The basic concepts of 3D-printed PBSs and PRs in integrated optical assemblies are illustrated in Fig. 1. This device connects a rotationally symmetric SMF with degenerate polarisation states to a highly polarisation-sensitive photonic integrated circuit. As an example, we illustrate a dual-polarisation receiver assembly for coherent communications in which data signals in orthogonal polarisation states of the SMF are split and independently detected using a pair of coherent optical receivers (Coh. Rx), which are fed by a joint local oscillator (LO). PBS/PR can be merged with additional 3D freeform waveguide elements, such as mode-field adapters, into a single monolithic structure. This structure can be fabricated in a single exposure step using high-resolution 3D-laser lithography that exploits multiphoton polymerisation in the focus of a pulsed femtosecond laser beam14. Fabricating the structure in situ onto readily positioned devices offers the freedom to adapt the geometry of the 3D-printed structures to the exact positions of the corresponding optical facets, thereby overcoming the need for high-precision mechanical alignment of the fibre with respect to the chip19,20,25,26. The assembly illustrated in Fig. 1 represents only one example of how 3D-printed polarisation-manipulating elements can be used in integrated optics. In general, structures can be printed on a wide range of optical devices, covering applications ranging from optical communications and signal processing27,28 to optical metrology29, imaging30, and quantum optics31.
The basic principle of our 3D freeform waveguide-based PBS is illustrated in Fig. 2. Fig. 2a depicts a 3D rendering of an exemplary device implementation, comprising an input waveguide port with a circular cross-section and a pair of output waveguide ports with rectangular cross-sections of a high aspect ratio. As explained in more detail, the separation of orthogonally polarised modes at the input port is accomplished by first transforming the circular cross section at the input port into a cross-shaped cross section formed by the superposition of the two high-aspect-ratio rectangular cross sections of the output waveguides. These initially overlapping partial waveguides are then separated adiabatically, thereby dragging the differently polarised modes to spatially separated output ports. In the following, the input port is denoted by superscript (I), whereas superscripts (H) and (V) refer to the output ports with horizontally and vertically oriented rectangular cross-sections, as shown in Fig. 2a. As an important feature of our PBS, we aimed to ensure identical behaviour of the two output ports H and V, and we therefore designed the PBS to have a geometrically symmetric structure with respect to a mirror plane that contains the axis of the input waveguide and is oriented at an angle of 45° with respect to the horizontally and vertically oriented rectangular waveguide cross-sections in the output plane, see Inset 1 of Fig. 2a. Note that the device is fully bidirectional and can also be used as a polarisation beam combiner, where the two rectangular waveguide ports H and V are used as inputs, whereas the circular port I acts as the output.
For a more detailed discussion, we subdivide the PBS into three segments, denoted by A, B, and C, where Segment A is directly adjacent to the input port. Owing to its circular cross section, the input port has two degenerate fundamental modes of orthogonal polarisations with identical effective refractive indices neff. Without loss of generality, we select two basis modes at the input with the dominant transverse component of the electric field aligned in the vertical and horizontal directions, as defined by the two output ports, and denote them as $ {E}_{H}^{\left(I\right)} $ and $ {E}_{V}^{\left(I\right)} $ respectively, as shown in the first row of Fig. 2b for the associated mode-field distributions. Within Segment A, the circular cross section at the input port is adiabatically morphed into a cross-shaped cross section at the transition to Segment B. At this transition, the waveguide can be represented by two spatially overlapping partial waveguides, WGH and WGV with high-aspect-ratio rectangular cross-sections. Owing to the adiabatic transition from a circular cross section to a cross-shaped one in Segment A, the two degenerate basis modes, denoted as $ {E}_{H}^{\left(I\right)} $ and $ {E}_{V}^{\left(I\right)} $ are transformed into the strongly guided modes of these rectangular partial waveguides. In this context, the term ‘strongly guided’ denotes the mode of a rectangular waveguide with its dominant transverse electric field component polarised along the long side of the rectangle. This mode exhibits a higher effective refractive index than its weakly guided counterpart, which is polarised along the short side of the rectangular waveguide core. In Segment B, partial waveguides WGH and WGV are gradually separated, dragging the corresponding strongly guided eigenmodes into two distinct waveguides at the input of Segment C.
