallels, and in some cases surpasses, that of their electronic counterparts.

[0148] Referring now to FIG. 8, a block diagram of a computing system 800 is illustrated, showing the interconnection of its various components. The computing system 800 may represent the hardware of the user device 702, database 704 and design / verification server 706 in FIG. 7.

[0149] Centrally connected to a communication bus 812 are processors 802. The processors 802 may be one or more central processing units (CPUs), graphics processing units (GPUs), or any other type of processing units that perform the computations and operations of the computing system 800. In some cases, the processors 802 may execute the software elements 810, which include the operating system 814 and applications 818.

[0150] Input devices 804 and display devices 806 are also connected to the communication bus 812. The input devices 804 may include keyboards, mice, touchscreens, or any other devices that allow a user to input commands or data into the computing system 800. The display devices 806, on the other hand, may include monitors, screens, or any other devices that visually present data or information to the user. In some examples, the input devices 804 and display devices 806 facilitate user interaction with the computing system 800.

[0151] Network interfaces 808, which are likewise connected to the communication bus 812, facilitate external connectivity. The network interfaces 808 may include wired or wireless interfaces that allow the computing system 800 to connect to external networks, such as the network 708. In some cases, the network interfaces 808 may enable the computing system 800 to communicate with other devices or servers over the network 708 (FIG. 7).

[0152] The software elements 810, which include the operating system 814 and applications 818, are shown as being part of the computing system 800. The operating system 814, In some examples, manages the hardware resources of the computing system 800 and provides various services for the applications 818. The applications 818, on the other hand, may include various software programs or applications that perform specific tasks or functions on the computing system 800. In some cases, the applications 818 may include the software components of the design / verification server 706.

[0153] Network communication 816 is depicted as a function of the operating system 814. The network communication 816 may involve various protocols and techniques for transmitting and receiving data over the network 708 (FIG. 7). In some examples, the network communication 816 may enable the computing system 800 to communicate with other devices or servers over the network 708, facilitating the exchange of data and information within the system 700 shown in FIG. 7.

[0154] FIG. 9 is a flowchart outlining a method 900 of performing phase-sensitive optical parametric amplification, according to aspects of the present disclosure.

[0155] The method of performing the phase-sensitive optical parametric amplification may begin at step 902 where an optical parametric amplifier may receive an optical signal to be amplified. The optical parametric amplifier may include a waveguide characterized by a waveguide geometry (e.g., width, height, thickness, etc.).

[0156] At step 904, the waveguide may parametrically amplify the optical signal by temporally gain trapping the optical signal by using the waveguide geometry and an optical pump. The temporal gain trapping may preserve the phase and temporal shape of the optical signal.

[0157] In one or more embodiments discussed above, gain trapping and OP As assume the pump- undepleted regime, where the nonlinearity of the OPA is sufficiently small so that the depletion of the pump field may be ignored. As the OPA becomes more nonlinear, however, large parametric gain of an OPA may start to deplete the pump field, which may classically induce nonlinear saturation effects. Under a sufficiently low loss, such saturating behaviors lead to non-Gaussian quantum features, e.g.,Wigner function negativities. Generally, such non-Gaussian quantum dynamics may occur in a highly multimodal manner, which may pose a significant challenge in utilizing them for quantum technologies, e.g., quantum information processing and computation.

[0158] The embodiments described herein may be used to confine such non-Gaussian dynamics to a two-mode subspace spanned by a signal and a pump supermodes. The effective interactions between these modes may take the form of a cubic quantum-nondemolition (QND) interaction (a.XaXb, whereand xbmay be quadrature operators for signal and pump, respectively. A cubic QND interaction is known to enable a deterministic implementation of a cubic QND gate, which completes a universal gate set for continuous-variable quantum information processing.

[0159] While the foregoing is directed to example embodiments described herein, other and further example embodiments may be devised without departing from the basic scope thereof. For example, aspects of the present disclosure may be implemented in hardware or software or a combination of hardware and software. One example embodiment described herein may be implemented as a program product for use with a computer system. The program(s) of the program product defines functions of the example embodiments (including the methods described herein) and may be contained on a variety of computer-readable storage media. Illustrative computer-readable storage media include, but are not limited to: (i) non-writable storage media (e.g., read-only memory (ROM) devices within a computer, such as CD-ROM disks readably by a CD-ROM drive, flash memory, ROM chips, or any type of solid- state non-volatile memory) on which information is permanently stored; and (ii) writable storage media (e.g., floppy disks within a diskette drive or hard-disk drive or any type of solid-state random-access memory) on which alterable information is stored. Such computer-readable storage media, when carrying computer-readable instructions that direct the functions of the disclosed example embodiments, are example embodiments of the present disclosure.

[0160] It will be appreciated by those skilled in the art that the preceding examples are example and not limiting. It is intended that all permutations, enhancements, equivalents, and improvements thereto are apparent to those skilled in the art upon a reading of the specification and a study of the drawings are included within the true spirit and scope of the present disclosure. It is therefore intended that the following appended claims include all such modifications, permutations, and equivalents as fall within the true spirit and scope of these teachings.

