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Photonic waveguide bundles using 3D laser writing and deep neural network image reconstruction

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Abstract

In recent years, three-dimensional (3D) printing with multi-photon laser writing has become an essential tool for the manufacturing of three-dimensional optical elements. Single-mode optical waveguides are one of the fundamental photonic components, and are the building block for compact multicore fiber bundles, where thousands of single-mode elements are closely packed, acting as individual pixels and delivering the local information to a sensor. In this work, we present the fabrication of polymer rectangular step-index (STIN) optical waveguide bundles in the IP-Dip photoresist, using a commercial 3D printer. Moreover, we reduce the core-to-core spacing of the imaging bundles by means of a deep neural network (DNN) which has been trained with a large synthetic dataset, demonstrating that the scrambling of information due to diffraction and cross-talk between fiber cores can be undone. The DNN-based approach can be adopted in applications such as on-chip platforms and microfluidic systems where accurate imaging from in-situ printed fiber bundles suffer cross-talk. In this respect, we provide a design and fabrication guideline for such scenarios by employing the DNN not only as a post-processing technique but also as a design optimization tool.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Additive manufacturing by multi-photon direct laser writing using nanoscale 3D printers has become an important tool for the fabrication of miniaturized three-dimensional optical elements such as micro-objectives [1], lenses [24], metalenses [5], low loss fiber-to-chip couplers [6], multi-layer diffractive elements [7], and other free-form coupling elements for photonic integration [8]. Because of high accuracy and precision [3] it became also possible to print directly on top of optical fibers [913], overcoming the delicate procedure of light coupling efficiency maximization.

Optical waveguides are one of the fundamental photonic components. The development of innovative technologies and materials for the fabrication of core-cladding structures has never stopped attracting the attention of the scientific community. Several groups have explored the potential of 3D printing for the realization of light guiding structures, such as polymer connections in photonic wire bonding applications [14,15], optical waveguides [4,16] and hollow-core light-cage systems [17,18]. Printing parameters such as laser power, motion speed, hatching and stitching greatly affect the printing outcome both in terms of refractive index and structural integrity, therefore proper choice of the parameters is extremely important for printing optical components, including optical waveguides and micro-scale volume holograms [1921].

Single-mode (SM) optical fibers are the building block for compact multicore fiber bundles, where thousands of single-mode elements are closely packed together acting as individual pixels, delivering the local information to a camera. Dense integration of fluidic and optical functionalities, such as imaging, becomes increasingly important, calling for compact, low-loss, three-dimensional (3D) optical fiber bundles in such devices [22,23]. In particular, in-situ printing solutions, such as chip-to-chip photonic wire bonding [14,15] represent a novel interconnection technology, capable of simplifying the fabrication process, avoiding the monolithic integration of multiple layers. In this regard, this work provides an alternative method for the implementation of multicore imaging fiber bundles, where the integration of conventional multicore fibers may lead to technically complex and costly high-precision alignment procedures [15,24].

The resolution of a waveguide bundle depends on the core-to-core spacing, which is limited by the cross-talk among the cores. Intensive research has focused on methodologies about how to increase the resolution in MCF bundles, such as by inducing small changes in the periodicity of the cores, and/or by slightly modifying the core size within the same fiber bundle [25,26]. Also the addition of distal lenses [27], as well as wavefront shaping techniques have shown remarkable resolution improvements by exploiting the NA of the fiber for point scanning imaging [2729]. Moreover, deep learning (DL) has shown pixelation-free imaging through fiber bundles [30,31] and undoing the scrambling in multimode fibers due to mode coupling [32,33].

In this work, we use 3D printing to record a fiber bundle using 2-photon polymerization (2PP) of the IP-Dip resin by means of a commercial 3D printer. We describe the calibration of the printing parameters, such as motion speed and laser power, identifying the optimal parameter range for the recording of two indices of refraction (core and cladding) required for the fabrication of rectangular step-index (STIN) optical waveguides and STIN multi-core fiber bundles. In all our experiments, we used the commercial 3D direct-laser writing system from Nanoscribe GmbH (Photonic Professional GT+). Optical phase reconstruction for refractive index measurements have been performed, as well as transmission loss measurements. Moreover, we show how deep neural networks (DNNs) can improve the imaging resolution of this type of waveguide bundles by undoing the scrambling due to the cross-talk, and remove the noise artifacts from the raw data. DNNs allowed us to quantify the reconstruction accuracy according to patterns of digits digitally propagated through various waveguide bundles with different core-to-core spacing, and finally, to set the optimal core-to-core spacing in the fabricated waveguide bundle according to highest reconstruction accuracy. Finally, we identified a successful 3D printing approach for the realization of 720 µm long STIN waveguide bundles, on which we performed experimental light coupling tests and used DNNs for image reconstruction from experimental data.

