On-chip beam rotators, adiabatic mode converters, and ...

Spherical phase-induced multicore waveguides (SPIM-WGs)

Historically, fs-laser-written waveguides operate with two different fabrication regimes: a non-heating regime with low laser repetition rate (<10&#;kHz); and heating regime with high laser repetition rate (>500&#;kHz). These two fabrication regimes involve different processes to create the RI profile in glass15,55 (Supplementary Note 1). We develop our technology based on the latter, which has much higher fabrication efficiency, reducing processing time from several hours to 1&#;2&#;min. Higher refractive index contrast (refractive index difference between waveguide core and substrate) can also be obtained which helps in our applications.

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In the rest of this paper, we refer to a common Cartesian coordinate system (Fig. 1a and inset of Fig. 2a) in which the waveguide was written along the y direction. The z axis (vertical direction) points along the optical axis of the laser-writing system. The x axis (horizontal direction) is perpendicular to the y and z axes. As briefly mentioned above, the &#;classic multi-scan&#; technique29,30,31 is a powerful method for creating rectangular shape waveguides in glass. The fabrication laser focus is scanned multiple times through the glass substrate with a x axis separation of about 0.4&#;µm between each pass to build up the waveguide RI profile. As shown in Fig. 1a, in the vertical z axis dimension, control over the cross-section is challenging since the z axis separation is limited (to ~8&#;µm, depending on objective NA). To enable fine control of sizes, and ultimately achieve arbitrary deformation of cross-section, it is essential to find a solution to reduce the step size along the z direction, without affecting the uniformity of the overall refractive index profile.

All images (LED, laser, simulation) excluding the phase pattern have the same frame size of 30&#;×&#;30&#;µm. Scale bars are 10&#;µm. a Classic multiscan laser fabrication technique has a large z step resolution (8&#;µm in this case). The red arrow marks laser propagation direction. Distances of core spacing along x axis (Δx), and z axis (Δz) are presented beside the diagram. b Three proposed fabrication schemes and the corresponding fabricated waveguides. In experimental demonstrations, Scheme I had Δx&#;=&#;Δz&#;=&#;0.4&#;µm, with 20 horizontal and 6 vertical scans. Scheme II had Δx&#;=&#;0.4&#;µm, Δz&#;=&#;1.5&#;µm, with 20 horizontal and 2 vertical scans. Scheme III had Δx&#;=&#;Δz&#;=&#;1.5&#;µm, with six horizontal and two vertical scans for the x-aligned rectangular waveguide, two horizontal and six vertical scans for the z-aligned rectangular waveguide. Labels: &#;LED&#;&#;images obtained with LED-illuminated microscope; &#;Laser&#;&#;785&#;nm laser transmission mode profile imaged at the waveguide output facet; &#;Z11&#;&#;manually induced primary spherical aberration61 (corresponding to Zernike mode 11 phase aberration) applied to spatial light modulator (SLM). &#;x-a.&#;&#;x-aligned rectangular waveguides. &#;z-a.&#;&#;z-aligned rectangular waveguides. c Simplified diagram of laser fabrication system with phase control. SLM is imaged to objective pupil with a 4&#;f telescope system. SLM spatial light modulator, Objective objective lens. d Manually induced additional spherical beam-shaping phases to SLM and their effects on laser focus and single-scan waveguides. Note that these phases are not used to correct spherical aberration caused by refractive index mismatch between air and sample, which was pre-corrected in all our experiments (please refer to &#;Phase pattern for SLM&#; section for details). Left: beam-shaping phase applied to SLM in addition to aberration corrections. Middle: simulated focal intensity distribution (enlarged images in Supplementary Fig. S1). Right: LED illumined microscopic image of single-scan waveguides. e Scheme III fabrication with negative spherical beam-shaping phase (Z11&#;=&#;&#;1), demonstrating significant improvement of cross-section control

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All images (LED, laser, simulation) have the same frame size of 30&#;×&#;30&#;µm. Scale bars are 10&#;µm. a Composition of a twisted waveguide. The lengths of z-aligned rectangular, twisted, x-aligned rectangular regions were 9.3&#;mm, 1.4&#;mm, 9.3&#;mm, respectively, for the studied waveguide. LED microscopic image top view of the fabricated sample is included, where a transition from 6&#;µm width to 12&#;µm width is clearly seen from the top 3D to 2D projection. Multi-scans of the laser spot at waveguide facets are shown as schematics. Coordinates: x/z transversal axis, y longitudinal axis. b Rectangular beam rotation can be achieved by a twisted waveguide, with 785&#;nm laser and &#;nm laser tested, respectively. Top: light guided from x-aligned rectangular input facet was converted to z-aligned rectangular modes. Bottom: light guided from z-aligned rectangular input facet was converted to x-aligned rectangular modes. c Measured refractive index profiles by a 3D tomographic microscope. Dashed boxes highlight positive refractive index regions which was able to guide laser light. Refractive index contrast was measured as high as 0.017. d COMSOL simulations of mode intensity distribution for 785&#;nm laser and &#;nm laser. The simulations were conducted based on measured refractive index data in the positive region from a tomographic microscope (highlighted by dashed boxed)

