Long-wavelength, high-resolution microscopy using upconversion in ultra-thin crystals

The demand for infrared (IR) spectroscopy and hyperspectral microscopy within the 5–12 μm range is steadily increasing, especially for achieving high-resolution spectral imaging of biological samples.¹ The measurements of vibrational absorption lines in biomolecules, such as lipids, proteins, and amides, without the need for staining, hold great potential in biomedical research.^2,3 The specificity, abundance, and distribution of biomolecules in tissue samples facilitate quantitative cancer screening, enabling label-free computer-assisted diagnostics based on machine learning algorithms.⁴ However, imaging at IR wavelengths faces limited spatial resolution as described by the Rayleigh criterion.

Several imaging techniques have been developed to overcome this limitation.^5–7 One example is Scanning Near-field Optical Microscopy (SNOM), which employs a needle-like tip to probe the surface’s dielectric constant while being illuminated by IR light.⁸ Relying on the tip dimensions rather than the illumination spot size, SNOM can achieve resolutions as small as 60–100 nm. However, SNOM suffers from slow and complex operation. A second example is Infrared Photothermal Heterodyne Imaging (IR-PHI), utilizing a tunable or broadband IR light source to probe the spectral absorbance of the sample. By modulating the amplitude of the IR light, the sample temperature experiences a corresponding modulation, leading to changes in the refractive index. When illuminating the sample with a strongly focused, short wavelength probe laser, the reflected probe light is modulated by the varying refractive index, thus indirectly probing the IR absorbance of the sample.⁹ Since the spatial resolution is determined by the short wavelength probe laser, rather than the IR signal wavelength, high resolution IR imaging can be achieved. However, the data obtained are not directly comparable to standard IR transmission data.

Raman spectroscopy is yet another technique that employs a short wavelength laser for spatial mapping of the vibrational energy levels. However, the Raman cross section is 6–8 orders of magnitude smaller than the corresponding IR vibrational absorption, therefore making it challenging to obtain fast acquisition of high contrast images.¹⁰ 

Another major challenge in IR imaging is the generally low signal-to-noise ratio obtained with IR detectors. One approach to overcome this challenge is to use upconversion detection, either in an imaging¹¹ or a raster scanning configuration.¹² Upconversion, where the IR signal is frequency converted to a shorter wavelength (typically in the 800–975 nm range) through sum-frequency mixing in a second order nonlinear material, has demonstrated an improved signal to noise ratio (SNR) compared to direct detection.¹³ 

This paper explores a novel approach for high-resolution raster scanning IR microscopy, utilizing upconversion hyperspectral imaging in ultra-thin crystals (optical thickness on the order of 10–20 wavelengths of the IR signal) after the IR probe beam has passed through the sample under investigation. The rationale behind this configuration is that the upconverted light is proportional to the product of the local IR signal intensity and the mixing laser intensity. Focusing the short wavelength mixing laser (e.g., 1064 nm) to a small spot size enables high resolution upconversion of the IR image (e.g., at 10 µm) carrying the spatial and spectral signature of the sample. The upconverted replica of the IR image enables better spatial resolution of the acquired image due to the shorter wavelength, given by the Rayleigh criterion.

Broadband upconversion detection is generally limited by the stringent requirements for phase matching associated with frequency conversion in cm-long nonlinear crystals. However, the use of ultra-short crystals has demonstrated several μm wide acceptance bandwidths and easy implementation.¹⁴ While the efficiency was low, the low noise nature of upconversion detection still provided a sufficient SNR for high resolution imaging in the spectral fingerprint region.

The present implementation is similar to the setup presented in Ref. 14, where a tunable narrowband IR Quantum Cascade Laser (QCL) probes the sample, followed by upconversion in an ultra-short Silver Gallium Sulfide, AgGaS₂ (AGS), crystal using a 1064 nm mixing laser (see schematics in Fig. 1). Using 20 mW mixing power at 1064 nm resulted in an upconversion efficiency of 0.3 µW/W, corresponding to 0.3 nW for an IR signal of 10 mW at 10 µm, using a 100 µm thick nonlinear crystal (SNR >55 for a measurement time of 50 µs). Furthermore, the use of an ultra-thin nonlinear crystal yields a large spectral acceptance bandwidth extending from 7 µm and well into the spectral absorption band of the nonlinear material at 12 µm, without any need for phase match tuning.

To minimize diffraction at the IR signal wavelength, the nonlinear material is positioned in close contact with a resolution target, mimicking the sample. The QCL was focused to form a beam waist of 30 µm at the plane of the resolution target. The 1064 nm mixing laser was focused to a beam waist of 2 µm to improve spatial resolution while keeping the angular acceptance parameter of the AGS crystal well above the divergence angles of the interacting beams. See further details on the acceptance angle calculations in the  Appendix.