Within Segment C, the two distinct output waveguides can be adiabatically tapered and bent to suppress unwanted higher-order modes and route the waveguides to the two output ports V and H. Furthermore, 3D-printed freeform waveguide structures can be directly connected to these output ports, for example, for polarisation rotation, see Fig. 1. The second and third rows of Fig. 2b show various mode-field profiles at the output, where $ {E}_{H}^{\left(V\right)} $ refers to the horizontally and $ {E}_{V}^{\left(V\right)} $ to the vertically polarised modes at the vertical output V, whereas $ {E}_{V}^{\left(H\right)} $denotes the vertically and $ {E}_{H}^{\left(H\right)} $ the horizontally polarised mode at the horizontal output H. In an ideal device, the powers of the degenerate $ {E}_{H}^{\left(I\right)} $ and $ {E}_{V}^{\left(I\right)} $ modes are completely coupled to the strongly guided modes $ {E}_{H}^{\left(H\right)} $ and $ {E}_{V}^{\left(V\right)} $, whereas the weakly guided modes $ {E}_{H}^{\left(V\right)} $ and $ {E}_{V}^{\left(H\right)} $are not excited.
The exact dimensions of the PBS structure shown in Fig. 2a were finally obtained from the numerical simulations. For good performance, the aspect ratio of the rectangular cross-sections of the partial waveguides in Section B should be as high as possible while maintaining compatibility with the resolution of the 3D printing system. In the simulated structure, the short side of the rectangular cross section was chosen to be $ {w}_{\mathrm{s}\mathrm{h}}=400\;\mathrm{n}\mathrm{m} $ based on the resolution of the underling lithography system, see Materials and Methods, whereas the long side varies in the range $ {w}_{\mathrm{l}\mathrm{o}}=$1.2−2.2 µm along the propagation direction. The exact shapes and lengths of the various waveguide sections were obtained by numerical optimisation, where the main goals were to maximise the transmission and PER while keeping the overall PBS structure as small as possible. During this optimisation, we designed the exact trajectories of various freeform waveguides, the trajectories of which were modelled using kink-free B-splines. The resulting length of the structure including all three segments amounts to $ L=21\; {\text {µm}} $. The overall design is reasonably robust with respect to variations in various geometric parameters, thus rendering the PBS concept amenable to high-throughput mass production by in situ laser printing (see Supplementary Information, Section S6).
In Fig. 2a, we illustrate the magnitude of the E-field within the device for operation at a wavelength of 1550 nm for horizontal polarisation at the input. The E-field distribution for vertical input polarisation is obtained by reflection about the symmetry plane. To describe the coupling between various modes at the input and output ports, we used the complex-valued scattering parameters (S-parameters) SIJ. In this description, SIJ refers to the amplitude transmission from $ J $ to $ I $ where $ I,J\in \left\{{E}_{H}^{\left(I\right)},{E}_{V}^{\left(I\right)},{E}_{H}^{\left(H\right)},{E}_{V}^{\left(H\right)},{E}_{H}^{\left(V\right)},{E}_{V}^{\left(V\right)}\right\} $ denote the various modes at the ports of the device. The results for the various simulated power-coupling coefficients, which are obtained by squaring the magnitudes of the corresponding S-parameters, are shown in Fig. 2c. Evaluating the power transmission $\big| $S${}_{{E}_{H}^{\left(H\right)}{E}_{H}^{\left(I\right)}}\big|^{2}=\big|$S${}_{{E}_{V}^{\left(V\right)}{E}_{V}^{\left(I\right)}}\big|^{2} $ from the input to the desired mode of the respective output port, we find an insertion loss of less than 2 dB over the entire wavelength range between 1250 nm and 1650 nm, with a minimum of 1.55 dB near 1550 nm, see green line in Fig. 2c. For each polarisation at the input port, we further extract the power that is coupled to the undesired mode at the corresponding ‘correct’ output port, which is quantified by the crosstalk $\big| $S$ {}_{{E}_{V}^{\left(H\right)}{E}_{H}^{\left(I\right)}}\big|^{2}=\big| $S${}_{{E}_{H}^{\left(V\right)}{E}_{V}^{\left(I\right)}}\big|^{2} $ and which is below –22 dB throughout the