We outline and interpret a recently developed theory of impedance matching or reflectionless excitation of arbitrary finite photonic structures in any dimension. The theory includes both the case of guided wave and free-space excitation. It describes the necessary and sufficient conditions for perfectly reflectionless excitation to be possible and specifies how many physical parameters must be tuned to achieve this. In the absence of geometric symmetries, such as parity and time-reversal, the product of parity and time-reversal, or rotational symmetry, the tuning of at least one structural parameter will be necessary to achieve reflectionless excitation. The theory employs a recently identified set of complex frequency solutions of the Maxwell equations as a starting point, which are defined by having zero reflection into a chosen set of input channels, and which are referred to as R-zeros. Tuning is generically necessary in order to move an R-zero to the real frequency axis, where it becomes a physical steady-state impedance-matched solution, which we refer to as a reflectionless scattering mode (RSM). In addition, except in single-channel systems, the RSM corresponds to a particular input wavefront, and any other wavefront will generally not be reflectionless. It is useful to consider the theory as representing a generalization of the concept of critical coupling of a resonator, but it holds in arbitrary dimension, for arbitrary number of channels, and even when resonances are not spectrally isolated. In a structure with parity and time-reversal symmetry (a real dielectric function) or with parity–time symmetry, generically a subset of the R-zeros has real frequencies, and reflectionless states exist at discrete frequencies without tuning. However, they do not exist within every spectral range, as they do in the special case of the Fabry–Pérot or two-mirror resonator, due to a spontaneous symmetry-breaking phenomenon when two RSMs meet. Such symmetry-breaking transitions correspond to a new kind of exceptional point, only recently identified, at which the shape of the reflection and transmission resonance lineshape is flattened. Numerical examples of RSMs are given for one-dimensional multimirror cavities, a two-dimensional multiwaveguide junction, and a multimode waveguide functioning as a perfect mode converter. Two solution methods to find R-zeros and RSMs are discussed. The first one is a straightforward generalization of the complex scaling or perfectly matched layer method and is applicable in a number of important cases; the second one involves a mode-specific boundary matching method that has only recently been demonstrated and can be applied to all geometries for which the theory is valid, including free space and multimode waveguide problems of the type solved here.

We demonstrate numerically and theoretically that the transverse-mode stability for a high-power fiber amplifier is greatly increased via simultaneous excitation of many high-order modes, while the amplified light maintains spatially coherent and high beam quality.

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. Significance: Monitoring the movement and vital signs of patients in hospitals and other healthcare environments is a significant burden on healthcare staff. Early warning systems using smart bed sensors hold promise to relieve this burden and improve patient outcomes. We propose a scalable and cost-effective optical fiber sensor array that can be embedded into a mattress to detect movement, both sensitively and spatially. Aim: Proof-of-concept demonstration that a multimode optical fiber (MMF) specklegram sensor array can be used to detect and image movement on a bed. Approach: Seven MMFs are attached to the upper surface of a mattress such that they cross in a array. The specklegram output is monitored using a single laser and single camera and movement on the fibers is monitored by calculating a rolling zero-normalized cross-correlation. A image is formed by comparing the signal at each crossing point between two fibers. Results: The MMF sensor array can detect and image movement on a bed, including getting on and off the bed, rolling on the bed, and breathing. Conclusions: The sensor array shows a high sensitivity to movement, which can be used for monitoring physiological parameters and patient movement for potential applications in healthcare settings.

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