Two-photon polymerization simulation and fabrication of 3D microprinted suspended waveguides for on-chip optical interconnects

Ricardo M. R. Adão; Tiago L. Alves; Christian Maibohm; Bruno Romeira; Jana B. Nieder

doi:10.1364/OE.449641

1. Introduction

In the current fast-forward technological and digital era, computation speed and energy efficiency are vital. Conventional electronic computing is reaching a miniaturization and heat dissipation efficiency bottleneck, with faster processors coming mainly at the expense of more and smaller transistors than fundamentally improved ones [1]. With fewer hardware improvement opportunities in sight, the future of conventional computation is ever more reliant on algorithm efficiency and smart resource deployment. On the other hand, Photonic Integrated Circuits (PIC) flourish as an up-and-coming hardware alternative [2], with negligible heating losses and speed-of-light signal processing as some of the most attractive properties of photonic over electronic computing. Furthermore, photonic technology supports emerging algorithmic approaches that can boost a future of high-speed and energy-efficient computing, such as quantum [3] and neuromorphic [4,5] computing. In particular, photonic artificial intelligence implementations such as photonic neural networks [6,7] arise as a valuable combination of hardware and algorithmic innovation.

In this work, we shall focus on the 3D interconnection technology in contrast to planar waveguiding for advanced PICs. We envision that the footprint of such systems could be minimized when coupling a significant number of vertically-emitting light sources /detectors such as on-chip lasers [8] and photonic sensors [9] since they enable highly-dense vertical-coupling approaches that are challenging to achieve with standard 2D waveguides or fiber-coupling packaging approaches due to inefficient coupling. Therefore, efficient optical interconnection of networks designs using flexible 3D waveguides [10] integrated with in/out couplers are urgently needed. Achieving this would greatly impact future emerging technologies such as photonic artificial neural networks, e.g. using bio-mimicking spiking micropillar [8,11] or Vertical Cavity Surface Emitting Laser (VCSEL)-based [12] artificial neurons. Moreover, approaches currently being explored in 2D PICs with 2D waveguide architectures to achieve reconfigurable waveguiding [13], e.g. reprogrammable by optical filtering different spectral bands - could be envisioned for more spatially versatile 3D interconnects.

True 3D architectures call for fabrication methods that provide free-form structures with high precision and control, ideally minimizing the number of fabrication steps typically required in lithography approaches. To accomplish this, femtosecond laser-based Two-photon polymerization (TPP), a 3D micro/nanoscale laser direct writing technology [10], is widely used. The most common implementations rely either on sample or beam translation systems, resorting to stage (motorized or piezo) [14] or galvo-scanning systems [15]. Stage-based systems are simpler to implement and can provide larger writing areas. Galvo-scanning systems enable much faster, vibrationless writing but are usually limited to the microscope objective field of view, often resorting to stage-synced mosaic stitching writing protocols for large-area fabrication. Alternatively, continuously-synchronized stage and galvo scanners can be used to write over larger areas, eliminating the mosaic stitching effects [16]. Similar to conventional macro-scale 3D printing, different meshing schemes can be considered depending on the structure shape and dimensions, the material, and the optical setup. The line tracing of the waveguide itself can be performed mainly via three strategies: writing along the trajectory, helix slicing, or line slicing [10]. Each method has its pros and cons, which shall be addressed ahead.

3D-printed polymeric photonic elements have recently gained massive attention, with examples including optical fiber taper couplers [17,18] and beam-shaping structures [19], fiber-to-chip-couplers [20], free-form inter-chip couplers [21,22], sub-micron waveguides [23], passive waveguide splitter-based convolution kernels for deep neural networks [24], among other waveguide devices [25,26]. High-resolution TPP – also known as two-photon nanoprinting, finds applications in artificial neural network CMOS chips for nanostructured decryption layers [27]. On the other hand, free-form on-chip 3D waveguides and couplers for individual device interconnections are relatively unexplored. Recent works have proposed designs based on continuously [28] and discretely [25] supported 3D waveguides for planar PIC and unsupported 3D splitter waveguides [29], the need for support structures varying with the waveguide shape, dimension, and material.

Although previous theoretical [30–32] and experimental [33] works have studied the TPP voxel shape, there is a lack of simulation tools to model the precise 3D shape of a TPP design depending on the experimental fabrication parameters. Such a tool could significantly facilitate the design, e.g., line spacing and meshing, enable shape visualization, and device performance optimization in a dedicated simulation software.

This work aims to provide a framework for the entire 3D waveguide process development from design to simulation, fabrication, and characterization. Here we introduce a simple Gaussian beam-based TPP shape simulation algorithm that considers experimental parameters including the material polymerization threshold and refractive index, laser power and wavelength, writing speed, and microscope objective type (air/oil/immersion) and numerical aperture. Horizontally-extended, elevated, discretely-supported on-chip 3D waveguides are designed and rendered in a custom-built MATLAB tool. A tapered waveguide allows the coupling of vertically-directed light into the 3D waveguides enabling light propagation over large distances (>100 μm) through the elevated planar waveguide sections, and re-coupling into the chip can be achieved by additional tapered and substrate anchored structures. The waveguide performance is analyzed using mode-solving and finite-difference time-domain (FDTD) photonic simulations. The structures are fabricated using a custom-built piezo sample translation-stage inverted microscope with bespoken python control software and subsequently analyzed using a custom-built optical waveguiding characterization setup.

2. Materials and methods

2.1 3D waveguide design and simulation

The 3D waveguide designs are developed in a custom-built graphical user interface (GUI) powered toolbox for MATLAB that implements the design functions described in Section 3.2. The TPP structure modeling considers an effective two-photon absorption (TPA) cross-section ${\sigma _2} = 5 \times {10^{ - 54}}$ cm⁴s for OrmoCore, with photoinitiator and TPA threshold radical densities ρ₀ = 2.4% and ρ_th = 0.25%, respectively. The TPP writing system parameters are: wavelength λ = 740 nm, repetition rate ν = 80 MHz, pulse duration τ = 80 fs, microscope objective numerical aperture NA = 0.75. The media refractive indices n₁= 1 and n₂ = 1.53 are considered for air and glass. The rendered 3D waveguide surfaces are exported to stereolithography (STL) files and imported to Lumerical’s FDTD or MODE software for coupling or bending loss analysis. Simulations are performed using plane-wave light sources and monitoring the power at the horizontal waveguide section. Multimode bending loss simulations are carried out by integrating the power coupling between the input fundamental TM mode and up to 75 waveguide-supported modes for λ = 830 nm, and a OrmoCore's n = 1.543. The final designs are exported as g-code files, imported, and executed in a Python custom-built instrumentation control software.