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One might test the idea, illustrated in Fig. 1b&#;Scheme I, where all laser spot scans closely stack together both along x and along z. However, as shown by the LED-illuminated transmission microscope image in Scheme I, the fabricated feature includes two large dark areas surrounded by bright regions, indicating a complicated structure of both positive and negative refractive index, which is most likely due to local thermal accumulation during processing15,55. During heating regime fs-laser fabrication, the high repetition rate laser creates a localized region of high-intensity plasma. If the multiple scans are chosen to be too close with each other (e.g., 0.4&#;µm in both the x and z directions), the high-intensity plasma generated by a newer scan melts the nearby feature created by existing scans, producing complicated structures. As shown in Fig. 1b&#;Scheme I, when the waveguide is tested with laser transmission, a nonuniform multimode profile was observed.

Observed from a single laser scan in Fig. 1d, we noticed that the refractive index asymmetry only exists along z direction but not x direction (which is consistent with existing reports53,56,57). We therefore explored the fabrication in Scheme II to see whether increased z scanning step of 1.5&#;µm from 0.4&#;µm could help. While there was a slight improvement, as shown in Fig. 1b&#;Scheme II, where positive RI region become wider along x direction, the transmitted laser mode was still far away from design. We therefore relaxed both horizontal and vertical scanning steps to 1.5&#;µm in Scheme III, and fabricated both x-aligned rectangular and z-aligned rectangular waveguides. As shown by the images in Fig. 1b, Scheme III gave us better-processed features. Comparing the laser-mode profiles of all the three schemes in Fig. 1b, waveguides fabricated by Scheme III presents a confined one-lobe laser guiding region instead of two laser guiding regions shown in Schemes I and II. We explored varying fabrication parameters (pulse energy 50&#;150&#;nJ, scanning speed 1&#;12&#;mm/s) and cross-section sizes, however neither Scheme I nor Scheme II was able to fabricate a feature close to the design.

For all the waveguide fabrications in this paper, system-induced aberrations were corrected by a wavefront sensorless adaptive optics method using a liquid crystal spatial light modulator (SLM) integrated into the laser fabrication system58,59. We experimentally verified the correction by the imaging of laser focus before each fabrication session. The spherical aberration that arose from refractive index mismatch between immersion and sample, was also pre-corrected by using the SLM60. It was important to ensure these aberrations were well corrected before our exploration (more details in &#;Materials and Methods&#;). For the convenience, we expressed this situation as &#;Zernike mode 11 equals 0&#; or &#;Z11&#;=&#;0&#;, where the 11th Zernike polynomial mode corresponds to the lowest order spherical aberration.

While Scheme III looked to give best results for fabrication strategy (Fig. 1b), there were however still large areas of complicated refractive index structure around the waveguide core. For the z-aligned rectangular waveguide, only the top region could guide light (bottom right images in Fig. 1b). Again, the problem was due to the fact that asymmetric complicated refractive index structure of the single-scan waveguide was along the z direction57. To resolve this problem, we introduced additional wavefront shaping, allowing us to gain a powerful capability to simplify and precisely control the fs-laser modified refractive index structure. The primary spherical aberration Zernike mode61 was chosen, as it can change laser focal shape along the z axis, while maintaining circular symmetry in the x&#;y plane (more analysis in Supplementary Fig. S1). We found that by deliberately introducing a negative spherical aberration phase, we were able to relocate more energy to the bottom half of the laser focus, shifting heat distribution along the z direction, thus producing a considerably simplified refractive index structure (Fig. 1d and Supplementary Fig. S1). Through extensive investigation, we found there was a difference in the waveguide formation process, that an applied spherical phase appears to limit heat accumulation at the top of laser focus, making it possible to generate a modified refractive index structure that matches the shape of laser focus. In comparison, using a conventional single scan without spherical aberrations, the shape of the modified refractive index structure was normally different to the laser focus. It was found empirically that an amplitude of &#;0.8 to &#;1.3 radians rms for Z11 worked well, so we chose negative one radian rms (Z11&#;=&#;&#;1) for subsequent fabrication. As shown in Fig. 1d, fabrication with Z11&#;=&#;&#;1 greatly simplified the single-scan-generated refractive index structure. Applying fabrication with Z11&#;=&#;&#;1 to multiscan x-aligned and z-aligned rectangular waveguides of Scheme III, we were able to produce structures which were well-matched to the original waveguide design (Fig. 1e and more results in Supplementary Figs. S2 and S3). The guided mode profiles showed well-confined elliptical modes.

