We develop the concept of degenerate distributed feedback (DDFB) laser operating close to Exceptional Points of Degeneracy (EPDs) of fourth-order, known as a Degenerate Band Edge (DBE), where four different Bloch eigenmodes coalesce. A waveguide operating near a DBE displays a large group delay that leads to a strong light-matter interaction enhancement upon the inclusion of a gain medium. This enhancement results in an ultralow lasing threshold that scales anomalously with cavity length. The resulting DDFB laser is expected to enforce mode selectivity and a coherent single-frequency operation that is resistant to small perturbations, load variations and distributed losses.
We generalize the concept of optimally chiral light (OCL), which encompasses all fields with maximum chirality at a given energy density, such as circularly polarized light (CPL), to light in an isotropic medium, where the optical chirality is not well defined. We find the generalized optimal chirality condition by enforcing the constructive scattering of the chiral response of chiral molecules with the phase shift between the incident electric and magnetic fields. The generalized OCL displays powerful electric-magnetic symmetries that maximize chiral light-matter interactions with simplified expressions.
Our investigation focuses on studying the forces induced on a chiral dipolar particle when exposed to optimally chiral light (OCL). The concept of OCL encompasses all structured light fields that achieve maximum helicity density at a given energy density. Examples of OCL include circularly polarized light (CPL) and the optimally chiral configurations of the azimuthally-radially polarized beam (ARPB), which is a phase-shifted superposition of an azimuthally and a radially polarized beams. The optimal chirality condition requires that light’s magnetic and electric fields along the same direction be phase-shifted by a quarter of a period and that the ratio of their magnitudes equals the characteristic impedance in free space [Hanifeh, Albooyeh, Capolino, ACS Phot 2020, 7, 10, 2682–2691]. By meeting these conditions, the resulting field also exhibits electric-magnetic symmetry in its energy and spin densities. Consequently, OCL simplifies the computation of forces induced on a chiral dipolar particle, while simultaneously boosting its ability to discern chirality. Notably, the gradient force depends exclusively on the gradient of the energy density (as opposed to a combination of gradients), whereas the remaining forces can be expressed using the Poynting vector and the field’s orbital momentum. Given these properties, optimally chiral fields represent a promising avenue for the precise manipulation of chiral nanoparticles. Additionally, the choice of the beam is dependent on the geometry of the optical trap, as different optimally chiral fields have different spatial features. While a beam with CPL induces more pronounced transverse forces that discriminate chirality perpendicular to the propagation direction, the optimally chiral ARPB produces strong longitudinal forces that discriminate chirality along the propagation direction, eliminating the problem of false chirality detection due to electric anisotropy of the nanoparticle.
We investigate the effect of fabrication tolerances on photonic multimode waveguides operating in the vicinity of a third-order exceptional point degeneracy (EPD), known as a stationary inflection point (SIP). An EPD is a point in the parameter space where two or more Bloch eigenmodes coalesce in an infinite periodic waveguide, and at an SIP three modes coalesce to form the frozen mode. Waveguides operating near an SIP exhibit slow-light behavior in finite-length waveguides with anomalous cubic scaling of the group delay with waveguide length. The frozen mode facilitates stronger light-matter interactions in active media, resulting in a significant increase in the effective gain within the cavity. However, systems operating near an EPD are also exceptionally sensitive to fabrication deviations. In this work, we explore wave propagation and the impact of various fabrication imperfections in analytic models and in fabricated photonic chips for three mirrorless devices operating near an SIP. To advance the concept of the SIP laser, we also analyze how the addition of gain and loss affects the SIP performance. Our results show that while minor deviations from the ideal parameters can prevent perfect mode coalescence at the EPD, the frozen mode remains resilient to small perturbations and a significant degree of mode degeneracy prevails. These findings provide critical insights into the design and fabrication of passive and active photonic devices operating near high-order EPDs, paving the way for their practical implementation in a wide range of applications.
We will discuss two kinds of exceptional points of degeneracy in waveguides and their respective application in lasers. Such exceptional points occur in waveguides with balanced loss and gain (e.g., PT symmetry), and in waveguides without loss and gain (e.g., periodic Si waveguides). Waveguides with such exceptional points have a strong degeneracy of their wavenumbers and polarization states that enables specific wave physics, only found in these degenerate systems. We will discuss advantages and disadvantages of both concepts to conceive laser regimes, related to high power, high spectral purity, high efficiency, etc, and show some realistic designs involving Si ridge waveguides.
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