A series of images were acquired at 10 µm in raster scanning mode, where a sandwiched structure consisting of a USAF 1951 resolution target and a 100 µm long AGS crystal was scanned, as illustrated in the inset in Fig. 1. The assembly was mounted in high precision translation stages (Attocube, ECS3030) for raster scanning. The upconverted signal at ∼960 nm was acquired using an avalanche photodetector (APD440A). The detected signal is plotted as a function of scanner position (see Fig. 2).

Examining group 5, element 6, with a measured visibility of 0.11 shows an experimental resolution limit of ∼17.5 µm (2 · 8.77 µm), thus significantly better than the 60 µm calculated from the Rayleigh limit using detection with the same objective lens. In Secs. III A–III C, a detailed analysis is given for the upconverted signal in an ultra-short AGS crystal placed a few wavelengths behind the sample structure. The analysis is based on the inhomogeneous Helmholtz equation using a two-dimensional (to decrease computation time) Green’s function.

A numerical model is developed to investigate upconversion in ultra-short nonlinear crystals behind targets with small spatial structures comparable to the wavelength of the illumination. The model is developed to estimate the spatial image resolution that can be obtained when the upconversion takes place immediately after the target. A raster scanning geometry is considered. It is shown that not only parameters such as IR wavelength and the NA of the objective lens are important but also the length of the nonlinear crystal plays a central role for the spatial resolution in the upconverted image.

The IR illumination beam (red, w_0,IR = 30 µm) is assumed to be large compared to the mixing beam (blue, w_0,Mi = 2 µm). When the IR beam is transmitted through the resolution target (see Fig. 3), the beam acquires high spatial frequencies in a direction transverse to the lines (in the following equations denoted as the x-direction). However, the beam can be considered unchanged in the orthogonal direction over the spot size of the mixing beam. Hence, a 2D numerical approach is implemented to minimize computation time.

The E-field of a 2D Gaussian beam can be calculated according to Eq. (3), where P_IR is the power of the IR beam, w_0,IR is the beam waist, w_IR(z) and R_IR(z) are the beam size and wave front radius of curvature, respectively, z is the position relative to the beam waist, k_IR is the wave-vector, and ζ(z) is the Goy phase shift.

The E-field behind a target, placed at a distance z_a after the beam waist of the illuminating beam, can be calculated according to Eq. (5), where $r(x,z)=((x−xa)2+(z−za)2)$ and a(x_a) is the field transmission of the resolution target. x_a and z_a are the relative transverse position and the longitudinal offset of the target compared to the center of the beam waist of the illuminating Gaussian IR beam, respectively.

The Gaussian intensity distribution is plotted in Fig. 4, where red and blue lines are the intensity, I(x = 0, z = 0) · e⁻², contours of the IR and mixing intensities, respectively. Figure 4(a) shows the IR intensity (gray scale) without resolution target, and Fig. 4(b) includes three slits with 16 µm slit width aligned with the centerline of the illumination beam, as illustrated in Fig. 3. Figure 4(c) is for a dark line of the resolution target centered with the illumination beam.

It is seen from Fig. 4 that the tightly focused mixing beam is highly diverging, resulting in a fast decay of the intensity at larger depths into the crystal. Furthermore, it is seen that the diffracted IR signal overlaps with the mixing beam further into the crystal even when obstructed by a dark line of the resolution target, which limits the image visibility [see Fig. 4(c)].

Note the local 1.7-fold increase in intensity behind the slit in Fig. 4(b) compared to the intensity distribution without the resolution target.

The upconverted local E-field amplitude inside the crystal is shown in Fig. 5 for different resolution target offsets. Figure 5(a) is for zero offset, whereas Figs. 5(b)–5(e) is for increasing offsets in steps of 8 µm, with a 16 µm slit width in the target. An off-axis E-field component is seen to emerge when the target is offset relative to the illumination beam center.

The generated E-field from each spatial positions in the crystal (spatial coordinate $xi,zi$⁠) can be propagated to a detector plane $xd,zd$ using the Hankel function as propagator, according to Eq. (7), where $rxd,zd,xi,zi=xi−xd2+zi−zd2$⁠.

Figure 6 shows the far-field amplitude of the upconverted E-field for different lengths of the nonlinear crystal. Figures 6(a)–6(e) illustrates the far-field as a function of target offsets ranging from zero to 32 µm in steps of 8 µm, all for a slit width of 16 µm.

To determine the visibility of raster scanned imaging, the upconverted power is calculated according to Eq. (9), as a function of transverse offset of the resolution target. Figure 7 shows the calculated normalized power at the detector plane as a function of target offset for different lengths of the nonlinear crystal. The calculation was made for three different slit widths of 16, 12, and 8 µm. The upconverted power is normalized with the power obtained without the target [see Fig. 4(a)]. It is clearly seen that the visibility of the fringes deteriorates for decreasing slit widths as well as for increasing length of the nonlinear crystal.