[0161] While various embodiments have been described above, it should be understood that they have been presented by way of example and not limitation. It will be apparent to persons skilled in the relevant art(s) that various changes in form and detail can be made therein without departing from the spirit and scope. In fact, after reading the above description, it will be apparent to one skilled in the relevant art(s) how to implement alternative embodiments. For example, other steps may be provided, or steps may be eliminated, from the described flows, and other components may be added to, or removed from, the described systems. Accordingly, other implementations are within the scope of the following claims.

[0162] In addition, it should be understood that any figures which highlight the functionality and advantages are presented for example purposes only. The disclosed methodology and system are each sufficiently flexible and configurable such that they may be utilized in ways other than that shown.

Claims

CLAIMSWhat is claimed is:

1. An optical parametric amplifier comprising: a waveguide with a waveguide geometry; and an optical pump optically coupled to the waveguide, the waveguide configured to use the optical pump and the waveguide geometry to temporally gain trap and perform phase-sensitive parametric amplification of an optical signal.

2. The optical parametric amplifier of claim 1, wherein the waveguide is configured to temporally gain trap the optical signal by lowering group velocity mismatch between the optical signal and the optical pump and / or by increasing group velocity dispersion of the optical signal.

3. The optical parametric amplifier of claim 1, wherein the waveguide geometry comprises at least one of a width, a height, or a thickness of the waveguide.

4. The optical parametric amplifier of claim 1, wherein the waveguide geometry comprises at least one of ridge waveguide type, multilayer cladding waveguide type, a coupled-core waveguide type, or a photonic crystal waveguide type.

5. The optical parametric amplifier of claim 1, wherein the optical signal is a distorted signal and wherein the waveguide is configured to lower the distortion while performing the optical parametric amplification.

6. The optical parametric amplifier of claim 1, wherein the optical signal is a continuous-wave signal and wherein the waveguide is configured to generate an ultra-fast pulse by performing the optical parametric amplification.

7. The optical parametric amplifier of claim 1, further comprising a phase shifter configured to phase shift the optical pump such that the waveguide selectively performs the phase-sensitive parametric amplification an in-phase component or a quadrature component of the optical signal.

8. The optical parametric amplifier of claim 1, further comprising a beam splitter configured to split the optical signal into an in-phase component and a quadrature component, and wherein the waveguide is configured to perform the phase-sensitive parametric amplification of the in-phase component or the quadrature component.

9. The optical parametric amplifier of claim 1, wherein the optical signal forms a vacuum input signal and an output after the phase-sensitive parametric amplification forms a squeezed vacuum signal.

10. The optical parametric amplifier of claim 1, wherein the optical signal is a pulse within an optical memory cavity.

11. The optical parametric amplifier of claim 1, wherein the waveguide geometry is determined in the steps of: selecting desired wavelengths for the optical signal and the optical pump,selecting the waveguide geometry to identify a range of parameters where a group velocity mismatch (GVM) between the optical signal and the optical pump is lowered and a signal group velocity dispersion (GVD) is increased, solving for a motion for the optical signal and the optical pump as a function of pump pulse energy using an eigenvalue solver, calculating eigenvalues, eigenvalue splitting, and mode purity as a function of pump pulse energy, and determining the waveguide geometry as being gain-trapped in response to confirming that the dominant eigenvalues are indicative of gain-trapped operation.

12. A method of performing phase sensitive optical parametric amplification comprising: receiving, by waveguide with a waveguide geometry, an optical signal to be parametrically amplified; and parametrically amplifying, by the waveguide using an optical pump and the waveguide geometry, by temporally gain trapping the optical signal.

13. The method of claim 12, further comprising: temporally gain trapping, by the waveguide, the optical signal by lowering group velocity mismatch between the optical signal and the optical pump and / or by increasing group velocity dispersion of the optical signal.

14. The method of claim 12, wherein the waveguide geometry comprises at least one of a width, a height, or a thickness of the waveguide.

15. The method of claim 12, wherein the waveguide geometry comprises at least one of ridge waveguide type, multilayer cladding waveguide type, a coupled-core waveguide type, or a photonic crystal waveguide type.

16. The method of claim 12, wherein the optical signal is a distorted signal, the method further comprising: lowering, by the waveguide, distortion while performing the optical parametric amplification.

17. The method of claim 12, wherein the optical signal is a continuous-wave signal, the method further comprising: generating, by the waveguide, ultra-fast pulse by performing the optical parametric amplification.

18. The method of claim 12, further comprising: phase shifting, by a phase shifter, the optical pump; and selectively performing, by the waveguide, . the phase-sensitive parametric amplification of an in-phase component or a quadrature component of the optical signal.

19. The method of claim 12, further comprising:splitting, by a beam splitter, the optical signal into in-phase component and a quadrature component; and performing, by the waveguide, the phase-sensitive parametric amplification of the in-phase component or the quadrature component.

20. The method of claim 12, wherein the optical signal forms vacuum input and an output after the phase-sensitive parametric amplification forms a squeezed vacuum signal.

21. The optical parametric amplifier of claim 1, wherein the optical signal is a distorted signal within an optical transmission line and wherein the waveguide is configured to periodically lower the distortion while performing the optical parametric amplification periodically.

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