2.2 TPP fabrication setup

A femtosecond pulsed laser (Tsunami, Spectra Physics) tuned to 740 nm wavelength and ∼80 fs pulse length is used as the TPP light source. An external SF10 glass prism compressor pair (AFS-SF10-SF10, Thorlabs) is used for pulse optimization counteracting the dispersion of the optical components. A reflective neutral-density filter wheel (NDC-50C-2M, Thorlabs) is used for power control and a beam sampler (10B20-01NC.2, Newport) deflects a fraction of the laser beam for a direct calibrated power reading (1918-R, Newport) indicating the laser power at the back aperture of the microscope objective. A periscope system raises the beam to the height of the input port of the microscope. In the beam path after the periscope, a TTL signal-controlled shutter (SHB1 T, Thorlabs) and beam expander consisting of two cemented achromats (f_BE1 = 40 mm, f_BE2 = 150 mm) are mounted via cage rods. A reflective ND filter (OD 0.2, NDUV02A, Thorlabs) directs the laser beam into a 40× dry objective (NA 0.75, MRH00401, Nikon) and is focused on the sample. The sample is translated using coupled XYZ micro-step motor and piezo stages (MicroStage Series, MCL; NanoLPS200, MCL; RM21 microscope, MCL), with traveling ranges of 20 mm (step motor) and 200 µm (piezo). Real-time monitoring of the fabrication is achieved via wide-field imaging, using an LED light source and a CMOS camera (MCE-B013-UW, MighTex). A bandpass filter (FSQ- BG39, Newport) protects the camera from laser reflections. A schematic of the experimental setup and instrumentation control can be found in Fig. S7 of the Supplement 1 (SD).

2.3 TPP sample preparation

Microscope coverslips (no. 1.5) are rinsed in isopropanol and DI water for cleaning, first dried by nitrogen, and subsequently dried on a hotplate at 100 ^°C for 10 min. OrmoCore is dropcasted onto the substrates, followed by a pre-baking at 80 ^°C for 10 min. After the fs laser exposure, the samples are post-baked at 130 ^°C for 20 min, cooled down to room temperature for 5 min, and developed in 1/3 v/v 4-methyl-2-pentanone dissolved in isopropanol for 12 min. After development, the samples are dipped in isopropanol for cleaning and dried under ambient conditions.

2.3 Photonic waveguide characterization

The 3D waveguide optical properties are characterized in a custom-built setup. A sample holder, a microlensed optical fiber (LFM1F-1, Thorlabs), and an imaging system are translated relative to each other using two XYZ manual fiber coupling stages (7TF2, Standa) and an XYZ manual translation stage (PT3, Thorlabs), respectively. The imaging system consists of a 4x dry objective (NA 0.1, PLN4X, Olympus), a 3.5 mm focal distance lens, and a 16-bit monochrome CMOS camera (CS2100M-USB, Quantalux, Thorlabs). The samples are placed inverted on a sample holder, the fiber focused onto the waveguide input, and the output intensity measured with the camera (2 ms collection time) as discussed in Section 3.4. After being optically characterized, the samples are coated with a 10 nm Au film for morphological characterization using a scanning electron microscope (SEM) (QUANTA 650FEG, FEI Europe B.V.).

3. Results

Towards the realization of 3D interconnects we developed a simulation software that take into account voxel shapes (described in Section 3.1), which is used to simulate and optimize generic 3D waveguide designs that follow parametric paths in horizontal and vertical directions (Section 3.2). For selected 3D interconnect designs, we simulated the waveguiding properties (Section 3.3), and compared them to the experimentally microfabricated and characterized 3D waveguides (Section 3.4).

3.1 TPP voxel modelling

The 3D TPP writing voxel shape can be approximated by modeling the intensity I(r,z) of a focused diffraction-limited Gaussian beam profile and considering the two-photon absorption with the material-specific polymerization threshold. The Gaussian beam profile can be expressed as

(1)$$I({r,z} )= \frac{{2P}}{{\pi \; {w^2}(z )}}\exp \left( { - 2\frac{{{r^2}}}{{{\textrm{w}^2}(\textrm{z} )}}} \right),$$

where P is the laser power and $r = \sqrt {{x^2} + {y^2}} $ is the radial cylindrical coordinate. The term w(z) is the beam radius

(2)$$w(z )= {w_0}\sqrt {1 + {{({({z - {z_0}} )/{z_R}} )}^2}} ,$$

where z₀ is the focus position relative to the substrate. For a diffraction-limited beam, ${z_r} = \pi w_0^2/\lambda $ is the Rayleigh length, ${w_0} = {\lambda _m}/({\pi {\theta_f}} )$ is the beam waist, and ${\lambda _m} = n\lambda $ is the medium wavelength. The far-field beam divergence ${\theta _f} = \arcsin ({\textrm{NA}/n} )$ depends on the objective’s numerical aperture (NA) and the medium refractive index n. It is well-known that the two-photon absorption is proportional to the square of the intensity. Figure 1(a) depicts the 3D spatial distribution of one and two-photon excitation intensities at the focus of the laser beam, illustrated by mapping I and I² (Eq. (1)). Since the TPA cross section is much lower than its one-photon counterpart, the nonlinear TPP writing voxel will be much more confined relative to the one-photon excitation voxel (far more than Fig. 1(a) lets on). The voxel dimensions (width and length) can be theoretically estimated by determining the region in space where the density of radicals ρ generated by two-photon absorption exceeds the two-photon polymerization threshold ρ_th.The polymerization threshold intensity I_th can thus be calculated [30,32] as (see derivation in Section S1 of the SD)

(3)$$I_{th}^2\mathrm{\Delta }t = \frac{{{{({\nu \tau \; \hbar \omega } )}^2}}}{{{\sigma _2}}}\log \frac{{{\rho _0}}}{{{\rho _0} - {\rho _{th}}}},$$

where Δt is the exposure time, ν, τ and ω are the laser repetition rate, pulse duration, and angular frequency, $\hbar$ is the reduced Planck’s constant, σ₂ is the effective two-photon absorption cross-section expressed in cm⁴s, and ρ₀ is the primary initiator density. Considering the intensity at the beam axis $I({r = 0,z = l} )= {I_{th}}$, the voxel vertical length l becomes

(4)$$l = {z_r}{\left( {\sqrt {{\sigma_2}\mathrm{\Delta }t\; N_0^2/C} - 1} \right)^{1/2}}$$

(5)$$C = \log \frac{{{\rho _0}}}{{{\rho _0} - {\rho _{th}}}}$$

Similarly, considering the intensity at the focal plane $I({r = d/2,z = 0} )= {I_{th}}$, the voxel width d becomes

(6)$$d = {w_0}\sqrt {\log {\sigma _2}\mathrm{\Delta }tN_0^2/C} $$

Fig. 1. Two-Photon Polymerization (TPP) writing voxel modeling. (a) Diagram of the simulation configuration. (b) 3D representation of the one and two-photon excitation intensities at the diffraction-limited focus of a Gaussian beam. (c) Theoretical writing voxel dimensions as a function of the laser power for materials of different two-photon absorption cross-section σ₂ values. (c-d) Comparison between the simulated and theoretical voxel length for OrmoCore (c) and width (d) as a function of the laser power for various writing speeds.

