A photonic crystal fiber (PCF) formed by a 2-dimensional photonic crystal (2D-PhC) with a missing hole as the core exhibits excellent single mode characteristics. In a PCF with a well-designed 2D-PhC, only the fundamental mode can be guided even if the core diameter is large compared to the guided wavelength. We are applying the same 2D-PhC structure to a vertical cavity surface emitting laser (VCSEL) to control lateral modes.
The device model used in this study is as follows. Air holes with diameter b are arranged to form a triangular 2D-PhC cladding. The center-to-center distance between adjacent holes is defined as the lattice constant a. The missing central hole acts as a core. To simplify the problem, we assume a uniform refractive index and neglect any heterostructures. We use the plane wave expansion method to obtain band diagrams for out-of-plane propagation and electric field distributions.
The out-of-plane band diagram for a 2D-PhC with relative hole diameter b/a of 0.95 (also a reasonable ratio for devices with an in-plane propagation configuration) is shown in Fig. 1. If we choose a fixed kz by assuming an optical cavity in the z direction, k0 for the confined mode must be close to kz/n. Since the photonic band gap at the normalized frequency k0 of around 0.5 never overlaps the line k0=kz/n and disappears at kz~1, the photonic band gap effect is not applicable to lateral confinement in VCSELs.
Fig. 1 Out-of-plane propagation band diagram of 2D-PhC.
In PCFs having the structure described above, number of guided modes is evaluated by the Veff-parameter,
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$$ V_{eff}=\frac{2\pi a}{\lambda}\sqrt{n^2-n_{eff}^2} $$
where neff is defined as the effective refractive index of the lowest mode in the 2D-PhC cladding (kz/k0).
If Veff is less than 2.405, the structure should be a single mode waveguide. We have calculated Veff by changing the relative hole diameter b/a as shown in Fig. 2. In this figure, normalized frequency a/l is used as the horizontal axis. If we choose an operating wavelength, the horizontal axis gives us the lattice constant a and the consequent core diameter 2a.
Fig. 2 Veff-parameter of the point defect structure.
If the relative hole diameter is designed to be 0.10, the single mode condition is satisfied for a/l greater than 10. From this result, single mode operation can be obtained at 1.3mm wavelength with a core diameter of more than 25mm. This means that the diameter of the core region is not of great concern in obtaining single mode operation. Electric field intensities of the lowest mode and the next higher order mode are shown in Fig. 3, where a/l is assumed to be 5. The lowest mode is well-confined in the center defect region, while the next higher order mode spreads over entire 2D-PhC cladding region. Thus single mode operation can be achieved by using 2D-PhC as a method of lateral confinement.
Fig. 3 Optical field intensities of the lowest mode and the next higher order mode.
N. Yokouchi, A. Danner, and K.D. Choquette, “Vertical cavity surface emitting lasers laterally confined by 2-dimensional photonic crystals,” Presented at 2002 LEOS Summer Topical Meetings, Mont Tremblant, Quebec, Canada, 15-17, July, 2002, Paper TuP2.
N. Yokouchi, A. Danner, and K.D. Choquette, “Lateral mode control of vertical cavity surface emitting lasers by using 2-dimensional photonic crystal structure,” to be Presented at Photonics West 2003, San Jose, CA, 25-31, Jan, 2003.
N. Yokouchi, A.J. Danner, and K.D. Choquette, “Etching depth dependence of the effective refractive index in 2-dimensional photonic crystal patterned vertical-cavity surface-emitting laser structure,” submitted to Appl. Phys. Lett.
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