Hybrid external-cavity lasers (ECL) using photonic wire bonds as coupling elements

Combining semiconductor optical amplifiers (SOA) on direct-bandgap III–V substrates with low-loss silicon or silicon-nitride photonic integrated circuits (PIC) has been key to chip-scale external-cavity lasers (ECL) that offer wideband tunability along with small optical linewidths. However, fabrication of such devices still relies on technologically demanding monolithic integration of heterogeneous material systems or requires costly high-precision package-level assembly, often based on active alignment, to achieve low-loss coupling between the SOA and the external feedback circuits. In this paper, we demonstrate a novel class of hybrid ECL that overcome these limitations by exploiting 3D-printed photonic wire bonds as intra-cavity coupling elements. Photonic wire bonds can be written in-situ in a fully automated process with shapes adapted to the mode-field sizes and the positions of the chips at both ends, thereby providing low-loss coupling even in presence of limited placement accuracy. In a proof-of-concept experiment, we use an InP-based reflective SOA (RSOA) along with a silicon photonic external feedback circuit and demonstrate a single-mode tuning range from 1515 to 1565 nm along with side mode suppression ratios above 40 dB and intrinsic linewidths down to 105 kHz. Our approach combines the scalability advantages of monolithic integration with the performance and flexibility of hybrid multi-chip assemblies and may thus open a path towards integrated ECL on a wide variety of integration platforms.


Experimental methods for RSOA characterization and bond loss estimation
To measure the small-signal gain and the saturation output power of the RSOA, we launch light to the device and measure the amplified signal using an AR-coated lensed single-mode fiber (SMF), see Inset of Fig. 2(a) of the main manuscript. To determine the coupling loss between the on-chip RSOA waveguide and the lensed SMF, we perform a two-step reference measurement: First, we operate the RSOA without the fiber coupled to it and use an integrating sphere (IS) to measure the overall emitted ASE power as a function of injection current, see Fig. S1(a). Next, the RSOA is coupled to the lensed SMF, and the position of the lensed SMF is left untouched for the remainder of the measurements. The fiber-coupled ASE power is measured with the same integrating sphere, Fig. S1(b). From this measurement, we extract the current-dependent ratio of the power ASE,SMF P captured by the lensed SMF and the overall ASE power ASE,tot P emitted by the RSOA and measured by the integrating sphere, see Fig. S1(c). At low currents, this ratio is extremely low, since spontaneous emission occurs into many transverse modes, which are all captured by the IS, whereas only the fundamental quasi-TE and quasi-TM mode is captured by the lensed SMF. With increasing current, the fundamental quasi-TE mode of the RSOA waveguide will experience stronger amplification and thus increasingly dominate the overall emitted ASE power. The ratio ASE,SMF ASE,tot PP thus converges asymptotically to the power-transmission factor RSOA,SMF  for coupling of light between the fundamental quasi-TE mode of the RSOA and the horizontally polarized fundamental mode of the lensed SMF. In our experiment, this fiber-chip coupling loss amounts to 10  . Note that this rather high loss is caused by the fact that we intentionally operated the SMF with a working distance larger than the specified one to reduce unwanted spurious back-reflections into the RSOA. Note also that for drive currents of I = 5 mA or higher, most of the ASE emitted by the bare RSOA is horizontally polarized and the measured ASE power can hence be attributed to the TE-polarized waveguide modes, see Fig. S1(e).
With the coupling loss at hand, we can now determine the RSOA gain. To this end, we launch a test signal through the SMF, extract the output signal via a circulator (CIRC), and estimate the incoming and the outgoing on-chip power in the quasi-TE mode of the RSOA, see Fig. S1(d) for the corresponding measurement setup. From our measurements, we find a small-signal on-chip gain of 23 dB along with an on-chip saturation output power of 12.5 dBm for a wavelength of 1550 nm   and a drive current of 100 mA, see Fig. 2 of the main manuscript.