Using manually induced spherical phase, we fabricated waveguides with core distances down to 0.3&#;µm and saw negligible difference in loss and mode properties. The distance of core spacing should be chosen based on practical applications. Larger spacing greatly increases fabrication efficiency and can be more suitable for longer wavelength applications. Smaller spacing gives higher resolution in control over cross-section shape and size and may be used for shorter wavelengths. As we targeted the design of devices to be optimized at the wavelength of &#;nm, 1.5&#;µm was chosen for the core distance of most waveguides in this paper. In Supplementary Fig. S2, we summarized and compared the fabrication of waveguides with varying core spacing from 0.5&#;µm to 3.5&#;µm. SPIM-WGs technique created waveguides with much better cross-section than classic multiscan technique for all the core spacings, and most importantly it enabled new capability to create waveguides with core spacing <2&#;µm, which is typically not easy through the classic multiscan method. Besides, the minimal sizes of SPIM-WGs created by 0.5-NA objective lens with 514&#;nm laser are around 3&#;×&#;0.5&#;µm. These minimal sizes are determined by the NA of objective lens and the wavelength of the fabrication laser. It is possible to create SPIM-WGs with cross-section sizes smaller than 2&#;×&#;0.3&#;µm with a >0.7&#;NA objective lens.

We named the waveguides fabricated by this technique as spherical phase-induced multicore waveguides (SPIM-WGs). We experimentally compared an alternative solution&#;to simply adopt a high NA objective lens in &#;classic multi-scan&#; (Fig. 1a), which could reduce the vertical separation down to ~3&#;µm with a 1.3&#;NA oil objective lens. However, our experimental results suggested that SPIM-WGs still hold several competitive advantages, including much higher fabrication efficiency (an order of magnitude reduction in fabrication time), more control over refractive index profile, and lower propagation loss. Some details of these will be analyzed further in this paper.

Beam rotators through twisted waveguides

Using the capability to finely control cross-section size along all transversal axes, we created waveguides with cross-section shape and size that varied along the length. The concept of these waveguides is illustrated in the schematics of Fig. 2a, where a single waveguide is composed of a straight z-aligned rectangular waveguide region at the input, twisted waveguide region at the middle, and x-aligned rectangular waveguide region at the output. To realize the concept in the experiment, waveguides were fabricated with 9&#;×&#;2 multiple scans, with each scan translating continuously through the entire sample. The transition in the twisted region from z-aligned rectangular to x-aligned rectangular was achieved by a smooth rotation of the 9&#;×&#;2 array by 90 degrees along a length of 1.4&#;mm. A transmission microscope image viewing from top of the fabricated sample (2D projection) shows the clear change in transverse waveguide dimension in the twisted region.

To demonstrate the laser-mode transition efficiency, we tested the twisted waveguide with both 785&#;nm and &#;nm lasers. As shown in Fig. 2b, when laser light was coupled from a x-aligned rectangular facet (right side of waveguide), the mode profiles obtained at the output of waveguide were rotated 90° to become z-aligned. Similarly, when light was coupled from the z-aligned rectangular facet, the output mode profiles were rotated 90° to be x-aligned (more results in Supplementary Fig. S3).

To accurately characterize the waveguide refractive index profile at various points along the device, measurements were made using 3D tomographic microscopy62. From the profiles in Fig. 2c, we can see that the multicore waveguides along the z axis were well combined and formed a smooth transition of positive refractive index regions along z (the vertical bright lines). The positive refractive index in each single core was highly uniform, significantly reducing scattering to achieve low waveguide loss. The shape and size of the positive refractive index regions were highly consistent across the whole multicore cross-section. The light-guiding region is highlighted with a dashed box; and there are surrounding areas of negative refractive index, which could further enhance mode confinement. As one of the SPIM-WGs&#; advantages, the refractive index contrast was measured to be 17&#;×&#;10&#;3, which is remarkably higher than that of most reported glass waveguides15. We believe this benefitted from both spherical phase control and partial overwriting (more details in Supplementary Fig. S4). Compared to a classic multiscan technique, the refractive index distribution of SPIM-WGs is better organized and highly predictable, contributing to much better waveguide qualities, especially low losses, which will be discussed later.

