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The SC source was pumped by a four-stage MOPA using an unfolded double-pass amplifier configuration based on a 1.55-μm directly modulated seed laser diode. The seed pulse duration is 1 ns, and the repetition rate is tunable between 10 and 10 MHz. The seed is subjected to three stages of amplification in erbium- and erbium-ytterbium-doped silica fibers, which extends the spectrum to 2.2 μm by in-amplifier nonlinear broadening. To further push the spectrum towards longer wavelengths, the erbium fiber was spliced to ~40 cm of the 10-μm core diameter thulium-doped double-clad fiber, which extended the spectrum to 2.7 μm. The thulium-doped fiber was subsequently spliced to a short piece of silica mode-field adapter fiber having a mode-field diameter of 8 μm, which provided a better match to the fluoride fiber. The mode adapter fiber is butt-coupled to a 6.5-μm core diameter single-mode ZrF4-BaF2-LaF3-AlF3-NaF (ZBLAN) fiber from FiberLabs Inc., with a short length of approximately 1.5 m to reduce the effect of strong multiphonon absorption beyond 4.3 μm.
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The interferometer is based on a Michelson design employing a gold-coated parabolic mirror collimator, a broadband CaF2 wedged plate beam splitter, a BaF2 plano-convex lens in the sample arm, and a BaF2 window and flat silver mirror in the reference arm. The BaF2 lens was chosen to minimize the effect of dispersion, while being available at a relatively short focal length of 15 mm. At 4 μm, the dispersion of BaF2 is relatively low at 16.4 ps/nm/km compared to other standard lens substrates, such as CaF2 (33.0), Si (−45.8), and ZnSe (−59.9), but most importantly, the dispersion slope is flat from 3.5-4.5 μm (13.6-19.1 ps/nm/km)33. Even so, the residual dispersion from the 6.3-mm center thickness lens was roughly compensated by a 5-mm window and the remaining dispersion was compensated numerically. Coupling to the upconversion module was performed using a 6-mm focal length aspheric chalcogenide lens and a 9-μm core diameter single-mode indium fluoride patch cable.
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Upconversion is realized by mixing the low-energy IR photons at a wavelength λIR with pump photons at a wavelength λP to generate upconverted photons with a wavelength λUP, under energy and momentum conservation:
$$ {{\lambda }}_{{P}}^{ - 1} + {{\lambda }}_{{{IR}}}^{ - 1} = {{\lambda }}_{{{UP}}}^{ - 1}, \:{{\Delta }}\vec k = \vec k_{{{UP}}} - \vec k_{{P}} - \vec k_{{{IR}}} $$ (1) where $\vec k$ is the wave propagation vector and ${{\Delta }}\vec k$ is a measure of the phase mismatch among the three interacting waves, which should ideally be zero for maximum QE. Furthermore, the QE scales linearly with the pump power and scales quadratically with the effective nonlinear coefficient (deff) and the length of the nonlinear medium27. The mid-IR OCT system is operated at a wavelength of 4 µm with a spectral bandwidth > 1 µm. Accordingly, the upconversion module was designed and optimized to upconvert the entire spectral range from 3.6 to 4.6 μm for the fastest detection. Among the various phase-matching configurations, quasi-phase matching in a PPLN crystal was chosen for the broadband upconversion, owing to its design flexibility, access to a high deff (14 pm/V), and optical transparency up to 5 µm26. The upconversion took place inside the PPLN crystal, where each wavelength was phase-matched at a different propagation angle. Thus, noncollinear interaction among the three participating waves was used to phase match over a wide spectral range (see Supplementary Fig. S3a). As the λUP is below λP, by choosing the pump wavelength λP=1 µm, conventional Si-CMOS detection can be engaged for λUP. Here, a solid-state (Nd:YVO4) CW linearly polarized laser operating at 1064 nm was used as the pump. This was driven by a broad area emitting laser diode (3 W, 880 nm). The high-finesse folded solid-state laser cavity was formed by mirrors M1-M7 (see Supplementary Fig. S4). All mirrors are high-reflective coated for 1064 nm and anti-reflective (AR) coated for 700-900 nm. The mirror M7 is based on an undoped YAG substrate and additionally high-transmission -coated for the 2-5-µm range. The mirror M6 acts as an output coupler for the upconverted light. The mirrors M4 and M5 are placed in a separate compartment to filter out the fluorescence from the laser crystal and 880-nm pump laser. A 20-mm-long 5% MgO-doped PPLN crystal is used for the experiment (Covesion, AR-coated for 1064 nm, 2.8-5.0 µm on both facets). The PPLN crystal consists of five different poling periods (Λ) ranging from 21 to 23 µm in steps of 0.5 µm. Each poled grating has a 1 mm × 1 mm aperture and is separated by 0.2-mm-wide regions of unpoled material. For different values of Λ, the phase mismatch and hence the overall upconversion spectral bandwidth varies (see Supplementary Fig. S3b). A wider bandwidth requires larger input angles for the IR beam, which reduces the overall QE as the effective interaction length is reduced. For a best-case scenario, Λ = 23 µm was considered in the setup. A CW intracavity power of > 30 W at 1064 nm was realized with a spot size (beam radius) of 180 µm inside the PPLN crystal. The entire system is operated at room temperature. The estimated maximum QE at each mid-IR wavelength is plotted in Supplementary Fig. S3c, considering an effective interaction length of 20 mm inside the PPLN crystal. The IR light (output of the fiber coupled 4-µm OCT signal) is collimated and then focused into the PPLN crystal using a pair of CaF2 aspheric lenses (f = 50 mm, AR coated for 2-5 µm). The upconverted light is collimated by a silica lens (f = 75 mm, AR coated for 650-1050 nm). A shortpass 1000-nm filter and a longpass 800-nm filter are inserted to block the leaked 1064-nm beam and 532-nm parasitic second harmonic light, respectively. A schematic representation of the radial wavelength distribution across the transverse upconverted beam profile is shown in Supplementary Fig. S4. The module is able to upconvert all wavelengths in a broad mid-IR spectral range of 3.6-4.8 µm to 820-870 nm, simultaneously.
