Abstract
A surfaceemitting distributed feedback (DFB) laser with secondorder gratings typically excites an antisymmetric mode that has low radiative efficiency and a doublelobed farfield beam. The radiative efficiency could be increased by using curved and chirped gratings for infrared diode lasers, plasmonassisted mode selection for midinfrared quantum cascade lasers (QCLs), and graded photonic structures for terahertz QCLs. Here, we demonstrate a new hybrid grating scheme that uses a superposition of second and fourthorder Bragg gratings that excite a symmetric mode with much greater radiative efficiency. The scheme is implemented for terahertz QCLs with metallic waveguides. Peak power output of 170 mW with a slopeefficiency of 993 mW A^{−1} is detected with robust singlemode singlelobed emission for a 3.4 THz QCL operating at 62 K. The hybrid grating scheme is arguably simpler to implement than aforementioned DFB schemes and could be used to increase power output for surfaceemitting DFB lasers at any wavelength.
Introduction
Highpower surfaceemitting (SE) semiconductor lasers^{1, 2} have significant advantages over their edgeemitting counterparts in multiple aspects related to coupling and alignment optics, testing and packaging, power scaling through arrays, wavelength stability, immunity to facet damage among others. The radiative efficiency of SE lasers has been increased by using different techniques, including use of curved and chirped gratings for infrared diode lasers^{3, 4}, implementation of central grating π shift for shortcavity devices^{5}, plasmonassisted mode selection for midinfrared quantum cascade lasers (QCLs)^{6,7,8}, and graded photonic structures for terahertz QCLs^{9}. At nearinfrared wavelengths, such highpower lasers are predominantly realized as verticalcavity SE lasers (VCSELs)^{10}. However, some of the highest power output for singlemode lasers has been demonstrated with secondorder DFB gratings^{3, 4}. For QCLs that emit at longer wavelengths^{11,12,13}, vertical cavities are not possible owing to the transversemagnetic polarization of the intersubband optical field, hence secondorder gratings are used for surfaceemission^{7, 8, 14,15,16,17,18}. Highbrightness singlemode QCLs are desired across the midIR and terahertz spectrum for applications in chemical and biomolecular sensing and spectroscopy. At midIR wavelengths, multiWatt level power was demonstrated for edgeemitting DFB QCLs^{19}; however, for surface (or substrate) emitting DFB QCLs with secondorder gratings, the power output is yet to reach such levels^{7, 8, 20} and there is considerable scope for improvement. For terahertz QCLs, the subwavelength confinement of the metallic cavities^{11} offered new challenges to development of DFB techniques. Consequently, a variety of DFB configurations have been demonstrated^{21, 22}. A modification of the onedimensional secondorder gratings with graded periodicity led to the previous highest power output of 103 mW at 20 K for singlemode terahertz QCLs^{9}. More recently, similar power levels have been realized with externalcavity SE terahertz QCLs^{23}, which offer the advantage of lowdivergence beams at the cost of frequencystability and specificity afforded by DFB lasers.
Here we describe a new scheme for enhancing radiative efficiency for surfaceemitting DFB QCLs in metallic cavities that achieves record high output power for singlemode terahertz QCLs. A record high slopeefficiency is realized that is more than four times greater than that in ref.^{9}, and is also considerably higher than that from terahertz QCLs with singleplasmon waveguides that have recently reached Watt level output powers^{24, 25}.
Results
Concept
A periodic perturbation in an optical waveguide leads to Bragg diffraction up to multiple higher orders that could be used to couple counterpropagating waves in the waveguide to establish DFB. The following equation describes the momentum conservation relation between the wavevectors of the incident guided wave inside the cavity k_{i} ≈ 2π/λ_{wg} = 2πn_{eff}/λ (where λ_{wg} is the wavelength inside the waveguide, λ is the free space wavelength, and n_{eff} is the effective index of propagation) and that of the diffracted wave k_{d}, which could be outside or inside the cavity at any angle θ_{d} (as defined with respect to the surfacenormal). This is also represented schematically in Fig. 1a.
here Λ is the grating period, 2π/Λ is the grating wavevector, and n is an integer (n = 1,2,3 …) that specifies the diffraction order. From this equation, it can be concluded that a nth order grating structure, where n is an even number, causes n/2th order diffraction to occur in the surfacenormal direction.
