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A lateral cavity photonic crystal surface emitting laser (LC-PCSEL) with airholes of cone-like shape etched near to the active layer is fabricated. It employs only a simple commercial epitaxial wafer without DBR and needs no wafer bonding technique. Surface emitting lasing action at 1575 nm with power of 1.8 mW is observed at room temperature, providing potential values for mass production of electrically driven PCSELs with low cost. Additionally, Fano resonance is utilized to analyze aperture equivalence of PC, and energy distribution in simplified laser structure is simulated to show oscillation and transmission characteristics of laser.
©2013 Optical Society of America
1. Introduction
Photonic crystal (PC) [1, 2] and surface plasmon polariton (SPP) [3] are two research hot spots in nanophotonics. Many devices related with PC or SPP have been demonstrated, such as beam splitters [4, 5], filters [6, 7], sensors [8, 9], and lasers [10–14], etc. In SPP lasers [15], the ultrasmall mode size has been achieved to maintain relatively high Q/V. However, the loss caused by metal absorption cannot be suppressed completely by inserting dielectric layer with low refractive index, thus efficiency and thermal stability of such lasers need to be considered. While to PC lasers, with the diamond as the heat sink [16], the working time can be continued much longer to about 18 hours. For new structures of PC lasers, recently, H. Yang et al. replaced top and bottom DBRs of traditional VCSEL with two thin, single-layer silicon PC Fano resonance membrane reflectors, and realized lasing under optical pump [17].
Among different types of PC lasers, surface emitting laser is a special kind of laser in which the resonant band edge mode can extend to a large area in the PC plane and eradiate laser beam normal to the plane with a narrow divergence angle and a symmetrical beam spot [18]. In Noda’s group, the non-planar wafer bonding process and the finely designed wafer pair have been adopted to achieve electrically driven laser [18]. The non-planar wafer bonding process requires advanced micro-nanofabrication technology. The matching between the wafers also demands advanced epitaxial growth technology. Furthermore, the PC region must be large enough to ensure the sufficient in-plane feedback because the quality (Q) factor of Γ2-1 varies with the region [19]. If the electron beam lithography (EBL) is used in the process of fabrication, the cost will be in direct proportion to the area of PC region.
In this article, we propose and fabricate a lateral cavity photonic crystal surface emitting laser (LC-PCSEL) based on the commercial AlGaInAs/InP multi-quantum-well (MQW) epitaxial wafer, a simple waveguide wafer which has no DBR and no use of wafer bonding, to desire mass production of electrically driven PCSELs with low cost. The basic properties of Γ2 are introduced in Sec. 2 and Γ2-1 mode is chosen for lasing, followed by the design and fabrication of LC-PCSEL in Sec. 3. Aperture equivalence of PC is analyzed and energy distribution in simplified laser structure is simulated in Sec. 4. Finally, the measured results of laser performance are given in Sec. 5, and some discussions in Sec. 6.
2. Γ2 modes
The two dimensional (2D) plane-wave expansion (PWE) method is utilized to calculate the band structure of square lattice PC slab with cylindric airhole, which is shown in Fig. 1. The lattice constant, area filling factor of airhole, dielectric constants of the slab and airhole in calculation are set to 1 μm, 0.2, 11.56 and 1, respectively. The thickness of the slab equals to the aperture of airhole. In Fig. 1, modes in light cone (shaded area) are leaky modes of the PC slab. For the modes at the high symmetry points, e.g. Γ2 (the second order of the Γ-point), the group velocities are nearly zeros, which results in the formation of standing-wave oscillations. Since we are interested in the surface-emitting effect of band edge modes, Γ2 will be selected and studied detailly.
Fig. 1 TE-like (thin line) / TM-like (thick line) band structure of two-dimensional square-lattice photonic crystal slab with cylindric airhole.