simulated wavelength range, see blue line in Fig. 2c. This crosstalk can be suppressed by subsequent polarisation filtering. We further calculate the power coupled to the desired output modes $ {E}_{H}^{\left(H\right)} $ and $ {E}_{V}^{\left(V\right)} $ from the ‘incorrect’ input modes $ {E}_{V}^{\left(I\right)} $ and $ {E}_{H}^{\left(I\right)} $, respectively, which cannot be suppressed by subsequent polarisation filters. This unfilterable crosstalk, $\big| $S${}_{{E}_{H}^{\left(H\right)}{E}_{V}^{\left(I\right)}}\big|^{2}=\big| $S${}_{{E}_{V}^{\left(V\right)}{E}_{H}^{\left(I\right)}}\big|^{2} $ is represented by the red line in Fig. 2c and is below –25 dB throughout the 400 nm-wide wavelength range of interest. We also extract the polarisation leakage $\big| $S${}_{{E}_{H}^{\left(V\right)}{E}_{H}^{\left(I\right)}}\big|^{2}=\big| $S${}_{{E}_{V}^{\left(H\right)}{E}_{V}^{\left(I\right)}}\big|^{2} $, which quantifies the power coupled to the undesired polarisation at the ‘incorrect’ output port for a given polarisation at the input port, thus maintaining its polarisation direction. For our structure, the polarisation leakage is below –17 dB throughout the simulated wavelength range, see orange line in Fig. 2c, and can be further suppressed by subsequent polarisation filters. Finally, we extracted the PER, that is, the ratio of the maximum and minimum powers observed in both modes of an output port when varying the excitation at the input over all possible polarisation states. For each output port, the PER can be obtained from the singular-value decomposition of the corresponding Jones matrix (see Supplementary Information Section S3 for details). We found that the PER was better than 16 dB within the investigated wavelength range and showed a strong increase towards longer wavelengths. Note that the PER and polarisation leakage are better than 30 dB over the wavelength range of 1250–1365 nm, and that this high-performance wavelength range can be shifted by adapting the design of the structure. Note also that, for practical applications, 3D-printed waveguides commonly need to be overclad by an additional material that may serve as mechanical support and environmental protection. However, the presence of the cladding material might require some design adaptations to deal with the associated changes in the refractive index contrast (see Supplementary Section S1), which also includes a more detailed discussion on the fabrication tolerances and robustness of the PBS and the PBS and PR designs in the presence of process variations.
To experimentally prove the viability of our concept, we fabricated a series of 3D-printed PBS that are directly connected to the cores of SMFs. We characterise the performance of these devices and use them as part of a receiver in a polarisation-division multiplexing (PDM) data transmission experiment.
In the first experiment, we fabricated a series of free-standing PBS on the facets of an SMF array and measured their performance using an infra-red (IR)-sensitive microscope IR microscope), see Fig. 3a. To ensure low-loss coupling to the SMF core, the structures were equipped with adiabatic mode-field adapters attached to Segment A of the PBS. A scanning electron microscope (SEM) image of the PBS and the mode-field adapter is shown in Fig. 3b. Light was fed to the SMF by a laser emitting at a wavelength of $ \lambda =1510\;{\rm{nm}} $, and a subsequent polarisation controller. At the two PBS outputs, light was radiated into free space and detected by an IR microscope. The centres of the white circles in the images in Fig. 3c match the centres of the corresponding PBS output ports, and the areas of the circles denote the areas that were considered in calculating the corresponding power levels. In the first set of measurements, we showed that the radiated light could be switched between the two output ports of the PBS by varying the polarisation at the input, see Column 1 of Fig. 3c. Specifically, Subfigures 1.1 and 2.1 refer to the cases where the polarisation controller was adjusted for maximum radiation from output ports V and H, with vertically and horizontally oriented waveguide cross-sections, respectively.
