A waveguide crossing comprising: a first waveguide; a second waveguide intersecting the first waveguide such that a gap equal to a width of the second waveguide is formed in the first waveguide, wherein the first and the second waveguides (200, 300) are silicon on isolator, SOI, waveguides for propagating optical signals in the 1550 nm band; wherein the first waveguide comprises a first waveguide section, wherein the first waveguide section is configured to support a single even-order optical mode, followed by a first non-adiabatic diverging taper, followed by a second waveguide section wider than the first waveguide section, wherein the second waveguide section is configured to support two even-order optical modes, followed by a second non-adiabatic diverging taper, followed by a third waveguide section wider than the second waveguide section, wherein the third waveguide section is configured to support three even-order optical modes; and wherein the first waveguide further comprises, downstream of the gap, a fourth waveguide section, followed by a first non-adiabatic converging taper, followed by a fifth waveguide section narrower than the fourth waveguide section, followed by a second non-adiabatic converging taper, followed by a sixth waveguide section narrower than the fifth waveguide section; wherein the second waveguide has a centerline defining a plane of symmetry, wherein the fourth, and fifth waveguide sections (212, 216) are symmetrical with respect to the plane of symmetry to the third, and second waveguide sections (210, 206), respectively, and wherein the first and second converging non-adiabatic tapers (214, 218) are symmetrical with respect to the plane of symmetry to the second and first diverging non-adiabatic tapers (208, 204), respectively; wherein the second waveguide section of a length L A is configured to adjust a phase offset between the two even-order optical modes, the third waveguide section of a length L B is configured to adjust a phase offset between the three even-order optical modes, the first and second non-adiabatic diverging tapers (204, 208) and the second and third waveguide sections (206, 210) are configured so that the three even-order modes are configured to interfere at a first interface between the third waveguide section and the gap to form a converging quasi-Gaussian beam across the gap, wherein the quasi-Gaussian beam is substantially symmetrical with respect to the plane of symmetry and self-images symmetrically across the gap. a first waveguide; a second waveguide intersecting the first waveguide such that a gap equal to a width of the second waveguide is formed in the first waveguide, wherein the first and the second waveguides (200, 300) are silicon on isolator, SOI, waveguides for propagating optical signals in the 1550 nm band; wherein the first waveguide comprises a first waveguide section, wherein the first waveguide section is configured to support a single even-order optical mode, followed by a first non-adiabatic diverging taper, followed by a second waveguide section wider than the first waveguide section, wherein the second waveguide section is configured to support two even-order optical modes, followed by a second non-adiabatic diverging taper, followed by a third waveguide section wider than the second waveguide section, wherein the third waveguide section is configured to support three even-order optical modes; and wherein the first waveguide further comprises, downstream of the gap, a fourth waveguide section, followed by a first non-adiabatic converging taper, followed by a fifth waveguide section narrower than the fourth waveguide section, followed by a second non-adiabatic converging taper, followed by a sixth waveguide section narrower than the fifth waveguide section; wherein the second waveguide has a centerline defining a plane of symmetry, wherein the fourth, and fifth waveguide sections (212, 216) are symmetrical with respect to the plane of symmetry to the third, and second waveguide sections (210, 206), respectively, and wherein the first and second converging non-adiabatic tapers (214, 218) are symmetrical with respect to the plane of symmetry to the second and first diverging non-adiabatic tapers (208, 204), respectively; wherein the second waveguide section of a length L A is configured to adjust a phase offset between the two even-order optical modes, the third waveguide section of a length L B is configured to adjust a phase offset between the three even-order optical modes, the first and second non-adiabatic diverging tapers (204, 208) and the second and third waveguide sections (206, 210) are configured so that the three even-order modes are configured to interfere at a first interface between the third waveguide section and the gap to form a converging quasi-Gaussian beam across the gap, wherein the quasi-Gaussian beam is substantially symmetrical with respect to the plane of symmetry and self-images symmetrically across the gap.