For Γ2 points, the Bragg diffraction conditions can be satisfied. According to the momentum and energy conservations, there are four diffractions in the plane forming the 2D coupling, which is shown in Fig. 2(a). The square in the center represents the first Brillouin zone, and the circle the energy conservation condition. and are the in-plane component wave vectors of the diffracted light and the incident light, respectively. and are the reciprocal lattice vectors, and (a is the lattice constant). It is interesting that when reaches Γ point, the incident light will diffract in the direction normal to the slab, forming the surface-emitting mode (see Fig. 2(b)).
We mainly analyze TE-like mode, because only TE-like mode occurs in our designed laser below. The band structure of TE-like modes around Γ2 points and the corresponding electromagnetic field distributions of Γ2 modes in one unit cell are shown in Figs. 3(a) and 3(b) respectively, which have ever been calculated by us in Ref [20]. Based on the number of mode distribution maximum, Γ2 is divided into Γ2-1(monopole mode), Γ2-2 (dipole mode) and Γ2-4 (quadrupole mode), which are shown as I, III, IV and II in Figs. 3(a) and 3(b), respectively. Among them, III and IV are two degenerate dipole modes.
Fig. 3 (a) Band structure of TE-like modes around Γ2 point. (b) Electromagnetic field distributions of corresponding Γ2 modes in one unit cell. Arrows indicate the electric vectors, and the brightness variation displays the distribution of magnetic intensity.
We calculate the Q factors of four modes using 3D finite-difference time-domain (FDTD) method. Table 1 shows the results of small structure with only 14 airholes in the Γ-X direction, which are consistent with that of Noda group’s [19]. The Q factor of Γ2-1 is larger than that of other modes, and it is more likely to become the lasing mode.
Table 1. Q factors of four Γ2 modes
3. Structure of LC-PCSEL
As we know, PCSEL can be classified into two types depending on the relative position between the PC and the active layer [21]. One is that the PC is defined on the cladding layer close to the active layer, and it modulates the modes in the active layer by modulating a fraction of field confined in the PC layer; the other is that the PC is defined directly on the active layer, and it modulates the modes in the active layer directly. In our early work [22], the laser of the second type was investigated. Both the quantum efficiency and the output power were too low, because the deep steep etching broke the active layer.
Here, we study the laser of the first type. As shown in Fig. 4(a), the designed structure is similar to our second type, but the PC is etched near to the active layer. The area of PC region is only 20 × 12 μm2, which results in not enough horizontal feedback of mode to realize lasing, so the FP cavity is employed as the lateral cavity due to its simple structure and low cost. Such structure of LC-PCSEL provides sufficient lateral Γ2-1 feedback, as well as large area for the current injection. The length of PC area is larger than the width, avoiding influences of the leaky light outside PC from the active layer on the oscillation of Γ2-1 around the center of PC.
Fig. 4 (a) Schematic structure of the LC-PCSEL. (b) and (c) are the PC SEMs of the side view and top view, respectively.
The LC-PCSEL is fabricated on the commercial epitaxial wafer by sequential processes, such as photolithography, EBL, inductively coupled plasma (ICP) etching, and wet etching. The detailed processes are the same as that in Ref [22]. The length and width of the ridge are 500 μm and 20 μm, respectively. Figures 4(b) and 4(c) show the PC SEMs of the side view and top view, and the measured top aperture, bottom aperture, depth and period of airhole with cone-like shape are 360 nm, 240 nm, 1.72 μm and 540 nm, respectively. In addition, the high reflection coating is introduced on the cleaved facets of FP cavity.
4. Equivalence of aperture and simulation
The etched airhole shown in Fig. 4(b) is not cylinder-like but cone-like, so 2D PWE cannot deal with the PC, and single 3D PWE is hard to calculate Γ2-1 mode. In order to save calculation resources and time, the equivalence of PC aperture is necessary. The detailed processes of equivalence are validated by rigorous coupled wave analysis (RCWA), an easy and time-saving method. In calculation, the refractive index of the slab is set to 3.1529.