2. 3D printing and optical characterization of step-index (STIN) multi-corewaveguide bundle

In this work, we selected the IP-dip photoresist in “dill” configuration (with the objective immersed in liquid monomer below) to obtain the highest optical quality and morphological smoothness by means of the 63× magnification objective. We demonstrated a single-step additive manufacturing of step-index refractive index photonic waveguides, where the high refractive index cores are surrounded by low refractive index cladding (see Section 1 of the Supplement 1). The waveguides are the result of constant laser power irradiation and speed across their core, embedded horizontally (perpendicularly to the optical axis of the optical setup of the printer) inside the shared cladding. The difference between the refractive indices is achieved by fine tuning the printing parameters after a careful optimization which maximized this difference, taking into account their final optical and structural properties, such as uniformity and geometrical fidelity. We implemented this calibration procedure both for the cladding and the cores.

2.1 Cladding calibration

The waveguide bundle cladding needs to have smaller refractive index than the core and must show a uniform profile along the entire sample length. Besides low refractive index, laser power and scanning speed need to be in the right combination to guarantee structural integrity and geometrical fidelity of the desired structure. To this end, we printed 40 × 13 × 200 µm objects (D x H x L in Fig. 1(a)), sweeping the laser power from 35% to 45% (with a step ΔP = 1%), and increasing speed from 6000 to 10000 µm/s (Δv = 1000 µm/s). The printing was executed layer by layer, with horizontal spacing of 0.1 µm (hatching distance) and vertical spacing of 0.3 µm (slicing distance). Following the completion of the 3D printing, we developed the sample in PGMEA and in isopropanol for about twelve and five minutes, respectively.

 figure: Fig. 1.

Fig. 1. (a) Schematic of a 40 × 13 x2 00 µm (D x H x L) block for the calibration of the cladding. Power percentage was swept between 35% and 45%; scanning speed ranged between 6000 and 10000 µm/s. (b-d) Hologram, wrapped and unwrapped 2D phase map of a 3D printed block at 40% laser power and 7000 µm/s scanning speed. A) and B) indicate the transversal and longitudinal cross cuts, respectively.

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We used digital holography to retrieve the phase accumulation throughout all the cladding structures, fully immersed into a refractive index matching Silicon oil. Details of the off-axis holographic set up can be found in the Supplement 1 (see Section 2). The raw hologram and the wrapped phase extraction from a printed object using 40% of the maximum average laser power (the laser power will be given in percentage of the maximum average power throughout the text) and 7000 µm/s are shown in Fig. 1(b) and (c), respectively. Many phase unwrapping methods have been proposed [34,35]; here we use the PUMA algorithm [36] for phase unwrapping and the reconstruction of the 3D printed object by means of this method is shown in Fig. 1(d). The 2D map of the extracted phase not only gives a quantitative measurement of the refractive index, but it also provides important information about the geometrical resemblance with the desired model. The transversal (A in Fig. 1(d)) and longitudinal (B in Fig. 1(d)) phase profiles are reported in Fig. 2(a) and (b) and they result from the profiles averaging over the entire length and width of the object. As it can be easily seen in both cross cuts, the effect of the power increase (and constant speed) is reflected in a higher phase accumulation across the printed volume. Moreover, the effects of the aberrations from the printing lens are more evident at lower laser power, yielding less polymerization because of the intensity decrease which takes place at the edges of the field of view. This can limit the applicability to bigger physical dimensions, in the face of the lowest refractive index. In order to guarantee both low refractive index, and good geometrical fidelity at reasonable sample length and fabrication time, we have set the calibration power to be 40% and the scanning speed at 7000 µm/s; the Supplement 1 (see Section 3) reports the full calibration of the cladding for all the scanning speeds and power percentages we have tested.

 figure: Fig. 2.

