Quantification of losses in bent waveguides within DBR-RW laser diodes emitting at 785 nm

An experimental study of straight and bent distributed Bragg reflector (DBR) ridge waveguide (RW) lasers and Fabry–Pérot (FP) RW lasers emitting at 785 nm is presented. To determine the losses introduced by the bent waveguides within DBR-RW lasers, different laser designs were manufactured and characterized. The bent waveguides investigated here within DBR-RW laser diodes are sine-shaped S-bends. S-bends with three different lateral offsets are manufactured. The experimental characterization of FP lasers and the straight DBR-RW lasers with different coatings at the rear facet enables a rough estimation of the losses caused by the DBR grating and the determination of the DBR reflectivity. Furthermore, additional losses in the bent DBR-RW lasers caused by the S-bend (i.e. radiation and scattering losses) are quantified by comparing them to the straight DBR-RW lasers. Within the active resonator, the S-bend losses amount to α Bend = 0.6 cm−1 (α Bend = 0.5 dB) for the smallest manufactured lateral S-bend offset H = 40 μm. For both straight and bent DBR-RW lasers spectrally narrow single-mode emission is obtained. A lateral beam width of 3.8 μm (using second moments) and a lateral far-field angle of about 18° and 19.5° (using second moments) for the straight and S-bend DBR-RW are measured, respectively. This gives a lateral beam propagation ratio of 1.2 and 1.3 (using second moments) for straight and S-bend DBR-RW, respectively. The radiation loss in dependency of the lateral S-bend offset is simulated and compared to experimentally estimated S-bend losses for bent DBR-RW lasers (H = 40 μm, H = 60 μm and H = 70 μm).


Introduction
Bent waveguides are basic photonic components that create a lateral offset to guide the light to any desired location.They are needed for example in photonic integrated circuits (PICs) Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.[1][2][3][4], where they connect the different monolithic devices on chip.While bent waveguides in PICs for example for telecommunication purposes mostly are passive structures, waveguide bends can also be put in an active laser resonator.For passive as well as for active S-bend shaped waveguides additional losses caused by the curvature (i.e.radiation and coupling/transission losses) have to be taken into account compared to straight waveguides.While passive S-bend waveguide structures are studied and modeled in depth [5][6][7][8][9], little attention has been given to active S-bends.An example of actively pumped S-bends is the dual-wavelength Y-branch distributed Bragg reflector (DBR) laser diode [10][11][12].In a Y-branch DBR laser diode, two S-bends merge to generate a common output aperture of two DBR resonators.Analyzing S-bend DBR laser diodes with respect to the losses introduced by the curvature can for example be interesting when designing such dual-wavelength Y-branch lasers.At an emission wavelength around 785 nm such lasers are for example used for Raman spectroscopy and the generation of THz radiation.
In this paper, Fabry-Pérot (FP) ridge waveguide (RW) lasers, DBR-RW lasers with straight RW, and S-bend DBR-RW lasers with bent waveguides emitting around 785 nm are investigated experimentally.First, electro-optical characteristics of the FP and straight DBR-RW laser structures are measured.The determined slope efficiencies are used to obtain internal losses, to estimate the DBR reflectivity, and to determine losses within the DBR grating.The obtained values are used to quantify additional losses caused by an S-bend within the active cavity.Second, a comparison of spectral properties and lateral beam quality measurements of the straight and S-bend DBR-RW lasers with lateral offset H = 40 µm is provided.To complete the study, losses caused by different lateral S-bend offsets are estimated.

Laser designs
Firstly, three different lateral laser designs are used for the presented experimental investigation.These are FP RW lasers, straight DBR-RW lasers and sine-shaped bent waveguide DBR-RW lasers (S-bend-DBR-RW lasers) with a lateral offset H = 40 µm.
All laser structures are based on the same vertical layer structure, which was grown using metalorganic vapor-phase epitaxy.Based on the tensile-strained GaAsP single quantum well (SQW) structure proposed in [13], a 14 nm thick SQW symmetrically embedded in a 1 µm thick Al 0.65 Ga 0.35 As vertical waveguide is used.The waveguide itself is surrounded by 1 µm thick Al 0.7 Ga 0.3 As n-and p-cladding.
To determine the figures of merits of the layer structure, uncoated, unmounted broad area (BA) lasers were measured on bar level.The measurements on BA lasers with a stripe width of 100 µm and different lengths from L BA = 1000 µm up to L BA = 6000 µm were carried out in pulsed mode (1 kHz, 1 µs).1000 µm long BA lasers showed a threshold current of I th = 230 mA and a slope efficiency of S = 0.67 W/A.The characteristic temperature of threshold current for these devices was found to be T 0 = 140 K.The other figure of merits results are summarized in table 1.
A more detailed description of the determination of the figures of merits of this vertical layer structure can be found in [14].The vertical far field has a Gaussian shape distribution.The full angle measured at half maximum (FWHM) is 29 • .
The lateral layouts of the laser designs are depicted in figure 1 (top view).The device length for all lasers is L = 3 mm and the RW width is w RW = 2.2 µm.All laser facets of the devices are passivated, and the coated front facet reflectivity is R front = 0.05.