It is known that the guided modes in PC can become leaky resonances when phase matched to radiation modes [23]. And FP oscillation occurs if a light transmits a uniform dielectric slab with the same thickness and effective refractive index as PC. But when leaky resonances interact with FP oscillation and satisfy the demands of constructive and destructive interferences, Fano resonances will appear, e.g. where circles 1, 2 and 3 show in Fig. 5. In other words, the Fano-resonance line shape in transmission spectrum proves the occurrence of guided resonance mode in PC slab. Figure 5 shows the transmission spectra of PC with cone-like airholes (Co-APC) and PC with cylinder-like airholes (Cy-APC). All the PC slabs have the same thicknesses of 1.72 μm, which easily leads to the formation of high order resonance mode. In the spectrum, the Fano-resonance line shape looks symmetric where the transmission related with FP oscillation reaches maximum, while at other places, the line shape becomes asymmetric.
Fig. 5 Transmission spectra of Co-APC and Cy-APC. The top and bottom apertures of the cone-like airhole are 360 nm and 240 nm, respectively. The cylinder-like airhole has one of apertures of cone-like airhole. The marked circles 1, 2, and 3 represent Fano resonances at three different wavelengths.
As described above, the dips marked with 1, 2, and 3 in Fig. 5 correspond to the first, third, and second order resonance modes of Co-APC, respectively, according to the number of magnetic field amplitude maximum along the direction of airhole axis. It is interesting that the second order resonance modes of Cy-APCs with apertures of 240 nm and 360 nm nearly overlap the first and third order resonance modes of Co-APC, which have the top aperture of 360 nm and the bottom aperture of 240 nm. We suppose resonance modes at 1 and 2 to be the engen-like modes and resonance mode at 3 between 1 and 2 to be the hybridized mode of Cy-APCs with two apertures due to their guided resonance characteristics, which will be proved later. The hybridized mode set up a link between Co-APC and Cy-APC. In a sense, based on the mode, the Cy-APC can be used as the equivalent of Co-APC.
The properties of the three resonant modes are analyzed from the characteristic parameters of cone-like airhole. The lattice constant is fixed to 540 nm. As shown in Figs. 6(a) and 6(b), the transmission spectrum blue shifts when the bottom and top apertures are independently increased. However, the increase of the bottom aperture Db from 230 nm to 250 nm makes resonant mode at 1 move faster than at 2 and 3 (see Fig. 6(a)), while the increase of the top aperture Dt from 350 nm to 370 nm causes the resonant modes at 2 and 3 shift faster than at 1 (see Fig. 6(b)). The difference of dip shift between 1 and 2 resulting from the change of corresponding aperture demonstrates the engen-like characteristics of resonant modes in Co-APC.
Fig. 6 (a), (b), (c) Transmission spectra of Co-APC as the bottom aperture, top aperture, and both are increased, respectively. D is the diameter of airhole in nm. (d) Transmission spectra of Co-APC when the depth of airhole and the thickness of slab are increased simultaneously. H represents the depth of the airhole in μm.
The tansmission spectra are investigated when the top and bottom apertures are increased in the increment of 5 nm simultaneously. As shown in Fig. 6(c), all the resonant modes at 1, 2 and 3 blue shift distinctly with nearly the same shift spacing. Figure 6(d) displays the variety of the spectrum as the height of airhole is increased from 1.69 μm to 1.75 μm in the increment of 10 nm. It is clear that the red shifts of modes at 1, 3 and 2 are small but monotonically increasing. However, the backgroud transmission spectrum has large shifts. Because the variation of resonant mode relies on the filling factor of airhole principally, and the increase of slab thickness results in the increase of effective refractive index, the resonant modes red shift slightly. While the backgroud transmission spectrum is directly affected by the effective index, thus its shift is considerable. Through the analysis of characteristic spectra, we can also evaluate the fabrication of sample as long as the scaling is set.
