Vertical high emission in photonic crystal nanocavities by band-folding design

We demonstrate reshaping of the radiation pattern emitted from photonic crystal nanocavities. More than 80% of the radiated power can be collected by an optics having numerical aperture of 0.6. This technique is very robust against disorders. The band folding method can be applied to almost any kind of cavity in order to reach stronger and more directive emission.

Figure 1

(Color online) Principle of band folding: schematic of a 1D cavity (b). Corresponding $E$-field distribution in the $k$ space (a) with minima at $k_x=0$ after $Q$-factor optimization. Modified design with additional subharmonic modulation (e). Resulting replica appearing at $k_x=0$ consequently to band-folding (d). Sketch of typical emission of 2D PhC cavities when optimized to achieve high $Q$ factor (c) and with addition to the subharmonic modulation (f) improving the directivity of the vertical emission.

Figure 2

(Color online) 1D PhC cavity: schematic of the 1D PhC cavity design used for band folding implementation (a). Calculated $E$-field distribution represented in real space (b) and $k$ space (c). Associated emission diagram with no significant radiated vertical component (d). $E$-field distribution of the modified design with subharmonic modulation in real (e) and reciprocal (f) spaces. Corresponding radiation pattern with directive vertical emission (g). Comparison of collection efficiency as a function of the NA for regular 1D cavity (squares) and new “extractor” design (open circles) (h). The blue circle in (d) and (g) represents the collection angle of optics having numerical aperture $\text{NA}=0.5$.

Figure 3

(Color online) $L3$ cavity: schematic of the $L3$ cavity with standard design (a) and with implementation of the band folding (d) through additional sub-harmonic modulation. Calculated $E$-field distribution in the $k$ space without (b) and with (e) band folding. Corresponding radiation pattern with broad emission for the standard $L3$ design (c) and highly directive for the modified (f).

Figure 4

(Color online) Heterostructure cavity: standard design (a) with two elongated periods forming the heterostructure cavity. Optimized design (d) for vertical emission including the new subharmonic periodicity. $E$-field distribution in reciprocal space for the original design (b) and the modified one (e). Associated emission diagrams, respectively (c) and (f).

Figure 5

(Color online) H0 cavity: schematic of the zero-point defect (H0) cavity without (a) and with (d) the band-folding structure. Associated $E$ field in reciprocal space (b) and (e), and emission diagrams (c) and (f).

Figure 6

(Color online) Hexapole cavity: calculated Hz-field distribution of the hexapole cavity (a). Corresponding $E$-field distribution in $k$ space (b) and far-field pattern (c). Schematic of the new design (d) including the band-folding principle. Associated field distribution in reciprocal space (e) and radiation diagram (f) showing directive emission perpendicular to the membrane.

Figure 7

(Color online) Collection efficiency as a function of NA: standard designs require large NA (left) whereas the modified designs improve collection efficiency for the same NA (right).

Figure 8

(Color online) Impact of disorder on radius: plot of the collection efficiency (a) versus the NA for the $L5$ extractor with and without disorder. Pseudocolor map (b) showing the collection efficiency as a function of the amount of disorder and the NA. Typical far-field patterns (c) of a $L5$ extractor for increasing disorder.

Figure 9

(Color online) Impact of disorder on position: plot of the collection efficiency (a) versus the NA for the $L5$ extractor with and without disorder. Calculated $E$-field distribution of the $L5$ extractor and related far-field patterns for 1% (b) and (c), and 2% (d) and (e), respectively.