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The exposure time Δt can be conveniently approximated as a function of the TPP writing speed v_vel as

(7)$$\mathrm{\Delta }t \approx \frac{{{w_0}}}{{{v_{vel}}}}\nu \tau $$

The material parameters σ₂, ρ₀, and ρ_th depend on the selected polymer and solution concentration. The parameters used for the morphological simulation of our structures, in OrmoCore, can be found in Section 2.1. Figure 1(b) plots the voxel width and length as a function of the laser power for other hypothetical materials with σ₂ = 10⁻⁵³, 10^−54, and 10⁻⁵⁵ cm⁴s, considering a writing speed of 75 µm/s. The voxel length varies considerably between 2 and 7 µm at 50 mW, while the voxel width varies significantly less, between 0.7 to 1.3 µm. Whereas the power P is the most straightforward parameter to determine experimentally with any conventional power meter, Eq. (1) shows that the intensity (power over the beam area) is the relevant parameter for the polymerization problem at hand. Moreover, the average intensity I₀ depends on the laser’s repetition rate ν and pulse length τ (see Eq. (3)). In this work, since all laser parameters other than the power are kept constant at λ = 740 nm, ν = 80 MHz, and τ = 80 fs for all simulations and experiments, P could be used as a valid parameter. However, for a more general readership using different experimental setups, we shall henceforth express our results in terms of the laser fluence F and the exposure dose D, where

(8)$$F = \frac{{{E_p}}}{A} = \frac{P}{{\nu A}} = \frac{P}{{\nu \pi w_0^2}},$$

where E_p is the pulse energy, A is the (wavelength-dependent) beam focus area, and

(9)$$D = \frac{P}{A}\mathrm{\Delta }t \approx \frac{P}{{\pi {{({{w_0}} )}^2}}}\left( {\frac{{2{w_0}}}{{{v_{vel}}}}\nu \tau } \right) = \frac{{2P\nu \tau }}{{\pi {w_0}{v_{vel}}}}\; $$

Despite having the same units, F quantifies the energy per area deposited by a single pulse within the focal spot, whereas D measures the cumulative energy per area resulting from the effective exposure time Δt (see Eq. (7)). Mapping the squared dose Δt I²(x,y,z) according to Eq. (1) and applying the polymerization threshold intensity from Eq. (3) allows modeling the precise voxel shape in 3D. The simulated voxel lengths and widths as a function of the laser power and writing speed are compared against theoretical predictions for the polymer Ormocore, in Fig. 1 (c-d). Three example voxel renderings are displayed as insets. While the voxel profile can be described as approximately an ellipsoid (cigar-shaped) for low laser powers, wider lobes start to form at the bottom for higher laser powers, leading to a peanut-like shape. The simulations and theory agree almost perfectly on the length prediction but display some width mismatch (${|{\mathrm{\Delta }d} |_{max}} = \; $0.45 µm, ${|{\mathrm{\Delta }d} |_{avg}} = $ 0.07 µm) that is partly compensated for by the wider voxel lobes neglected by the theoretical approach.

The refractive index mismatch between air and the glass substrate induces a distortion in the vertical beam translation distortion that is accounted for by applying a linear correction

(10)$$\frac{{\mathrm{\Delta }{z_2}}}{{\mathrm{\Delta }{z_1}}} = \sqrt {\frac{{n_2^2 - N{A^2}}}{{n_1^2 - N{A^2}}}} ,$$

where NA is the microscope objective numerical aperture, Δz₁ and Δz₂ are the vertical beam displacements in media 1 and 2 (air and glass, respectively), and n₁ and n₂ are the respective media refractive indices. The derivation of Eq. (10) can be found in Section S2 of the SD. For the experimental setup used in this work (c.f. Section 3.4), $\mathrm{\Delta }{\textrm{z}_2}/\mathrm{\Delta }{\textrm{z}_1} \approx 2$.

The TPP structure shape can be modeled by calculating the accumulated squared dose $\sum \mathrm{\Delta }t{I^2}({x,z,y} )$ throughout the design tracing and applying the polymerization threshold $\mathrm{\Delta }tI_{th}^2$. The following section presents the developed 3D waveguide designs and applies this method to precisely predict the shape of the TPP structures.

3.2 3D waveguide design

This section describes the proposed 3D waveguide designs for out-of-plane interconnections. The waveguide trajectory designs are developed in a custom-built script-based software via mathematical parametric functions. Let the symbol f represents general waveguide parameterization

(11)$$\vec{f}({x,y,z} )= {f_x}(s ){\hat{\rm e}_x} + {f_y}(s ){\hat{\rm e}_y} + {f_z}(s ){\hat{\rm e}_z},$$

where f_i(s) and ê_i, i = {x,y,z} are the three-dimensional components of f as a function of the parameter s, and ê_i are the unit vectors related to the three dimensions. For simplicity, consider the case where x ≡ f_x(s) = s, so that f_y(s) ≡ f_y(x) and f_z(s) ≡ f_z(x). Doing so allows designing waveguides that extend along the x direction, while expressing the y and z components of f as a function of x. Having defined the waveguide design coordinates in an $N \times 3$ matrix dataset, the full waveguide design can then be rotated around the z axis by applying a basic rotation matrix. In the following, we propose four parameterizations: two parametrizations to modulate the waveguide shape in the vertical plane and two others for the vertical plane.

3.2.1 Vertical-plane parametric functions: f_z(x)

The vertical plane parameterization defines the waveguide shape along the axial direction. Importantly, it also determines the method of light coupling to the waveguide, which can be categorized into three types: evanescent coupling, butt coupling, and vertical coupling. In terms of waveguide coupler shape, evanescent and butt coupling can be achieved using similar geometries, since both typically occur at planar waveguide segments. We shall refer to both of these coupling types as horizontal coupling. Vertical coupling, however, requires vertical (or oblique) waveguide segments, relative to the substrate plane. Conceivably, a 3D waveguide can be designed for different types of coupling at each end, e.g. vertical coupling from a vertically-emitting device (or a grating) in one end, and evanescent coupling to a planar waveguide on the other end. However, let us focus on a symmetric waveguide design.