In both cases, we measured the ratio $ \Gamma $ of the optical power at the targeted output port to the residual power emitted at the respective other output port, which amounts to 9.8 dB and 9.7 dB, respectively. We also adjusted the input polarisation to yield equal power at both ports, see Subfigure 3.1 in Fig. 3c. To check the polarisation states of the light radiated from the two outputs, we repeated the experiment with a vertically and horizontally oriented polarisation filter (PF) between the microscope objective and the IR camera, as shown in Columns 2 and 3 of Fig. 3c. The PF has an extinction ratio greater than 34 dB. Assuming an excitation with pure vertical polarisation in Row 1 of Fig. 3c, the vertically oriented PF in Subfigure 1.2 suppresses the spurious horizontal polarisation at Port V, which corresponds to the crosstalk S${}_{{E}_{H}^{\left(V\right)}{E}_{V}^{\left(I\right)}}$, and the spurious horizontal polarisation at Port H, which represents the unfilterable crosstalk S${}_{{E}_{H}^{\left(H\right)}{E}_{V}^{\left(I\right)}} $. The measured power ratio $ \Gamma $ of the emitted light after the PF amounts to 12.1 dB and corresponds to the ratio $\big| $S$ {}_{{E}_{V}^{\left(V\right)}{E}_{V}^{\left(I\right)}}\big|^{2}\big/\big| $S${}_{{E}_{V}^{\left(H\right)}{E}_{V}^{\left(I\right)}}\big|^{2} $ of the power transmission at Port V and the leakage at Port H. The measured ratio is smaller than approximately 18 dB expected from the simulation results, see Fig. 2c. We attribute these deviations to the geometrical inaccuracies of the fabricated structures. In Subfigure 2.2, the polarisation controller is adjusted for the maximum radiation from output H, but the PF is oriented vertically such that only spurious horizontal polarisations at both outputs, $\big| $S${}_{{E}_{H}^{\left(H\right)}{E}_{V}^{\left(I\right)}}\big|^{2} $ and $\big| $S${}_{{E}_{H}^{\left(V\right)}{E}_{V}^{\left(I\right)}}\big|^{2} $ can be seen on the IR camera. As expected, the camera image does not exhibit significant power. In Subfigure 3.2, where light exits both the output arms of the PBS, the light radiated from Port H is completely suppressed by the vertically oriented PF, whereas the light radiated from Port V does not experience significant attenuation. The same experiment was repeated with a horizontally oriented PF, see Column 3 of Fig. 3c, thereby reproducing the findings described for the data in the second column. This simple experiment demonstrated that the device works qualitatively as expected.
In the second experiment, we tested our PBS structures by measuring the PER over a broad range of wavelengths. To this end, the polarisation at the input of the structure was varied randomly using a polarisation scrambler, while the Stokes vector and power at the device output were continuously recorded using a polarimeter (see Supplementary Information Sections S2–S4). The measurement was repeated for each output port to reveal the output polarisation state of the maximum and minimum power transmissions as well as the associated PER. The PBS test structure used in this experiment was again 3D-printed on the facet of an SMF array connected to a polarisation scrambler. At the output, the structure was equipped with a pair of PRs realised by rectangular waveguides twisted along the propagation direction32,33. Twisting one waveguide by +45° and the other by –45° thus leads to identical polarisations at both output ports, see Fig. 1 and Fig. 4a. For better probing of the output, the structure was equipped with adiabatic mode field adapters held by a table-like mechanical support structure, as shown in Fig. 4a. Hence, the output ports can be individually read out by an SMF (see Supplementary Information, Section S2, for details on the experiment). We obtained a measured PER better than 11 dB in the wavelength range of 1270–1620 nm, which was limited by the tuning range of the underlying laser sources (see Fig. 4b). The measured insertion losses at 1550 nm for Output I and Output II correspond to 4.4 dB and 3.8 dB, respectively, including the loss of the PBS, of the subsequent PR, and of the adiabatic mode-field adapters see Fig. 2c. A more detailed comparison of the measurement results and simulations is provided in Supplementary Information, Section S2.
To demonstrate the technical viability of the 3D-printed PBS, we performed a polarisation-division multiplexing (PDM) data transmission experiment that emulates the application scenario illustrated in Fig. 1. The experimental setup and results are shown in Figs. 4a, c, d. Details of the experimental setup can be found in Supplementary Information, Section S5. The experiment relied on a PBS/PR combination, as used in the previous experiment, complemented by an additional fan-out structure, see Fig. 4a. This fan-out structure is 3D-printed on a second fibre array and allows to simultaneously couple both PBS outputs to a pair of outgoing SMF with a standard pitch of 127 µm. The fan-out structure is equipped with two lenses with a pitch of 25 µm that pick-up light from the two PBS outputs, followed by a pair of total-internal-reflection (TIR) mirrors in each path to adjust the lateral offset of the beams at the output. At $ \lambda =1550\;\mathrm{n}\mathrm{m} $, the measured insertion losses of the two channels of the fan-out are 1.2 dB and 1.9 dB, with a crosstalk between channels below –46 dB.
