Integrated Photonic Device for Wavelength-Stable Laser Oscillation and Simultaneous Input Coupling

A guided-mode-resonance device for both narrow-band retroreflection and waveguide input coupling was designed and fabricated for operation wavelength of 1550 nm. It consists of a focusing grating coupler (FGC) integrated in a waveguide cavity resonator constructed by a pair of distributed Bragg reflectors (DBRs) on a reflection substrate. The size of the FGC was 31 × 20 μm2. The device was used as a laser mirror of an external cavity laser. The oscillation wavelength was fixed to the retroreflection wavelength, and the laser power was coupled to a waveguide. The coupled power depends on the length of one DBR. The optimal length for the maximum coupling was also discussed theoretically and experimentally.


I. INTRODUCTION
A GUIDED-MODE resonance filter (GMRF) consists of a surface grating on a thin-film waveguide on a transparent substrate and shows a narrowband reflection spectrum for an vertically-incident free-space wave [1], [2], [3], [4], [5], [6], [7]. The grating excites and out-couples a guided wave in a resonance wavelength band. A GMRF has advantages in fabrication convenience and design flexibility in comparison to a dielectric multilayer mirror. A GMRF requires only a few layers whereas a dielectric multilayer mirror requires hundreds of layers for narrowband reflection. Various spectra, including narrowband reflection, narrowband transmission, and wideband reflection, can be obtained by appropriate design of the waveguide structure and grating coupling strength. Narrowband reflection and transmission are useful for laser mirrors [8], [9], [10], [11], [12], [13], [14] and chromatic filters [15], [16], respectively. Wideband reflection is attractive for achromatic mirrors [17], [18]. Moderate bandwidth can be used for color filters [19], [20], [21], [22], [23]. Moreover, intentional introduction of absorptive loss into the guided mode can provide high-extinction absorbers [24], [25]. Since the resonance wavelength is sensitive to an effective refractive index of the guided mode, the GMRF can act as high-precision index sensors applicable to bio-chemical sensing [26], [27]. Another essential feature is polarization selectivity. The GMRF brings not only reflection but also phase shift to only certain polarization component. This feature is exploited for polarizers [28], [29] and depolarizers [30], [31]. Thus, GMRFs have been used as bulk-optic components in most of applications so far. On the other hand, the configuration of guided mode utilization inspires us an application to integrated photonics.
We are investigating utilization of GMR in photonic integrated circuit. However, a normal GMRF needs a sub-millimetersize interaction aperture for nanometer-order reflection bandwidth. For miniaturizing the aperture, a new type of GMRF, namely, cavity-resonator-integrated guided-mode resonance filter (CRIGF) was proposed [32], [33], [34]. It has a small grating coupler within a waveguide cavity resonator constructed by two distributed Bragg reflectors (DBRs). In addition to the small aperture, the excited guided wave can be extracted from the CRIGF through one of the DBRs [35]. Because of the multifunctionality of input coupling and narrowband reflection, it is expected that a CRIGF serves as an external laser mirror which stabilizes oscillation wavelength to the reflection wavelength and couples the laser light to the waveguide. A combination of semiconductor optical amplifiers (SOAs) integrated on a gain chip and cascaded CRIGFs of different resonance wavelengths integrated on a bus waveguide would provide an ultra-compact multi-wavelength light source without separate multiplexers, such as an arrayed waveguide grating or a multi-mode interference coupler [36]. An SOA and a CRIGF construct a laser cavity. A light launched from an anti-reflection coated facet of the SOA is reflected back by the CRIGF. However, here is an issue to be solved. The diameter of an incident beam to the CRIGF must coincide with the aperture size to obtain high reflectance. The aperture size will be several microns at least even though it is much smaller than GMRF. Meanwhile, a field diameter of the guided mode of an SOA is a few microns. We cannot expect high-efficiency direct butt coupling of the SOA to the CRIGF and need some beam-size conversion. We proposed a focusing CRIGF (F-CRIGF) for reflecting and focusing a diverging wave back to the diverging point. A focusing grating coupler (FGC) and a reflection substrate are used in the F-CRIGF [37]. An F-CRIGF can retroreflect the emitted light from the SOA. As a result, we can avoid the unpreferable integration of additional lens for the beamsize conversion. Stabilization of oscillation wavelength by an F-CRIGF was demonstrated in previous work [38]. This time, we designed