An optical isolator, comprising: a first polarizer including first and second ports, the first polarizer coupled to receive a forward propagating wave at the first port and to output at the second port a polarized forward propagating wave having a first plane of polarization; a non-reciprocal rotator coupled to receive the polarized forward propagating wave from the second port of the first polarizer and to rotate the polarized forward propagating wave from the first plane of polarization by an angle to a second plane of polarization; a reciprocal rotator coupled to the non-reciprocal rotator to receive the polarized forward propagating wave and to rotate the polarized forward propagating wave from the second plane of polarization back to the first plane of polarization; and a second polarizer including third and fourth ports (P3,P4), the third port coupled to the reciprocal rotator to receive the polarized forward propagating wave and to pass the polarized forward propagating wave having the first plane of polarization to the fourth port, wherein the first and second polarizers are monolithically integrated into a multilayer semiconductor die, characterised in that the non- reciprocal rotator and the reciprocal rotator are monolithically integrated into said die, wherein the non-reciprocal rotator comprises a substrate layer included in said die; a ferromagnetic semiconductor layer comprising manganese, silicon and germanium disposed on the substrate layer; a first, p-doped layer comprising silicon and germanium disposed on the ferromagnetic layer; a heterostructure disposed on the first, p-doped layer, wherein the heterostructure comprises one or more layers comprising silicon alternating with one or more layers comprising silicon and germanium; and a second, n-doped layer comprising silicon disposed on the heterostructure. a first polarizer including first and second ports, the first polarizer coupled to receive a forward propagating wave at the first port and to output at the second port a polarized forward propagating wave having a first plane of polarization; a non-reciprocal rotator coupled to receive the polarized forward propagating wave from the second port of the first polarizer and to rotate the polarized forward propagating wave from the first plane of polarization by an angle to a second plane of polarization; a reciprocal rotator coupled to the non-reciprocal rotator to receive the polarized forward propagating wave and to rotate the polarized forward propagating wave from the second plane of polarization back to the first plane of polarization; and a second polarizer including third and fourth ports (P3,P4), the third port coupled to the reciprocal rotator to receive the polarized forward propagating wave and to pass the polarized forward propagating wave having the first plane of polarization to the fourth port, wherein the first and second polarizers are monolithically integrated into a multilayer semiconductor die, characterised in that the non- reciprocal rotator and the reciprocal rotator are monolithically integrated into said die, wherein the non-reciprocal rotator comprises a substrate layer included in said die; a ferromagnetic semiconductor layer comprising manganese, silicon and germanium disposed on the substrate layer; a first, p-doped layer comprising silicon and germanium disposed on the ferromagnetic layer; a heterostructure disposed on the first, p-doped layer, wherein the heterostructure comprises one or more layers comprising silicon alternating with one or more layers comprising silicon and germanium; and a second, n-doped layer comprising silicon disposed on the heterostructure.