In order to investigate the waveguiding properties from spatially separated regions of positive index change, we conducted simulations using the experimentally measured refractive index data. As shown in Fig. 2d, the guiding modes at both wavelengths were uniform without any evidence of deterioration. We note that the mode profile was dependent on spacing of multicore as well as refractive index contrast. In our design, choosing 1.5&#;µm core distance with 17&#;×&#;10&#;3 refractive index contrast was sufficient to produce a uniform laser guiding mode with excellent confinement for both the 785&#;nm and the &#;nm laser. As seen from Fig. 2b, d, the mode size was smaller for the shorter wavelength, which is expected. Based on a large number of simulations for varying waveguide cross-sections, we found by appropriate design that these periodic positive-negative refractive index transection profiles were well able to produce mode profiles similar to a homogeneous step-index waveguide, and had negligible impact to waveguide losses, which will be discussed in the following text.

Light-guiding performance

It is essential to evaluate waveguide losses to inspect whether the multicore structure or the twisted region may introduce additional losses to the waveguide. In order to have a comprehensive understanding of losses, we fabricated several sets of waveguides with different cross-section shapes and sizes, as illustrated in Fig. 3a. We here used waveguides fabricated with a single pass of laser focus15 (referred to here as &#;classic single-scan waveguide&#;) as the basis for comparison. Loss measurements were conducted by a cut-back method (details in &#;Materials and methods&#;) at 785&#;nm wavelength. We first evaluated whether the multicore structures introduced additional loss compared to the classic single-scan waveguide. The average measured waveguide propagation losses are summarized in Fig. 3b. The numbers were averaged across several waveguides with the same configuration to show repeatability. Except for the x-aligned rectangular waveguide with 10&#;×&#;4&#;µm cross-section, all the other SPIM-WGs had propagation losses lower than that of classic single-scan waveguide. We therefore concluded that overall, SPIM-WGs had lower propagation losses than that of classic single-scan waveguides. We believe this is due to higher refractive index uniformity and contrast of SPIM-WGs.

All images (LED, laser) have the same frame size of 30&#;×&#;30&#;µm. Scale bars are 10&#;µm. a Sets of waveguides were fabricated with different cross-section shapes and sizes. Classic single-scan, x-aligned, z-aligned waveguides were two waveguides per set, while twisted waveguides (twisted length of 1.4&#;mm) were four (two z-aligned input facet, two x-aligned input facet) per set. Cross-section images are included in Supplementary Fig. S3. b Comparison of propagation losses for classic single-scan, x-aligned, z-aligned and twisted waveguides. Each number presented in the figure is an average of two measured waveguides for single-scan, x-aligned, and z-aligned sets; an average of four waveguides for twisted sets. The fabrication speed was 8&#;mm/s. c Twisted waveguides&#; propagation losses versus laser focal spot scanning speed. The cross-section size was 20&#;×&#;4&#;µm, twisted length was 1.4&#;mm, twisted angle was 90°. d Twisted waveguides propagation losses versus twisted region length. Cross-section size was 10&#;×&#;4&#;µm, laser scanning speed was 8&#;mm/s (sacrificing loss to gain fabrication efficiency), twisted angle was 90°. e Twisted waveguide propagation losses versus twisted angle. Cross-section size was 20&#;×&#;4&#;µm, laser scanning speed was 8&#;mm/s (sacrificing loss to reduce fabrication time), twisted length was 1.4&#;mm. f Demonstration of beam rotation by several sets of twisted waveguides with varying twisted angle. Left: LED transmission microscopic images of waveguide facet. Middle: measured &#;nm laser-mode profile images. Right: diagrams of twisted SPIM-WGs with different angles

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We then investigated whether the twisted region inside SPIM-WGs introduced additional losses compared to the straight region. In the measured results of Fig. 3b, we found twisted waveguides have on average a propagation loss that lies between that of x-aligned rectangular waveguides and z-aligned rectangular waveguides. It was therefore concluded that additional loss induced by waveguide cross-section twisting should be negligible. On the other hand, twisting SPIM-WGs were demonstrated with even lower propagation losses than classic single-scan waveguides in Fig. 3b. We note that for single-scan waveguides, the conventional method with Z11&#;=&#;0 provides slightly lower loss and better circularity, while SPIM-WGs with Z11&#;=&#;&#;1 hold advantages in nearly all the aspects whenever a multiscan approach is needed.

We conducted experiments to evaluate how the fabrication parameters affected the performance of twisted waveguides. Figure 3c summarized how the twisted waveguide&#;s propagation loss could be optimized by changing laser scanning speed. It appeared that with pulse energy of 78&#;nJ, a scanning speed around 4&#;mm/s was optimal. A waveguide fabricated with these parameters was measured with propagation loss as low as 0.14&#;dB/cm, which is close to the limit of EAGLE glass absorption at 785&#;nm63. During our experiments, we constantly measured propagation losses in the range of 0.13&#;0.2&#;dB/cm for twisted shape SPIM-WGs fabricated with 4&#;mm/s scanning speed, further confirming these low propagation losses were easily repeatable.

