An Investigation of Relative CEP Cycling in Birefringent Delay Lines

Sammanfattning

Ultrafast pump-probe laser experiments often require precise control of both the temporal delay and electric field between pulses. Birefringent delay lines offer a compact alternative to traditional mirror-based systems, but introducing a group delay through material dispersion inherently causes the Carrier-Envelope Phase (CEP) to cycle differently in the pulses. This Relative CEP Cycling (RCC) prevents control of the electric field, limiting applications in few-cycle laser pulse experiments. This work demonstrates that by pairing the birefringent materials \ce{MgF2} and sapphire, this cycling can be eliminated at a specific central wavelength. Through analytical calculations, computer simulations using Fourier Transform Spectral Interferometry (FTSI), and experimental characterization, a zero-cycling-rate central wavelength ($\lambda_{ZCR}$) is identified. This wavelength is where the Relative CEP Cycling Rate (RCCR) remains zero regardless of relative group delay. The experimentally measured ($\lambda_{ZCR}=778.38 \pm 0.78 $ nm) deviates from the analytically predicted value (749.59 nm) and the simulated value ($747.11 \pm 0.62$ nm), partly due to variations in reported Sellmeier coefficients for these materials. Despite the identified discrepancy between values of $\lambda_{ZCR}$, the fundamental principle is validated: careful material selection enables birefringent delay lines that have precise control over the electric field, opening pathways for compact, robust few-cycle pulse control.