As aforementioned, the hybridized resonant mode may be excited in an equivalent PC slab with cylindric airholes. As shown in Fig. 7, we obtain the equivalent aperture of cylinder-like airhole by employing the relation of equal effective refractive index between Co-APC and Cy-APC. In the case of airholes with equivalent aperture, Cy-APC should reserve characters of Co-APC as many as possible. The bulk effective refractive index approximation is validated as following:
where Vcone, Vcylinder and Vcubic are the volumes of cone-like airhole, cylider-like airhole and PC cell, respectively. n1 and nair are the refractive indices of dielectric and air. The parameters of every structure are substituded into Eq. (1), and the calculated equivalent aperture of cylinder-like airhole is achieved as 302 nm. We will scan the apertures around 302 nm to testify the validity of equivalent aperture by the transmission spectrum.Figure 8 shows the transmission spectra of Cy-APC with different airhole apertures increased from 291 nm to 311 nm. It is so lucky that the resonant mode in Cy-APC with aperture of 311 nm can match with the predicted hybridized mode, which is shown at 3 in Fig. 5 and now at 2 in Fig. 8. Additionally, for the first order resonant mode of Co-APC, we get another aperture of 291 nm to satisfy the mode match. However, the background transmission spectra for the two apertures both deviate greatly from that of Co-APC, and lie at two sides, respectively. It means the effective indices of the two Cy-APCs are not consistent with that of Co-APC. But they set a range, i.e. 291 nm < D < 311 nm, for the equivalent aperture of Co-APC. We reduce the range further from 301 nm to 306 nm, and find that the calculated equivalent aperture of 302 nm is the optimal aperture for the well agreement of background spectrum with that of Co-APC in our interested communication wavelength range. For the range, the refractive index of the relatively large wavelength is close to the average index of PC, namely the aforementioned effective index.
Figure 9(a) shows the distribution of the magnetic field amplitude for resonant mode 1 with wavelength of 1.5291 μm in Co-APC cell. The resonant mode of Cy-APC near to mode 1 has the wavelength of 1.5293 μm, whose distribution of the magnetic field amplitude is diplayed in Fig. 9(b). The wavelength difference of only 0.2 nm occurs between the two resonant modes. Along the Z direction, there is only one maximum of magnetic field amplitude, showing both the two modes are the first order resonant modes. They mainly lie in the dielectric of PC. However, the distribution of Co-APC is suppressed gradually along the positive Z direction due to the influence of cone-like airhole, while that of Cy-APC is unaffected and expanded equably. Figure 9(c) demonstrates the distribution of resonant mode 2 in Co-APC cell, and Fig. 9(d) the resonant mode near to mode 2 in Cy-APC cell. It is clear that there are two maximums of magnetic field amplitude in the Z direction, which means both the two modes are the second order resonant modes. The wavelength difference between them is 0.8 nm. Like the first order resonant modes, they are also distributed mostly in the dielectric of PC, and the mode distribution of Co-APC is also squeezed in the positive Z direction and looks nonuniform.
Fig. 9 Distribution of the magnetic field amplitude for (a) resonant mode 1 with wavelength of 1.5291 μm in Co-APC cell, (b) resonant mode near to mode 1 with wavelength of 1.5293 μm in Cy-APC cell with aperture of 291 nm, (c) resonant mode 2 with wavelength of 1.4546 μm in Co-APC cell, and (d) resonant mode near to mode 2 with wavelength of 1.4538 μm in Cy-APC cell with aperture of 311 nm. The inset gives the coordinate and parameters of Co-APC cell.
By the distribution of the magnetic field amplitude, we can testify the equivalent aperture of 302 nm. Figures 10(a)-10(d) show the distributions of the magnetic field amplitude for light with wavelength 1.572 μm in Co-APC and Cy-APC, respectively. They provide some information about shapes and sizes of airholes of PC. On the other hand, the strength of distribution in PC cell demonstrates Co-APC is similar to Cy-APC with equivalent aperture of 302 nm, and much different from that with aperture of 291 nm or 311 nm. This also proves the effectiveness of equivalent aperture of 302 nm.