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After the upconversion module, the near-IR light is collected by a 100-µm core multimode silica fiber guiding the light to a line scan spectrometer (Cobra UDC, Wasatch Photonics, USA) operating with a maximum line rate of 45 kHz (for a bit depth of 10). The spectral range covered the wavelengths of 796 to 879 nm, which is sampled by 4096 pixels. To scan the sample, it is mounted on a double translation stage (2 × ILS50CC from Newport) with a maximum travel speed of 100 mm/s, a travel range of 50 mm and a stepping resolution of 1 µm. The detected raw spectra are dark signal subtracted and normalized to the reference arm signal. Pixel to wavenumber translation and interferometer dispersion compensation are achieved by exploiting the phase information across the pixel array retrieved for two reference interferograms showing clear interference fringes. In this way, spectral resampling is performed to linearize wavenumber sampling34, after which a phase shift is applied for compensating the unevenly matched dispersion in the arms of the interferometer. To suppress the effects stemming from the spectral envelope of the interferograms, a Hanning spectral filter is applied to the spectral region of the interferometric signals. Finally, a fast Fourier transform is applied to generate a reflectivity profile, that is, an A-scan. A compromise between signal strength and acquisition time is made that leads to an A-scan acquisition time of 3 ms. To build B-scans (2D images), the horizontal stage (X) is programmed to move continuously over a specified distance, achieving a 500 line B-scan in 1.5 s. 3D scans are built by stepping the vertical (Y) stage at a proportionately slower rate to assemble multiple B-scans.
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The MC simulations are performed using the open source software MCX35. The simulated domain consists of 1400 × 9 × 230 uniform voxels in XYZ with a size of 5 × 5 × 5 μm3 each, corresponding to a total size of 7000 × 45 × 1150 μm3. The structure is considered uniform along the Y direction, similar to what is shown in the ridge/valley part of Fig. 3a. The slab thicknesses and the valley depths in the simulation are identical to the real ones, but the valley widths in the simulation increase along the horizontal direction from 5 μm at one side of the domain to 180 μm to the other side in steps of 5 μm for the sake of simplicity. The optical properties of zirconia and alumina used in the MC simulations are taken from Su et al19. The MC software launches a number of photons into the defined structure and tracks their path taking into account the refractive index, absorption, scattering, and scattering anisotropy using a random number generator to emulate scattering statistics. The simulated source uses a beam with a Gaussian transverse distribution with a constant width (5 μm for 1.3-µm center wavelength, and 15 μm for 4-µm center wavelength), due to the MC simulations being pure geometrical optics, which hinders the use of a diverging Gaussian beam. The OCT signal in a single A-scan is extracted from the MC simulation by, at each time step, summing the flux of photons that return to the top layer of the simulation within an angle corresponding to the NA of the system, which is 0.1 for both 1.3 and 4 µm. The simulations thus emulate a time-domain OCT implementation. The simulations ran for T = 14.4 ps, in steps of dt = 24 fs, giving a digital sampling of dz = (c dt)/ 2 = 3.6 µm in air. Due to the lack of wave nature of light in the MC simulations, both the axial and lateral resolutions are limited by the digital sampling only, which is unphysical of course, but accepted here because the investigation focuses on the comparison of the penetration depth. The B-scans are constructed by collecting A-scans obtained by moving the source 10 µm laterally, which gives 700 A-scans in a B-scan. Each A-scan simulation is performed using a different seed for the random number generator. To make the raw B-scans represent their experimental counterparts, they are corrected for roll-off by multiplying each A-scan with the measured roll-off curve, as well as corrected for the reduction in signal strength caused by the divergence of the Gaussian beam. This correction is introduced by multiplying the signal at a given depth, z, by the overlap integral, C, between the fundamental mode of the fiber that collects the light and the transverse distribution of the light reflected at z. This overlap integral is approximated here by the overlap integral between the Gaussian distribution of the propagating beam at the focal point U(x, y, zF) and the transverse distribution of light that is reflected at another point z > zF. Due to the double pass of light, the second distribution becomes Gaussian like the input beam at a distance 2(z − zF) from the focal point:
$$ C \approx \frac{{\left( {{\int} {{\int}_{ - \infty }^\infty {U\left( {x, y, 2z - z_{{F}}} \right)U\left( {x, y, z_{{F}}} \right){{d}}x{{d}}y} } } \right)^2}}{{{\int} {{\int}_{ - \infty }^\infty {U\left( {x, y, 2z - z_{{F}}} \right)^2{{d}}x{{d}}y} } {\int} {{\int}_{ - \infty }^\infty {U\left( {x, y, z_{{F}}} \right)^2{{d}}x{{d}}y} } }} \\ = \frac{{4w_0^4\pi ^2\left( {4\left( {z - z_{{F}}} \right)^2\lambda ^2 + \pi ^2w_0^4} \right)}}{{\left( {4\left( {z - z_{{F}}} \right)^2\lambda ^2 + 2\pi ^2w_0^4} \right)^2}} $$ (2) where U(x, y, z) represents a Gaussian beam with e-2 width w0. The focal point, zF, is placed 50 µm below the top surface of C1 to emulate the experimental conditions. The exact parameters and options input to the MCX software as well as the files specifying the spatial domain and the overlap integrals are freely available from the authors upon request.