Here we propose two f_z(x) symmetric parametric functions, one for horizontal, another for vertical coupling. For the horizontal coupling we use a squared cosine-based function $f_z^{cos2}(x )$

(12)$$f_z^{cos2}(x )= \; \left\{ {\begin{array}{cc} {{R_z}\left( {{{\cos }^2}\left( {\frac{{{\phi_z}}}{{{R_x}}}({x - {x_0}} )} \right)\; - {{\cos }^2}({{\phi_z}} )\; } \right)}&{,\; |{x - {x_0}} |< {R_x}}\\ 0&{,\; \textrm{otherwise}\; \; \; \; \; } \end{array}} \right.,$$

where R_x and R_z define the waveguide length and height. For an oblique waveguide end (rather than a horizontal end) the phase term ${\phi _z} \in \left[ {0,\pi /2} \right[$ can be used to change the coupling angle θ₀, via the cos² slope, albeit non-linearly, since ${\theta _0} = \arctan ({ - 2\sin (\phi )\cos (\phi )} )$, and ${\theta _0} \in [{0,45} ]^\circ $ (relative to the substrate surface). Radian and degree units are used to emphasize the distinction between phase terms and geometrical angles, respectively.

The vertical coupling can be achieved via an ellipsoidal parametrization

(13)$$f_z^{elli}({sx} )= \left\{ {\begin{array}{cc} {{R_z}\sqrt {1 - {{\left( {\frac{{({x - {x_0}} )\cos ({{\theta_0}} )}}{{{R_x}}}} \right)}^2}} - {R_z}\sin ({{\theta_0}} )}&{,\; |{x - {x_0}} |\le {R_x}}\\ 0&0 \end{array}} \right.,$$

where again θ₀ is the coupling angle relative to the substrate surface. Several parameter sweep illustrating the waveguide geometries achievable with both parameterizations can be found in Fig. S3 of the SD.

3.2.2 Horizontal-plane parametric functions: f_y(x)

This work focuses on two illustrative s-bend parameterizations: the sigmoid and the circle arc. The sigmoid is a continuous function that provides the most straightforward definition

(14)$$f_y^{sig}(s )= \frac{{2{R_y}}}{{1\; + \; {e^{ - 2\pi ({x\; - \; {x_0}} )/{R_c}\; }}}} + {y_0},$$

where y₀ is the starting ordinate, x₀ is the curvature center, and R_c and R_y are the lengths along x and y directions. We shall refer to R_y as the curvature amplitude, i.e., the distance along y between the two straight segments of the s-bend. In contrast to the sigmoid parameterization, building a continuous circular arc-based s-bend requires a more complicated branch function

(15)$$f_y^{circ}\left( {x'} \right) = \left\{ {\begin{array}{c} { - {R_c}\left( {1 - \sin {\phi _y}} \right)\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; ,\; \; x' \le - {x_c}\; }\\ { - \sqrt {R_c^2 - {{\left( {x' + {x_c}} \right)}^2}} + {y_c}\; \; \; \; \; \; \;\;\;\;\;\;,\; \; - {x_c} < x' \le 0}\\ {\sqrt {R_c^2 - {{\left( {x' - {x_c}} \right)}^2}} - {y_c}\; \; \; \; \; \; \; \; \;\; \; \; \; \; ,\; \; 0 < x' \le {x_c}}\\ {{R_c}\left( {1 - \sin {\phi _y}} \right)\; \; \; \; \; \; \;\; \; \; \; \; \; \; \;\; ,\; \; \;{x_c} < x'} \end{array}} \right.,$$

where x’ = x – x₀ simplifies the notation, ${x_c} = {R_c}\cos {\phi _y}\; $and ${y_c} = {R_c}\sin {\phi _y}$ are the offsets from the curvature center, and R_c is the circle radius. For a circular arc s-bend, the curvature amplitude is ${R_y} = {R_c}({1 - \sin {\phi_y}} )$, where ${\phi _y} \in [{0,\pi /2} ]$ is the phase term that controls the curvature amplitude. The bending losses in curved waveguides depend on the bend radius and the curvature angle Θ. It can be demonstrated that for the circle arc and sigmoid parametrizations,

(16)$${\mathrm{\Theta }_{circ}} = \pi - 2{\phi _y} = \pi - 2\textrm{asin}\left( {1 - \frac{{{R_y}}}{{{R_c}}}} \right)$$

(17)$${\mathrm{\Theta }_{sig}} \approx 2\textrm{atan}\frac{{\pi {R_y}}}{{{R_x}}}$$

In Section S3 of the Supplement 1 we present the Θ_circ,sig calculation and compare it as a function of the s-bend amplitude. The sigmoid function displays an irregular angle variation, with a curvature angle larger than the circular arc for R_y/R_c ∈ [0.05, 0.81]) and a lower one otherwise (see Fig. S4 of the SD). Since in this work the interval of interest lies within the region where Θ_circ < Θ_sig, the circular parametrization was selected as the preferred one.

The implemented software was equipped with a GUI and several functions that facilitate the design process, such as automatic supporting and tapered structures were included. Figure S5 of the SD shows screenshots of the GUI. For a writing-along-the-trajectory approach, an algorithm that uses discrete unit vectors perpendicular to the waveguide profile allows setting the waveguide width for a constant section area. Fabrication tests with OrmoCore demonstrated that optimal mechanical properties are obtained with a laser fluence F = 20.3 mJ/cm² (P = 18.5 mW). With this information, morphological simulations of the waveguide core section systematically sweeping over the number of line traces per waveguide and the traced spacing showed that 26 traces spaced by 0.3 µm lead to smooth rectangular waveguide sections (further discussed in Sections 3.3 and 3.4). Figure 2(a) shows 3D waveguide design examples based on the $f_z^{elli}$ parametrization for a straight and two s-bend configurations obtained using $f_y^{circ}$. Both s-bend structures have bending amplitudes of R_y = 40 µm but different bending radii R_c of 40 and 80 µm. Figure 2(b) illustrates the three main 3D waveguide building blocks: the waveguide core, light coupling taperings, and support structures. The red lines indicate the writing beam path lines, while the simulated TPP structure surface is shown in gray.

Fig. 2. Two-Photon Polymerization (TPP) structure modeling and 3D waveguide design. (a) 3D waveguide structure design (writing beam path trajectories) identifying the ellipsoid vertical $f_z^{elli}$ and circular horizontal $f_y^{circ}$ parametrizations for various bending amplitudes R_y and bending radii R_c. The line colors indicate the tracing order starting in red and ending in blue. The blue labels identify the three main building blocks. (b) 3D structure surface rendering and waveguide building blocks. The black labels describe structural design

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The photonic taperings for out-of-plane light coupling to the 3D elevated waveguide are designed using hollow cones with circular meshing traced around the waveguide core. The design parameters w_t and l_t define taper bottom width and extension, respectively, while δr_t and δz_t define the horizontal and vertical mesh resolutions, respectively. In Section 3.3 the photonic simulations of the light coupling into the waveguide as a function of w_t and l_t are described.

Depending on the design and material, the 3D waveguides may require support structures for increased stability. The implemented design algorithm automatically defines support structures along the 3D waveguide parametric curve, here rectangular meshed extruded triangles (see Fig. 2(b)). The parameters w_s and l_s define the support structure width and length, respectively, while δxy_s and δz_s define the horizontal and vertical mesh resolutions, respectively. In Section 3.3 and 3.4 the simulation and experimental quantification of waveguiding losses introduced by each support structure is described, respectively.

