2020/06/22 by Mohamed Y. Nada, Filippo Capolino · 2 citations
Engineering · Physics and Astronomy · #Photonic and Optical Devices #Photorefractive and Nonlinear Optics #Quantum optics and atomic interactions
paper · doi:10.1364/josab.385198
openalex publication_date 2020/06/22 · openalex created_date 2020/06/25 · openalex updated_date 2026/08/01
We demonstrate for the first time, to our knowledge, the occurrence of a sixth -order exceptional point of degeneracy (EPD) in a realistic multimode optical photonic structure by using a modified periodic coupled-resonator optical waveguide (CROW) at the optical wavelength <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>λ</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>1550</mml:mn> <mml:mspace width="thinmathspace"/> <mml:mspace width="thinmathspace"/> <mml:mtext>nm</mml:mtext> </mml:math> . The sixth-order EPD is obtained in a CROW without the need of loss or gain, and such an EPD corresponds to a very special band edge of the periodic photonic structure where six eigenmodes coalesce, so we refer to it as the sixth-order degenerate band edge (6DBE). Moreover, we report a new scaling law of the quality factor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>Q</mml:mi> </mml:mrow> </mml:math> of an optical cavity made of such a periodic 6DBE-CROW with cavity length as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Q</mml:mi> <mml:mo>∝</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>N</mml:mi> <mml:mn>7</mml:mn> </mml:msup> </mml:mrow> </mml:math> , when operating near the 6DBE with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>N</mml:mi> </mml:math> being the number of unit cells in the periodic finite-length CROW. Furthermore, we elaborate on the application of the 6DBE to ultralow-threshold lasers. We present a novel scaling law of the lasing threshold that scales as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>N</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> when operating near the 6DBE. Also, we show the superiority of the threshold scaling of the 6DBE-CROW to the scaling of another CROW with the same size operating near a fourth-order EPD that is often referred to as the degenerate band edge (DBE). The lasing threshold scaling of the DBE-CROW laser is shown here for the first time to our knowledge. We also discuss the high sensitivity of the proposed 6DBE-CROW to perturbations, which may find applications in sensors, modulators, optical switches, nonlinear devices, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Q</mml:mi> </mml:math> -switching cavities.