In the data transmission experiment, we launched a 16QAM PDM signal at a symbol rate of 80 GBd and a centre wavelength of λ = 1550 nm into the PBS/PR input, and fed the two output signals of the device to a pair of coherent receivers (see Supplementary Information Section S5 for details). We performed the experiment both with our 3D-printed PBS assembly and with a commercially available fibre-coupled PBS having a PER in excess of 30 dB. In both cases, we swept the optical signal-to-noise ratio (OSNR) at the input of the PBS and recorded constellation diagrams along with the corresponding bit error ratios (BER), as shown in Figs. 4c, d. At a BER of 1.25 × 10–2, our transmission setup exhibits an OSNR penalty of approximately 3 dB with respect to an ideal intradyne transmission system, as shown in Fig. 4d. This rather high implementation penalty occurs because our experiment had to rely on a heterodyne receiver scheme, which leads to additional impairments caused by amplified spontaneous emission (ASE) noise that would not be observed in a more commonly used intradyne receiver. The additional ASE impairments are responsible for approximately 2 dB of the measured 3 dB OSNR implementation penalty (see Supplementary Information Section S5 for details). Nevertheless, our experiments show that the 3D-printed PBS/PR assembly does not introduce any additional OSNR penalty with respect to commercial PBS, although the respective PER differ significantly. This may be attributed to the fact that the polarisation-sensitive mixing of data signals with the LO of the coherent optical receiver in combination with the digital polarisation demultiplexing algorithms of the PDM receiver can easily compensate for the finite PER of our 3D-printed PBS. Hence, even though there is still room for improvement in the performance of our 3D-printed PBS/PR assemblies, the current devices already offer an attractive route towards highly scalable ultra-compact dual-polarisation receivers, as shown in Fig. 1.
Finally, we compared the performance of our PBS/PR assembly with that of competing approaches. Our device exhibited a measured PER of better than 11 dB for wavelengths between 1270 and 1620 nm. The insertion loss is between 3.8 dB and 4.4 dB at a wavelength of 1550 nm and may be further reduced towards 2.5 dB, see Section S2 of the Supplementary Information. These loss figures are comparable to those obtained from polarisation-splitting grating couplers (PS-GC) with backside metal mirrors12, which exhibit measured insertion losses of 2.4 dB for both polarisations at a wavelength of 1550 nm. However, note that these insertion losses were measured by optimising the position of the optical fibre with respect to the PS-GC individually for each polarisation, and that they are expected to increase to 3.8 dB for a fixed fibre position12. Note also that the PS-GC is intrinsically narrowband and the insertion loss increases by at least 7 dB within a wavelength range of 60 nm, as shown in Fig. 3 of Ref. 12. Moreover, PS-GC often leads to technically unfavourable packaging geometries, with fibres mounted too close to the surface-normal position of the chip. Nevertheless, the measured PER of the PS-GC is 25 dB at a wavelength of 1550 nm, which clearly outperforms our current devices; however, we believe that these deficiencies can be overcome by further optimisation of the 3D-printed structures (see Section S2 for details). Other approaches9,34,35 rely on waveguide-based polarisation splitters and rotators that can be fabricated in multilayer silicon nitride structures. Such devices were demonstrated34,35 to exhibit a PER greater than 16 dB within a 60 nm-wide wavelength range35, whereas the measured insertion losses34 were approximately 1 dB. Similar performance was obtained7 for PBS/PR structures based on mode conversion in standard silicon photonic (SiP) waveguides, offering a 13 dB PER and a 1.5 dB insertion loss over a wavelength range of 50 nm. These losses, however, do not include the coupling between an optical fibre and an on-chip waveguide, which would typically add another 1.5–2 dB of loss36, thus leading to overall losses of 3–3.5 dB. These values are comparable to the losses achieved using our devices. Note also that integrated waveguide-based PBS/PR rely on rather long structures with typical lengths9,34,35 of 400 µm to 800 µm. Hence, our approach should also be able to compete with PBS/PR concepts based on rather large on-chip structures in terms of both PER and insertion loss.