Dispersion Characteristics of the Multi-mode Fiber-fed VIPA Spectrograph

A high-resolution (${ \mathcal R }\gt {10}^{5}$), multi-mode fiber-fed spectrograph on large telescopes with a reasonable size is desirable in astronomy. In this work, the dispersion characteristics of a multi-mode fiber-fed Virtually Imaged Phased Array (VIPA) spectrograph are studied theoretically and experimentally. A VIPA spectrograph, fed by multi-mode optical fibers with the operating wavelength at 750 ∼ 770 nm, is designed and built in our laboratory. After calibration with a homemade Yb:fiber ring laser frequency comb (with a repetition frequency of 808 MHz), the measured spectral resolution fed by multi-mode fibers with core diameters $\varnothing =10$, 25, 50, and 105 μm is comparable with that of the single-mode fiber, i.e., ${ \mathcal R }=7.62\times {10}^{5}\sim 8.97\times {10}^{5}$, with equivalent transmission efficiencies. This verifies experimentally that the spectral resolution is much less affected by the core diameters of the input fibers when compared with that of échelle spectrographs. It is also found that the diffraction envelope of the VIPA spectrograph relies on the coherence of light sources and the width of the point-spread function is inversely proportional to the spatial position on the detector. Since the VIPA spectrograph has no imaging process in the main dispersion direction, the spectral resolution is insensitive to the width of the input slit or the fiber diameter. This makes the VIPA spectrograph a promising instrument to attain an ultra-high spectral resolution (${ \mathcal R }\gt 3\times {10}^{5}$) on very large telescopes.