3.3 Photonic simulations

The 3D renderings allow visualization of the waveguides and furthermore can directly be loaded into the photonic simulation software. Here we study three key aspects: bending losses associated with vertical and horizontal waveguide curvatures and losses introduced by the waveguide itself and the support structures.

Fig. 3. Waveguiding mode-solving simulations of simulated TPP 3D waveguides. (a) Simulated waveguide section profile obtained with the proposed TPP structure simulation algorithm. Fundamental TM waveguiding modes for fixed waveguide design and writing speed but varying laser fluences F = 10.2, 20.3, 40.6 mJ/cm² (powers P = 9.25, 18.5, and 37 mW). Considering a writing speed v_vel = 75 µm/s leads to exposure doses D = 84, 167, 334 mJ/cm². (b-c) Simulated TM multimode waveguide transmission associated with horizontal (b) and vertical (c) bending as a function of the waveguide bending radius, over 90° curvatures.

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Figure 3(a) shows a diagram of the model configuration used to simulate the waveguide optical properties in Lumerical’s MODE solver. The mode solving is performed using the morphological simulations of waveguide segments, using Lumerical’s STL file import functionality. Figure 3(b) shows the morphological simulations and associated fundamental waveguiding TM₀₀ modes for waveguide core segments designed with 26 parallel lines separated by 0.3 µm, assuming a fabrication writing speed of 75 µm/s, and three different laser fluences F = 10.2, 20.3, 40.6 mJ/cm² (P = 9.25, 18.5, and 37 mW), respectively. As expected, if the speed and line spacing are kept constant, the vertical elongation scales with the laser fluence, which will modify the waveguide mode confinement properties. Modifying other design parameters, such as the line spacing or the tracing trajectory (e.g., square wave instead of parallel traces) and writing speeds, could lead to other core geometries. For instance, decreasing either the line spacing or the writing speed (increasing the exposure dose) will lead to narrower and taller structures (see Fig. 1(c)). However, inadequate line spacing and dose combinations could introduce surface roughness (e.g., if the line spacing is too large for a given exposure dose) or detached line traces, leading to severely deformed structures or even structural collapse. As mentioned above and further discussed in Sections 3.4 and 4, experimental tests demonstrated that an optimal balance between the mechanical stiffness and voxel elongation is obtained for a dose D = 167 mJ/cm² for OmoCore, leading to an effective (reproducible) minimum vertical extension of 9 µm. Hence, the D = 84 mJ/cm² core geometry shown in Fig. 3(b) could prove challenging to achieve experimentally, and thus, some prior knowledge of the material’s mechanical properties is essential.

Figure 3(c-d) shows the simulated multimode waveguide transmission as a function of the vertical and horizontal bending radii (Θ = 90°) for the three evaluated design parameter combinations. It can be observed that wider cores increase the bending losses, especially in the vertical direction. For these parameters, the square-sectioned waveguides sustain a minimum bending radius of about 80 µm in both directions.

The waveguide transmission T considering N lossy elements can be generally quantified as

(18)$$T = \mathop \prod \limits_{i = 1}^N {T_i}, $$

where T_i is the transmission associated with the lossy element i. The bend transmission T_b as a function of the curvature angle Θ can be generalized as

(19)$${T_b}(\mathrm{\Theta } )= {T_b}{({90^\circ } )^{\mathrm{\Theta }/90^\circ }}, $$

where T(90°) is the simulated bending loss for a curvature angle of 90°. Eqs. (18,19) shall be used to analyze the experimental characterization of the waveguide transmission properties.

The waveguide incoupling efficiency can be improved using light-funneling tapers. Figure 4(a) illustrates a 3D FDTD simulation (maximum-normalized dB scale) across a tapered waveguide. The tapering performance is analyzed by monitoring the fraction of light coupled to the horizontal waveguide section (vertical output monitor) using a plane wave source with a 20° tipping angle (relative to the substrate normal, aligned with curvature of the waveguide) that matches the experimental characterization configuration. The color and transparency-scale bottom limits are set to -15 dB, matching the light intensity that escaped the waveguide coupler (visualization purposes). Figure 4(b) shows a systematic output for taper widths w_t and lengths l_t varying between 10 and 30 µm. The integrated power (top left corner label) generally increases with the width and remains approximately unchanged by the taper length, except for w_t = 10 and 30 µm, for which the sharp angle imposed at l_t = 10 µm cancels the advantage of having a larger taper area. The taper-free waveguide mode (P = 5.16 nW) and the plotted results of Fig. 4(b) are shown in Fig. S6 of the SD. The [w_t,l_t] [30,20] µm is chosen as the most beneficial compromise between performance, mechanical stability, and fabrication time.

Fig. 4. Finite-Difference Time-Domain (FDTD) simulations of 3D photonic waveguides. (a) 3D FDTD simulation of a bottom incoming plane wave coupling to the 3D waveguide with tapering parameters w_t = 30 and l_t = 20 µm. The electric field intensity I is represented logarithmically relative to the maximum. An output monitor (normalized linear scale) quantifies the amount of light coupled to the waveguide. The black and blue labels describe simulation elements and waveguide structural features, respectively. (b) Systematic characterization of the waveguide output power as a function of [w_t,t_l]. The top-left corner labels indicate the integrated power within the waveguide area. The scale bar is 4 µm wide. (c) 3D FDTD simulation of the losses induced by a 30 × 8 × 60 µm³ support structure, using a waveguiding input mode similar to the output in (a). The power is represented logarithmically using the same normalization reference as (a). The simulations used much higher surface mesh resolutions than shown in (a) and (c), thus chosen for visualization (transparency) purposes.

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Figure 4(c) illustrates the simulation of the losses induced by a 30 × 8 × 60 µm³ support structure. An input mode roughly matching the previously simulated waveguide propagating mode is injected before the support structure (as visible in the vertical monitor Fig. 4(a)). The 3D FDTD simulation illustrates the scattering at the support structure edges, which leads to leakage towards the waveguide surroundings and incoupling to the support structure itself. It should be noted that Fig. 4(a) and (b) share the same normalization reference, meaning that the losses highlighted in (b) are highly contrasted for visualization purposes. The inset images show input and output waveguiding modes revealing a 5.3% intensity loss per support structure. Both surface rendering and photonic simulations were crucial to obtaining the final waveguide designs, whose fabrication and experimental characterization are reported in the following section.

