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Spectroscopy and hyperspectral imaging are widely used tools for identifying compounds and materials. One optical design is a polarization interferometer that uses birefringent wedges, like a Babinet-Soleil compensator, to create the interferograms that are Fourier transformed to give the spectra. Such designs have lateral spatial offset between then_oandn_eoptical beams, which reduces the interferogram intensity and creates a spatially dependent phase that is problematic for hyperspectral imaging. The lateral separation between the beams is wavelength dependent, created by the achromatic nature of Babinet-Soleil compensators. We introduce a birefringent wedge design for Fourier transform spectroscopy that creates collinearn_oandn_eoptical beams for optimal interference and no spatial dependent phase. Our 3-wedge design, which we call a Wisconsin interferometer, improves the signal strength of polarization spectrometers, and eliminates phase shifts in hyperspectral imaging. We anticipate that it will find use in analytical, remote sensing, and ultrafast spectroscopy applications. 

A comparative study was conducted to investigate the 3.9 µm mid-IR emission properties of Ho³⁺doped NaYF₄and CsCdCl₃crystals as well as Ho³⁺doped Ga₂Ge₅S₁₃glass. Following optical excitation at ∼890 nm, all the studied materials exhibited broad mid-IR emissions centered at ∼3.9 µm at room temperature. The mid-IR emission at 3.9 µm, originating from the⁵I₅→⁵I₆transition, showed long emission lifetime values of ∼16.5 ms and ∼1.61 ms for Ho³⁺doped CsCdCl₃crystal and Ga₂Ge₅S₁₃glass, respectively. Conversely, the Ho³⁺doped NaYF₄crystal exhibited a relatively short lifetime of ∼120 µs. Temperature dependent decay time measurements were performed for the⁵I₅excited state for all three samples. The results showed that the emission lifetimes of Ho³⁺:CsCdCl₃and Ho³⁺:Ga₂Ge₅S₁₃were nearly temperature independent over the range studied, while significant emission quenching of the⁵I₅level was observed in Ho³⁺:NaYF₄. The temperature dependence of the multi-phonon relaxation rate for 3.9 µm mid-IR emission in Ho³⁺:NaYF₄crystal was determined. The room temperature stimulated emission cross-sections for all three samples were calculated using the Füchtbauer-Landenburg equation. Furthermore, the results of Judd-Ofelt analysis are presented and discussed. 

The mid-IR spectroscopic properties of ${\mathrm{E}\mathrm{r}}^{3+}$doped low-phonon ${\mathrm{C}\mathrm{s}\mathrm{C}\mathrm{d}\mathrm{C}\mathrm{l}}_3$and ${\mathrm{C}\mathrm{s}\mathrm{P}\mathrm{b}\mathrm{C}\mathrm{l}}_3$crystals grown by the Bridgman technique have been investigated. Using optical excitations at $\sim <\#comment/>800\mathrm{n}\mathrm{m}$and $\sim <\#comment/>660\mathrm{n}\mathrm{m}$, both crystals exhibited IR emissions at $\sim <\#comment/>1.55$, $\sim <\#comment/>2.75$, $\sim <\#comment/>3.5$, and $\sim <\#comment/>4.5\text{µ<\#comment/>}\mathrm{m}$at room temperature. The mid-IR emission at 4.5 µm, originating from the ${}^4{\mathrm{I}}_{9/2}\to <\#comment/>{}^4{\mathrm{I}}_{11/2}$transition, showed a long emission lifetime of $\sim <\#comment/>11.6\mathrm{m}\mathrm{s}$for ${\mathrm{E}\mathrm{r}}^{3+}$doped ${\mathrm{C}\mathrm{s}\mathrm{C}\mathrm{d}\mathrm{C}\mathrm{l}}_3$, whereas ${\mathrm{E}\mathrm{r}}^{3+}$doped ${\mathrm{C}\mathrm{s}\mathrm{P}\mathrm{b}\mathrm{C}\mathrm{l}}_3$exhibited a shorter lifetime of $\sim <\#comment/>1.8\mathrm{m}\mathrm{s}$. The measured emission lifetimes of the ${}^4{\mathrm{I}}_{9/2}$state were nearly independent of the temperature, indicating a negligibly small nonradiative decay rate through multiphonon relaxation, as predicted by the energy-gap law for low-maximum-phonon energy hosts. The room temperature stimulated emission cross sections for the ${}^4{\mathrm{I}}_{9/2}\to <\#comment/>{}^4{\mathrm{I}}_{11/2}$transition in ${\mathrm{E}\mathrm{r}}^{3+}$doped ${\mathrm{C}\mathrm{s}\mathrm{C}\mathrm{d}\mathrm{C}\mathrm{l}}_3$and ${\mathrm{C}\mathrm{s}\mathrm{P}\mathrm{b}\mathrm{C}\mathrm{l}}_3$were determined to be $\sim <\#comment/>0.14\times <\#comment/>{10}^{-<\#comment/>20}{\mathrm{c}\mathrm{m}}^2$and $\sim <\#comment/>0.41\times <\#comment/>{10}^{-<\#comment/>20}{\mathrm{c}\mathrm{m}}^2$, respectively. The results of Judd–Ofelt analysis are presented and discussed.