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1. A vectorial envelope Maxwell formulation for electromagnetic waveguides with application to nonlinear fiber optics

   https://doi.org/10.1016/j.camwa.2025.05.026  

   Henneking, Stefan; Grosek, Jacob; Demkowicz, Leszek (September 2025, Computers & Mathematics with Applications)

   This article presents an ultraweak discontinuous Petrov-Galerkin (DPG) formulation of the time-harmonic Maxwell equations for the vectorial envelope of the electromagnetic field in a weakly-guiding multi-mode fiber waveguide. This formulation is derived using an envelope ansatz for the vector-valued electric and magnetic field components, factoring out an oscillatory term of exp(-ikz) with a user-defined wavenumber k, where z is the longitudinal fiber axis and field propagation direction. The resulting formulation is a modified system of the time-harmonic Maxwell equations for the vectorial envelope of the propagating field. This envelope is less oscillatory in the z-direction than the original field, so that it can be more efficiently discretized and computed, enabling solutions to the vectorial DPG Maxwell system in fibers that are 1000x longer than previously possible. Different approaches for incorporating a perfectly matched layer for absorbing the outgoing wave modes at the fiber end are derived and compared numerically. The resulting formulation is used to solve a 3D Maxwell model of an ytterbium-doped active gain fiber amplifier, coupled with the heat equation for including thermal effects. The nonlinear model is then used to simulate thermally-induced transverse mode instability (TMI). The numerical experiments demonstrate that it is computationally feasible to perform simulations and analysis of real-length optical fiber laser amplifiers using discretizations of the full vectorial time-harmonic Maxwell equations. The approach promises a new high-fidelity methodology for analyzing TMI in high-power fiber laser systems and is extendable to including other nonlinearities. 

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2. Novel Measurement-Based Efficient Computational Approach to Modeling Optical Power Transmission in Step-Index Polymer Optical Fiber

   https://doi.org/10.3390/photonics9040260  

   Guerrero, Jorge; Losada, M. Angeles; Lopez, Alicia; Mateo, Javier; Richards, Dwight; Antoniades, N.; Jiang, Xin; Madamopoulos, Nicholas (April 2022, Photonics)

   Polymer optical fibers (POFs) are playing an important role in industrial applications nowadays due to their ease of handling and resilience to bending and environmental effects. A POF can tolerate a bending radius of less than 20 mm, it can work in environments with temperatures ranging from −55 °C to +105 °C, and its lifetime is around 20 years. In this paper, we propose a novel, rigorous, and efficient computational model to estimate the most important parameters that determine the characteristics of light propagation through a step-index polymer optical fiber (SI-POF). The model uses attenuation, diffusion, and mode group delay as functions of the propagation angle to characterize the optical power transmission in the SI-POF. Taking into consideration the mode group delay allows us to generalize the computational model to be applicable to POFs with different index profiles. In particular, we use experimental measurements of spatial distributions and frequency responses to derive accurate parameters for our SI-POF simulation model. The experimental data were measured at different fiber lengths according to the cut-back method. This method consists of taking several measurements such as frequency responses, angular intensity distributions, and optical power measurements over a long length of fiber (>100 m), then cutting back the fiber while maintaining the same launching conditions and repeating the measurements on the shorter lengths of fiber. The model derivation uses an objective function to minimize the differences between the experimental measurements and the simulated results. The use of the matrix exponential method (MEM) to implement the SI-POF model results in a computationally efficient model that is suitable for POF-based system-level studies. The efficiency gain is due to the independence of the calculation time with respect to the fiber length, in contrast to the classic analytical solutions of the time-dependent power flow equation. The robustness of the proposed model is validated by calculating the goodness-of-fit of the model predictions relative to experimental data. 