We fabricated waveguides with different twisted region lengths to evaluate how this parameter affects the overall performance. As shown in Fig. 3d, the total propagation losses (straight plus twisted regions) remained almost constant when reducing the length of twisted region, which means the SPIM-WGs with twisted region as short as 0.05&#;mm had similar overall loss to one with a 1.4-mm twisted region. Moreover, we found that the waveguides with different twisted lengths had comparable performance in z-aligned to x-aligned mode conversion. It is notable that waveguides in Fig. 3d were fabricated with a higher scanning speed of 8&#;mm/s, which reduced fabrication time by half. Optimizing scanning speed could easily bring down the losses as indicated in Fig. 3c.

Finally, we demonstrated SPIM-WGs&#; flexibility in controlling the twisted angles, providing versatile beam rotation capability. We fabricated twisted waveguides starting from a z-aligned rectangular shape into twisted angles of 0°, 30°, 45°, 60°, 90°. Figure 3f includes both LED-illuminated microscopic images and &#;nm laser transmission mode profiles, showing not only good control over cross-section shape, but also the flexibility to rotate the orientation of elliptical laser guiding modes. Moreover, as demonstrated in Fig. 3e, varying the twisted angle did not have noticeable effects on SPIM-WGs&#; propagation losses.

Adiabatic mode converters with advanced mode matching

We demonstrate that SPIM-WGs enable a new capability to flexibly create mode converters that can arbitrarily transform modes regardless of their symmetry. There are many photonic chip applications that require mode manipulation, for example, when mode matching is needed. We highlight four common application cases to demonstrate this capability. In most optical chips, coupling of laser light in/out of a single-mode fiber is important3. In terms of direct laser-written waveguides, researchers have adopted methods to achieve higher coupling efficiency52,53 by controlling the fabrication laser power. Based on SPIM-WGs, we created converters whose cross-sections were transformed between circular and rectangular shapes (diagram on the left of Fig. 4a). The mode conversion performance is demonstrated in Fig. 4a, where the mode intensity plots indicate a clear transition between circular and elliptical modes. Both the circular or rectangular shapes and sizes can be flexibly and precisely controlled. In our experiments, the circular facet of the mode converter was designed to have the same physical dimensions as the core of the &#;nm single-mode fiber (a diameter of 8&#;µm). This provided excellent mode matching; we observed that 95.7% light was coupled from the fiber tip to the circular facet of SPIM-WGs mode converter. This represents a significant decrease of coupling loss after advanced mode matching, from 1.69&#;dB in the case of rectangular facet to 0.19&#;dB in the case of circular facet based on our measurement with &#;nm laser. The total loss (coupling&#;+&#;propagation) of a mode converter with length of 1.32&#;cm was measured to be remarkably as low as 0.59&#;dB, where the waveguide was fabricated with a scanning speed of 6&#;mm/s. During our experiments, the total losses of ten converters fabricated in the same configuration were measured to be in the range of 0.59&#;0.75&#;dB, confirming high consistency of light-guiding performance.

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All images (LED, laser) in a and b have the same frame size of 30&#;×&#;30&#;µm. Scale bars are 10&#;µm. a Left: circular&#;Rectangular mode converter that couples single-mode fibers (circular shape mode) to rectangular shape waveguides (elliptical shape mode). A waveguide with length of 1.32&#;cm was measured to have ultra-low total loss of 0.59&#;dB (coupling&#;+&#;propagation). The coupling loss was calculated to be 0.19&#;dB (95.7% light coupled). Middle: LED-illuminated microscopic images demonstrating classic multiscan technique is not capable to fabricate these high-quality mode converters while SPIM-WGs technique enables this capability. About -nm laser-mode profiles are presented for SPIM-WGs. Right: plots of intensity versus distance for corresponding SPIM-WGs circular and elliptical mode profiles. Plotting lines are indicated in mode profiles. b Circular-ppKTP mode converter that couples single-mode fibers to ppKTP waveguides. A waveguide with length of 1.38&#;cm was measured at &#;nm wavelength to have total loss of 0.65&#;dB (coupling&#;+&#;propagation). The coupling loss was 0.24&#;dB (94.6% light coupled). c Circular&#;rectangular TE01 mode converter that converts between Gaussian circular mode with rectangular TE01 mode (also called LP11 mode in waveguide theory). A waveguide with length of 1.27&#;cm was measured at 785&#;nm wavelength to have ultra-low total loss of 0.78&#;dB (coupling&#;+&#;propagation). The coupling loss was calculated to be as low as 0.2&#;dB (95.5% light coupled). d Circular&#;circular TE01 mode converter that converts between Gaussian circular mode with circular TE01 mode or a hollow ring shape intensity distribution. A waveguide with length of 1.27&#;cm was measured at 785&#;nm wavelength to have total loss of 0.73&#;dB (coupling&#;+&#;propagation). The coupling loss was calculated to be 0.21&#;dB (95.3% light coupled). e Top: COMSOL simulated field distribution of designed circular shape mode profile to match a single-mode fiber at &#;nm. Middle: COMSOL simulated field distribution of designed mode profile to match ppKTP waveguide at &#;nm. Bottom: designed refractive index profile for matching ppKTP waveguide mode. f Top: COMSOL simulated field distribution of designed circular shape mode profile to match a single-mode fiber at 785&#;nm. Middle: COMSOL simulated field distribution of designed rectangular TE01 mode profile at 785&#;nm. Bottom: COMSOL simulated field distribution of designed circular TE01 mode profile at 785&#;nm

