Observation of exceptional points between different Hermite-Gaussian transverse modes in a birefringent Fabry-Perot cavity = 복굴절성 페브리–페로 공진기에서의 서로 다른 에르미트–가우시안 횡모드 간 예외점 관측

다국어 초록 (Multilingual Abstract)

We demonstrate the formation of an exceptional point (EP) between distinct Hermite–Gaussian transverse modes in a Fabry–Perot cavity by combining tunable intracavity birefringence with controllable, polarization-dependent loss. By inserting two quarter-waveplates and a thin pellicle beamsplitter inside the cavity, we mix orthogonal polarization modes and introduce differential attenuation. Tuning the waveplate rotation angle as well as the beamsplitter’s loss drives the cavity’s round-trip Jones matrix to a non-Hermitian degeneracy, at which both the resonance frequencies and linewidths of two interacting modes coalesce. Experimentally, we excite either the fundamental (TEM00) and firstorder transverse modes (TEM10) or two orthogonally polarized TEM00 modes, and we probe their Stokes parameters and transmission spectra as the system approaches the EP. We observe that, at the critical tuning, the two modes merge into a single circularly polarized eigenstate, exhibiting identical frequency and linewidth. Our results agree quantitatively with the analytic Jones-matrix model, confirming that precise control of birefringence and loss in a standard Fabry–Perot cavity suffices to engineer non-Hermitian singularities. This work opens new avenues for exploring and enhanced sensing in precision photonics as well as EP physics in cavity quantum electrodynamics.

목차 (Table of Contents)

• Contents
• Abstract i
• Chapter 1 Introduction 1
• Chapter 2 Theoretical Background 6
• 2.1 Jones matrix and EP formation 6
• 2.2 Polarization variation 12
• 2.3 Eigenvalue justification 12
• 2.4 Eigenvectors of J 14
• 2.5 Exceptional Point Condition 21
• 2.6 Breakdown of Orthogonality between TEM0,0 mode and TEM1,0 mode 22
• 2.6.1 Eigenvalue justification23
• Chapter 3 Experimental Methods 25
• 3.1 Fabry-Perot cavity 25
• 3.1.1 Fabry-Perot cavity design 27
• Chapter 4 Results 35
• 4.1 Exceptional points between TEM0,0 and TEM1,0 35
• ii4.2 Exceptional points between TEM1,0 and TEM2,0 45
• 4.3 Simultaneous occurrence of exceptional points between TEMn,0 modes 49
• Chapter 5 Conclusion 54
• 5.1 Summary 54
• 5.2 Future Work 55
• Chapter 6 Appendix 58
• 6.1 Fabry-Perot cavity drawing 58
• Acknowledgements 75
• 요약 76