Fig. 2. Longitudinal (a) and transversal (b) averaged cross cut profiles as a function of laser power percentage (and constant speed v = 7000 µm/s).The effect of the lens aberrations results in a lower polymerization efficiency at the edges of the field of view, limiting the printable length dimension when lower laser power percentages are used; this effect is more evident across the longitudinal dimension compared to the transversal dimension which measures only 40 µm. (c) 2D mapping of the refractive index difference between the printed objects and the index matching oil as a function of the laser power percentage and the scanning speed, extrapolated from the cladding calibration; we have measured a minimum and a maximum $\Delta n$ of 0.02 and 0.04, respectively.

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For a better understanding of the optical behavior of the material, and to facilitate the choice of the proper parameters to use, we have mapped the refractive index difference between the polymerized objects and the background, as a function of power percentage and speed (Fig. 2(c)). We have measured a minimum and a maximum $\Delta n$ of 0.02 and 0.045 between the 3D-printed structures and the background, respectively.

2.2 Core to cladding refractive index contrast

We have implemented two possible configurations for the 3D structuring of STIN optical waveguides to identify the suitable parameters range for the printing of the cores, and to further explore the printing potentials of the printing system: one horizontal (Fig. 3(a)) and one vertical (Fig. 3(b)) bottom-up printing approach.

 figure: Fig. 3.

Fig. 3. Vertical (a) and horizontal (b) bottom-up printing approach of STIN multicore fiber bundles using Nanoscribe GmbH Photonic Professional GT+. In (a) the waveguide cores lay perpendicularly to the x-y plane, while in (b) they are printed in a parallel fashion, perpendicularly to the optical axis. (c) Unwrapped 2D phase map PUMA reconstruction of a 20 µm high STIN multicore fiber bundle printed using the Photonic Professional GT+ system. The cladding and core power percentage are set at 40% and 64%, respectively; the speed is 7000 µm/s for both cores and cladding. (d) Phase profile along the cross-cut (highlighted in red in (a)); the phase difference between cores and cladding measures 3 rad on average.

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First we 3D-printed rectangular waveguides with a width D = 3 µm and height H = 20 µm, in a vertical, bottom-up printing configuration. We determined that 55%−65% is the correct power percentage range for printing the cores, above which we would damage the structures. In order to extrapolate the refractive index difference scaling law as a function of the parameters, we printed waveguides at 58% (11.6 mW), 61% (12.2 mW), and 64% (12.8 mW), and varying speeds from 6000 to 10000 µm/s. Digital holography revealed the difference in the accumulated phase through the 20 µm high cores and the shared cladding. The 2D unwrapped phase map for a 20 µm high waveguide bundle, with vcore= vcladding = 7000 µm/s and Pcore = 64% and Pcladding = 40% is shown in Fig. 3(c), and the profile cross sections traced along the sample base dimension in Fig. 3(d).

Knowing the real physical dimension of the object is necessary to retrieve the correct refractive index. For this purpose, we coated the 3D printed structures with 10 nm thin layer of gold using a single chamber sputterer (Alliance Concept DP-650) and observed them into a scanning electron microscope (SEM Zeiss LEO 1550). As one can observe in Fig. 4(a), different exposure zones yield a different size of polymerization due to the dependence of voxel size on exposure and a different shrinkage, resulting in an additional protrusion in correspondence of the cores (inset in Fig. 4(a)). This ledge measures 300 nm circa, which leads to additional 1.5774 rad in the phase accumulation measured by the interferogram. Taking this into consideration, the refractive index difference scaling law at the experimental parameters we have tested is depicted in Fig. 4(b), ranging from a minimum of ${\sim}$ 0.002 to a maximum of ${\sim}$ 0.008; the mean and standard deviation values have been measured over five waveguides.

 figure: Fig. 4.

Fig. 4. (a) SEM image of a 7 × 7, 20 µm high waveguide bundle fabricated at Pcladding = 40%, Pcore = 64%, and v = 7000 µm/s; as it can be seen in the red framed inset, different exposure zones experience a different shrinkage, resulting in an additional protrusion in correspondence of the cores. The waveguides measure ∼3 µm in size. (b) Refractive index difference scaling law of waveguides fabricated at 58% (11.6 mW), 61% (12.2 mW), 64% (12.8 mW), and varying speed from 6000 to 10000 µm/s; the experimental fabrication parameters for the cladding are constant (Pcladding = 40%, v = 7000 µm/s). The mean and standard deviation values have been measured over five waveguides.