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As a second example, we consider ppKTP (periodically poled potassium titanyl phosphate) waveguides64,65,66,67,68, which are used in nonlinear optics, in particular for frequency conversion and quantum light sources. The waveguiding mode is defined via a rubidium ion-exchange process beginning at the surface of the material and penetrating below with gradually reduced concentration. This typically leads to a skewed Gaussian mode profile69,70,71, inducing high coupling losses to single-mode fiber due to mode mismatch, which is a major hurdle for effective integration of these devices. Based on our previous measurements, the coupling loss between single-mode fiber and a ppKTP waveguide is around 70%67. We observed that improving efficiency from 70% to >80% for each mode would allow one to beat the shot-noise limit in phase-sensing without post-selection67. We demonstrate that our SPIM-WGs technique can easily create a converter to transform between a ppKTP waveguide mode and a circular mode from an external single-mode fiber, therefore provide a significantly improved coupling. We designed a refractive index profile, presented in Fig. 4b, that was able to generate a mode profile matched to the mode from a typical ppKTP waveguide. The designed refractive index profile was created by fine-tuning the size and shape with feedback from COMSOL simulation. We fabricated this type of mode converter from an 8&#;µm diameter circular shape (matching to the core size of single-mode fiber) to the designed ppKTP refractive index with sizes of 8&#;×&#;8&#;µm, 6&#;×&#;6&#;µm, and 4&#;×&#;4&#;µm. A typical mode converter with length of 1.38&#;cm was measured to have total loss remarkably as low as 0.65&#;dB, with coupling loss of 0.24&#;dB (94.6% light coupled). In total, 18 converters were fabricated, and their total losses were measured in the range of 0.65&#;0.8&#;dB. The mode profiles of one converter with mock ppKTP waveguide of 8&#;×&#;8&#;µm size are presented in Fig. 4c, where the mode shape transition is clearly seen. In practical applications, mode converters could be cut to be shorter (e.g., ~0.5&#;cm), easily reducing the propagation loss and raising overall efficiency to be >90%.

The advantage of creating adiabatic mode converters inside the glass is that devices can be designed for a particular wavelength across a broad range from visible to near-infrared, as glass has low absorption in these wavelengths. To demonstrate the applicability of our technique in another wavelength band, we created another two mode converters (presented in Fig. 4c, d) for 785&#;nm laser conversion. Mode converters for other target wavelengths would also be easily achievable, as the design would differ mostly in size.

As the third example, we created a mode converter that can convert between a Gaussian mode and a rectangular TE10 mode. We excited the TE01 mode with two lobes along x direction, however, it is easy to switch to the design of the other orientation (z-aligned) as we demonstrated above (sometimes TE01 and TE10 are used to distinguish the orientation of the lobes). This conventional TE01 mode has the same mode intensity profile as LP11 modes in waveguide theory72, meaning TE01 mode we generated can be coupled to either a rectangular waveguide or a circular waveguide. Either a TE01 mode (Fig. 4c), or an elliptical shape mode (e.g., Fig. 2) can be excited at the rectangular shape output facet. The transition between them can be easily controlled by either a slight shift in the input angle (~5°) or a slight shift in the position (~0.5&#;1&#;µm) of input beam relative to the waveguide. In practical applications, we used optical glue to fix the angle or position between fiber and waveguide sample. As the demonstration in Fig. 4c, we chose to shift the angle, which also brought slightly higher propagation loss. The total loss (coupling&#;+&#;propagation) of this mode converter with length of 1.27&#;cm was measured to be 0.78&#;dB at 785&#;nm laser, where the waveguide was fabricated with scanning speed of 8&#;mm/s.