Using the graphs in Fig. 7, the visibility of the fringes can be calculated according to Eq. (1). The visibility is plotted as a function of slit width for different crystal lengths in Fig. 8. Using an IR illumination beam waist of 30 µm at the plane of the aperture and a mixing beam waist of 2 µm at the same plane. The gray area indicates a visibility below the Rayleigh criterion, V_Rc ≈ 0.11, i.e., not spatially resolved. The spatial resolution is seen to increase for the decreasing length of the nonlinear crystal. Figure 8 shows the theoretically calculated visibility together with measured data points for the 100 µm long AGS crystal (data listed in Table I). The measured data points highlighted by solid markers are seen to be outliers. The reason for this discrepancy is believed to be a small unwanted angle between the resolution target and the nonlinear crystal, increasing the propagation distance (diffraction) from the resolution target to the volume where the upconversion takes place. Generally, a good agreement is seen between the developed upconversion theory and the measured data.

The effective NA of both lenses used in the experiment is ∼0.1, However, the NA of the detection lens should be scaled with the wavelength conversion ratio due to the upconversion process, corresponding to NA_De ≈ 1. The theoretical resolution calculated from Eq. (10) is 11 µm, i.e., the minimal distance between two distinguishable points according to the Rayleigh criterion. This corresponds to a slit width of the resolution target of 5.5 µm, indicated with red asterisk in Fig. 8. This corresponds to the maximum resolution that can be obtained with the applied lens combination for a crystal length going toward zero.

This paper demonstrates the feasibility of using ultra-short nonlinear crystals for long-wavelength upconversion raster scanning microscopy. The use of short crystals for the upconversion process makes phase match tuning obsolete even when using broadband or broadly tunable narrowband sources. The current implementation, using a 100 µm thick AGS crystal with a cut angle of θ = 39°, enables type I phase matching over the range from 7 to 12 µm for normal incidence on the crystal.

The upconversion technique enables the use of existing near-IR instrumentation, such as fast high gain detectors. At the same time, the use of short crystals broadens the range of useful nonlinear materials for upconversion applications since the IR absorption of the material is substantially reduced when ∼100 µm crystal lengths are used, both in terms of signal reduction due to absorption and in terms of noise induced by upconverted thermal radiation.¹⁴ 

A theoretical description of upconversion in short crystals close to the resolution target is presented for the first time, calculating the upconverted efficiency and visibility of spatial features. Experimental measurements are in good agreement with theory. Close to a fourfold improvement of the spatial resolution of an upconversion raster scanning microscope was realized compared to the theoretical limit of a classical IR microscope with similar NA. Several aspects of this novel approach can be investigated and optimized in the future work, e.g., using even shorter nonlinear crystals or thin-films to obtain the ultimate spatial resolution ultimately limited by the beam size of the shorter wavelength mixing laser.

Other nonlinear crystals such as OP:GaAs or AgGaSe₂ could be considered, improving the upconversion efficiency or wavelength coverage. Increasing the mixing power to the Watt level should be possible, while still being below the damage threshold of AGS (∼10 MW/cm²), thus improving the upconversion efficiency significantly.

We would like to acknowledge the financial support from the Villum Foundation Grant: V.K.R Grant No. 00028112. We further acknowledge financial support from the Lundbeck Foundation “Ultra sensitive mid-infrared spectrometer for imaging wet bio samples,” Grant No. R346-2020-1538.

The authors have no conflicts to disclose.

P. Tidemand-Lichtenberg: Conceptualization (equal); Funding acquisition (supporting); Investigation (lead); Software (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). C. Pedersen: Conceptualization (equal); Funding acquisition (lead); Investigation (supporting); Project administration (lead); Software (supporting); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

A numerical evaluation of the angular acceptance parameter for upconversion in short nonlinear crystals can be based on Ref. 19. Type I phase matching is considered, where the IR and mixing field are ordinarily polarized, while the upconverted signal is extraordinarily polarized. To calculate the angular acceptance as a function of crystal length, the crystal is assumed to be cut at θ_cut = 39° and the mixing laser angle is assumed to be normal to the crystal surface. Since the material is uniaxial, the acceptance parameter depends on whether the angle is in the ordinary or extraordinary plane (containing the optical axis of the material).

The angle of the upconverted field is optimized to minimize the transverse phase mismatch, i.e., the upconverted field has an angle approximately given by the IR input angle scaled with the shift in wavelength φ_up ≈ φ_IRλ_up/λ_IR. The normalized efficiency is plotted as a function of angle for different crystal lengths in Fig. 9.