The modal characteristics of a Photonic-Crystal Vertical-Cavity Surface-Emitting diode Laser (PC-VCSEL) have been investigated. Photonic crystal structure, realized by a regular net of air holes within the layers, has been etched in the upper DBR mirror. An advanced three-dimensional, vectorial electromagnetic model has been applied to a phosphide – based device design featuring InGaAlAs active region, AlGaAs/GaAs mirrors and a tunnel junction to confine the current flow. For the structure under consideration a single mode operation has been found for the hole diameter over photonic crystal lattice constant ratio between 0.1–0.3.
© 2007 Optical Society of America
Intensive research on Photonic-Crystal (PC) structures bore in modification of the Vertical-Cavity Surface-Emitting diode Lasers (VCSEL) with PC structures (PC-VCSEL). The light within such a device is confined with respect to all three dimensions: along axial direction it is reflected from the top and the bottom Distributed Bragg Reflectors (DBRs), and radially it is confined by a two-dimensional, hexagonal PC lattice within the upper DBR with a single PC defect. To fully take advantage of the PC, the hole etching depth should be as deep as the whole structure, to protect the field from radial leakage out of the cavity and to minimize the threshold current. However the state of the art of the technology allows for a limited ratio between the hole depth and diameter. Therefore in this paper we consider PC introduced in the top DBR. The aperture of the holes should be large enough to increase the waveguiding effect however; too wide holes introduce diffraction losses. The goal of this paper is to determine the optimal aperture of the holes in order to achieve the lowest modal losses.
2. Laser structure and computational method
Several works have addressed recently the electromagnetic wave problem within a PC VCSEL cavity [1,2] however, all of them are based on a simple effective index/frequency method. Such an approach can be erroneous since the separability of the optical field in longitudinal and transverse components, which is a common assumption for effective methods , is not possible for PC-VCSEL.
Using the 3D fully vectorial Plane Wave Admittance Method (PWAM) we investigate here the influence of the geometry of the PC structure on the fundamental mode distribution, the wavelength of the emitted light and the modal gain within an InP-based VCSEL. Our model combines two very effective approaches. In the plane of the active region, the field is expanded in a basis of exponential functions and, using the Admittance Method, it is transformed through the layers determining an eigenvalue problem, which gives as a solution the effective wavelength of the mode and the distribution of the mode within the structure. Details of the model are described elsewhere . In the present paper we will focus on InP based VCSELs with a PC structure etched in the top mirror. The structure is expected to exhibit more advantages over other typical VCSEL designs. The InP-based VCSELs suffer from the lack of an effective optical confinement, which would ensure stable, polarized, single mode operation necessary in telecommunication applications. In contrast to the GaAs-based VCSELs, the InP-based technology provides no method to create oxide apertures, which effectively confine the light. On the other hand, there is a big demand on InP-based lasers since they can cover both telecommunication wavelengths: 1.3 and 1.55 μm. The GaAs-based GaInAsN lasers are the biggest competitors for the InP lasers, since they proved excellent lasing performance for the 1.3 μm wavelength [5,6]. However, similar results have not been achieved for longer wavelengths since material technology is still imperfect for higher content of nitride allowing for longer wavelength emission. The InP materials are characterized by a similar lattice constant as the InAlGaAs active region material, which covers both wavelengths and provides high material gain. Hence it seems to be the most effective solution  according to the current stage of technology.
Our theoretical study is based on the 1.3 μm PC VCSEL structure, of a design shown in Fig. 1. The multiquantum well active region within the 3-λ InP cavity consists of four 10-nm-thick Al0.0152Ga0.495In0.49As quantum wells and 15-nm-wide Al0.218Ga0.25In0.532As barriers. The cavity is bounded by the Al0.9Ga0.1As/GaAs DBRs. The upper one consists of 27 DBR pairs and the bottom one of 35 pairs. An optical confinement is realized by three rings of hexagonal air-hole PC in the whole upper DBR with a lattice constant of 4 μm. We consider here a simple single defect PC cavity. The uniform injection of carriers in the active region is assured by a proton implanted tunnel junction placed at a node position of the standing wave. In our computational model, the refractive indices of the layers are complex. We take into account the losses originating from the free carrier absorption in the passive layers and the intraband absorption within the active region and the tunnel junction. The distributions of the refractive indices are assumed to be uniform within each layer (see table 1).
Figure 2 shows the dependence of the emitted wavelength of the fundamental HE11 mode as a function of (1/N) where N stands for the number of the nodes. The nodes are related to the number of the plane waves in PWAM by the relation: (2N +1)2. The different curves in Fig. 2 correspond to different a/L ratios where a is the hole diameter and L is the lattice constant. A change of the a/L ratio does not change the single defect aperture, which is defined here as a 10 μm circle, touching the inner ring of the holes.