The concept of the hybrid secondorder and fourthorder DFB gratings for increased radiative efficiency of SE lasers is described next. Figure 1b shows the conventional secondorder gratings in an optical cavity that are used to realize broadarea surface (or substrate) normal emission from the cavity, since the firstorder Bragg diffraction is perpendicular to the guided wave direction in the cavity as per Eq. (1)^{1}. Coupledmode^{2} or finiteelement modeling of the periodic structures are used to compute the photonic bandstructure. Typically, the bandedge modes in a longitudinal cavity are termed as symmetric and antisymmetric with high and low radiative efficiencies respectively, where the latter is excited for a SE DFB laser thereby limiting its output power. The radiative efficiency depends on the precise amplitude and phase of the standingwave (resonantmode) with respect to the periodicity of the grating. This behavior is typical of different types waveguides and DFB gratings and not just metallic cavities that are shown in Fig. 1b. Figure 1c shows conceptually how superposing a fourthorder grating structure on the existing secondorder grating serves to enhance the overall radiative efficiency. Due to weaker Bragg diffraction for feedback, the fourthorder grating does not alter the modeshapes of bandedge modes significantly, which changes the electromagnetic field distribution along the length of cavity only slightly, that is, the maximum point of E_{ x } would slight offset the slit center and reduce the radiative efficiency of symmetric mode. An array of antennalike dipoles with opposite polarities are introduced in each repeat period of the hybrid grating that causes destructive interference for the outcoupled radiation (marked as competing dipole from 4th order DFB as shown in Fig. 1c), which in turn reduces the outcoupling efficiency of symmetric mode. However, since the secondorder Bragg diffraction is in the surfacenormal direction, the fourthorder grating could be located so as to increase radiative loss for the original antisymmetric mode of the secondorder DFB structure. Such a hybrid grating enhances the radiative efficiency of the antisymmetric mode and reduces that of the symmetric mode, and hence, either of those bandedge modes could possibly be excited as per the precise implementation of the fourthorder grating. In either case, the radiative efficiency is enhanced when compared to the excited mode for the original secondorder DFB structure. It is to be noted that the 1st and 3rd order diffraction from the fourthorder gratings DFB could potentially produce offnormalradiation since they are not diffracted perpendicularly or parallel to the surface. However, the possibility of such radiation does not exist in such a cavity, which can be shown through straightforward analysis based on Eq. (1). Finiteelementsimulations were also carried out to validate this claim, which is described further in the Supplementary Note 6.
Implementing hybrid DFB scheme for terahertz QCLs
To describe the specific implementation of the hybrid DFB scheme for terahertz QCLs with metallic cavities, and a comparison with the conventional secondorder DFB in such QCLs^{18}, results from finiteelement simulations are shown in Fig. 2. The radiative surface losses of the resonant modes, their frequencies, and electric field profiles for the bandedge modes for finitelength cavities with gratings implemented in the top metal cladding are shown. It is argued that the value of radiative loss itself is a direct indicator of the outcoupling efficiency from such DFB cavities. Supplementary Note 7 further elaborates this aspect about the outcoupling efficiency from the cavity. For a conventional secondorder DFB, the radiative loss for the upper bandedge mode (symmetric inplane (E_{ x }) field) is considerably larger than the nonradiative lower bandedge mode (antisymmetric inplane (E_{ x }) field)^{18}. In comparison, the cavity with the hybrid secondorder and fourthorder gratings greatly enhances the surfaceloss for the antisymmetric lower bandedge mode due to additional radiation from the slit corresponding to the fourthorder superposed grating. The loss for the symmetric upper bandedge mode is reduced from that of the secondorder DFB structure. For the simulated case of d/Λ in Fig. 2, the upper bandedge mode is of lower loss for the hybrid DFB grating, and will be excited in a lasing cavity. More importantly, the surface loss of the excited mode in laser cavity with hybrid DFB can be enhanced by an order of magnitude from that of the secondorder DFB cavity. It may be noted that bandgap of the hybrid DFB cavity has a redshift of ~0.08 THz in the shown simulation, which is due to the fact that a larger fraction of evanescent field propagates outside the active medium that lowers the effective propagation index n_{eff} of the guided waves.
For the symmetric mode excited in the case of hybrid DFB with a specific d/Λ = 3/8, n_{eff} is close to ~3.2 according to Eq. (1), this relatively low n_{eff} is due to the establishment of a strong surface plasmon polariton (SPP) field that propagates on the top of the active region as shown in Fig. 2b. In contrast, the antisymmetric mode has a larger n_{eff} ~ 3.45, which translates to a larger fraction of resonant mode confined inside the active medium.