and fabricated F-CRIGFs for input coupling as well as wavelength stabilization. We constructed external-cavity diode lasers (ECDLs) using the F-CRIGFs, and demonstrated wavelength-stable laser oscillation and simultaneous input coupling for the first time. The extraction ratio through one DBR to the waveguide depends on length of the DBR. Shorter DBR gives lower retroreflection to the SOA but higher-efficiency input coupling to the waveguide. We discuss the optimal DBR length with experimental results. Fig. 1 shows a schematic diagram of an ECDL using an F-CRIGF and wave propagation. An F-CRIGF consists of an FGC integrated in a waveguide resonator and an underneath reflection substrate. The waveguide is constructed with an optical buffer layer, a guiding core layer, and relief gratings forming FGC and DBRs [39], [40]. A diverging wave is launched from an anti-reflection coated facet of an SOA. A part of the diverging wave is coupled to counter-propagating guided waves by the FGC in a resonance wavelength band. The rest is specularly reflected by the reflection substrate. The guided waves propagate back and forth in the waveguide resonator. The FGC out-couples the guided waves to diverging and focusing radiation waves depending on the direction of the guided wave propagation. The diverging radiation wave interferes with the specularly reflected wave. They vanish at a wavelength λ rc where complete destructive interference occurs when both DBRs have 100% reflectance. As a result, only the focusing radiation wave remains. The interference destruction degrades in other wavelengths. It means that the maximum retroreflection is obtained at λ rc . Thus, the laser oscillation wavelength is fixed to λ rc . We can extract the resonant guided wave from the F-CRIGF by reducing reflectance of one of DBRs. It is worth noting that the retroreflection for laser oscillation and the excitation of guided mode occur simultaneously. This is a great advantage in integration of an input coupler in comparison to a case of usual grating coupler where adjustments in wavelength and incidence-angle are required for high efficiency coupling. You can reduce DBR reflectance by shortening its coupling length. A shortened DBR (S-DBR) is integrated on the side of input coupling port. Shorter S-DBR extracts more guided-wave power, but degrades the guided mode resonance leading to reduction of the retroreflection to the SOA. Therefore, the S-DBR length should be designed to maximize the device efficiency of the guided-mode launching ECDL. Fig. 2 shows a schematic view of the designed F-CRIGF for λ rc of 1550 nm. We assumed y-polarized incident light and designed F-CRIGFs operating with transverse-electric guided mode. A 370-nm-thick Si-N guiding core layer (refractive index of 1.954) and a 1820-nm-thick SiO 2 optical buffer layer (refractive index of 1.468) are stacked on a reflection substrate. The reflection substrate is made of a dielectric multilayer mirror of 10.5 pairs of 174.1-nm-thick Nb 2 O 5 (refractive index of 2.216) and 263.4-nm-thick SiO 2 deposited on a SiO 2 substrate to give 100% reflectance. Si-N/air gratings of 50-nm height are formed on the core layer. The fill factor of the gratings was set to 0.5. The effective refractive index N of the guided mode was estimated to be 1.678 with an assumption of a simplified structure replacing the gratings by a uniform layer with a dielectric-constant-averaged refractive index. Coupling length L GC , width W GC , and focal length f of the FGC were set to 31, 20, and 67 μm, respectively, corresponding to divergence angles from the SOA facet of 17°in z-direction and 27°in y-direction. These angles are the same as the ones of the SOA used in the experiment described in Section IV. Grating line patterns can be expressed with use of difference in spatial phase between the incident and diffracted waves. The phase of +z propagation guided wave φ g can be written as

A. F-CRIGF Structure
The phase of -z propagation guided wave is -φ g . The m-th grating line pattern of the DBR reflecting +z propagation guided wave to -z propagation guided wave is expressed by The phase of the incident free space wave diverging from a point (f, 0, 0) to the FGC is expressed by A half part of FGC located in negative z area (-L GC /2 < z < 0) was designed to launch a guided wave propagating +z direction while the other part (0 < z < L GC /2) was designed to launch -z propagating guided wave. The m-th line pattern of the FGC for negative and positive z area on the waveguide plane can be written as respectively. The FGC has curved and chirped pattern [37]. The grating period was calculated to be from 920 to 810 nm in the current case. The grating period of the DBR was determined to be 462.5 nm (=λ rc /2N). The distance between the two DBRs must be integer multiple of λ rc /N for occurring retroreflection at