3.4 Fabrication and characterization

The proposed simulation algorithm provides a key starting point on the design and fabrication parameters. This section reports the simulated and fabricated structures and the optical characterization of the waveguide transmission depending on the number of support structures (straight waveguides) and bending radius (curved waveguides). Figure 5 compares full-structure morphological simulations with SEM images of the experimental realizations. Figure 5(a) shows the line-trace design of an $f_z^{cos2}$-parameterized waveguide with hollow support structures. The red-yellow-green-blue line color gradient represents the tracing order, where red lines are traced first and blue ones last. Figure 5(b) shows the full-structure simulation obtained with the proposed morphological prediction method, considering a laser power P = 18 mW, corresponding to a fluence F = 20 mJ/cm². Considering also the writing speed v_vel = 50 µm/s leads to an exposure dose D = 244 mJ/cm². Figure 5(c) shows the Scanning Electron Microscopy (SEM) image of the fabricated structure. Besides their overall shape, the simulated and fabricated structures can be compared in terms of the simulations’ ability to accurately reproduce the voxel elongation in the central trace (waveguide core), the surface features (roughness) of the support structure faces, the appearance of deformations (such as wrinkles, surface bending, torsion, and shearing), and structural stability or breakdown in the latter.

Fig. 5. Design, morphological simulation, and fabrication of $f_z^{cos2}$-parameterized waveguides with hollow support structures via Two-Photon Polymerization (TPP) 3D microprinting. (a) Structure design (writing beam path trajectories). (b) Morphological simulation using a fluence F = 20 mJ/cm² (per pulse) and a writing speed v = 50 µm/s, thus leading to an exposure dose D = 244 mJ/cm². (c) Scanning Electron Microscopy (SEM) image of the fabricated structure in OrmoCore. (d) Systematic sweep over the laser fluence and writing speed, comparing the simulation (left) and experimental fabrication (right) results. The inset labels represent the exposure dose D(F,v) shared by the corresponding simulation and fabrication counterparts. The colors highlight structures obtained using a similar dose. The laser, optical setup, and polymer parameters are for all structures reported in this manuscript and can be found in Section 2.

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The examples highlighted in Fig. 5(b-c) were chosen for their remarkable agreement in all parameters. However, Fig. 5(c) shows support structure surface deformations that are not reproduced in the simulations due to the absence of mechanical strain information in the morphological model. Figure 5(d) compares the simulation (left) and fabrication (right) results as a function of laser power (fluence F) and writing speed. The colored labels indicate structures obtained with an equivalent exposure dose D. An overall agreement is observed for high laser fluences and lower writing speeds (F ≥ 15 mJ/cm², v_vel ≤ 25 µm/s) with all parameters accurately reproduced. However, for decreasing laser fluence and increasing writing speed, the polymerization density reduces. The simulations present small fissures in the support structure surface but fail to reproduce the lack of structural integrity observed in the fabricated structures, leading to strong deformations, support structure folding, and structural collapse. Furthermore, the fabrication results reveal how the mechanical stability of the exposed polymer depends strongly on the laser power. The red labels show the most contrasting scenario of same-dosed structures written with the minimum and maximum laser powers. The former is completely collapsed, while the latter is structurally robust.

Figure 6 shows SEM images of fabricated TPP structures with different designs. Figure 6(a) shows four example $f_z^{cos2}$ designs (horizontal coupling) as a function of support structure number and gap length. The structures are stable with support structures as small as 17 µm long and gaps up to 100 µm with a negligible waveguide curvature change. Figure 6(b) shows a top view of the systematic fabrication of 3D $f_z^{elli}$ (vertical coupling) waveguides with bending radii varying between 50 µm and 500 µm ($f_y^{circ}$-parameterized). Figure 6(c) and 6(d) show examples of straight and bent, respectively.

Fig. 6. Scanning electron microscopy (SEM) images of two-photon polymerization (TPP) fabricated structures. (a) Single-trace $f_z^{cos2}$-parameterized waveguides on hollow support structures, sweeping over the support structure and gap length. (b) Top-view SEM image of systematic fabrication of $f_z^{elli}$-parameterized bent waveguides ($f_y^{circ}$) with bending radii varying from 50 to 500 µm in steps of 50 µm, from the left to the right. (c-d) Perspective views of straight (c) and bent ($f_y^{circ}$) (d) $f_z^{elli}$-parameterized waveguides on meshed support structures.

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The 3D waveguides’ optical transmission is characterized experimentally using a custom-built setup in Fig. 7(a). The sample is probed in an inverted configuration, where a microlensed optical fiber focuses the laser light (λ = 830 nm) into the waveguide input. An optical microscopy system quantifies the waveguide output intensity from a top view. An example readout measurement is shown in the bottom inset of Fig. 7(a). From left to right, the first bright spot corresponds to the optical fiber probe, followed by three bright spots from support structure light scattering. The rightmost bright spot corresponds to the waveguide output.

Fig. 7. Experimental characterization of 3D waveguide transmission. (a) Characterization setup schematic and (inset) example of top-view intensity measurement for a vertical radius R_z = 45 µm and the number of Support Structures N_SS = 8. Laser wavelength λ = 830 nm. (b) Log plot of the output intensity as a function of the number of support structures for R_z = {45, 60, 90} µm. The inset shows a Scanning Electron Microscopy (SEM) image of the fabricated R_z = 90 µm sample. (c) Plot of the normalized output intensity as a function of the bending radius for a fixed amplitude R_y = 50 µm

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Figure 7(b) plots the optical transmission of variable-length 3D waveguides with equally spaced support structures (see top-right inset SEM image). Apart from the input and output structures, which are the same for all waveguides and can therefore be neglected in this relative comparison, the geometry of straight waveguides can be approximated as straight constant-sectioned segments separated by support structures. Given the high refractive index contrast between OrmoCore and air, the transmission losses associated with the straight, unsupported waveguide segments are relatively low for the lengths at study. Meanwhile, the sudden section variations at the support structure sites introduce intense scattering hotspots. Hence, we consider the support structures the primary sources of loss and neglect the waveguide length variation, plotting Fig. 7(b) solely as a function of the number of support structures. This assumption allows estimating the (exponential) loss per support structure by calculating the slope of the transmission curves. The characterization was carried out for 3D waveguides fabricated with the same writing speed (75 µm/s) and laser power (18.5 mW) parameters (D = 67 mJ/cm²), three different heights R_z = {45, 60, 90} µm, (2/3) R_z× 8 × R_z µm³ support structures, and otherwise analogous $f_z^{elli}$ designs. The losses of each support structure scale with the waveguide height, with R_z = 45, 60, and 80 µm showing losses of 0.454, 0.640, and 0.925 dB/SS, which translates into 9.16, 13.7, and 19.2% per SS, respectively.

