Enhanced rotation sensing and exceptional points in a parity–time-symmetric coupled-ring gyroscope
Matthew J. Grant, Michel J. F. Digonnet
Abstract
Enhancement in rotation sensitivity is achieved in a parity–time-symmetric gyroscope consisting of a ring with gain coupled to a lossy ring, operated below laser threshold and in the vicinity of its exceptional point (EP). An external laser and a conventional readout system are used to measure the large rotation-induced shifts in resonance frequency known to occur in this device. A complete model of the rotation sensitivity is derived that accounts for gain saturation caused by the large circulating power. Compared to a single-ring gyro, the sensitivity is enhanced by a factor of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>∼</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>300</mml:mn> </mml:mrow> </mml:mrow> </mml:math> when the inter-ring coupling is tuned to its EP value <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>κ</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext class="MJX-tex-mathit" mathvariant="italic">EP</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>∼</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2400</mml:mn> </mml:mrow> </mml:mrow> </mml:math> when it is decreased from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>κ</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext class="MJX-tex-mathit" mathvariant="italic">EP</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , even though the Sagnac frequency shift is then much smaller. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>∼</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>40</mml:mn> </mml:mrow> </mml:mrow> <mml:mi mathvariant="normal">%</mml:mi> </mml:math> of this 2400-fold enhancement is assigned to a new sensing mechanism where rotation alters the gain saturation. These results show that this compact gyro has a far greater sensitivity than a conventional ring gyro, and that this improvement arises mostly from the gain compensating the loss, as opposed to the enhanced Sagnac frequency shift from the EP. This gyro is also shown to be much more stable against gain fluctuations than a single-ring gyro with gain.