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Finally, we established the final printing power and speed for both cladding (Pcladding = 40%, v = 7000 µm/s) and cores (Pcore = 64%, v = 7000 µm/s); in order to explore the system’s potential for the printing of high structures, we have printed rectangular waveguides with a diameter D = 3 µm at variable heights. The printing outcome following this approach results in damaged polymerized structures, due to cumulative overexposure (see Section 4 of the Supplement 1). Observing the different indices reported in Fig. 4(b), we conclude that the available dynamic range is approximately 0.008 between the polymer of low exposure and the polymer that reaches saturation. However, there is a trade-off between dynamic range and structural fidelity in terms of resemblance and damage threshold, which is unique for each geometry and application. Here, having a small volume of highly exposed regions (cores) enables us to utilize higher laser powers without observing material damage, which yields a higher dynamic range than what is reported in [19], where a similar approach is employed.

The 3D printing of mm-long, highly resolved polymer structures using the dill configuration and the 63× magnification objective requires blocks’ stitching. Once the object exceeds the field of view of the printing optics, the stage needs to move sequentially in x-y, in order to allow for the following block to be printed. The waveguide cores need to be continuous and homogeneous at the block-block interface, and therefore the stitching should guarantee adhesion and structural integrity from one printed block to the other. To this end, we have explored two possible printing configurations for the fabrication of horizontal STIN multicore fiber bundles. Good quality waveguides can be printed in a layer-by-layer fashion, perpendicularly to the optical axis of the printing optics. Details about the printing procedure and parameters are encompassed in the Supplement 1, Section 5.

2.3 Transmission loss measurements

Together with the refractive index difference between core and cladding, we quantified the transmission loss of these types of waveguides by means of the in-out light coupling platform depicted (see Section 6 of the Supplement 1). To measure the transmission loss properties of STIN waveguides printed using IP-dip and the Nanoscribe apparatus, we have printed two identical samples at two different lengths, 840 and 600 µm, respectively; rectangular cores dimensions measured 2 µm × 2.5 µm. We have used Pcladding = 38%, Pcore = 61%, and v = 7000 µm/s for both cores and cladding. We have coupled a 10 µm diameter incoherent white light beam into three different waveguides at each of the printed lengths, 30 µm distant from one another, and measured the output intensities at 535/43, 561/14, 592/43 nm, 609/50 nm, and 675/53 nm colored filters. Propagation losses primarily depend on strong scattering and material absorption [37]. Figure 5 shows the transmission loss we have measured as a result of the intensity power ratios between the outputs recorded at the major length and the ones measured at the shorter length, averaged over three waveguides; the inset in Fig. 5 shows the waveguide output recorded at 609/50 nm. These waveguides exhibit losses of 8 dB/mm at shorter wavelengths, down to ∼2.5 dB/mm above 600 nm wavelength. Despite material absorption, the high losses we have measured in the 500–600 nm wavelength region of the electromagnetic spectrum are mostly due to scattering caused by the rough polymerized surface, which proceeds voxel by voxel.

 figure: Fig. 5.

Fig. 5. Transmission loss in dB/mm of the rectangular STIN optical waveguides fabricated Nanoscribe Photonic Professional GT+. Inset shows the output intensity profile of one waveguide recorded at 609/50 nm wavelength filter. The loss at short wavelengths is highly affected from scattering, most probably due to material roughness.

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3. Image reconstruction using a convolutional deep neural network (CNN)

In order to investigate and predict the optimal core-to-core spacing between the waveguides to be set for the fabrication of the final bundle, we verified how a ‘U-net‘ type CNN reconstructs output images from the waveguide bundles at varying waveguide pitch. Information about the U-net structure can be found in the Supplement 1, Section 7.