The hybrid DFB grating offers flexibility in design by simply altering the offset d at which the fourthorder grating is implemented as shown in the schematic in Fig. 2a. The relative radiative losses of the two bandedge modes could be modulated by adjusting d/Λ, which is useful to design for selective excitation of a lower or upper bandedge mode. This is shown in the plot of computed surface losses of the bandedge modes of the infinitely wide but finitelength terahertz QCL cavity in Fig. 3a, where simulation is done with same parameters for the grating as in Fig. 2. For a certain range of d/Λ values, the loss of the upper bandedge mode could be lowered and hence such a mode could be selectively excited. For experimental results presented later, d/Λ = 3/8 was implemented to selectively excite an upper bandedge mode. Note that in this case, both bandedge modes lead to singlelobed beams in the farfield and symmetric/antisymmetric designations lose significance due to an overall constructive interference in the farfield for both bandedge modes (Supplementary Note 2 shows an intuitive explanation on singlelobed beam profile for both bangedge modes), when considering the net radiation from every 2Λ length of the DFB structure. In this sense, the hybrid DFB structure could instead simply be called a fourthorder DFB scheme, but one that has a specific requirement for its unit cell of periodicity 2Λ. We choose not to use this terminology since then it does not clearly indicate the operating mechanism of the DFB.
Given that the hybrid DFB for terahertz QCLs presented here is implemented with dualslits in metal cladding in every alternate period of length Λ, it is intuitively compelling to consider whether the radiative loss for a secondorder DFB for such QCLs could also be increased by introducing dualslits in each period to avoid the nulls of the radiative field E_{ x } in one of the two slits. Such a DFB structure was indeed investigated experimentally in ref. ^{26}. However, it turns out, such a DFB structure also has an antisymmetric mode for one of its bandedge modes, which has negligible radiative coupling. In this case, the role of symmetry is reversed for the bandedge modes, and the upper bandedge mode now becomes the lowloss mode with destructive interference for radiative coupling into the farfield. The behavior of the surfacelosses for the two bandedge modes and the representative electric field profiles for the dualslit secondorder grating structure are shown in Fig. 3b. This type of structure could potentially be used to increase output power if a large d/Λ was chosen to make the photonic bandgap large, such that the upper bandedge modes lie outside the gain region of the active medium. This was indeed the strategy employed in ref. ^{26} to increase power output from SE DFB terahertz QCLs moderately. While the dualslit structure may appear to offer somewhat similar functionality to the hybrid DFB structure, the latter is fundamentally different in its functionality and effectiveness to improve radiative efficiency for surfaceemission.
Experimental results
Experimental results from representative SE terahertz QCLs implemented with hybrid DFB gratings in pulsed mode of operation and mounted inside a Stirling cooler are shown in Fig. 4. The scanning electron microscope (SEM) image of the fabricated and mounted QCL chip in Fig. 4a shows several QCLs of varying dimensions located side by side. The results presented here are from QCLs of dimension 10×200 μm×1.5 mm. The choice of the length of cavity is made based on estimation of the DFB coupling strength, and is described in the Supplementary Note 1 and Supplementary Note 2, where the simulated energydensity profile along the length of the cavity for the chosen length is shown in Supplementary Figure 1. The hybrid DFB grating in the form of slits is implemented in the top metal cladding. Figure 4b shows the light–current (L–I) curves versus heatsink temperature, current–voltage (I–V) curve at 62 K, and also spectra as a function of bias at 62 K. The QCL emits in singlemode at all bias conditions at ~3.39 THz, and operated up to maximum temperature of 105 K. Figure 4c shows the measured farfield radiation pattern, which is singlelobed and a characteristic of symmetric mode excitation for the resonantmode of the DFB structure. The fullwidth halfmaximum divergence is ~5° × 25° that closely matches the result from fullwave finiteelement simulation of the DFB cavity as presented in Supplementary Figure 1. Finally, the robustness of the DFB scheme in exciting the desired mode based on lithographically defined periodicity is exemplified from the lasing spectra of three different QCLs with different Λ shown in Fig. 4d. All QCLs showed singlemode operation in the entire dynamic range and the lasing frequencies scale with Λ with an effective propagation index n_{eff} ~ 3.16 for the guided modes. This relatively low n_{eff} certifies that the upper bandedge mode is excited for these QCLs as designed.