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3. General framework for ultrafast nonlinear photonics: unifying single and multi-envelope treatments [Invited]

   https://doi.org/10.1364/OE.513856  

   Phillips, C_R; Jankowski, M.; Flemens, N.; Fejer, M_M (February 2024, Optics Express)

   Numerical modeling of ultrashort pulse propagation is important for designing and understanding the underlying dynamical processes in devices that take advantage of highly nonlinear interactions in dispersion-engineered optical waveguides. Once the spectral bandwidth reaches an octave or more, multiple types of nonlinear polarization terms can drive individual optical frequencies. This issue is particularly prominent inχ⁽²⁾devices where all harmonics of the input pulse are generated and there can be extensive spectral overlap between them. Single-envelope approaches to pulse propagation have been developed to address these complexities; this has led to a significant mismatch between the strategies used to analyze moderate-bandwidth devices (usually involving multi-envelope models) and those used to analyze octave-spanning devices (usually involving models with one envelope per waveguide mode). Here we unify the different strategies by developing a common framework, applicable to any optical bandwidth, that allows for a side-by-side comparison between single- and multi-envelope models. We include bothχ⁽²⁾andχ⁽³⁾interactions in these models, with emphasis onχ⁽²⁾interactions. We show a detailed example based on recent supercontinuum generation experiments in a thin-film LiNbO₃on sapphire quasi-phase-matching waveguide. Our simulations of this device show good agreement between single- and multi-envelope models in terms of the frequency comb properties of the electric field, even for multi-octave-spanning spectra. Building on this finding, we explore how the multi-envelope approach can be used to develop reduced models that help build physical insights about new ultrafast photonics devices enabled by modern dispersion-engineered waveguides, and discuss practical considerations for the choice of such models. More broadly, we give guidelines on the pros and cons of the different modeling strategies in the context of device design, numerical efficiency, and accuracy of the simulations. 

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4. Low-loss fiber-to-chip interface for lithium niobate photonic integrated circuits

   Lingyan He, Mian Zhang (January 2019, Optics letters)

   Integrated lithium niobate (LN) photonic circuits have recently emerged as a promising candidate for advanced photonic functions such as high-speed modulation, nonlinear frequency conversion, and frequency comb generation. For practical applications, optical interfaces that feature low fiber-to-chip coupling losses are essential. So far, the fiber-to-chip loss (commonly >10  dB/facet) has dominated the total insertion losses of typical LN photonic integrated circuits, where on-chip losses can be as low as 0.03–0.1 dB/cm. Here we experimentally demonstrate a low-loss mode size converter for coupling between a standard lensed fiber and sub-micrometer LN rib waveguides. The coupler consists of two inverse tapers that convert the small optical mode of a rib waveguide into a symmetrically guided mode of a LN nanowire, featuring a larger mode area matched to that of a tapered optical fiber. The measured fiber-to-chip coupling loss is lower than 1.7 dB/facet with high fabrication tolerance and repeatability. Our results open the door for practical integrated LN photonic circuits efficiently interfaced with optical fibers. 

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5. Wafer-scale fabrication of InGaP-on-insulator for nonlinear and quantum photonic applications

   https://doi.org/10.1063/5.0225747  

   Thiel, Lillian; Castro, Joshua_E; Steiner, Trevor_J; Nguyen, Catherine_L; Pechilis, Audrey; Duan, Liao; Lewis, Nicholas; Cole, Garrett_D; Bowers, John_E; Moody, Galan (September 2024, Applied Physics Letters)

   The development of manufacturable and scalable integrated nonlinear photonic materials is driving key technologies in diverse areas, such as high-speed communications, signal processing, sensing, and quantum information. Here, we demonstrate a nonlinear platform—InGaP-on-insulator—optimized for visible-to-telecommunication wavelength χ(2) nonlinear optical processes. In this work, we detail our 100 mm wafer-scale InGaP-on-insulator fabrication process realized via wafer bonding, optical lithography, and dry-etching techniques. The resulting wafers yield 1000 s of components in each fabrication cycle, with initial designs that include chip-to-fiber couplers, 12.5-cm-long nested spiral waveguides, and arrays of microring resonators with free-spectral ranges spanning 400–900 GHz. We demonstrate intrinsic resonator quality factors as high as 324 000 (440 000) for single-resonance (split-resonance) modes near 1550 nm corresponding to 1.56 dB/cm (1.22 dB/cm) propagation loss. We analyze the loss vs waveguide width and resonator radius to establish the operating regime for optimal 775–1550 nm phase matching. By combining the high χ(2) and χ(3) optical nonlinearity of InGaP with wafer-scale fabrication and low propagation loss, these results open promising possibilities for entangled-photon, multi-photon, and squeezed light generation. 

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