3.1 Training and testing a U-net with a synthetic dataset for the prediction of the correct core-to-core spacing D

For a better estimate of the final optimal bundle configuration, we evaluated the quality of the reconstruction performed by the network, calculating the mean squared error (MSE) and the mean absolute error (MAE) for different core-to-core spacing D and at a bundle length of 1 cm (see Section 8 of the Supplement 1). This has been done following the conceptual procedure schematically shown in Fig. 6. First, we synthetically enlarged the network training dataset by propagating through a 1 cm long waveguide bundle, 1170 different replicas of digits using the beam propagation method (BPM). In particular, the synthetic dataset was created by rotating and scaling the layout of the digits we have patterned to be used as the physical imaging sample (Supplement 1, Section 9) in the experiments. In a second step, the bundle output images produced by the BPM served as an input to the U-net type convolutional neural network, where the resulting 1170 distal pattern images were randomly split into 1053 for training and 117 for testing (10%). The training set has been split, in turn, into 210 examples for validation (20%) and 843 examples for training (80%), and processed in batches of 20, shuffling them at every epoch to minimize over fitting. The training proceeded for a maximum of 150 epochs. The Adam optimizer we used had a learning rate of 1 × 10−5. We recorded every output intensity by simulating the STIN waveguide bundles with =0.007 and core dimensions W = 2 µm and H = 2.5 µm, where these values are extracted from the fabricated samples. The source wavelength in the simulation is λ=600 nm and the waveguide pitch D is varied between 3 and 40 µm where the bundle is bounded in a 120 µm by 120 µm area.

 figure: Fig. 6.

Fig. 6. Schematic of synthetic dataset creation for the training of the network. 1170 digits have been propagated through a 12 × 12 STIN waveguide bundle with core dimensions W = 2 µm, H = 2.5 µm and refractive index difference Δn = 0.007. We set the illumination wavelength λ=600 nm, the sample length L = 1 cm at variable waveguide pitch D.

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We monitored the learning curves for both the training and the validation datasets, displaying the MSE and MAE for the different waveguide pitches D. Preliminary experimental data from light coupling experiments exhibited moderate to low contrast, as well as additional background noise, most likely due to stray light. For this reason, we have tested the reconstruction both in the absence and in the presence of a background noise randomly changing for every sample and having a Gaussian distribution to mimic the experimental data, where the peak value of the noise is 20% of the peak value of the signal within the dataset. We additionally simulated the propagation of a plane wave through the bundle and added the result to each of the digit output intensities, so that the ratio between the intensities of the cores illuminated by the input pattern and the others is on average 20%. Figure 7(a) and (b) display the two metrics as a function of the core-to-core spacing, suggesting an optimal pitch D of 10 µm to be used for the fabrication of the waveguide bundle, both in the presence and without noise. Figure 7(c) reports one example of digit used as a ground truth, while Fig. 7(d) show the propagated (upper panel) and the reconstructed (lower panel) version of the digit performed by the network for a uniform bundle, D = 4 µm, D = 10 µm, D = 20 and D = 30, respectively in the absence of noise. Figure 7(e) reports the similar results when we add the background noise to the digitally propagated fields. All the results from the propagation performed by the BPM method and the network reconstruction for all the different core-to-core spacing D we have simulated are shown in the Supplement 1, Section 8. These results demonstrate that a U-net type CNN roughly reconstructs the input pattern in all scenarios presented when the field is scrambled by Fresnel diffraction and weakly waveguiding. However, it exhibits an optimal point in terms of waveguide pitch where the reconstruction is the best by both visual inspection and mean squared/absolute error metrics. This behavior becomes more evident when the noise is introduced in the dataset. To show how much the DNN relies on the cladding light, we have retrained the U-net with the simulated dataset, removing the cladding light information by setting the intensity to zero everywhere except in the waveguide cores. We provide these results in Fig. 8 showing an increased MSE and MAE for all the waveguide pitches D, suggesting that the information encoded in the cladding light is still helpful during reconstruction. However, we observe that the network still reconstructs the input patterns at the different waveguide pitches D even without the cladding light contribution, proving no strong reliance on this information especially around the optimal pitch value as exemplified in Fig. 8(d) and (e). Further details are provided in the section 8 of the Supplement 1.

 figure: Fig. 7.

Fig. 7. Mean squared error (a) and mean absolute error (b) of the synthetic test datasets as a function of the waveguide pitch D. (c) Example of a ground truth digit. Upper panel and lower panel in (d) report the propagated digit and its reconstruction provided by the network when there is no noise for a uniform bundle, D= 4 µm, D= 10 µm, D= 20 µm and D= 30 µm, respectively. Upper panel and lower panel in (e) report the propagated digit and its reconstruction provided by the network when there is noise added to the propagated fields for a uniform bundle, D= 4 µm, D= 10 µm, D= 20 µm and D= 30 µm, respectively. Scale bars measure 20 µm.