The primary contribution of this work is the high radiative efficiency of the hybrid DFB scheme. A peak optical power output of 170 ± 3 mW at 62 K was measured for the QCL reported in Fig. 4b, which is the power detected from the power meter without making any corrections for the imperfect collection efficiency and optical losses from the cryostat window. The wallplug efficiency of this device is ~0.78% and a slope efficiency of 993 ± 15 mW A^{−1} (differential quantum efficiency of 71 photons/electron) is estimated from the slope of the 62 K L–I using linear curve fitting in the range of 20−80% of bias range of the QCL. The differential and slopeefficiencies are highest achieved todate from any terahertz QCL including that from Fabry–Pérot QCLs with singleplasmon waveguides, which had demonstrated the best radiative efficiencies previously. For comparison, terahertz QCLs with conventional secondorder gratings were also fabricated from the same MBE wafer. L–I data from one such representative QCL with similar cavity dimensions is shown in Supplementary Note 3, which achieved a peak power output of 50 mW, a maximum operating temperature of 129 K, a wallplug efficiency of ~0.18% and a slope efficiency of ~80 mW A^{−1} at 63 K. While the peak power outputs cannot be compared since the dynamic range for lasing is higher for the conventional secondorder DFB device, the slope efficiency for the QCL with hybrid DFB is more than an order of magnitude higher compared to the conventional secondorder DFB QCL that validates the strong enhancement of radiation due to the new DFB technique. However, it has to be noted that the comparison of power output of hybrid DFB with conventional secondorder DFB is not truly reflective of improvement in outcoupling efficiency due to the fact that any variation of the boundary condition near the ends of cavities would significantly influence the emission loss of conventional secondorder DFB^{18}. Therefore L–I data from a Fabry–Pérot QCL with a dimension of 10 μm×150 μm×1.5 mm is also shown in Supplementary Note 4 for comparison, which shows that the maximum operating temperature of this active medium is 137 K. The temperature performance from this active medium is relatively modest compared to stateofthe art terahertz QCLs, and hence, a significant increase in power performance is expected with better performing active medium that could achieve a greater dynamic range in lasing with high temperature performance. To futher reveal the high performance of this hybrid secondorder and fourthorder DFB mechanism, a comparison of this scheme with graded photonic structure^{9} based on numerical simulation is presented in Supplementary Note 5.
Discussion
In conclusion, here we have described a new DFB method to significantly increase radiative efficiency for surfaceemitting solidstate lasers based on the widely used secondorder Bragg gratings. A hybrid secondorder and fourthorder DFB grating is shown as an effective method to excite a symmetric radiative mode with large radiative outcoupling in a singlelobed beam, which is also simpler to implement compared to existing modifications to secondorder gratings in literature. The hybrid DFB scheme is implemented for terahertz QCLs to realize a singlemode QCL with highest reported optical power output (170 mW) todate. A recordhighest slopeefficiency (993 mW A^{−1}) and differential quantum efficiency (71 photons per electron) is also experimentally demonstrated when compared to all previously reported terahertz QCLs in literature (including that from multimoded Fabry–Pérot QCLs). These values suggest that the radiative efficiency realized for the QCL is approximately onethird of the maximum theoretically possible in absence of any loss mechanisms. In principle, the hybrid DFB technique should also be applicable to semiconductor lasers at nearinfrared and midinfrared wavelengths to increase the power output for singlemode surfaceemitting lasers at those wavelengths.
Methods
Finiteelement modeling
All of the simulations were carried out by using COMSOL Multiphysics 4.4. A module of Electromagnetic waves, Frequency Domain (ewfd) under the catalog of Optics was utilized to calculate the eigenmodes of various kinds of DFB laser structures shown in this paper. In order to obtain accurate information of the emission loss, The active region is modeled as lossless and the metal is modeled to be perfect electrical conductors, the highly doped contact layer serving as absorbing boundaries of the cavity is implemented using a complex dielectric constant computed using Drudemodel and a perfectmatching layer for absorbing boundary echoes was adopted to wrap all the borders. The specific details of the modeling for both 2D and 3D simulations are same as that in ref. ^{27}, in which case, the computed loss is the sum of loss at absorbing boundaries as well as that due to radiation (outcoupling). By analyzing the eigenfrequencies and their corresponding radiation losses, the lasing frequency as well as the farfield beam patterns can be estimated.
