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Single-mode surface-emitting distributed feedback terahertz (THz) quantum cascade lasers (QCLs) operating around 2.76 THz are investigated in metal-metal waveguide. The design consists of one conventional long slit and two additional short slits aside in a single unit cell. Based on the symmetric modes, the two short slits provide radiating components in phase to form higher beam quality. Meanwhile the long slit provides the main feedback and lower extracted power with out-of-phased components, which contributes less to the beam. The surface-current analysis method is first introduced in QCL to analyze the losses between symmetric and anti-symmetric modes as the distance of the two short slits changes. The designed band-edge mode operates at a relative low loss, and a main single lobe is achieved with low side lobe level.
© 2016 Optical Society of America
1. Introduction
Terahertz (THz) quantum cascade lasers (QCLs) go through rapid development [1] since they were first demonstrated in 2002 [2]. As a novel compact source, the research on the THz radiation of QCLs becomes a hot topic. The semi-insulating surface-plasmon (SISP) [3] and Metal-Metal (MM) [4] waveguides are the two typical types of waveguides, which are widely studied. The former one featuring only one side metal cladding provides good output power through edge-emitting, but it has poor temperature performance and high threshold current for its loose mode confinement in the active region. In the latter one, the active region is sandwiched by two metal claddings with field confinement close to one. Since the thickness of the active region is subwavelength, the edge-emitted light emission is highly divergent from the small radiating aperture. Besides, the extracted power is low because of the impedance mismatch at the facet. The horn antenna [5] and lens [6] are implemented to improve beam quality, but they demand complicated manufacturing technologies or assembling. However, with easier fabrication process, the third-order distributed feedback (DFB) grating [7] and an antenna coupled method [8] are introduced to improve the edge emission while the second-order DFB grating [9–11] is introduced to provide the vertical emission. Recently, a novel coupling scheme, the global antenna mutual coupling, is proposed by Q. Hu et al. to phase lock two-dimensional (2D) laser arrays, and a narrow symmetric beam in the vertical emission is achieved with beam divergence <10° × 10° [12]. More recently, the antenna-feedback method is implemented into THz QCL to achieve single-mode operating with beam divergence 4° × 4° [13]. As for the one-dimensional (1D) single laser, with respect to the bandgap formed by DFB, the lower and upper band-edge modes feature different field distributions. According to the spatial symmetry of their vertical electric field components, the lower and upper band-edge modes can be classified as symmetric and anti-symmetric modes respectively with respect to the single slit in a unit cell. The radiating components on the edges of the slits are in phase in the anti-symmetric modes, which generate constructive interference with low divergent light beam. But with its higher radiation loss and higher threshold current density, it can be hardly favoured in normal DFB laser. Recently, graded photonic heterostructure (GPH) [14–16] is implemented into THz QCL to localize the anti-symmetric mode in the centre of the device and confine the other modes to the lossy laser facets. Therefore, the anti-symmetric mode maintains a relatively lower threshold current density and can be favoured. Meanwhile, the symmetric mode at lower band-edge generates divergent beam with lower surface loss [10] in the conventional structure. The insertion of a π-phase shift [10, 17] into the central device makes the field distribution along the device in phase. But the field distribution is still out of phase on the level of a single slit and the amplitude of near-field distribution is null in the centre of the device [17], which results in a high sidelobe level (SLL) [10, 17]. Optimization has been done to the device operating in symmetric modes [18], but it still remains a high SLL in the calculated far-field radiation.
In this paper, the potential of the operation on the symmetric mode is exploited to achieve higher beam quality. In the proposed structure, besides remaining the normal long slit in the centre of the unit cell, two shorter slits are added at the same side of the long slit and separated in the lateral direction. The exposed top doped GaAs contact layer operates as absorbing boundary conditions at the surrounding of the designed grating, which can increase the cavity loss of higher order lateral modes and provide anti-reflecting boundary conditions at each end of the ridge [11, 14, 19–22]. Furthermore, the distance of the two short slits determines the loss ratio between the symmetric and anti-symmetric fundamental modes in a single unit cell. The surface-current analysis method is first introduced in QCL to analyze the mechanism of the loss ratio. In this structure, the long slit provides the main feedback and also helps to increase the radiation loss adjacent to the designed mode. Meanwhile, the field distributions of the two short slits are in phase both at the unit cell level and with respect to the whole device, which provides the constructive interference in far-field region. The radiation from the long slit is divergent and only gives a weak contribution to the SLL, which is still kept at a low level. Therefore, the higher beam quality than [10, 18] is achieved based on the symmetric mode of the proposed structure.