Figure 7(c) shows the characterization of the bending losses in $f_y^{circ}$-parameterized 3D waveguides with R_y = 50 µm for all structures, as a function of the horizontal bending radius R_c ranging from 37.5 to 400 µm. The transmittance is estimated by measuring the waveguide output intensity normalized by the average intensity for R_c ≥ 150 µm, resulting in a few experimental values larger than one. The experimental measurements are compared against the simulations from Fig. 3(b). The curvature angle variation between the different structures is eliminated using Eq. (18), i.e., calculating T_b(90°) from the measured T_b(Θ) (Fig. S8 of the SD plots examples of the Θ(R_c,R_y)-dependent correction). Similar to the analysis in Fig. 7(b), the slight length variations can be neglected, and the input and output losses are the same for all structures and thus ignorable. The experimentally characterized transmission decays more prominently for R_b < 100 µm than the simulated D = 67 mJ/cm² curve. Nevertheless, the transmission behavior agrees well with the simulations.

4. Discussion

This work proposes a simple Gaussian-beam method to predict the 3D structure shape based on cumulative two-photon polymerization. While similar principles were used before to analyze single and double-voxel geometries [31], here it is proposed for the first time in the context of full-structure morphological simulations that take instrument and optical parameters into account. This allows simulating photonic properties of structures that match the experimental realization with high precision. The morphology predictions consider a linear correction to compensate for the focus length distortion effect induced by the air-glass refractive index mismatch in the case of an air objective. Previous works have analyzed this distortion effect, observing the Light-Induced Damage Threshold (LIDT) and voxel length increase and decrease changing approximately linearly with the laser focus depth [34,35]. The presented model considers a constant voxel length distortion factor (Eq. (10)), but Section S2 of the SD presents a straightforward approach to include a linear depth dependence. Nevertheless, the SEM images of the fabricated structures indicate that even the most simplified approach provides excellent 3D morphology predictions.

The proposed method provides a massive advantage compared to systematic experimental optimization, reducing lab working time, materials, and femtosecond laser equipment utilization. However, the model does not contemplate all physical phenomena, which partly explains the mismatch between modeled and fabricated structures in Fig. 5(d). It is known that the laser power influences the post-exposure polymer mechanical properties, with higher laser power leading to higher polymer rigidity in same-exposure-dosed structures [32]. This effect results from the more efficient polymer cross-linking at higher powers, leading to larger Young’s moduli and thus better mechanical stability. Furthermore, high power can burn or boil the polymer at the laser focus. Structure shrinkage and other mechanical instabilities resulting from the sample development step are also not considered here. This can be observed particularly in Fig. 5(d) for structures fabricated with high writing speed and low laser power (fluence). For such combinations, the polymerized structure lacks structural integrity and collapses during the development stage. However, the model fails to recognize this effect and shows unrealistic still-standing structures. Therefore, some prior knowledge of the polymer specifications is still required. Other simulation errors can be observed at very low laser powers and writing speeds, where the cumulative energy deposited during the slow-motion writing leads to an over-estimation of the polymerized volume. In reality, the low pulse energy leads to a tiny polymerization voxel, which may not be enough to generate a coherent structure despite the large exposure dose. Furthermore, very low laser powers lead to low rigidity and thus poor mechanical stability. As a result, Fig. 5(d) shows that even though some polymerization occurs, the structure lacks mechanical robustness and collapses, which the model does not take into account. Hence, the accuracy of the proposed model’s morphological predictions can be optimized by a prior calibration of the adequate laser power and writing speed according to the material specifications. Still, the proposed method is far more comprehensive than previous attempts to render TPP structure surfaces based on the stacking of solid ellipsoid [32] or cigar-shaped voxels [29], which serve as mere visualization methods and cannot be used for performance simulations. Future works might include Finite-Element Analysis (FEA) simulations to analyze surface tension and resulting deformations of the rendered structures [36]. Finally, the proposed model neglects the possible presence of (linear) thermal effects that could lead to polymerization alongside the nonlinear TPP [37]. Thermal effects are particularly relevant at high repetition rates (higher than the thermal relaxation rate, which leads to thermal accumulation), high laser fluence, and long pulse durations. This work, however, is developed primarily in a low-power regime. Our maximum experimental fluence F_max = 20.3 mJ/cm² and pulse length τ = 80 fs are both far below the 200–5000 mJ/cm² and 8-25 ps reported in Ref. [37]. Furthermore, our typical exposure dose D = 167 mJ/cm² is one order of magnitude below the 1000-3000 mJ/cm² suggested in OrmoCore’s manufacturer processing guidelines. Therefore, we neglect the occurrence of thermal effects in this work. Recent works have demonstrated that defining the polymerization processes in terms of the energy density (J/cm³), rather than fluence, can account for the decreasing depth of energy deposition into the skin depth at the focus, regardless of the absorption nonlinearity [38].

The proposed 3D waveguide design method is based on parametric curves that can be defined analytically or via discrete point interpolations. Writing along the trajectory can provide high fidelity structures with smooth waveguide surfaces but is only applicable to gel-like polymers such as OrmoCore that withstand movements during the lithography step, otherwise, the single writing lines detach and introduce severe surface roughness [10]. Sliced writing methods are better suited for liquid polymers but decrease the design accuracy and lead to surface heterogeneities that might need to be corrected by an extra contour trace, thereby increasing the minimum structure size. Helix slicing along thin waveguide trajectories can be particularly challenging for motorized stages with limited angular acceleration and thus significantly increase the writing time. The experimental optimization stages of this work comprised TPP fabrications tests using different materials: 1) SZ2080 showed good mechanical properties, but the use of photoinitiators makes it too optically absorbent; 2) EpoCore shows no signs of TPP using our laser settings; 3) OrmoComp showed optimal mechanical properties, but a refractive index lower than the microscope coverslip substrates, preventing mode guiding in planar waveguides; 4) OmorCore revealed sub-optimal mechanical properties but high refractive index. Still, OrmoCore proved viscous enough to support writing along the trajectory. Hence, we use this simplified method for the waveguide core tracing and different meshing types, densities, and writing speeds for the filled elements (support structures and tapers) in OrmoCore. Ideally, future works should consider alternative optically clear, mechanically stable materials, such as IP-S, IP-Dip, [39], and SU8 [40].

The optical interconnection between optical elements can be achieved mainly through horizontal or vertical coupling (according to the conventions from Section 3.2.1), depending on the device emission or light guiding profile. This work proposes parametric curves for both scenarios but focuses mainly on vertical coupling, which, for several reasons, can be the more challenging to implement experimentally. Such challenges include the limited microscope objective working distance, structure instability, and various distortion effects. In particular, the support structures lead to waveguide profile heterogeneities due to microlensing and scattering effects during the writing, which are more pronounced in the meshed case. Such heterogeneities scale with the 3D waveguide height since larger support structures induce increased lensing effects, as shown in Fig. 7(b). Future works could avoid the stitching errors (small but noticeable in Fig. 7(a,d)) using the continuously-synchronized stage implementation reported in Ref. [16].

