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A low-loss surface plasmonic polariton (SPP) laser is designed as a candidate for the light-source in large-scale integrated (LSI) photonic circuits. Key design parameters of the laser are discussed and optimized to enhance the optical gain and minimize the metallic absorption loss. Performance of the laser is calculated to verify the device feasibility in the designed application.
© 2015 Optical Society of America
1. Introduction
As the growing demands for high-performance optical interconnections between the super-computing systems, surface plasmonic polariton (SPP) waveguide based lasers [1–3] have been considered as a promising candidate for the light source in the next generation photonic circuits. This plasmonic nanolaser structure, as categorized along with the other main stream of the all-three-dimensional sub-wavelength device, i.e., surface plasmon amplification by stimulated emission of radiation (SPASER) [4], has been studied intensively for their achievements in breaking the diffraction limit. This high-integration ability can potentially minimize the device’s cross-section or full dimensions to nanometer range, so that large-scale integration (LSI) of the functional components, including transmitters and receivers, on one chip can be possible [5]. Also, from the circuit design point of view, the SPP laser’s natural compatibility with the newly designed various passive plasmonic waveguides and interconnections could be a direct advantage for the signal couplings between light sources and transmission channels [5]. However, one main hurdle for the wide application of plasmonic based devices is the high metallic loss due to photon-metal interaction [6–8]. Many efforts have been devoted to this aspect for several years [9–11], trying to provide a good balance between the SPP guiding and absorption loss. Here, in this paper, we explore a novel strategy for the plasmonic nanolaser design, by focusing on the separation of SPP wave from the metal contact to minimize the loss [12–14], while providing optical gain through the photonic wave to maintain generation and amplification of the desirable plasmonic feature.
When studying the plasmonic waveguide structure, it is discovered that light can interact with the induced charges on surface of the dielectric interface, away from directly contacting the metal [12]. This means the SPP wave can still be guided by those surface charges along the dielectric material, with the distant and non-contact help of the metal plate [13–15]. The scheme ameliorates the heavy loss from plasma absorption and potentially enables the nanometer-size laser sources to work under electrical pumping. Therefore, we design this new type of plasmonic laser using the hybrid waveguide structure, which can help photons to stay away from the major metallic absorptions. The waveguide ridge is designed to be quasi-triangular or trapezoid shape so that plasmonic wave can be laterally well confined at the top, while the photonic wave overlaps as much as possible with the active material in the lower multi-quantum well (MQW) region to obtain sufficient gain. The cross-section and hybrid-mode profile of the laser structure can be schematically shown in Fig. 1.
Here, the III-V type active materials in form of MQWs, are sandwiched between the InP layers as spacer (top) and substrate (bottom) of the P-N heterjunction, so that both the e-/h+ carriers and the photonic wave can be simultaneously well confined in the active region. A thin layer of low refractive-index conductive (or semi-conductive) material is used to cover the PN junction, as in Fig. 1(a), in order to separate the major part of optical wave from directly contacting the metal plate to minimize absorption loss. When the ridge-shape PN diode (i.e., III-V heterjunction) is placed close to the metal contact, high intensity of the plasmonic wave can be induced at the cover-to-semiconductor interface under the low-index cover layer, because photons can interact with the E-field-induced electrons at that interface to trigger SPP excitation [15]. Modal gain of the laser can be calculated from the confinement factor Γ and material gain gm of the active region. And the total loss γ comes mainly from the metal absorption and the photon leakage out of the ultra-small sub-micron core region.
2. Device design parameters
To characterize performance of the laser design, we carry out sensitivity studies of the structure to provide a guideline for the device’s further optimizations, especially in how to maximize the plasmonic wave while minimizing the SPP absorption. Here, the ridge upper-base (w1), height (h), tilting angle (θ) and gap distance to the metal contact (d) are the main parameters of the structure, as indicated in Fig. 2(a). To overcome the loss, photonic wave of the hybrid mode has to remain in the active region and interacts with the gain material as much as possible to obtain the maximum amount of stimulated photons. Then, we can quantitatively compare the modal gain <g> and total loss γ to calculate the net gain G, which describes the laser’s ability in converting the electrically pumped energy into photonic light. The material used in MQW is InAlGaAs/InP, whose gain spectrum around 1.3µm can be calculated as in Fig. 2(b) from the k-p method simulation [16]. The modal loss γ can also be obtained from the finite element method calculation of the laser’s cross-section, by COMSOL multiphysics electromagnetics package, considering the metallic absorption effects. The refractive indices for the metal and semiconductors are set as nAu = 0.403-8.25j, nInAlGaAs = 3.45, nInP = 3.2, and npolymer = 1.45, which is a simplification from the frequency dispersive model and is approximated under the assumption that single-mode oscillation of the photonic wave is obtained in the longitudinal cavity at 1320 nm wavelength. The insert in Fig. 2(b) shows the material gain difference between adjacent longitudinal modes to be greater than 20 cm−1, and the mode spacing is approximately 5nm at 50µm cavity length.
