1. Introduction

High power, single mode vertical cavity surface emitting lasers (VCSELs) have attracted significant interest in the past few years [1–4]. The conventional VCSEL structure incorporates a waveguide whose core refractive index is larger than its cladding’s. Small core size is always necessary in order for such so-called positive-index waveguide to support only a single fundamental mode. This inevitably leads to small emission aperture size, in turn limited maximum output power, for single -mode VCSELs designed in a conventional way. There are increasing demands for larger-aperture single -mode operation, and hence higher continuous output powers. Due to the fact that multiple modes will exist in larger aperture waveguide, one of the solutions is to increase the modal discrimination and make the devices favor fundamental mode only [2]. Recently, ring-type anti-resonant-reflecting optical waveguide (ARROW) VCSELs [3] have been reported to operate at single mode with emitting aperture size as large as 8 ~ 12μm. The cladding of the ring-type ARROW VCSEL can be approximately regarded as a stack of high- and low-index Bragg reflectors. Average refractive index of the stack is higher than core index. Such waveguide’s strong leakage discrimination on high-order modes is responsible for achieving single mode operation with large aperture.

Index-guiding photonic crystal (PC) waveguide has recently been applied in VCSEL design to get single-fundamental-mode operation by Dae-Sung Song et al. [4]. The microstructured waveguide incorporated has a holey cladding structure and a solid core. This kind of VCSEL is expected to provide good single-mode operation. However, the single mode operation can be provided only if the ratio of the hole diameter to the hole-to-hole distance stays smaller than a certain value. This threshold value could be very small if index contrast involved is relatively high, which would make fabrication a difficult process. Though partial etching of the air holes would be a solution to this problem [5–6], it may be a difficult controlling process during fabrication.

In this paper, we propose an alternative design. In top DBR mirror region, a hexagonal array of high-index cylinders is introduced in the cladding region. These high-index cylinders are tuned in dimension to strongly reflect light back to the core region. We refer to this design as anti-resonant reflecting photonic crystal vertical cavity surface emitting lasers (ARPC-VCSEL). In contrast to a positive-index waveguide, the ARPC-VCSEL can operate with only a fundamental mode even cylinder dimension is relatively big compared to cylinder-to-cylinder distance, since high order modes suffer excessively large loss in this structure.

2. Design of anti-resonant reflecting PC-VCSEL

The proposed ARPC-VCSEL is shown in Fig. 1(a). As stated in reference (Fig. 2 in Ref. 3), one proper way to get the cylindrical ARROW structure is by chemically etching a thin GaAs-GaInP spacer layer. Following by regrowth process, the high- and low-index ring reflectors can be defined. Our proposed APRC-VCSEL can be realized exactly in the same way. That is, the GaAs-GaInP spacer layer is selectively etched with a photomask whose pattern matches the array of high index cylinders. The places where the spacer layer remains (an array of circular regions in this case) are responsible for the formation of high index cylinders after Hadley’s effective index modeling [7]. After our proposed structure is converted to Hardley’s effective index model [2][7] , the waveguide adopted in our proposed VCSEL can be schematically shown in Fig. 1(b). Background region is of lower index. Black regions represent high-index rods that run along the waveguide’s axial direction. As the average index of cladding is higher than that of core, index-guiding is dismissed in such waveguide. In fact, PC formed by the hexagonal array of rods in cladding region reflects light strongly at certain wavelength ranges. Such light confinement in low-index core region is attributed to Bragg reflections at cylinder boundaries along any propagation direction in the entire transverse plane [8]. Photonic bandgap (PBG) is another explanation for the Bragg reflection mentioned here [9].

The cross section of the ARPC-VCSEL is shown in the Fig. 1(c). d is the diameter of the high index cylinders and Λ is the pitch of the cladding PC. In our design, the effective refractive indices of cylinder n_cylinder (black areas) and core (or the background region, white areas) n_core are assumed to be 3.35 and 3.3, respectively. Λ is chosen at 7.36μm , and diameter of the cylinder d 3.31μm. The emission wavelength is 0.98 μm. The core diameter is roughly 2Λ =14.7μm , which is considered very big.

 

Fig. 1. (a) Schematic of anti-resonant reflecting photonic crystal VCSEL. (b) Waveguide incorporated in ARRP -VCSEL after Hardley model. (c) Cross section of the ARRP -VCSEL, the black regions represent high index cylinders.

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3. Results and discussions

The structure we proposed in the Section 2 is relatively a complex one compared to conventional VCSELs. In this section, we employ multipole method [10], which is originally developed for calculating the modes of micro-structured optical fibers, to analyze this APRC-VCSEL structure. This method gives the most accurate results as it is semi -analytical. Also it employs an open boundary formulation, hence it is capable to calculate modal leakage losses. It is should be noted that we only use one ring of rods in our simulation. That is because transverse modal property for ARPC-VCSELs with more rings of rods in cladding is supposed to have similar characteristics [11]. The calculated effective indices n_eff of the first four modes at λ = 0.98μm are given in Table 1.