2. Unit cell design
In the structure, the 10μm-thick GaAs/AlGaAs active region with an average n-doping of 2 × 1015 cm−3 is sandwiched between gold layers and highly-doped contact layers at 5 × 1018 cm−3. Normally, the losses of the metal are not take into account [7, 12, 14], and only the real part of the refractive index of the active region is taken into account in the simulation [14]. Therefore, the refractive index of the semiconductor active region is taken to be 3.6 [10, 14], and the gold layer is approximated as perfect electric conductor [14, 23] in the modelling. The unmetallized top contact layer is unpumped directly, and the highly doped semiconductor operates as an absorbing layer [7, 14, 19–21]. Therefore, the losses of the higher-order lateral modes are increased to a large extent and those modes are suppressed in the mode competition during the pumping. In our design, the width of the ridge L = 120μm, the width of the unmetalized top contact layer w = 10μm at each side of the ridge, the length of the centered slit is 90μm, and the duty cycle is 86.6% with the period Λ = 30μm. The periodic boundary conditions are applied to the unit cell in the x-axis direction in the simulation. The eigen-modes with complex eigen-frequencies are solved by the finite element method (FEM). The simulated results for the unit cell with a single slit are shown in Fig. 1. According to the symmetry of the vertical electric fields (Ez) with respect to the centered slit, the modes in Figs. 1(a) and (b) are clarified as symmetric mode and anti-symmetric mode, respectively, in this paper. Meanwhile, the corresponding surface current intensity on the underlying surface of the top metal is plotted in Figs. 1(c) and (d). The positions of the maximum of the current intensity are separated by those of Ez at a quarter guided wavelength in the x-axis direction reasonably according to the electromagnetic relations. The envelope of the guided fieldintensity along the cavity of the symmetric and anti-symmetric modes is shown in Fig. 1(e) and (f). Because of the neutralization of Ex, Fig. 1(e) shows a depression in the middle. Furthermore, because of the strong radiating of the anti-symmetric mode, the envelope in the middle is not null. It also can be seen that the envelope has maximum at the edge of the slit.
Fig. 1 Top view of the Ez components in the active region: (a) symmetric mode and (b) anti-symmetric mode. Top view of the surface current intensity on the underlying surface of the top metal: (c) symmetric mode and (d) anti-symmetric mode. The envelope of the guided fieldintensity along the cavity with single slit: (e) symmetric mode and (f) anti-symmetric mode.
In the proposed structure, two additional short slits are added on the top metal symmetrically with respect to the longitudinal centre of the ridge and located at one side of the long slit with a separation of Λ/4. It can be seen in Figs. 1 and 2 that the Ez component distributions of the modes are similar with and without the two slits except that there are two maximum fields in the symmetric mode in the lateral direction in the proposed structure. In Fig. 2(d), the radiating components Ex from the two short slits are out of phase with weak emission in the anti-symmetric mode, and those from the long slit are strong and cause high radiation loss, which means that it can be hardly favoured in the structure with uniform periodicity. However, in the symmetric mode, the Ex components above the long slit are out of phase, leading to a low level of radiation with the destructive interference. Comparatively, the Ex components above the short slits are in phase with the constructive interference. Therefore, the corresponding radiation loss is mainly determined and controlled by the sizes of the two short slits and can be smaller than that of the anti-symmetric mode. Under the condition of the constructive interference, a single main lobe can be formed and the output power from the two short slits is higher than that from the long slit. Additionally, the contribution of the destructive interference from the long slits in the symmetric modes is mainly reflected in the sidelobe with a low level. As for the envelope, it can be seen in Fig. 2(e) and (f) that they are distorted slightly and the sides with additional slits have larger density.