Internal efficiency
η i = 0.9 Internal absorption α i = 0.9 cm −1 Transparency current density jtr = 115 A cm −2 Threshold current for devices with infinite length

Modal gain coefficient
Γg 0 = 18 cm −1  The RW section equals the pump region and the corresponding length is referred to as L pump .The 10th-order deeply etched DBR grating is processed using e-beam lithography.
The etch depth of the grating is 1470 nm.The grating period is about 1210 nm and the width of the trenches is about 150 nm.Please refer to [14] for more details.The DBR width at the connection to the RW is 2.2 µm.The DBR width is tapered up to a width of 10 µm at the rear facet.Tapering the ridge width of the DBR grating improves the diffraction efficiency of the grating compared to DBR gratings with a constant width [15].Two different designs of coatings were used for the rear facets of straight DBR-RW devices.Straight DBR-RW laser with high reflection coating (figure 1(b.1)) on the rear facet (R rear = 0.95) were fabricated as well as devices with antireflection coating (figure 1(b.2)), which leads to a rear facet reflectivity of R rear ≈ 5 × 10 −4 .
In figure 1(c), the S-bend DBR-RW laser can be seen.The shape of the DBR grating is identical to the grating of the straight DBR-RW laser.The shape of the RW is different and can be split into a 500 µm long straight part (out) at the front facet and a 2 mm curved part in the middle of the device (Sbend).The sine-shaped S-bend with length L S = 2 mm and lateral offset of H = 40 µm is based on Liu et al [16] defined by: The lateral offset H = 40 µm ensures that the S-bend is adiabatic.As will be discussed later in this paper, the simulated radiation loss is almost neglectable for H = 40 µm (see figure 5).
All devices were soldered p-side up on a CuW submount passively cooled by a heat sink.The electrical contacts on the p-side are made by wire bonds.