Table 1. Mode effective refractive index for the first four modes

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From Table 1, we note that n_eff < n_core < n_cladding , the results indicate that the effective modal index is outside the range of bound modes in the individual cylinders. From the values of the effective modal index, we can observe that TE ₀₁, TM ₀₁ and HE ₂₁ modes nearly have the same real part and imaginary part, which indicates that these three modes have roughly the same propagation constant and also have nearly the same mode losses. The loss for fundamental HE ₁₁ mode is four times smaller than that for the other three high-order modes.

 

Fig. 2. Transverse electric field of: (a) ${\mathit{\text{HE}}}_{11}^{\mathrm{y}}$ mode; (b) TE ₀₁ mode; (c) TM ₀₁ mode; (d) HE ₂₁ mode. (e) is for E_y field of ${\mathit{\text{HE}}}_{11}^{\mathrm{y}}$ mode and (f) for E_y field of TE ₀₁ mode.

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The transverse modal field E_t (E_t = E_x + iE_y ) of HE ₁₁,TE ₀₁, TM ₀₁ and HE ₂₁ modes are shown in Fig. 2(a) to Fig. 2(d), respectively. The intensity distribution of E_y field for HE ₁₁ and TE ₀₁ modes are shown in Fig. 2(e) and Fig. 2(f) separately.

The modal confinement loss α can be obtained from the imaginary part of the effective mode index ℑ(n_eff ) by using $\alpha =\frac{\mathrm{\pi \Im }\left(n_{\mathit{eff}}\right)}{25\lambda }.$. We have investigated the modal confinement losses with the change of lasing wavelength. The modal losses of HE ₁₁ and TE ₀₁ modes are calculated over a range of wavelengths from 0.65 ~ 1.3μm and the results are shown in Fig. 8.

From Fig. 8, it is noticed that the confinement losses for both modes consists of a number of lower regions separated by narrow regions where the loss increases rapidly. This behavior is fundamentally different from the index guiding VCSELs for which the loss increases monotonically with the wavelength. And the explanation of the characteristics was given by T.P.White et al. in [11–12]. Generally speaking, when the resonant condition of the photonic crystal cladding is met, field tends to be confined in the cladding cylinders, and core mode will hence suffer from high loss. Good confinement of the core mode will happen when the photonic crystal cladding is highly anti-resonant. The resonant condition of the photonic crystal cladding (where the large modal loss located) can be written as

where k_ex is the transverse component of the wavevector κ in high index regions. If we assume n_eff ≈ n_core , the peak-loss wavelength points can then be predicted by the following expression

where roots(J_l ) means the roots of Bessel function of order l.

 

Fig. 3. The modal loss of HE ₁₁ (dotted line) and TE ₀₁ (solid line) modes with the change of the wavelength.

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In Fig. 3, loss peaks appear around λ = 0.695μm, λ = 0.85μm and λ = 1.05μm. These values are in good agreement with the calculated ones. For example, λ = 0.695μm corresponds to k_exd/2 = 8.63 in equation (1), which is quite near to the third root of Bessel function J ₀. Loss rate for fundamental mode is always below that for high-order modes. At λ = 0.98μm (lasing wavelength), we can get large modal discrimination as well as keep the fundamental modal loss relatively small. The modal loss difference between HE ₁₁ mode and TE ₀₁ mode at that wavelength approaches to maximum, which is about 7.5cm^-1 . Hence, our proposed VCSEL is supposed to favor the fundamental model, and the high-order modes are greatly depressed.

Another method for loss peaks prediction is to employ the PBG theory. PBG-map for photonic crystal cladding depicted in Fig. 1 has been calculated by using the plane wave expansion (PWE) method. Fig. 4 shows the gap-map obtained in the coordinate of n_eff versus of wavelength λ. Shaded regions are PBG gap regions, within which no propagating mode is supported by the cladding structure. As a result the light is rejected back to the core region.

In order to make the z-propagating light to be confined in the core region, the modal effective index n_eff should be less than but very close to 3.30. As an approximation, we draw a level line at this n_eff = 3.3 in Fig. 4. From the figure, we can see n_eff = 3.3 line crosses several gap regions. Light can be confined in the core region if the level line stays within the gap region. Light will experience large leakage loss and can’t be confined in the core region if the level line is outside the gap regions. We notice in Fig. 4, the level line stay outside gap regions around 0.71um, 0.87um, and 1.1um wavelength points, which agree with loss peak positions in Fig. 3 very well.

 

Fig. 4. Map of phtonics bandgaps found for cladding photonic crystal structure.

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4. Conclusions

We have introduced anti-resonant reflecting photonic crystal structure in vertical cavity surface emitting lasers (VCSELs) to achieve large-aperture single-mode operation. The modal loss properties of the proposed structures with one ring of high index cylinders have been investigated by using multipole method. It was found the loss properties of the modes are varied periodically with the lasing wavelength. High-order modes always have about four times higher loss than the fundamental mode. Our proposed VCSEL is supposed to have single-mode operation with such large modal discrimination. Explanations of modal loss properties by photonic bandgap method have also been provided.