Fig. 10 Distribution of the magnetic field amplitude for the incident light with wavelength of 1.572 μm in Co-APC cell (a) and Cy-APC cells with apertures of (b) 302 nm, (c) 291 nm, (d) 311 nm.
We use the equivalent aperture of 302 nm to calculate Γ2-1 mode of Cy-APC and light energy distribution. Based on the commercial waveguide epitaxy wafer, we set up a 3-layer slab equivalent model for the LC-PCSEL except the ultra thick substrate, which is shown in Fig. 11. The refractive index and thickness of each layer are (3.1529, 1.8 μm), (3.2827, 0.3 μm) and (3.1681, 0.8 μm), respectively. Light is excited in the middle layer, i.e. active layer. The width of the FP ridge is 20 μm, and the length is set to 48 μm for the qualitative simulation. In the middle of the FP ridge, PC is etched close to the active layer with the depth of 1.72 μm and the area of 32 a × 32 a.
The size of PC and the thickness of active layer determine the Γ2-1 mode [23]. The thickness of PC more than triple lattice constant, and the thickness of active layer only 300 nm, and the nice local resonance of Γ2-1 mode in PC make the 2D PWE effective in calculating Γ2-1 mode [24]. The obtained Γ2-1 mode lies at the wavelength of 1.572 μm.
Figures 12(a) and 12(b) show the 3D FDTD simulated light energy distribution of LC-PCSEL in the longitudinal and lateral cross sections, respectively. It can be seen that light mainly resonates in the active layer and PC area, but a part of light diffuses into the top and bottom cladding layers. The part hardly satisfies the wave vector matching condition of Γ2-1, so it nearly cannot output along the vertical direction. This causes a large loss for the laser. Although only about 1% of light comes out of the PC forming the surface emitting laser, Γ2-1 mode can oscillate in a large area around the center of PC. Light in the active layer extends more down to the bottom cladding layer, which is clearly indicated in Fig. 12(b). In this simplified 3-layer structure, the refractive indices above and below PC are different. The asymmetric PC slab, and the small thickness of active layer, have some destroying effects on the TE-like polarization.
Fig. 12 Longitudinal (a) and lateral (b) light energe distribution cross sections of LC-PCSEL. The unit for axes is μm, and the colorbar dB.
5. Measurement
In the measurement, the device is pumped by the continue current at room temperature. The surface emitting light is collected by a photodetector placed 3 cm away from the device in the direction vertical to the substrate to ignore the edge emission. The light-current-voltage curve of the device is shown in Fig. 13. It is clear that the threshold current is 200 mA, smaller than that of the laser of the second type [22], the major reason of which we think is the high reflection coating of FP cavity facets. Under the working current of 480 mA, the output power reaches 1.8 mW, much higher than that of the second type.
The surface emitting spectrum is measured under the current of 400 mA by the focused optical path connected to an optical spectrum analyzer. Figure 14 shows the result and indicates the center wavelength of the surface emitting mode Γ2-1 at 1575 nm, and the full width at half maximum (FWHM) of 0.1 nm. The measured Γ2-1 agrees well with previous calculation result, though there is a difference of 3 nm between them due to unavoidable fabrication discrepancies; and the FWHM is already smaller than Noda group’s result of 0.12 nm [25]. The Q factor estimated according to λ/Δλ and the side mode suppression ratio (SMSR) are about 15750 and 29 dB, respectively. Meanwhile, we measure the surface emitting light at a relatively small solid angle (see Fig. 15), and obtain the far-field divergence angles of 4.5° along the longitudinal direction and 10.7° along the lateral direction, respectively. All the results demonstrate that the electrically driven single mode surface emitting laser is achieved on a commercial epitaxial waveguide wafer without DBR utilizing the characteristics of PC band edge mode.