B. Theoretically Predicted Characteristics
Reflectance spectra of designed F-CRIGFs were calculated using a model developed by ourselves [41]. Focusing reflectance R f and specular reflectance R s of F-CRIGF are given by where c, L Cav , ω, ω rc , R DBR , and R S-DBR are the speed of light in a vacuum, length of the waveguide cavity, angular frequencies of incident-wave wavelength and of λ rc and reflectances of the normal DBR and the S-DBR, respectively. Here r a and t a are reflection and transmission coefficients on the assumption that no coupling occurs by the gratings, respectively. Then, κ ga , κ gs , α, E ν a 0 , E ν s 0 , Δ, and τ are coupling coefficients for couplings from the guided wave to the air-and substrate-radiation waves, the radiation decay factor of the FGC, normalized electric fields of the air-and substrate-radiation modes, a phase mismatch factor in z-direction between incident and radiation waves and photon lifetime in the waveguide resonator.
Equation (6) includes only radiation waves, whereas (7) includes multilayer reflection r a as well. In the case of the designed F-CRIGF, κ gs = 0 and t a = 0 because of substrate reflection of 100% efficiency. Therefore, only terms of multilayer reflection and air radiation remain. The first and second terms of (8) show contributions from the radiation from the FGC and the leakage through both the DBRs, respectively. The specular reflectance R s vanishes by substituting ω = ω rc and (8) into (7) when R DBR = R S-DBR = 1. Only R f remains at λ rc resultantly. When R DBR and R S-DBR < 1, the incident power is divided into a focusing reflection, a specular reflection, and the guided-wave leakage from the waveguide resonator. An extraction through the S-DBR is a portion of the guided-wave leakage. The extraction ratio E is given by where T DBR and T S-DBR are transmittances of the normal DBR and S-DBR, respectively. The first and the second factors are the total leakage power and distribution ratio of the powers transmitted through the S-DBR. Fig. 3 shows the calculated dependences of R f , R s , and E on S-DBR length. The values of r a , t a , κ ga , κ gs , E ν a 0 , E ν s 0 and Δ slightly vary in the FGC aperture due to incidence angle variation in a precise sense. In the calculation, we approximated these values as the ones for vertical incidence for simplicity. Longer S-DBR gives higher Q-factor of the ECDL but lower extraction efficiency. In other words, there is an optimal S-DBR length for the maximum efficiency of the guided-mode launching ECDL. Transmission power P t from a typical Fabry-Perot laser through a front mirror is written by where , q, w a , d a , L a , Г, N g , D 0 , A g , τ s , τ ph , γ int , J, J th , R 1 , and R 2 are the reduced Planck constant, the elementary charge, the width, thickness, and length of the active region, the confinement factor of the guided mode in the active region, a group refractive index of the guided mode, a transparency carrier density, a differential gain, a relaxation time of a spontaneous emission, a photon lifetime in the ECDL, an internal loss of the laser cavity, an injection current density, a threshold injection current density, and reflectances of front and back mirrors, respectively. The second and third factors of (13) are external differential quantum efficiency and the number of injection carrier, respectively. The threshold current density J th is given by (14) showing that round-trip gain needs to beat round-trip cavity loss. The photon lifetime τ ph is related with the internal and reflection losses as shown (15). We use the F-CRIGF as a front mirror, then R 1 = R f . The incident power P in to the F-CRIGF and the extracted power P ex to the waveguide are given by We calculated dependence of P ex on S-DBR length. We consider an SOA with R 2 of 0.9, w a of 4 μm, d a of 1.0 μm, L a of 1000 μm, Г of 0.035, N g of 3.2, D 0 of 0.9 × 10 18 cm −3 , A g of 1.5 × 10 −16 cm 2 , τ s of 3.5 ns, and γ int of 0 mm −1 . Fig. 4 shows the calculated P ex for several injection currents I, which is given by J×w a L a . The S-DBR length for the maximum P ex was about 50 μm in this case. On the other hand, longer S-DBR gives higher R f and lower threshold injection current.