Device characterization
The power-current-characteristics (P-I-characteristics) of the devices with different lateral designs from figure 1  To determine the internal loss α i of the FP laser, the following expression for the slope efficiency S measured at the front facet is used: where h, ν and q are Planck's constant, laser frequency, and elementary charge, respectively.The internal efficiency η i is assumed to be equal to the determined internal efficiency of the BA lasers and amounts to η i = 0.9 (see table 1).R front and R rear are the reflectivities of the front and rear facet, respectively.The mirror losses α mirror are defined by: where L is the cavity length of 3 mm.With the measured FP slope efficiency of S = 1.07 W/A and the front and rear facet reflectivities of R front = 0.05 and R rear = 0.95, the internal losses of the FP RW laser is estimated to be Looking at the DBR-RW laser with high-reflection coating (R rear = 0.95) in figure 2(b.1), the threshold current is I th = 40 mA, the slope efficiency is S = 0.88 W/A and the optical output power at 250 mA is P = 185 mW.Assuming that the reflectivity of the DBR-grating is smaller than the rear side reflectivity and therefore neglecting the reflectivity of the DBR grating and ignoring any interference between the resonators formed with the DBR and the rear facet, the losses of the DBR grating α DBR caused by absorption and scattering can be approximated.In this case, the resonator comprises the pump section (RW) and the DBR section.In contrast to the FP RW laser, grating losses α DBR have to be taken into account and the internal absorption ⟨α i ⟩ in formula (2) can be expressed as: where L DBR = 500 µm is the length of the DBR grating.
With α i = 1.8 cm −1 known from the FP RW laser and the measured slope efficiency of the DBR-RW laser with R rear = 0.95, this leads to approximated DBR grating losses of α DBR = 9.0 cm −1 .Please note, that the measured optical spectra from the high reflection coated DBR-RW laser are longitudinal multi-mode with a mode distance of 27 pm.
Considering the device length of 3 mm to be the cavity and using the group refractive index of 3.7, this is in very good agreement to the observed mode distance of 27 pm.This  4) in ( 2) with the previously calculated values for α i and α DBR , the reflectivity of the rear mirror, hence the DBR grating reflectivity R rear = R DBR , can be determined to be R DBR = 0.45.Please note, that the optical spectra measured for the anti-reflection coated DBR-RW laser are longitudinal single mode.As expected for DBR lasers, mode hops occur.The measured mode hop size using a HighFinesse WS6-600 wavemeter (accuracy specified by manufacturer: 600 MHz) is 29.5 pm.This correlates to a cavity length of 2.8 mm (group refractive index: 3.7), which is as expected smaller than the cavity length of the high reflection coated DBR-RW laser discussed before.
The P-I-characteristic of the S-bend DBR-RW laser from figure 1(c) is shown in figure 2(c).The threshold current for the S-bend DBR-RW laser is I th = 40 mA.The optical output power at 250 mA is P = 160 mA and the slope efficiency between 100 mA and 200 mA is S = 0.78 W/A.For the calculation of the S-bend losses, the expression for ⟨α i ⟩ is modified in the following way: where the length of the straight output RW is L out = 500 µm and the length of the sine-shaped S-bend is L S = 2 mm.With the previously estimated values of the DBR grating reflectivity and the internal and DBR losses, formula (5) used in (2) offers a calculated S-bend loss of α S = 0.6 cm −1 for L S = 2 mm.The determined S-bend loss includes radiation as well as scattering losses.
The results extracted from the slope efficiency evaluations of the different device designs are summarized in table 2.
Both the straight and the S-bend DBR-RW laser from figure 1 (R rear ≈ 5 × 10 −4 ) provide narrow spectral emission.Figure 3 shows optical spectra of both laser designs at exemplary optical output powers (measured with DEMON LTB Berlin spectrometer; spectral resolution about 11 pm at 785 nm).At P = 50 mW, the emission wavelength of the straight and the S-bend DBR-RW laser is 783.84 nm.Slight differences in emission wavelength can be seen for P = 100 mW and P = 150 mW when straight and S-bend DBR-RW lasers are compared.The emission wavelengths are 783.90nm and 783.91 nm at 100 mW and 783.96 nm and 783.98 nm at 150 mW for the straight and the S-bend DBR-RW laser, respectively.Due to the additional losses in the bent waveguide of the S-bend DBR-RW laser, higher injection current is needed to reach the same optical output powers.Hence, the laser heats up slightly more than the straight DBR-RW laser.This is the reason for a slightly higher wavelength shift for the S-bend DBR-RW laser when increasing the optical output power.
As expected for RW lasers, beam quality measurements show Gaussian shaped beam-waist profiles as well as Gaussian shaped far-field distributions for straight and S-bend DBR-RW lasers.As depicted in figure 4(a), no difference in lateral beam waist profile can be found for straight and S-bend lasers.
At all shown optical output powers, the lateral beam width using second moments is w 2nd = 3.8 µm for both straight and S-bend DBR-RW lasers.In the lateral far-field measurements, only a minor difference between straight and S-bend DBR-RW lasers can be observed.For the straight DBR-RW laser at 50 mW, 100 mW and 150 mW optical output power, the lateral far-field angle using second moments is 18 • .For the S-bend DBR-RW laser the lateral far-field angle using second moments is slightly larger with 19.5 • .This leads to a lateral beam propagation ratio M 2 of 1.2 and 1.3 (second moments) of the straight and S-bend DBR-RW laser, respectively.