Materials
The active medium of the THzQCLs is based on a threewell resonantphonon design with GaAs/Al_{0.15}Ga_{0.85}As superlattice (design RT3W221YR16A, MBE wafer VB832, with a layer sequence of 57/18.5/ 31/9/28.5/16.5 (starting from the injector barrier) where the thicknesses are in monolayers (ML, 1 ML = 2.825 Å), and was grown by molecular beam epitaxy, with 221 cascaded periods, leading to an overall thickness of 10 μm. The design is similar to the threewell QCL designs in^{28, 29} with minor modifications to achieve peak gain centered around a frequency of 3.3 THz. The QCL superlattice has an average ndoping of 5.7e15 cm^{−3} and surrounded by 0.1 μm and 0.05 μm thick highly doped GaAs contact layers doped at 5e18 cm^{−3} on either sides of the superlattice. A 200 nm thick Al_{0.50}Ga_{0.50}As layer was grown as an etchstop layer preceding the entire stack.
Device fabrication
Cu–Cu based metallic waveguides were fabricated using standard thermo compression waferbonding technique. Following waferbonding and substrate removal, positiveresist lithography was used to selectively etch away the 0.1 μm thick highly doped GaAs layer from almost all locations where topmetal cladding would exist on individual cavities by H_{2}SO_{4}:H_{2}O_{2}:H_{2}O etchant in 1:8:80 concentration. A 10 μm wide highly doped GaAs layer below the topmetal cladding was left unetched at the regions close to both longitudinal and lateral facets, serving as the longitudinal and lateral absorbing boundary to ensure the excitation of the desired mode as the lowestloss lasing mode as described in ref. ^{27}. A sequence of Ti/Cu/Au were deposited as top (20/200/100 nm) metallic layers, in which an imagereversal lithography was implemented to form metallic gratings. DFB ridge cavities then were processed by wetetching using H_{2}SO_{4}:H_{2}O_{2}:H_{2}O etchant in 1:8:80 concentration. A Ti/Cu/Au (20/250/100 nm) contact was also used as the backsidemetal contact for the finally fabricated QCL chips to assist in soldering. Before deposition of backsidemetal of the wafer, the substrate was mechanically polished down to a thickness of 250 μm to improve heatsinking.
Experimental characterization
During the light–current–voltage measurements, A pulse of 300 ns duration with 100 kHz signal cycle (3.0 % duty cycle) was chosen to drive the devices presented in this paper on a coldstage of a Stirlingcooler (which is operating at ~62 K). Under the same conditions, the absolute power was calibrated using a thermopile power meter (model number: Scientech AC2500 with AC25H) as is reported without any corrections to the detected signal. No focusing optics were used in this process except a highdensity polyethylene window on the cryocooler. The reported spectra were measured using a Fouriertransform infraredspectrometer (BRUKER; VERTEX 70 v) by operating the devices at 100 kHz with a 300 ns pulse duration (3.0 % duty cycle). Farfield beam patterns were measured with a pyroelectric detector mounted on a 2D motorized scanning stage, which was placed at 40 cm from the DFB lasers, with maximum scan angle ± 26.5° in both two directions. The devices was operated near the peak power operated at 100 kHz with a 300 ns pulse duration and electronically modulated with pulsetrains at 1000 Hz (1.5 % duty cycle).
Data Availiability
All relevant data related to numerical simulation, experimental results will be preserved with Sushil Kumar at Lehigh University, the data sets are accessible via the corresponding author.
Additional information
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Change history
14 May 2018
The original PDF version of this Article contained an error in Equation 1. The ‘Λ’ was missing from the denominator. This has been corrected in the PDF version of the Article. The HTML version was correct from the time of publication.
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Acknowledgements
This work is supported by the U.S. National Science Foundation under Grants: ECCS 1351142, ECCS 1609168, and CMMI 1437168. It was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DENA0003525.
Author information
Affiliations
Contributions
S.K. conceived the original idea of a hybrid grating and supervised the project. Y.J. further developed the idea through analysis and simulations, and techniques for the practical implementation. Y.J. and C.W. performed numerical simulations. L.G. and Y.J. fabricated the devices. Y.J., J.C., and L.G. developed the experimental setup and conducted the measurements. J.L.R. was responsible for growth of the QCL material by molecular beam epitaxy. S.K. and Y.J. wrote the manuscript with inputs from all other authors.
Competing interests
The authors declare no competing interests.
Corresponding authors
Correspondence to Yuan Jin or Sushil Kumar.
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