To estimate the insertion loss of the photonic wire bond, we again use the fiber-coupled ASE power ASE,SMF P and compare it to the ASE power ASE,SiP P in the on-chip silicon photonic waveguide that is directly connected to the photonic wire bond. To extract the ASE power ASE,SiP P in the on-chip waveguide, we operate the assembled module, see Fig. 1(b) in the main manuscript, with the rings R1 and R2 detuned to one another to avoid feedback into the RSOA. We then measure the ASE spectra through GC 4 and calculate the corresponding power levels ASE,SiP P in the SiP waveguide directly connected to the PWB by taking into account the wavelength-dependent loss of GC 4 and of the MMI as well as the 0.5 dB of wavelengthindependent on-chip propagation loss in the 2.5 mm-long waveguide between the PWB and GC 4. For this analysis, we only consider the ASE power emitted into an approximately 0.8 nm-wide band centered at 1550 nm, which does not contain any resonance of R2. The position of the 0.8 nm-wide band is illustrated by a dashed line in Fig. S1 Note that a small part of the ASE power ASE,SMF P measured in the fiber should even originate from quasi-TM modes of the RSOA, which cannot be extracted through the highly polarization-sensitive grating coupler (GC 4). To take this effect into account, the measured value of ASE,SMF P would have to be reduced to only represent the portion coming from quasi-TE modes of the RSOA. This would increase the coupling efficiency according to Eq. (S1) and hence reduce the coupling loss, such that the number specified above may be considered a conservative estimate of the PWB loss. Note also that the ASE power is extracted around 1550 nm, close to the long-wavelength edge of the ASE spectrum, see Fig. S1(f). In this region, the power spectral density of the ASE saturates for large pump currents, Fig. S1(f), thereby reducing the uncertainty of the measurement technique and eliminating the impact of spurious lasing lines that might occur at short wavelengths during measurement of the ASE spectrum through the SiP chip.

Characterization and modelling of add-drop ring resonators
In Section "Component characterization" of the main manuscript, we describe our ring resonators based on a simple model illustrated in Fig. S2(a) 1,2 . In this representation, the complex amplitudes of the electric mode fields at the input, the drop, the through, and the add ports are denoted as i E , d E , t E , and a E , respectively. Due to the bidirectional operation of the ring filter, the coupling zones between the bus waveguides and the ring are designed symmetrically. Assuming for simplicity that the coupling zones are lossless, the device can be described by . The complex through-port amplitude transmission ti / EE is then given by 2 PP of the power captured by the lensed SMF and the overall ASE power emitted by the RSOA. In the high-current limit, this ratio converges to the coupling loss between the fundamental quasi-TE mode of the RSOA waveguide and the horizontally polarized fundamental mode of the lensed SMF. (d) Measurement setup for small-signal gain, saturation output power and ASE spectrum. A tunable laser source (TLS) and an optical circulator are used to launch test signals to the RSOA and to extract the amplified output signals. (e) Polarization-filtered ASE power emitted by the bare RSOA, measured with an infrared microscope and a linear polarizer in the camera path. The abscissa indicates the orientation of the polarizer, where 0° corresponds to maximum transmission for horizontally-polarized light. For drive currents of I = 5 mA or higher, most of the emitted ASE is polarized along this direction and may hence be attributed to quasi-TE modes of the on-chip RSOA waveguide. (f) ASE power spectra measured through the SMF that is directly coupled to the RSOA, see Subfigure (d). The ASE power levels used for estimating the PWB insertion loss are extracted from a 0.8 nm-wide wavelength band centered at 1550 nm (indicated by a vertical line), i.e., close to the long-wavelength edge of the ASE. In this region, the power spectral density of the ASE saturates for large pump currents, thereby reducing the uncertainty of the measurement technique. (g) PWB coupling loss of 10 We determine the parameters a,  , eg,SiP n , and 0  from through-port power transmission measurements via grating couplers GC 1 and GC 3, see Section "Component characterization" and Fig. 1 in a first step and use this value to fit Eq. (S2) to the shape of the individual resonances, assuming a constant eg,SiP n . Since the measured data contains resonances of both rings, we first cut out relevant data segments around each resonance and assign them to the corresponding ring. Measurement data and fit curve are shown for one exemplary resonance dip in Fig. S2(b). The phase offset 0  in Eq. (3) can be adjusted by the thermal phase tuners and is responsible for the absolute frequency position of the transmission spectra 2 ti ( )) ( EE  and 2 di ( )) ( EE  on the frequency axis. For the plot in Fig. 3(a)

Vernier tuning range and tuning enhancement factor
In many cases of practical interest, the tuning range of an ECL with a feedback circuit of two cascaded rings is dictated by the frequency spacing between the main reflection peak and the most prominent side peaks that arise from nearly-overlapping ring resonances. To estimate this frequency spacing, we assume that the two rings R1 and R2 are tuned to a common central resonance frequency 0 f and we express all other resonance frequencies as  The precise frequency of the side mode, that can occur due to the partially overlapping resonances of R1 and R2, depends on the resonance line shapes of the individual rings and lies in the interval limited by 02 FSR fm   and   01 1 FSR fm   . The error when approximating the side mode frequency with either interval limit is smaller than FSR 2  .