Fig. 2 Top view of the Ez components of the proposed structure: (a) symmetric mode and (b) anti-symmetric mode. Top view of radiating electric field components Ex on a reference plane 1um above the slits: (c) symmetric mode and (d) anti-symmetric mode. The size of the two additional slits: a = 12μm and b = 6μm. The envelope of the guided fieldintensity along the cavity with three slits in a unit cell: (e) symmetric mode and (f) anti-symmetric mode.
To get a deeper physical understanding, the effect of variation of d on loss is studied. It can be seen in Fig. 3(a) that the losses of the anti-symmetric modes remain independent on d, while those of the symmetric modes arise as d increases. Meanwhile, the variation of d has a little effect on the real part of the eigen-frequency in Fig. 3(b). The real part of the eigen-frequency of the anti-symmetric modes and symmetric modes decreases and increases individually as d increases, which means a wider bandgap for a smaller d. The reason is that the feedback will be stronger when the two short slits are closer to the centre of the ridge.
Fig. 3 The effect of the variation of d on (a) the losses and (b) the real part of the eigen-frequency.
The normalized amplitudes of the electric fields of the symmetric and anti-symmetric modes are plotted in Figs. 4(c) and 4(d). In the symmetric modes, the two maximum fields move laterally as the separation of the two short slits increases laterally, and the positions of the maximum fields and slits are almost same in the transverse direction. However, the distributions of the electric fields in the anti-symmetric modes almost remain independent on d.
Fig. 4 Top view of the surface current intensity on the underlying surface of the top metal of the proposed structure: (a) symmetric mode and (b) anti-symmetric mode, the contact layer under the slits should be removed in the fabrication. (c) The normalized amplitude of the electric fields of the symmetric mode along the centre of the active region below the long slit, where the maximum of the fields is located. (d) The normalized amplitude of the electric fields of the anti-symmetric mode along the centre of the active region below the two short slits in the transverse direction.
The current intensity distribution can give the expression to the lateral movement of the fields and the variation of the loss with the variation of d. To the best of our knowledge, the surface-current analysis method is first introduced in QCL to analyze the lateral intensity of the electric fields and the losses between symmetric and anti-symmetric modes. The surface current intensity on the underlying surface of the top metal is plotted in Figs. 4(a) and 4(b) for the symmetric and anti-symmetric modes respectively. It can be seen in Figs. 1(c) and 4(a) that the two short slits are located in the plane where the current intensity of the symmetric mode is maximum. Therefore, the two short slits cut off the original path of the current and make the current resonate strongly around the slits. The changed distribution of the current intensity induce the change of the corresponding magnetic and electric field distributions. The positions of the short slits, the maximum of the current intensity and the maximum of the electric fields are aligned in the transverse direction as shown Figs. 4(a) and 4(c). Furthermore, when the positions of the maximum of the electric fields move outwards, the overlap of the mode in the cavity and absorbing boundary conditions increases, causing an increase of the cavity loss which dominates the increase of the loss in Fig. 3(a). On the contrary, the short slits are located at the minimum of the current intensity in the anti-symmetric mode and does not cut off the path of the current during the movement as shown in Figs. 4(b) and 4(d). Therefore, the two short slits have less influence on the current and the field distributions as well as the loss of the anti-symmetric mode.
3. Near field and far field
According to the above discussion, the symmetric mode as in Fig. 2(a) and 2(c) can be favoured only if d is less than 50μm, and a single lobe can be predicted. The designed three slit unit cell constitutes the finite structure, and the field distribution of the symmetric mode similar to that of the unit cell is located at each slit in the ridge as the lower band-edge mode, which is desired for lasering. As for the modes with frequencies lower than that of the lower band-edge mode, the field distribution changes with respect to the slits and more long slits give the radiating components Ex in phase theoretically. With the larger radiation losses, these undesired modes are hardly favoured in the mode competition. In Fig. 5(a), the modes adjacent to the band-edge modes have much larger losses than that of the band-edge modes. Besides the radiation losses, these modes also suffer from larger cavity losses. According to Fig. 5(c), the maximum amplitude field of the lower band-edge mode is in the centre of the ridge and the amplitude decays towards the ends. Comparatively in Fig. 5(g), the maximum amplitude field of the adjacent mode is located at the ends of the ridge and have more overlap with the lossy absorbing boundary. Compared with Figs. 5(d) and 5(f), the upper band-edge mode gives more radiating components in phase above the slits, and it has larger losses than lower band-edge mode as shown in Fig. 5(a). Before and after the loss of metal is considered, the ratio of loss between modes A and B is 0.80 and 0.85, respectively. Therefore, a gain spectrum in the shade with the maximum gain located around the frequency of the lower band-edge mode can be used to laser single mode.
