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Group IV photonic materials such as Si and Ge have been used for monolithic applications including on-chip sensors and optical devices in the mid-IR spectral range. The optical properties of germanium have not been reported experimentally to the same extent as silicon in spite of expected merits over silicon. Germanium is expected to possess advantages as large nonlinear optical coefficients, a broad transparency beyond 10um, and large carrier mobility.
In this paper, we report nonlinear refractive indices and multi-photon absorption coefficients over the wavelength range between 2um-5um, measured using closed and open z-scan measurements. Samples are scanned through the focal point of a plano-convex spherical CaF2 lens, where an intensity variation with respect to its spatial location exists. The transmitted laser power is measured by a power meter at different sample positions relative to the focal region. Closed Z-scan measurements utilize an aperture in front of the detector whereas open Z-scan measurements do not. Closed Z-scan measurements are typically used for the quantification of nonlinear refractive indices while open Z-scan measurements are used for the characterization of nonlinear absorption coefficients. The closed Z-scan measurement values are then divided by the open Z-scan measurement values to remove the effects of nonlinear absorption before the nonlinear refractive index is measured by fitting [B.-U. Sohn et al., APL 111(2017)]
Ultrashort pulses with a temporal width of 150fs at a1kHz repetition rate are used for the measurements. The mid-infrared optical pulses originate from an optical parametric amplifier and difference frequency pumped by a Ti:sapphire regenerative amplifier. The low repetition rate of the pulses and ultrashort temporal pulse width which is much shorter than the thermal diffusion time scale of 40µs in Ge, is ideal to mitigate effects of heat phonons on the nonlinear effects under study. The nonlinear refractive index of Ge is characterized to possess the highest value, 9.1*10-5cm2/GW at a wavelength of 3um, corresponding to the two photon absorption edge. This result is supported by Kramers-Kronig relation between two photon absorption and nonlinear refractive index n2. The value of n2 is observed to vary between 4*10-5cm2/GW to 5*10-5 cm2/GW within the 3.5-5µm wavelength range.
Considering Ge’s bandgap of 0.66eV, two photon absorption and three photon absorption occur in Ge at wavelengths between 2-3.6µm and 3.6-5.5µm respectively. The two photon absorption coefficient has the largest value, 25.6cm/GW at 2.2µm and possesses a relatively constant value with average of 0.71cm3/GW2 between 4-5.5µm. The four photon absorption coefficient is measured to be 0.007cm5/GW3 at 6µm.
We further investigate the nonlinear figure of merit (FOM), which is proportional to n2 and inversely related to multi photon absorption coefficient. A large FOM is achieved in wavelengths where n2 is large and multi-photon absorption effects are weak. The FOM has a high value of 0.08 between 2.5 - 3 µm making germanium an efficient material for applications in nonlinear optical devices.
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