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 figure: Fig. 8.

Fig. 8. Mean squared error (a) and mean absolute error (b) of the synthetic test datasets as a function of the waveguide pitch D when the cladding light is removed (c) Example of a ground truth digit. Upper panel and lower panel in (d) report the propagated digit and its reconstruction provided by the network when there is no noise for D= 4 µm, D= 10 µm, D= 20 µm and D= 30 µm, respectively. Upper panel and lower panel in (e) report the propagated digit and its reconstruction provided by the network when there is noise added to the propagated fields for D= 4 µm, D= 10 µm, D= 20 µm and D= 30 µm, respectively. Scale bars measure 20 µm. Cladding light is digitally removed.

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3.2 Training and testing with synthetic data that mimics experimental conditions

As a proof of concept and based on the optimal pitch D identified from the network, we fabricated a 12 × 12 STIN, 720 µm long waveguide bundle, with an inter-waveguide distance D= 10 µm, $\Delta n$ =0.007 and core dimensions W = 2 µm and H = 2.5 µm. For the sake of clarity, Fig. 9 reports an example of simulated and recorded digit at the optimal pitch D= 10 µm, after 1 cm propagation, without any additional background noise (a), with a superimposed propagated planewave (b) and Gaussian-like distribution noise (c).

 figure: Fig. 9.

Fig. 9. BPM output intensity of a digit, propagated in the bundle for 1 cm propagation distance; digit output intensity with a superimposed propagated plane wave (b) and a Gaussian noise distribution (c); scale bar measures 20 µm.

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For the sake of consistency with the experiment, we retrained the network simulating a waveguide bundle at a length L = 720 µm. Figure 10 shows five examples of the DNN image reconstruction using the synthetic testing dataset: the first row shows five pixelated digits obtained from the BPM simulations and added noise, which now serve as inputs to the DNN, while the second and the third rows report the reconstructed digits and the ground truths, respectively. The transverse computation window of BPM is set as 2048 × 2048 to properly simulate wave propagation. Then the output intensity is recorded and down sampled to 256 × 256 to reduce the computational load in DNN training. We registered a MSE = 0.015 and a MAE = 0.03 over the test dataset. In general, we can see that the DNN can reconstruct quality enhanced images from the fiber bundle, removing the pixelation effect due to the fiber cores and bypassing the blurring and scrambling effect due to core-to-core coupling.

 figure: Fig. 10.

Fig. 10. Five examples of synthetic inputs we used to test the DNN (first row), their corresponding reconstruction (second row) and the ground truths used for the training (third row); the waveguide pitch and the scale bars measure 10 and 20 µm, respectively.

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3.3 Image patterns projection, imaging and test results with experimental data

In order to explore the imaging capabilities of the fabricated waveguide bundle, we have fabricated a custom made sample target containing digits from 0 to 9, with different sizes and feature thicknesses. The pattern has been realized on a glass wafer and fabricated by means of standard photolithographic techniques. An image and the process flow for the fabrication of the sample target is encompassed in the Supplement 1, Section 9.

The custom-made target of digits, whose layout is used to generate an augmented synthetic dataset, as described in the previous section of this manuscript, has been used to train the network with many examples. Then this network is tested with the experimental recordings. We have measured the output intensity from the 720 µm long waveguide bundle we fabricated using Nanoscribe, when the digits from the custom made sample target are projected to the proximal bundle facet (Supplement 1, Section 8). The U-net shows good reconstruction performances, despite the light cross-talk and the pixelated nature of the images, as depicted in Fig. 10. The first row in Fig. 10 shows some of the waveguide bundle output intensities, which now correspond to the DNN input, while the second and the third rows show the reconstructed digit from the DNN and the corresponding ground truth, respectively. MSE and MAE for each reconstructed digit are also reported, reaching minimum values of 0.036 and 0.069, respectively; scale bars measure 20 µm. Depending on the thickness, size and complexity of the patterned digit, the delivering and recognition of the image at the fiber end can be challenging, as one can notice by observing the images in the first row of Fig. 11. In addition, the network also successfully reconstructs the digits when the cladding light is removed after retraining (see Fig. S14 in section 8 of the Supplement 1). To conclude, the use of DNN for image reconstruction provides an efficient platform for improved and accurate rendering of fiber bundle images and proves to be a valuable tool to extract the desired information from the raw images captured on a camera.

 figure: Fig. 11.