S-bend DBR-RW laser with different lateral offset H
Secondly, the presented analysis for the estimation of S-bend loss α S within an active resonator is also applied for S-bend DBR-RW lasers with bends with different lateral offsets H.The devices are based on the same vertical layer structure design and have a slightly different lateral layout with a longer overall device length of 4 mm and a longer output RW section of 1.5 mm compared to the above-mentioned devices.The included sine-shaped S-bends have the same lengths of 2 mm and are defined by equation (1) as well.The fabricated S-bend offsets are H = 40 µm, H = 60 µm and H = 70 µm.As expected, the S-bend loss α S = 0.6 cm −1 is again found for the identical S-bend with an offset of 40 µm.For H = 60 µm and H = 70 µm the determined S-bend loss is α S,60 = 1.6 cm −1 and α S,70 = 3.2 cm −1 , respectively.As expected from literature, the increase in radiation loss is non-linear when the S-bend offset H is increased [17].
Figure 5 shows the estimated S-bend losses (including radiation and scattering losses) for the different lateral offsets from the measurements in comparison to the simulated radiation loss of passive S-bends with different offsets (used simulation software: FIMMPROP from Photon Design).
The discrepancy between the experimentally determined and simulated losses is assumed to be mainly due to scattering losses, which are not included in the simulation.Nevertheless, the experimental results reproduce the expected tendency of an non-linear dependency of the S-bend losses on the lateral offset H.

Summary
By analyzing experimental results of FP RW, straight DBR-RW, and S-bend DBR-RW lasers, losses within the DBR grating and losses caused by an active sine-shaped S-bend are estimated.A grating loss of about α DBR = 9.0 cm −1 is approximated.Additionally, the DBR reflectivity was estimated to be R DBR = 0.45.The S-bend loss within the active resonator of the bent DBR-RW laser was evaluated to be α S = 0.6 cm −1 for a lateral S-bend offset of H = 40 µm.
The S-bend DBR-RW laser (H = 40 µm) reaches an optical output power of P = 160 mW at an injection current of I pump = 250 mA.Narrow spectral emission is obtained from the straight as well as the S-bend DBR-RW laser.
Lateral beam width and far-field distribution are comparable for the straight and S-bend DBR-RW laser and lead to a lateral beam propagation ratio of 1.2 and 1.3 (using second moments).
For three different lateral S-bend offsets H, the S-bend loss was determined experimentally.In agreement with the simulation, a non-linear increase of S-bend loss with increasing lateral offset was found.For H = 60 µm and H = 70 µm, the S-bend loss is α S = 1.6 cm −1 and α S = 3.2 cm −1 , respectively.

Figure 1 (
b.1) and (b.2) illustrate the straight DBR-RW laser, which comprises a 0.5 mm long DBR grating and a 2.5 mm long RW section.
are depicted in figure 2. The FP RW laser (figure 2(a)) exhibits a threshold current of I th = 35 mA.The maximal optical output power at I RW = 250 mA amounts to P = 230 mW.Between I RW = 100 mA and I RW = 200 mA, the slope efficiency is determined to be S = 1.07 W/A.

Table 2 .
Estimated losses and reflectivity based on the P-I-analysis of the different devices from figure 1. Internal loss FP RW laser α i = 1.8 cm −1 DBR loss α DBR = 9.0 cm −1 DBR reflectivity R DBR = 0.45 S-bend loss α S = 0.6 cm −1 encouraged us to make the above assumption to neglect the DBR reflectivity for a rough approximation of the losses α DBR within the DBR grating.To estimate the DBR grating reflectivity, the P-I-curve of the DBR-RW laser with anti-reflection coated rear facet (R rear ≈ 5 × 10 −4 ) from figure 1(b.2) is used.The threshold current for this laser is I th = 40 mA and the optical output power at 250 mA is P = 170 mA.The slope efficiency determined between I pump = 100 mA and I pump = 200 mA is S = 0.81 W/A.Using formula (

Figure 4 .
Figure 4. (a) Measured lateral beam-waist profiles of straight (black) and S-bend DBR-RW (red) at optical output powers of 50 mW, 100 mW and 150 mW at T = 25 • C. Dashed light blue line shows Gaussian fit of measured profile.(b) Measured lateral far-field angle of straight (black) and S-bend DBR-RW (red) at optical output powers of 50 mW, 100 mW and 150 mW at T = 25 • C. Dashed light blue line shows a Gaussian fit of measured profile.

Figure 5 .
Figure 5. Experimentally estimated S-bend loss α S (black dots) in dependency of lateral S-bend offset H within the active laser resonator.Simulated radiation loss of passive S-bend (red dots) in dependency of lateral S-bend offset H.

'
Forschungsfabrik Mikroelektronik Deutschland (FMD)' framework under ref.16FMD02.Additional financial support was provided by the European Commission for the Project MIB under Grant Number 667933-2.

Table 1 .
Figures of merits of tensile-strained GaAsP SQW inAlGaAs determined for BA lasers with a stripe width of 100 µm.