Tuning map
The ECL emission wavelength is selected by aligning the two ring resonators for a common resonance and by optimizing the cavity phase for maximum output power. Once the appropriate tuning parameters are found, they can be stored in a look-up table for later use and for rapid tuning. A simple example of such a tuning map is shown in Fig. S3. When heating only one ring, the corresponding resonance is detuned in proportion to the heating power, while the resonance of the other ring stays nearly constant, indicating very low thermal crosstalk. The vertical offset of the traces obtained from neighboring resonances corresponds to twice the π-power Pπ of the respective ring heater, which amounts to ,R1 24.4 mW P   for R1 and ,R2 24.1 mW P   for R2. To operate the laser at, e.g., 1549 nm, one can choose the heating powers R1 34.8 mW P  and R2 25.0 mW P  based on the tuning map, see dashed lines in Fig. S3. Due to residual thermal crosstalk, the final operation point needs to be fine-tuned in an iterative approach.

Two-photon absorption (TPA) and TPAinduced free carrier absorption in the external cavity circuit
The high optical power in the ring-resonator waveguides of the silicon photonic (SiP) external-cavity circuit might lead to detrimental nonlinear effects. To quantify these effects at least approximately, we have performed further estimations and measurements. The power enhancement in a ring resonator as compared to the power in the corresponding bus waveguide can be described by the buildup factor B, see Eq.   power of approximately 9 dBm that is fed to each of the rings through the bus waveguide connected to the MMI. Assuming an unperturbed resonator in perfect resonance, the power propagating into a single direction within the rings would then amount to more than 19.5 dBm. The overall intra-cavity power is even higher, since the rings are fed from both sides. To estimate the impact of nonlinear losses, we have measured the powerdependent transmission characteristics of a 2.25 mm-long straight silicon photonic waveguide with a cross section of 500 nm × 220 nm that is identical to that of our ring resonator. The results are shown in Fig. S4, exhibiting signs of nonlinear losses such as TPA and TPA-induced FCA for on-chip powers of approximately 19 dBm (80 mW). We should hence expect that the rings of our silicon photonic feedback circuit are affected by such effects as well.
We experimentally confirm this notion by conducting transmission measurements between grating couplers GC 1 and GC 3 of our ECL chip at different optical power levels. To avoid destroying the ECL during the experiment, we used a SiP chip that is nominally identical to the one contained in the ECL and that was fed by a test laser and an EDFA. We tune the laser to an emission wavelength slightly below a resonance of ring R1 and then ramp the heater current of ring R1 up and down to scan the resonance across the fixed laser wavelength while measuring the output power. Figure S5 shows the on-chip transmission through the bus waveguide of the ring resonator, measured as a function of heater power for different optical input power levels Bus P . For increasing laser power, we make three observations similar to Fig. 20 of Ref 3 : Starting from a power level Bus P of 4 dBm, we first find that the resonance peaks become increasingly skewed, see Fig. S5(c). At around 5 dBm, we further observe the onset of hysteresis and bi-stable behavior, which becomes more pronounced with increasing power, Fig. S5(d,e,f). At the same time we find that the depth of the transmission dip decreases, Fig. S5 an effect that sets on already at power levels around 0 dBm in the bus waveguide. Heating of the ring due to linear absorption may explain skewing and bi-stability 5 , but the reduction of the depth of the resonance dips is a clear indication of nonlinear losses such as TPA and TPA-induced FCA in the rings 6 . These experimental findings are in reasonable agreement with the estimated build-up factor B of 11.8 dB and the fact that nonlinear losses in silicon nanowire waveguides start to become relevant at power levels around 19 dBm, see Fig. S4. Based on these estimations, we should expect that operation of our device is not only subject to heating of the rings due to linear optical intra-cavity losses, but also to TPA and TPA-induced FCA in the ringat least to some degree. In our experiments, we did not