As the fourth example, we created a mode converter that can convert between circular shape Gaussian mode and a circular TE10 mode, which has a ring shape intensity with a hollow core73,74. In order to generate a ring shape intensity with symmetric and uniform intensity, we used COMSOL simulations to precisely design the position for each single laser scan (in total 18 scans for one converter). We note the position of each single scan is not evenly distributed along the circle, since the structure generated by single scan is elongated along the z direction. This is seen in the last COMSOL simulated image of Fig. 4f. As the result, the measured ring shape mode profile at 785&#;nm has high symmetry and uniform intensity. The total loss (coupling&#;+&#;propagation) of the mode converter with length of 1.27&#;cm was measured to be 0.73&#;dB at 785&#;nm laser, where the waveguide was fabricated with a scanning speed of 8&#;mm/s. In total, we created 24 mode converters with ring diameter varying from 6.5&#;µm to 13&#;µm, with total insertion loss measured in the range of 0.73 to 0.88&#;dB.

To demonstrate SPIM-WGs&#; capability in creating high-quality adiabatic mode converters, we also added the fabrication results from classic multiscan for comparison in Fig. 4. As we can see that the structures created by classic multiscan are very complicated. The situation becomes even worse for the application in shorter wavelengths (Fig. 4c, d). Mode converters require precise fabrication, so that we can conclude that the classic multiscan fabrication in the heating regime is not capable of creating these mode converters.

The capability of SPIM-WGs in creating adiabatic mode converters is not restricted to the above four examples. We also found that the adiabatic transitions of the cross-sections introduced negligible additional loss in SPIM-WGs mode converters. The propagation losses of the mode converters were found to be nearly the same as the waveguides with fixed cross-section with same sizes. We also conducted experimental verification of the adiabatic process for the mode converters, with results summarized in Supplementary Fig. S7.

On-chip wavelength-dependent waveplates

In this section, we extend the capability of SPIM-WGs by demonstrating the polarization state manipulation of guided linear polarized light, to enhance the toolbox of SPIM-WGs photonic circuits. To prove this concept on a chip, we constructed polarization-controlled experimental apparatus (details in &#;Materials and methods&#;). The waveguide was tested with linearly polarized light from either a monochromatic or wide-band supercontinuum laser source. SPIM-WGs were studied to evaluate their polarization conversion efficiency (PCE) for propagated light, which is defined as,

$$PCE_{TE \to TM} = \frac{{P_{TM}}}{{P_{TE} + P_{TM}}}$$

$$PCE_{TM \to TE} = \frac{{P_{TE}}}{{P_{TE} + P_{TM}}}$$

in which, PTE(TM) is the power in the TE (TM) polarization at the waveguide output facet.

We investigated 90° twisted waveguides with varying twisted length and total length (diagram in Fig. 2a). When tested with 0°/90° linear polarized -nm monochromatic laser, we found that appropriately designed twisted waveguides were able to rotate the polarization of transmitted laser light, through the mechanism of adiabatic mode evolution in the twisted region34,39,42,75. When light propagates along the twisted region with such a rotated rectangular shape, not only does the mode shape undergo an adiabatic evolution, but the polarization of the photons also gradually changes together with the evolution of fundamental modes. Figure 5a compared two twisted waveguides with same total length of 30&#;mm, but different twisted length of 25&#;mm (top) and 15&#;mm (bottom). As seen in the mode images, the twisted waveguide with 25&#;mm twisted length maintained the same polarization state of guided laser light at &#;nm. In comparison, the twisted waveguide with 15&#;mm length was able to convert the polarization state with efficiency up to 60% as demonstrated in bottom images of Fig. 5a. With a TE input, TM mode was strongly observed at the output of twisted waveguide, while a similar case was seen for TM mode conversion into TE mode.

All images (LED, laser) have the same frame size of 30&#;×&#;30&#;µm. Scale bars are 10&#;µm. a Results of polarization-controlled experiments at &#;nm wavelength laser. Top: twisted waveguide with 25&#;mm twisted length. Bottom: twisted waveguide with 15&#;mm twisted length. Images are waveguide mode profiles observed for particular output polarization state, with input laser light of either pure TE or pure TM polarization. Both waveguides have total length of 30&#;mm. b Measured polarization conversion PCE for twisted waveguides with total length of 30&#;mm, different twisted lengths of 25&#;mm and 15&#;mm, at wide near-infrared wavelengths. PCEs are controllable for any target wavelength by modifying twisted length while fixing total length. Red curve is measured with horizontally polarized input laser, while orange curve is vertical polarized input laser. c Measured polarization conversion PCE for twisted waveguides with total length of 10&#;mm, twisted lengths of 1.4&#;mm, at wide near-infrared wavelengths. The polarization manipulation behavior of straight rectangular waveguides was measured for comparison in Supplementary Fig. S9. In this figure, Waveguide cross-section sizes are 20&#;×&#;4&#;µm for all. Twisted waveguides are with 90° twisting angle

