Abstract

We study the interaction of a mode propagating in a planar waveguide with a three–dimensional rectangular defect (protrusion or notch) in the structure. The scattering by the defect disturbes the propagation of the mode and light is coupled out of the waveguide. To investigate these phenomena we compute electric field distributions with the Green’s tensor technique and show movies with varying defect geometries and different mode polarizations. These calculations should be useful for optimizing specific elements in complex photonic circuits.

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References

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  1. R.G. Hunsperger, Integrated Optics: Theory and Technology, 3rd ed. (Springer, Berlin, 1991).
  2. T. Tamir and S. T. Peng, "Analysis and Design of Grating Couplers," Appl. Phys. 14, 235-254 (1977).
    [CrossRef]
  3. M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Green's tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
    [CrossRef]
  4. M. Paulus and O. J. F. Martin, "Light propagation and scattering in stratified media: A Green's tensor approach," J. Opt. Soc. Am. A 18, 854-861 (2001).
    [CrossRef]
  5. D. Marcuse, Light transmission optics, 2nd ed. (Krieger, Malabar, 1989).
  6. M. Born and E. Wolf, Principles of Optics, 6th. ed. (Pergamon Press, Oxford, 1987).

Other

R.G. Hunsperger, Integrated Optics: Theory and Technology, 3rd ed. (Springer, Berlin, 1991).

T. Tamir and S. T. Peng, "Analysis and Design of Grating Couplers," Appl. Phys. 14, 235-254 (1977).
[CrossRef]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Green's tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
[CrossRef]

M. Paulus and O. J. F. Martin, "Light propagation and scattering in stratified media: A Green's tensor approach," J. Opt. Soc. Am. A 18, 854-861 (2001).
[CrossRef]

D. Marcuse, Light transmission optics, 2nd ed. (Krieger, Malabar, 1989).

M. Born and E. Wolf, Principles of Optics, 6th. ed. (Pergamon Press, Oxford, 1987).

Supplementary Material (6)

» Media 1: MOV (431 KB)     
» Media 2: MOV (448 KB)     
» Media 3: MOV (425 KB)     
» Media 4: MOV (434 KB)     
» Media 5: MOV (399 KB)     
» Media 6: MOV (405 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Geometry of the investigated InP/InGaAsP planar waveguide structure (permittivities ε InP=10.05, εInGaAsP=11.42, wavelength λ=1.55 µm. Either (a) a protrusion with height h>0 is deposited on or (b) a notch with depth h<0 is etched through the structure. This scattering element has a finite lateral extension (500 nm) in both the x and the y directions.

Fig. 2.
Fig. 2.

Movies of the electric field amplitude for the investigated waveguide structure (Fig. 1) with varying defect height/depth h. A TE0 mode propagating in the x direction is used as illumination. Side view through the center of the structure (y=0) with a (a) linear (441 KB) and a (b) logarithmic (459 KB) color scale.

Fig. 3.
Fig. 3.

Electric field amplitude in the symmetry plane (y=0) 500 nm above the InP/air interface for two different defects (protrusion with h=100 nm and notch with h=-100 nm) and two different illumination polarizations. The bar represents the extension of the defect in the x direction.

Fig. 4.
Fig. 4.

Same situation as in Fig. 2 but with a TM0 mode as illumination. The movies have a (a) linear (435 KB) and a (b) logarithmic (444 KB) color scale.

Fig. 5.
Fig. 5.

Movies of the electric field amplitude in the InGaAsP layer (z=-525 nm) for varying defect height/depth h. Top view for a (a) TE0 (408 KB, see Fig. 2) and a (b) TM0 illumination (415 KB, see Fig. 4). The white box represents the extension of the defect in the xy plane.

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