A. Fabrication
The multilayer structure for the bottom mirror, waveguide, and gratings were deposited by radical assisted sputtering by Shincron Co., Ltd. The grating relief structure was formed by electron-beam (EB) direct writing lithography. The waveguide channel was obtained by remaining grating teeth. In other words, grating grooves and outside the channel were etched out. Fig. 5 shows a scanning electron microscope (SEM) image of grating patterns of the fabricated F-CRIGF.

B. Experimental Setup
A gain chip (SAF-1126-55-90-HTS, Thorlabs) was combined with the fabricated F-CRIGFs to construct ECDLs. We measured laser oscillation spectra and the extracted powers of the guided wave simultaneously. A schematic diagram of the experimental setup is shown in Fig. 6. An output GC was integrated next to the S-DBR for measuring P ex . We inserted relay lenses and a beam splitter in order to measure lasing spectra by an optical spectrum analyzer. The emitted wave from the SOA was collimated, deflected by the beam splitter, and focused on the focal point of the F-CRIGF. The reflected wave returned to the SOA. Alignment tolerance is determined by the emission diameter of the SOA, typically a few micrometers. We should align the focal point of the F-CRIGF to the emission point. In the experiment, the F-CRIGF and the SOA were aligned actively for obtaining the highest laser power. Optical stages with micrometers were used, and the alignment accuracy was about 1 μm. Alignment error of 1 μm results in a mode-field matching ratio of −1 dB. Effect of this coupling loss is discussed below. The extracted guided wave from the F-CRIGF was out-coupled by the output GC, and was detected by a photodetector. Fig. 7 shows the measured dependences of P ex on S-DBR length for several injection currents. The S-DBR length for the maximum extraction was shorter than the prediction shown in Fig. 4. This difference must be attributed to extra cavity loss caused by the insertion of optical components between the SOA and the F-CRIGF. The insertion loss should be counted in γ int and can be written as

C. Experimental Results
where T lens is transmittance of the lenses, R BS is reflectance of the beam splitter, and η c is a mode-field matching ratio between emitted and returned waves at the end of the SOA. The estimated value of T lens , R BS , and η c were 0.75, 0.90, and 0.8, respectively. The value of η c was calculated on the assumption that the optical axis shift between the emitted wave and returned wave is 1 μm. We calculated the dependence of P ex on S-DBR length with the γ int . The calculated dependences are shown in Fig. 8 by lines and show good agreement with the experimental results. It is found that the fabricated F-CRIGF with S-DBR length of 25 μm gives the maximum extraction power. Fig. 8 shows relationship between the measured laser power and the injection current for the F-CRIGF with the S-DBR length of 25 μm. The laser power was linearly increased from the threshold current of 50 mA. Fig. 9 shows the measured laser oscillation spectra. The peak wavelength did not shift and stayed at 1553 nm even when injection current increased. On the other hand, the oscillation bandwidth broadened. This broadening   means increase of longitudinal modes in oscillation. We cannot distinguish each longitudinal mode because the cavity length was extremely long. We can also see some small spikes corresponding to the longitudinal modes of a cavity length of 1 mm constructed by facets of the SOA. Fig. 10 shows the measured dependence of the peak wavelength on the injection current. The average wavelength was 1552.83 nm, and the fluctuation from the average was within 0.18 nm. It indicates that the F-CRIGF works well as a wavelength-stabilizing external laser mirror. Slight shifts of the oscillation wavelength from the designed λ rc of 1550 nm can be attributed to the fabrication errors on the layer thickness and the grating fill factor.

V. CONCLUSION
We proposed an F-CRIGF serving as a wavelength-stabilizing laser mirror as well as a waveguide input coupler. We designed and fabricated the F-CRIGFs of the resonance wavelength of 1550 nm with several S-DBR lengths. We constructed ECDLs using the F-CRIGFs, and measured oscillation wavelengths and extracted guided wave powers. The dependences of the extracted powers on S-DBR length showed good agreement with the theoretically calculated results. The S-DBR length for the maximum extraction was shown to be 25 μm. We confirmed simultaneous wavelength stabilized lasing and input coupling even though some extra optical components were inserted in the laser cavity for experimental characterization.