encounter any detrimental effects such as hysteretic wavelength- Fig. S5. Transmission measurements through ring R1 between grating couplers GC 1 and GC 3 at different optical input power levels PBus in the bus waveguide. To avoid destroying the ECL during the experiment, we used a SiP chip that is nominally identical to the one contained in the ECL and that was fed by a test laser and an EDFA. We tune the laser to an emission wavelength slightly below a resonance of ring R1 and then ramp the heater current of ring R1 up and down to scan the resonance across the fixed laser wavelength while measuring the output power. This experiment is repeated at different levels of the on-chip input power PBus. Starting from a power level PBus of 4 dBm, we first find that the resonance peaks become increasingly skewed, see Subfigure (c). At around 5 dBm, we further observe the onset of hysteresis and bi-stable behavior, which becomes more pronounced with increasing power, Subfigures (d),(e),(f). At the same time, we find that the depth of the transmission dip decreases, see Fig. R3 for details. Heating of the ring due to linear absorption may explain skewing and bi-stability 5 , but the reduction of the depth of the resonance dips is a clear indication for nonlinear losses such as TPA and TPA-induced FCA in the rings 6 . Fig. S6. Resonance depths for different optical power levels PBus in the bus waveguide, extracted from transmission measurements between grating couplers GC 1 and GC 3, see Fig. S5. The resonance depths start to decrease already at power levels around 0 dBm in the bus waveguide. At around 5 dBm, we observe the onset of hysteresis and bi-stable behavior, which becomes more pronounced with increasing power. The blue trace shows the resonance depths recorded when ramping the heating power up ("forward") and the orange trace shows the ones when ramping the heating power down ("reverse"). tuning behavior or unwanted pulsation of the laser emission. Still, implementing ECL with higher emission power might either require large-area SiP waveguides 7 , active removal of free carriers by reverse-biased p-i-n junctions integrated into the ring waveguide 8,9 , or feedback circuits base on waveguides made from large-bandgap silicon dioxide 10 or silicon nitride 11,12 . 6. Theoretical discussion of the ECL linewidth As a reference for the experimentally measured phase-noise properties of our ECL, we theoretically estimate the linewidth that could be expected based on the characteristics of the RSOA and the external feedback circuit. To this end, we follow the formalism described in Ref 7,11,13 , which is based on Ref 14 . In this model, the laser is simplified to an active section in between two reflecting facets. The back facet has a frequency-independent amplitude reflection coefficient coefficient b r , while the front facet is represented by a frequency-dependent complex amplitude reflection coefficient    (S17) For simplicity, we assume that the resonance frequencies of both rings are tuned to perfectly coincide at or near the lasing frequency, leading to a reflection spectrum as shown in Fig. 3(b) of the main manuscript. Tuning of the intra-cavity phase shifts the frequency of the lasing resonator mode with respect to the peak of the reflection spectrum of the external feedback circuit, and the exact linewidth depends on the detuning between the laser emission frequency and the peak of the reflection spectrum. (S18) With these numbers at hand, we can use the estimation of Henry 15 for the Fabry-Pérot linewidth, which then leads to the estimated ECL linewidth Equations (S12)…(S20) allow to estimate the linewidth of our ECL, using numerical values for the various parameters as specified in Table S1. For the Henry factor, we consider a typical value range of H 2...7   for InP/InGaAsP lasers at a wavelength of 1.5 µm, see Ref 16 . For the population inversion   (a) Calculated parameters A, B, and F according to Eqs. (S15) -(S17). To account for the uncertainties of the various input parameters listed in Table S1, we plot two traces for B, F, and , indicating the corresponding lower (subscript "lo") and the upper (subscript "up") boundary. (b) Corresponding linewidth according to Eqs. (S19) and (S20). Assuming optimum detuning, we expect linewidths between 90 kHz and 460 kHz. This is in reasonable agreement with the experimentally measured linewidth of approximately 105 kHz.