Fig. 2 (a) Detailed structural and material parameters of the InAlGaAs/InP QW diode cross-section (drawn in half). (b) Material gain gm of the 8-layer MQW at different injection sheet carrier densities. The insert is to show the mode spacing and their gain difference.
Because the tilting angle θ can be related to the discussion of upper base w1, so in the following Fig. 3, we compare cases of different w1 (with the lower base w2, height h and gap distance d kept the same) in evaluating the top-width or angle effect on the wave confinement and modal gain properties. From the plot, it can be seen that without direct contact to the metal, loss of the plasmonic wave is quantitatively the same even when w1 shrinks to a point, at which SPP has the smallest spot size [13]. However, the photonic wave is squeezed and less confined, as summarized in a later Γ-curve. Therefore, we have to optimize the structure by setting the ridge shape to be trapezoidal to balance the plasmonic size and photonic confinement (i.e., gain). The ridge symmetry is chosen only to simplify our discussions.
Fig. 3 Evolution of the hybrid mode field pattern with fixed distance d = 50nm from the contact, and at different upper base widths w1 = (a) 10nm, (b) 50nm, (c) 250nm. Here, w2 = 250nm, and h = 200nm are kept the same.
Next, we compare cases of identical ridge shapes but with different gap distances d to the metal contact as in Fig. 4. From the plots, we can see that the plasmonic wave is maximized when d approaches 0. But the smallest d case has the maximum SPP loss, as in Fig. 5(b) modal-loss curve. Therefore, an intermedium value of the gap distance d has to be properly chosen to minimize the metal absorption, while not jeopardizing the SPP wave from distinguishing.
Fig. 4 Evolution of the hybrid mode field pattern with increasing distance from the contact as d = (a) 10nm, (b) 50nm, (c) 100nm. Here, w1 = 50nm, w2 = 250nm and h = 200nm are not changed.
Fig. 5 Evolution of (a) the confinement factor Γ and imaginary part of neff, (b) the modal gain <g> and loss γ, of the structure with different upper base widths w1 and gap distances d.
As summarized in Fig. 5(a), the mode confinement factor Γ of photonic wave in the MQW as , and the imaginary part of the mode effective index neff are plotted as a function of the upper base width w1 and the gap distance d. The modal gain and modal loss γ = −2πIm(neff) / λ are also plotted in Fig. 5(b) for easier comparison. Here, the material gain gm and wavelength λ are approximately fixed on the peak gain value at 1.3µm, due to the single-mode lasing behavior as we have mentioned before. For the large d case, a wider upper base width w1 can improve the confinement factor Γ much more in obtaining more gain; and for the small d case, a wider w1 brings in more loss due to the increased direct-contacting area of metal to the plasmonic wave. Also, the modal loss curves exhibit more variations compared to the gain at different d, so the gap distance should affect the structure more dramatically in determining whether the laser can work at practical injections to give an optimum SPP output.
In the net gain G ( = <g>-γ) plot in Fig. 6(a), as w1 and d increase, G can become positive for photonic amplification and resonance, because more of the light stays in the active region to interact with the gain material. However, a wider w1 brings down the inverse of the plasmonic wave scaling factor (SF−1) [12,13] as in Fig. 6(b), and an enlarged gap distance d can also diminish the plasmonic wave directly [13].
Fig. 6 (a) Net gain of the hybrid mode as a function of the ridge-contact distance d and upper base width w1. (b) Inverse scaling factor (SF−1) of the plasmonic wave.
Here, the SF parameter is defined [12] as
where is the effective modal area, and A0 = (λ/2n)2 is the diffraction spot size in the waveguide. W(x,y) is the sum of total electrical and magnetic energies of the plasmonic wave, and the SF parameter is used to compare the spot-size shrinking ability of SPP in different w1 or d cases, i.e., the smaller SF, or the bigger SF−1, the better SPP confinement. We have plotted the inverse of SF in log scale in Fig. 6(b), and we can see that as w1 or d increases, the plasmonic wave deteriorates, which is against the trend in Fig. 6(a) if we prefer more net gain.To miniaturize the device and achieve new functionalities, the SPP wave with a bigger SF−1 factor is more desirable for the plasmon extraction in the LSI photonic circuits design. Therefore, the photonic wave, although source of the optical gain, has to be sacrificed in order to maintain a suitable portion of the plasmonic feature. From Fig. 6, we can find that the values of w1 = 50nm and d = 50nm are a qualitatively optimized combination in this specific designed structure, where loss and gain can be balanced, and the plasmonic wave can be maximized with an acceptable SF−1 factor.
As for other parameters, height of the upper p-InP layer can also be viewed as part of the d parameter, so we will not discuss here in further details. The ridge height h is mainly determined by the number of QWs needed in the active region, and is therefore decided by the required material gain and photonic wave confinement for the design. The refractive index of the cover material is also directly related to the plasmonic wave confinement [17] and has to be set as low as possible, provided it is a conductive material to be able to pass high density of carriers to the PN junction.