Fig. 11. Output intensity from the fiber bundle, fabricated using Nanoscribe Photonic Professional GT+, recorded by means of CAM1 (first row) and DNN reconstructed images and corresponding ground truths (second and third rows); scale bars measure 20 µm.

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4. Conclusions

In this work, we report the fabrication of STIN rectangular optical waveguides in a horizontal, bottom-up printing approach, using Nanoscribe GmbH Photonic Professional GT+. We show a full calibration of the printing parameters, such as laser power and motion speed for the realization of undamaged structures with maximized refractive index contrast between the cores and the surrounding cladding. We identified Pcladding = 38% (7.6 mW), Pcore = 61% (12.2 mW), and v = 7000 µm/s for both cores and cladding as the optimal parameter combination for the fabrication of STIN waveguides using this technique. We characterized the waveguides in terms of refractive index difference and transmission loss, reporting $\Delta n$=0.007 and transmission loss of ∼2.5 dB/mm above 600 nm wavelength.

We identify a successful 3D printing strategy for STIN waveguide bundles, using a horizontal printing configuration, according to which the waveguides are structured in a layer-by-layer fashion. We built a convolutional neural network (CNN) of the U-net type and monitored the mean squared error (MSE) and the mean absolute error (MAE) provided by the network, after 1 cm length propagation. By doing so, we showed that the DNN can undo the coupling due to cross-talk on various core-to-core spacing. We used the MSE and MAE as the metric to set the optimum core-to-core spacing for the fabricated sample. Finally, after we have trained the network with an enlarged synthetic dataset we show how DNN techniques can improve the imaging resolution from the fabricated, 12 × 12 step-index (STIN) waveguide bundle at the optimal waveguide pitch of 10 µm, both from simulation and experimental datasets. The network is capable of removing pixelation effects and noise artifacts, turning out to be an efficient platform for improved and accurate rendering of fiber bundle images. The DNN-based optimization approach can be adopted in applications to obtain accurate imaging where in-situ printed fiber bundles suffer from cross-talk. In this respect, we provide a design and fabrication guideline for such scenarios.

Acknowledgments

We would like to thank Dr. Pooria Hadikhani for the help he kindly provided for the fabrication of the custom made sample target by means of a standard photolithographic process. We also thank Dr. Ye Pu for fruitful discussions.

Disclosures

A large fraction of this work is encompassed in the PhD thesis titled Three-dimensional fabrication of sub-micron optical waveguides in PDMS and other polymer materials [38]. The authors declare no conflicts of interest.

Data availability

The dataset of digits, the BPM code, and the U-net type CNN underlying the results presented in this paper are available at the GitHub repository in Ref. [39].

Supplemental document

See Supplement 1 for supporting content.

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Supplementary Material (1)

NameDescription
Supplement 1       Supplemental Document

Data availability

The dataset of digits, the BPM code, and the U-net type CNN underlying the results presented in this paper are available at the GitHub repository in Ref. [39].

39. G. Panusa, N. U. Dinc, and D. Psaltis, “Photonic waveguide bundles using 3D laser writing and deep neural network image reconstruction,” GitHub (2021), https://github.com/ulasdinc/WgdBundle_DNN.

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Figures (11)