To the LC-PCSEL of the first type, the airholes are etched artificially with cone-like shape for two reasons: one is the effective refractive index of PC changes gradually from bottom to top, forming the index microlens effect beneficial to the decrease of far-field divergence angle; the other is helping reduce the FP-like effect when the light in the compound cavity transmits along the vertical direction, and thus increase output efficiency. In reality, Γ2-1 mode of Cy-APC with equivalent aperture cannot be excited completely. But if most of Γ2-1 mode can be excited in Co-APC to support surface emitting laser, the LC-PCSEL should have potential application values.
6. Discussions
The band structure of Co-APC may be calculated by 3D FDTD [19], but we can use RCWA to recognize PC with different shape airholes even defects once the intuitive transmission spectrum is obtained. On the other hand, the model transformation assisted by RCWA is effective, providing opportunities to get Γ2 using 2D PWE.
For Cy-APC, we try to build up a relation between 2D or 3D PWE results and that of RCWA by using the same parameters. But unfortunately, we have not find out the rigorously matched results, for both the in-plane Γ2 resonance and the out-of-plane Fano resonance are strict with wavelength. Perhaps different methods make results different. In physical mechanisms, the guided resonance brought about by Γ2 mode leads to the appearance of Fano-resonance line style of transmission spectrum [26].
To separate the loss of the guided mode in the PC slab and the out-of-plane radiation loss in the direction normal to the PC plane, the factor () can be decomposed into horizontal factor () and vertical factor () [19]. To realize lasing by small PC region, the FP cavity has been hybridized with PC to provide enough horizontal feedback, namely large , which was calculated by us in Ref [22]. Actually, for this special hybridized cavity formed in the commercial epitaxial wafer, according to the loss mechanism such as the radiation loss (~) and non-radiation loss (~), should be redefined as
whileIn Eq. (2), is caused by the surface emitting light from PC. It is directly related with of PC. In Eq. (3), depends on whether high reflection coating is introduced on the cleaved facets of FP cavity, and represents the absorption loss occurring in dielectric. indicates the in-plane loss of light in PC, which has a close relation with of PC.Compared with the laser of the second type, which has a destroyed active layer and no cavity facet coating, our present laser has larger and . This leads to larger which results in the decrease of lasing threshold though there are smaller and due to small PC region with cone-like airholes.
In order to increase radiation efficiency of a plasmon laser, reducing the radiation quality factor to a certain level was adopted [27]. For our PC and FP hybridized laser, we take the same measure to improve the vertical output efficiency. The efficiency defined by can be written in terms of quality factors in the following way.
In our work, is reduced by the slant etching of PC airholes. To an optically very thick PC slab, can reach 105 for certain slab resonant mode [28]. As aforementioned ~, the decrease of has nonsignificant effect on . Therefore, according to Eq. (4), is increased.7. Summary
In summary, a LC-PCSEL based on the mechanism of photonic band edge mode lateral resonance and vertical output is fabricated. The deep cone-like airholes of the PC are etched near to the active layer of the commercial AlGaInAs/InP MQW epitaxial wafer. The PC surface emitting lasing action is observed at 1575 nm with power of 1.8 mW at room temperature. Equivalence of Co-APC aperture is analyzed by the PC Fano resonance, and energy distribution in a simplified 3-layer slab structure of laser is simulated to demonstrate oscillation and transmission characteristics of laser. Our LC-PCSEL opens up a new way to fabricate the electrically driven surface emitting laser, and might make big progress for mass production with low cost.
Acknowledgments
This work is supported by the Chinese National Key Basic Research Special Fund/CNKBRSF (Grant Nos. 2012CB933501 and 2011CB922002), the National Natural Science Foundation of China (Grant Nos. 61025025, 61274070, 61021003, 61234004, 61205043, 61137003 and 60838003) and the National High Technology Research and Development Program of China (Grant Nos. 2012AA012202 and 2013AA030501).
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