3. Electrical pumping properties
To check the feasibility of our designed plasmonic nanolaser device in achieving functionality under the direct current injection, we have to study the electrical properties of the diode. Here we calculate [13] the band structures and quasi-Fermi levels (QFL) of the d = 50nm case under electrical pumping at 1.5V bias, as in Fig. 7(a), as well as the e-/h+ current densities and the stimulated recombination rate in Fig. 7(b). The cover layer in our design uses a low refractive index (semi-)conductive material (e.g., wide-bandgap doped polymer) that has to be of high contrast to the III-V core layers and has high mobilities of e- or h+ for the current injection. There are various choices of materials [18] that can be used for this cover layer, which we will not expand in our discussion here in context of this paper. From the plot, we can see that the photons are generated with sufficient amount of recombination rate (~1027 cm−3s−1) in the InAlGaAs gain layer of the heterojunction, and are then collected to form both the photonic wave in the high-index active layer and the plasmonic wave in the low-index cover layer. The hybrid mode is therefore relatively kept away from directly contacting the metal plate, so that the absorption loss is minimized.
Fig. 7 (a) Band structure and quasi-Fermi level of the laser’s heterojunction; (b) Electron/hole current density and stimulated recombination rate for the diode, at 1.5V electrical pumping. In the plot, the “0”-depth reference is set at the interface between the metal contact and the cover layer, and “positive” direction points downwards into the substrate.
The output power of the hybrid mode laser is calculated [17] and compared to the standard DFB [19] and VCSEL [20] lasers using the same material systems, i.e., InAlGaAs/InP around 1.3µm, as shown in Fig. 8(a). From the plot, it can be seen that the plasmonic wave power is much larger (~µW) than that of the purely metal-guided plasmonic one (~nW) [9,10], but is still two/one magnitude smaller than that of the DFB/VCSEL lasers, due to its intrinsic loss from the SPP wave. The threshold current density J is also higher than the DFB lasers, but can be comparable to the VCSEL, as the contact area for current injection is the largest for DFB and the smallest for VCSEL, if we assume the same gain to be generated.
Fig. 8 (a) Comparison of the output power v.s. injection current density curves for conventional DFB [19], VCSEL [20] and our SPP lasers; (b) 3D hybrid SPP laser structure (in red) with HR-coated facets, connected to a passive SPP waveguide (in cyan green) by interface-coupling.
Here, both the longitudinal emitting facets of the laser, as shown in Fig. 8(b), are covered with highly reflective (HR) coatings (approximately 100% reflectivity), so that only the photonic wave can oscillate coherently inside the cavity forever without exiting. And as the excitation and generation of non-coherent SPPs by photons, the plasmonic wave is extracted out of the laser through the interface between the low-index cover and the upper InP layer, to the passive SPP waveguide. The connection between the interface port to the SPP waveguide should be as smooth as possible, if can be AR coated or directly connected, to minimize the coupling loss. This HR-coated configuration can improve resonance of the stimulated amplifications for photons inside the active cavity, and can provide the maximum converted energy to the plasmonic wave via the photonic wave interaction. Therefore, we prefer a structure with greater SF−1 for the SPP wave, as mentioned in Section 2, to facilitate the interface-coupling of SPP wave as much as possible out of the total hybrid mode, under the constraint of the “SF v.s. loss” trade-off.
We have to note that it is different from the designs [10,11] that put the active region directly onto the metal waveguide, as here SPP is conducted via the non-metallic materials to reduce the loss. To couple the plasmonic wave out of the laser section, various loss-optimized schemes of the SPP waveguide [5] can be used to transport light signal further into the photonic circuit, so that plasmonic wave can contact the lossy metal media as minimized as possible. Therefore, with this hybrid SPP laser fully compatible with the designs of low-loss passive SPP waveguides, we can form fast and robust on-board communication channel instead of the metal wire, and use it as a potential light source for the LSI photonic circuit.
4. Discussion and conclusion
We have discussed the basic configuration and key parameters of a low-loss surface plasmonic polariton (SPP) laser design. Modal properties of the laser with respect to different design parameters are also discussed and optimized, to enhance the optical amplification and minimize the metallic absorption loss for the plasmonic wave. We calculated the electrical properties of the laser to verify its performance for use as a compact light-source candidate under electrical pumping for the large-scale integrated photonic circuits. With the optimized plasmonic wave generation and amplification, via III-V active material and non-direct contact to metal, the all-SPP based high bandwidth on-board transmission channels can be feasible in the next generation high speed data communication systems.
Acknowledgments
The research is supported by the “National Natural Science Foundation of China, NSFC” (Grant No. 11304181) and the “Shandong Province Natural Science Foundation” (Grant No. ZR2013FQ018). LY acknowledges the helps on COMSOL modeling from Guo-Dong Zhang during the project. We also thank Dr. Xun Li for the simulation program on the material gain calculations.
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