A directional coupler for optically coupling waveguides, the directional coupler comprising: a first input; a second input; a first output; a second output; a shoulder disposed on a substrate, wherein: the shoulder extends from the first input to the first output, from the second input to the second output, from the first input to the second output, and from the second input to the first output; and the shoulder comprises a material; a first ridge disposed on the shoulder and extending from the first input to the first output, wherein the first ridge comprises the material; and a second ridge disposed on the shoulder and extending from the second input to the second output, wherein: the second ridge comprises the material; and the second ridge is separate from the first ridge; characterized by the directional coupler further comprising: a first region comprising the inputs, wherein, at the inputs, the shoulder is separated into two portions, a first portion of the shoulder under the first ridge and a second portion of the shoulder under the second ridge, wherein, at the inputs, the first portion of the shoulder is separated from the second portion of the shoulder by a first gap, where the shoulder tapers inward in a longitudinal direction toward a longitudinal axis until a first portion of the shoulder under the first ridge merges with a second portion of the shoulder under the second ridge; a second region longitudinally adjacent to the first region where outside edges of the shoulder, the first ridge and the second ridge taper such that they narrow longitudinally; a third region longitudinally adjacent to the second region where the outside edges, the first ridge and the second ridge taper in an opposite direction than in the second region; and a fourth region longitudinally adjacent to the third region where the shoulder splits and tapers in an opposite direction than in the first region, until the first portion of the shoulder is separated from the second portion of the shoulder by a second gap. a first input; a second input; a first output; a second output; a shoulder disposed on a substrate, wherein: the shoulder extends from the first input to the first output, from the second input to the second output, from the first input to the second output, and from the second input to the first output; and the shoulder comprises a material; the shoulder extends from the first input to the first output, from the second input to the second output, from the first input to the second output, and from the second input to the first output; and the shoulder comprises a material; a first ridge disposed on the shoulder and extending from the first input to the first output, wherein the first ridge comprises the material; and a second ridge disposed on the shoulder and extending from the second input to the second output, wherein: the second ridge comprises the material; and the second ridge is separate from the first ridge; the second ridge comprises the material; and the second ridge is separate from the first ridge; characterized by the directional coupler further comprising: a first region comprising the inputs, wherein, at the inputs, the shoulder is separated into two portions, a first portion of the shoulder under the first ridge and a second portion of the shoulder under the second ridge, wherein, at the inputs, the first portion of the shoulder is separated from the second portion of the shoulder by a first gap, where the shoulder tapers inward in a longitudinal direction toward a longitudinal axis until a first portion of the shoulder under the first ridge merges with a second portion of the shoulder under the second ridge; a second region longitudinally adjacent to the first region where outside edges of the shoulder, the first ridge and the second ridge taper such that they narrow longitudinally; a third region longitudinally adjacent to the second region where the outside edges, the first ridge and the second ridge taper in an opposite direction than in the second region; and a fourth region longitudinally adjacent to the third region where the shoulder splits and tapers in an opposite direction than in the first region, until the first portion of the shoulder is separated from the second portion of the shoulder by a second gap. a first region comprising the inputs, wherein, at the inputs, the shoulder is separated into two portions, a first portion of the shoulder under the first ridge and a second portion of the shoulder under the second ridge, wherein, at the inputs, the first portion of the shoulder is separated from the second portion of the shoulder by a first gap, where the shoulder tapers inward in a longitudinal direction toward a longitudinal axis until a first portion of the shoulder under the first ridge merges with a second portion of the shoulder under the second ridge; a second region longitudinally adjacent to the first region where outside edges of the shoulder, the first ridge and the second ridge taper such that they narrow longitudinally; a third region longitudinally adjacent to the second region where the outside edges, the first ridge and the second ridge taper in an opposite direction than in the second region; and a fourth region longitudinally adjacent to the third region where the shoulder splits and tapers in an opposite direction than in the first region, until the first portion of the shoulder is separated from the second portion of the shoulder by a second gap.