The best convergence is achieved for the narrowest holes. In that case the interaction between the optical field and the holes is weak and the field penetrates transversely the regions placed outside the active region aperture. More attention should be paid to the case of broad holes. The convergence with the number of nodes is slower than in the case of narrow holes. The reason lies in the strong confinement mechanism, which is similar to the one observed in oxide VCSELs. The behavior of PWAM for strong confinement mechanism has been reported in .
3.1. Passive structure
We consider two different cases: a VCSEL structure as just described and the same VCSEL with a step gain function. Figure 3(a) presents the dependence of the emitted wavelength on the hole aperture for two guided modes in the structure (HE11 and HE12). The holes serve to provide the optical confinement. Broadening of the holes causes narrowing of the active region and strengthening of the mode confinement. The impact of the mode squeezing by the holes is observed in a typical blue shift of the emitted wavelength. The structure supports only the fundamental mode for narrow holes in the range 0.1 – 0.3 of the a/L ratio.
From among the hybrid modes, only the fundamental and first order modes are supported by the structure. The aperture created by the single defect photonic crystal is too small to support higher order modes. Figure 3(b) presents the imaginary part of the wavelength in the same domain as in Fig. 3(a). The imaginary part of the wavelength is proportional to the mode extinction. The main tendency is an increase of the modal losses with increasing of air hole aperture, mainly because of the fact that expanding the air holes disturbs to more extend the periodicity of the DBR mirror and therefore contributes to the lowering of the refractivity as well as to the scattering of the light by the low refractive air columns.
3.2. Active structure
The next simulation presents the influence of the gain region on the PC VCSEL modal characteristics. A gain profile has been introduced to the active region as a step-like function of the imaginary part of the refractive index. Within a radius of 3 μm the gain has been set to be equal to 2000 cm−1  and outside of the region to 1000 cm−1. The analysis of the real part of the wavelength does not reveals any major changes comparing to the case 3.1 of a passive structure, reflecting the fact that the introduction of a gain profile does not disturb the distribution of the real refractive index. More dramatic change is observed for the imaginary wavelength characteristics (Fig. 3(b)). The modal losses of the modes have been affected positively by the existence of the gain region, revealing positive, or close to positive values of the imaginary part of the wavelength. The narrow holes favor a single mode action with the cost of higher modal losses due to the weak waveguiding effect and the consequent filed penetration in the high loss region. Figure 4(a) illustrates that indeed, the fundamental mode is weakly confined by the holes of 0.1 L aperture. Further increase of the hole aperture (Fig. 3(b)) leads to a larger modal gain of the fundamental mode, while HE12 mode remains cut off for a/L < 0.3. That allows for a single mode operation, which is characterized by the highest modal gain for an aperture hole of 0.3 L. In this case, the dynamical behavior of the device can be significantly improved, since high-speed modulation will not cause the appearance of higher order modes. The fundamental mode becomes perfectly confined to the single defect of the PC and simultaneously to the active region (Fig. 4(b)). Hence optimal hole apertures supporting single mode action are in the range 0.2 – 0.3 L. Further increase of the air holes diameter does not improve the fundamental mode characteristics (Fig. 3(a)) instead the HE12 mode appears and becomes gained, leading to a reduction of the fundamental mode discrimination. The difference between the modes in terms of imaginary part of the wavelength reaches its minimum for 0.7 L hole aperture. In that case the fundamental mode begins to suffer diffraction losses, which is visible as oscillations of the mode distribution in the outer region (Fig. 4(c)).
We demonstrate that careless use of a photonic crystal within a DBR could deteriorate the VCSEL characteristics. From one side, it may cause severe optical field leakage for narrow holes. From the other side, too broad holes can cause diffraction losses, reduction of higher order mode discrimination as well as reduction of DBR mirror reflection. We find that the optimal aperture of holes is in the range of a/L ratio values from 0.2 to 0.3. In that region of a/L we achieve a single mode operation with the highest modal gain of the fundamental mode. Such a laser configuration can be very useful for further CW hot cavity analysis as an optimized for a single mode operation structure with the lowest threshold current and electrical power. We show that the Photonic Crystal structure etched in the top DBR of a VCSEL confines the light within a small active region in a very efficient way, which discriminates higher order modes and stabilizes the single mode operation. This can significantly improve the dynamical behavior of the devices.
T. C. acknowledges the support of the Belgian Federal Science Policy Office for providing Research Fellowships. This work was supported by the IAP Program of the Belgian government, as well as GOA, FWO, and OZR of the VUB.
References and links
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