Fig. 1.
Fig. 1. (a) Schematic of a 40 × 13 x2 00 µm (D x H x L) block for the calibration of the cladding. Power percentage was swept between 35% and 45%; scanning speed ranged between 6000 and 10000 µm/s. (b-d) Hologram, wrapped and unwrapped 2D phase map of a 3D printed block at 40% laser power and 7000 µm/s scanning speed. A) and B) indicate the transversal and longitudinal cross cuts, respectively.
Fig. 2.
Fig. 2. Longitudinal (a) and transversal (b) averaged cross cut profiles as a function of laser power percentage (and constant speed v = 7000 µm/s).The effect of the lens aberrations results in a lower polymerization efficiency at the edges of the field of view, limiting the printable length dimension when lower laser power percentages are used; this effect is more evident across the longitudinal dimension compared to the transversal dimension which measures only 40 µm. (c) 2D mapping of the refractive index difference between the printed objects and the index matching oil as a function of the laser power percentage and the scanning speed, extrapolated from the cladding calibration; we have measured a minimum and a maximum $\Delta n$ of 0.02 and 0.04, respectively.
Fig. 3.
Fig. 3. Vertical (a) and horizontal (b) bottom-up printing approach of STIN multicore fiber bundles using Nanoscribe GmbH Photonic Professional GT+. In (a) the waveguide cores lay perpendicularly to the x-y plane, while in (b) they are printed in a parallel fashion, perpendicularly to the optical axis. (c) Unwrapped 2D phase map PUMA reconstruction of a 20 µm high STIN multicore fiber bundle printed using the Photonic Professional GT+ system. The cladding and core power percentage are set at 40% and 64%, respectively; the speed is 7000 µm/s for both cores and cladding. (d) Phase profile along the cross-cut (highlighted in red in (a)); the phase difference between cores and cladding measures 3 rad on average.
Fig. 4.
Fig. 4. (a) SEM image of a 7 × 7, 20 µm high waveguide bundle fabricated at Pcladding = 40%, Pcore = 64%, and v = 7000 µm/s; as it can be seen in the red framed inset, different exposure zones experience a different shrinkage, resulting in an additional protrusion in correspondence of the cores. The waveguides measure ∼3 µm in size. (b) Refractive index difference scaling law of waveguides fabricated at 58% (11.6 mW), 61% (12.2 mW), 64% (12.8 mW), and varying speed from 6000 to 10000 µm/s; the experimental fabrication parameters for the cladding are constant (Pcladding = 40%, v = 7000 µm/s). The mean and standard deviation values have been measured over five waveguides.
Fig. 5.
Fig. 5. Transmission loss in dB/mm of the rectangular STIN optical waveguides fabricated Nanoscribe Photonic Professional GT+. Inset shows the output intensity profile of one waveguide recorded at 609/50 nm wavelength filter. The loss at short wavelengths is highly affected from scattering, most probably due to material roughness.
Fig. 6.
Fig. 6. Schematic of synthetic dataset creation for the training of the network. 1170 digits have been propagated through a 12 × 12 STIN waveguide bundle with core dimensions W = 2 µm, H = 2.5 µm and refractive index difference Δn = 0.007. We set the illumination wavelength λ=600 nm, the sample length L = 1 cm at variable waveguide pitch D.
Fig. 7.
Fig. 7. Mean squared error (a) and mean absolute error (b) of the synthetic test datasets as a function of the waveguide pitch D. (c) Example of a ground truth digit. Upper panel and lower panel in (d) report the propagated digit and its reconstruction provided by the network when there is no noise for a uniform bundle, D= 4 µm, D= 10 µm, D= 20 µm and D= 30 µm, respectively. Upper panel and lower panel in (e) report the propagated digit and its reconstruction provided by the network when there is noise added to the propagated fields for a uniform bundle, D= 4 µm, D= 10 µm, D= 20 µm and D= 30 µm, respectively. Scale bars measure 20 µm.
Fig. 8.
Fig. 8. Mean squared error (a) and mean absolute error (b) of the synthetic test datasets as a function of the waveguide pitch D when the cladding light is removed (c) Example of a ground truth digit. Upper panel and lower panel in (d) report the propagated digit and its reconstruction provided by the network when there is no noise for D= 4 µm, D= 10 µm, D= 20 µm and D= 30 µm, respectively. Upper panel and lower panel in (e) report the propagated digit and its reconstruction provided by the network when there is noise added to the propagated fields for D= 4 µm, D= 10 µm, D= 20 µm and D= 30 µm, respectively. Scale bars measure 20 µm. Cladding light is digitally removed.
Fig. 9.
Fig. 9. BPM output intensity of a digit, propagated in the bundle for 1 cm propagation distance; digit output intensity with a superimposed propagated plane wave (b) and a Gaussian noise distribution (c); scale bar measures 20 µm.
Fig. 10.
Fig. 10. Five examples of synthetic inputs we used to test the DNN (first row), their corresponding reconstruction (second row) and the ground truths used for the training (third row); the waveguide pitch and the scale bars measure 10 and 20 µm, respectively.
Fig. 11.
Fig. 11. Output intensity from the fiber bundle, fabricated using Nanoscribe Photonic Professional GT+, recorded by means of CAM1 (first row) and DNN reconstructed images and corresponding ground truths (second and third rows); scale bars measure 20 µm.
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