Optical apparatus and method having predetermined group velocity dispersion

An optical apparatus comprising:

• a slab waveguide;
• and
• a plurality of channel waveguides optically coupled to said slab waveguide, each of said plurality of channel waveguides optically coupled to said slab waveguide via a transition segment, said transition segment comprising:
• a taper comprising a narrow end and a wide end and increasing not more than 2 μm in width per 1 μm in length, wherein said narrow end of said taper is configured to optically couple to said channel waveguide, and said transition segment further comprising an extension comprising a first end, a second end, and a constant width wherein said first end of said extension is configured to optically couple to said wide end of said taper and said second end of said extension is configured to optically couple to said slab waveguide and wherein said extension is equal in width to said wide end of said taper.

An optical apparatus comprising:

• a slab waveguide;
• and
• a plurality of channel waveguides optically coupled to said slab waveguide, each of said channel waveguides coupled to said slab waveguide via a transition segment, each said transition segment comprising
• a taper comprising a narrow end and a wide end and an intermediate mode conversion structure therebetween, said intermediate mode conversion structure configured to substantially couple a first mode at the narrow end and an optical field at the wide end wherein said optical field comprises a component in the first mode and a component in a third mode, said taper further configured such that optical power propagating in said optical field at said wide end is substantially equal to optical power propagating in said first mode at said narrow end, and said transition segment further comprising an extension comprising a first end and a second end and an intermediate mode conserving structure therebetween, said intermediate mode conserving structure configured to substantially couple the first mode at said first end and the first mode at said second end, to substantially couple the third mode at said first end and the third mode at said second end, to prevent substantial coupling between the first mode at said first end and the third mode at the said second end, and to prevent substantial coupling between the third mode at said first end and the first mode at said second end.