Performing the waveguide trace before the support structures reduces these issues, but this can only be done if the polymer viscosity is high enough so that the unsupported waveguide traces can withstand powerful micro-positioner vibrations during the support structure tracing. Using this approach in OrmoCore led to severe structural distortion and was discarded. Inverting the sample and design might be a good strategy to mitigate this problem. However, it might cause the polymer to drip onto the microscope objective or create an irregular polymer thickness profile (e.g., elongated droplet) that changes working distance throughout the sample, leading to highly distorted structures. Spin-coating the polymer on the substrate is also challenging given the large thicknesses used (up to 100 µm) that introduce challenges in the spin-coating process and promote considerable material wastage.

The vertical voxel elongation can lead to irregular waveguide core widths depending on its slope. Strategies similar to the parallel line tracing used to widen the waveguide design can compensate the core height as a function of the design slope.

In terms of waveguiding performance, discrete support structures introduce sudden waveguide profile variations, leading to scattering losses and mode perturbations. Such scattering losses can be reduced by minimizing the contact area between the waveguide core and the support structure, for which we identify three strategies: 1) using hollow support structures; 2) reducing the structure length along the propagation direction; and 3) avoiding overexposure regions at welding points,e.g., by increasing the designed distance between the upper support structure trace and the waveguide. However, all three strategies reduce the mechanical stability of the structure. Ultimately, support structure minimization will be highly dependent on the mechanical properties of the polymer. Continuous support structures could constitute an alternative for reduced scattering hotspots. However, this approach reduces the mode confinement (light can leak towards the support structures), significantly increases the writing time, and severely hinders the waveguide overlapping, making it unsuited for interconnection applications.

The experiments reveal significantly larger losses from the support structures (see Fig. 7(b)) than the simulation predictions (see Fig. 4(c)), indicating that the simulations do not fully reproduce the surface roughness and heterogeneities around the support structures. Also, the 3D FDTD simulations considered a single propagation mode, which can overlook contributions from additional modes coupling to the support structures. Still, and despite not having been systematically analyzed, the simulation provided reasonable order of magnitude prediction. The number of support structures should therefore be minimized, according to the polymer rigidity specifications.

Despite the referenceless (unknown input power) waveguide transmission characterization method employed, which leads to the fluctuations around T = 1 observed in Fig. 7(c), the experimental results display a good agreement with the simulated curves, albeit with some discrepancy. The lower experimental transmission compared to the simulations (see Fig. 3(b)) can be explained by core elongations (e.g., due to a higher laser power than the intended 18.5 mW) or other experimental loss sources overlooked by the simulations, such as surface roughness and characterization probe misalignment. It should be noted that while the comparative characterization method employed proved sufficient to gauge the losses introduced by support structures and bends, it fails to provide an absolute reading of the transmission. Obtaining such information would require an exact characterization of the coupling efficiency between the input fiber and the waveguides, which is challenging to achieve in the present characterization configuration. Future works should consider calibrated characterization systems to monitor, for instance, the coupling efficiency between a reference planar waveguide and the 3D ones, where the coupling efficiency between the input fiber and the reference waveguide is known.

It is important to notice that all design, fabrication, and characterization tools were custom-made, thus enabling a flexible 3D microprinting solution. This paper reports the methods employed so that a broader range of researchers can access the proposed 3D photonic interconnection technology. However, most of the structure heterogeneities discussed here are efficiently avoidable in high-fidelity commercial TPP platforms such as Nanoscribe that resort to dip-in objective technology, eliminating most refractive index mismatch and dripping polymer issues. The proposed simulation method becomes even more relevant for such systems since the simulated surfaces are fabricated with higher reproducibility, and the morphology of the simulated structures is more closely related to the fabricated ones.

Future work beyond this proof-of-concept study could focus on strategies to characterize and reduce the 3D couplers’ insertion loss. The simulations from Fig. 4(b) demonstrate the ability to couple light from an optical fiber (through the glass substrate) into the 3D waveguides. Since the fiber field is modeled as a plane wave injected from the substrate, it is not surprising that the systematic taper parameter sweep shows larger power collections for larger taper base diameters. However, a more careful numerical analysis of the insertion losses would require a better knowledge of the fiber field profile. Such knowledge would allow the taper geometry optimization to minimize back reflections, e.g., via the tapering angle. Experimental insertion loss characterizations would require a calibrated optical setup employing, for instance, the procedure described in Feldmann’s recent work from Ref. [7], which reports experimental insertion losses of about -1.5 dB in broadband 3D polymeric couplers.

The proposed design and surface simulation tools may find applications in vast TPP-based 3D systems that require precise structure shape predictions. Such include polymeric micromachines, micro-scaffolds for biological cell mobility studies, and other polymeric photonic elements. The proposed parametric curve, support structures, and taper designs can interconnect many PIC devices, becoming particularly interesting for systems requiring complex inter-device interconnections, such as photonic neural networks.

5. Conclusion

This work proposes a method to predict the 3D morphology of TPP-written structures based on the physical parameters of the microfabrication setup such as the laser power, microscope objective numerical aperture, use of oil immersion; as well as material parameters, such as the TPA cross-section, photo initiator concentration and TPP threshold. The simulations agree with the theory and provide versatile structure predictions. We demonstrate how a custom-build TPP 3D microprinting station can be obtained using a multi-photon fluorescence microscope instrumentation. Parametric curve-based designs are proposed for 3D waveguides for the photonic interconnection on-chip devices, including support structures and light funneling tapers. The parametrizations directly translate into laser tracing trajectories, allowing fine structure tuning and excluding the need for (and the error introduced by) 3D slicing software. Optimization protocols based on variation approaches, where writing parameters are systematically varied and results compared until the optimal writing parameters, are found to require longer writing times and may lead to excessive material usage. Here, FDTD and mode propagation simulations using the simulated structure surfaces enable waveguide performance predictions and design optimizations, thereby potentially reducing the optimization costs.

The experimental optical characterization of the waveguide bending losses displays a good agreement with the simulations. The observed discrepancies are expected to be reduced in high-fidelity commercial TPP systems, for which the surface simulations provide more accurate predictions. The developed design and simulation tools can be used for any TPP application. However, the developed design functions are particularly relevant for PIC 3D photonic interconnections, such as in photonic neural networks.

Funding

European Commission (H2020-FET-OPEN No. 828841 “ChipAI”); ERDF INTERREG V-A España-Portugal (POCTEP) (2014–2020 0181_NANOEATERS_1_EP).

Acknowledgments

We thank Beatriz Costa for testing the developed simulation and microfabrication techniques, and Filipe Camarneiro for support on Python device control implementation. This work benefitted form the access to and support by the Nanophotonics and Bioimaging, the Nanofabrication and the AEMIS Research Core facilities of INL. RA acknowledges the Laser Photonics & Vision Ph.D. program, U. Vigo.

Disclosures

The authors declare no conflicts of interest

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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Two-photon polymerization simulation and fabrication of 3D microprinted suspended waveguides for on-chip optical interconnects

Abstract

1. Introduction