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The capability of polarization manipulation of twisted waveguides is demonstrated for near-infrared light in the results of Fig. 5b, c. We observed that the polarization conversion had periodic variation across a wide range of wavelengths. We think the oscillations can be the consequence of excitation and interference of higher order modes in our waveguides. Supplementary Note 2 provides details of the mathematical representation of this mode interference. With the definition of modal group index76 \(n_g = - \frac{{\lambda ^2}}{{2\pi }}\frac{{d\beta }}{{d\lambda }} = n_{eff} - \lambda \frac{{dn_{eff}}}{{d\lambda }}\), where β is the propagation constant, λ is the wavelength of transmitted laser light and neff is effective refractive index, we obtained the following expression for the period of spectral oscillations in wavelength (more details in Supplementary Note 2):

$${{\Delta }}\lambda = \pm \frac{{\lambda ^2}}{{(n_{g1} - n_{g2})L}}$$

ng has relatively weaker dependence over λ, so that Δλ is almost a function of λ2 and L. The obtained expression explains faster oscillations for waveguides with longer total length (larger L, comparing Fig. 5b, c), and narrowing of the wavelength period at shorter wavelengths. The period of the observed oscillations may indicate that the interference occurs between modes of different order rather than between polarization modes of the same order. The energies of these modes are interfering and coupling along the length of the twisted region where both mode conversion and polarization conversion take place. Some mode interferences are constructive to polarization conversion, while others are destructive (details in Supplementary Note 2). In some particular wavelength bands, the destructive effects of mode interferences are heavier than that of other wavelength bands, where we observed nearly zero polarization conversion for these wavelengths. The fact that the polarization conversion is differently affected by mode interference explains the oscillation effect of PCE across wide wavelength ranges.

Modification of the total waveguide length makes it possible to adjust the period of polarization conversion oscillation, which provides a useful tool for on-chip polarization manipulation. When the total waveguide length was fixed, but the length of the twisted region was changed, we found that the periodical oscillation can shift, as shown in Fig. 5b. Fixing the total length and controlling the length of twisted region thus becomes a second method for tunable polarization manipulation. Based on these observations, it is possible to design a waveplate which provides rotated polarization state at several target wavelengths while more or less maintaining the original polarization state at the other wavelengths. For an example, as shown as middle figure of Fig. 5b, one waveplate with 15&#;mm twisted length operates as a waveplate at &#;nm (telecom. C band) and &#;nm (telecom. E band), but maintains the original polarization state at &#;nm (telecom. S band). Conversely, the waveguide with 25&#;mm twisted length (top figure) maintains the original polarization state at &#;nm (telecom. C band) and &#;nm (telecom. E band), but operates as a waveplate at &#;nm (telecom. S band). It is thus possible to design and achieve a waveplate with desired rotated polarization angle for a particular wavelength. We achieved a PCE of around 70% through further reduction of the spacing between multiple cores to 0.65&#;µm to produce a more uniform refractive index cross-section. As the first extensive report of experimental investigations on the polarization conversion effect for the weak refractive index contrast 90° twisted waveguides embedded inside glass, these results show the polarization conversion effect seems to be weaker than those waveguides with a high contrast step index34 if same twisted length is applied.

Though it is not easy to access a full polarization conversion, with low losses and multi-wavelength applicability, the designed waveplate could still be applied to some important applications which do not need full polarization conversion, such as, various integrated quantum-entangled photons sources23, quantum study of polarization photons47 and many other photonic devices which need integration of an on-chip waveplate. Another capability arises with the wavelength dependence, where the waveguide acts as a rotated waveplate at one or several wavelengths and while barely effecting the polarization at other different wavelengths which might be interesting for frequency-division multiplexing (FDM) telecommunication systems. Thirdly, the waveplate can be designed as a polarization-maintaining beam rotator, where the beam intensity profile can be rotated 90° with little change of the original polarization state. These cases are experimentally shown in Fig. 5b, c) where the polarization conversion approaches zero but beam profile itself was rotated 90°. Finally, the functionalities of polarization conversion can be incorporated together with adiabatic mode conversion in a single waveguide design, for devices exhibiting multiple functionalities, which is important for the future development of ultra-compact integrated photonic circuits.

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