Fig. 5 (a) Mode spectrum for the finite length (15 periods) of the designed structure with d = 48μm. The estimated effective refractive index is 3.52. The estimated gain spectrum of the gain medium plotted is in the shaded region, which can be used to favour the laser of single mode. Lower band-edge mode operating in symmetric electric field distribution denoted by A: (b) Ez components and (c) the amplitude of electric fields in the centre of the active region, Ex components (d) 5μm and (e) 20μm above the top metal. (f) Ex components 5μm above the top metal of the upper band-edge mode operating in anti-symmetric electric field distribution denoted by B. (g) Amplitude of electric fields in the centre of the active region of the mode with frequency 2.62THz denoted by C. Figure 5(d), (b) and (f) share one scale bar. The maximum value of the scale bar is 0.2 in Fig. 5(e) in line with Fig. 5(b)(d)(e) numerically. The width of the exposed contact layer on either side of the ridge in the y-axis direction is 10μm and that on the end of the ridge Lend is 50μm.
In Fig. 5(b), the distributions of Ez components below each both long and short slit in the finite structure are very similar with those in the infinite one as predicated, except the long slits at the ends. Due to the end effects, the long slits at the ends do not give strictly out-of-phased radiating components as shown in Fig. 5(d), which will make a little distortion in the main beam. As shown in Fig. 5(e), most of the out-of-phased radiating components from the long slits are neutralized on the plane above but very close to the top metal. The near field in Fig. 5(e) can be used to calculate the far field beam patterns by Stratton-Chu formula. Along the ridge in the x-axis direction in Fig. 5(e), the amplitude of the fields increases from the left to the right part gradually, resulting in the SLL below −10dB in the copolarization (co-pol) radiation in the E-plane in Fig. 6. Besides, due to the end effect, the out-of-phased Ex components on the left part slightly deteriorate the symmetry of the main beam as shown in Fig. 6(a) and lead to a small fluctuation from 4° to 8° in the E-plane as shown in Fig. 6(b). Due to the boundary conditions provided by the narrow slits, the cross-polarization (cr-pol) radiation both E-plane and H-plane is below −30dB as shown in Fig. 6(b). Since the radiating aperture is smaller in the y-axis direction, the beam width in the H-plane is broader than that in the E-plane in Fig. 6(a). The full width half maxima (FWHM) of the calculated farfield beam pattern is 22° and 50° in the E- and H-plane, respectively, and longer ridge and phase locking [16] can be applied to achieve a narrower beam.
Fig. 6 (a) Calculated far-field beam pattern in the UV coordinate system (U = sinθ*cosφ, V = sinθ*sinφ). The color bar is in logarithmic scale. (b) Calculated normalized co-pol and cr-pol radiation patterns in both the E-plane and H-plane.
4. Conclusion
In the paper, surface emission in MM waveguide THz QCLs is demonstrated with second-order DFB metal grating. In the designed structure, two additional slits are located at the one side of the conventional long slit in each unit cell. The two short slits are not only designed to give consist radiation with high beam quality, but also used to control the loss ratio between symmetric and anti-symmetric modes. The surface-current analysis method is first implemented in QCL to analyze the losses, which provides another point of view to investigate the physical mechanism of QCLs. Single lobe can be achieved because of the radiating components from the two short slits based on the symmetric modes, and it maintains lower loss than that from long slits based on anti-symmetric modes. Since the amplitude of the radiating components gradually increases along the ridge, the SLL is kept at a low level and better than that has null amplitude in the centre along the ridge with π-phase shift. Because of the in-phased radiating components in each small slit and constructive interference, the outcoupling of this structure will be better than FabryPerot cavity and conventional secondorder surface emitting THz QCLs. It can be conceived that this kind of additional short slits can be extended to 2D photonic crystal [19] [23] for loss control and improvement of beam quality.
Funding
Natural Science Foundation of China (NSFC) (61371051); Sichuan Youth Science and Technology Foundation (2014JQ0012).
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