A tunable Bragg grating comprising: a first substrate section; first and second spaced apart support bars extending upwardly from the first substrate section; a first waveguide for guiding light therein, wherein the first waveguide has an optical axis and is supported by the first and second support bars above the first substrate section so that a first gap exists between the first substrate section and the first waveguide, wherein an effective refractive index of the first waveguide is spatially modulated along the optical axis, forming a grating for reflecting an optical frequency component of the light guided by the first waveguide to propagate back therein, wherein at least one of phase or amplitude of the spatial modulation of the effective refractive index is varying along the optical axis, forming modulation crests and valleys, wherein the crests are spaced apart at a first spatial frequency along the optical axis; and a first resistive heater disposed on the first waveguide, for heating the first waveguide for tuning an optical frequency of the reflected optical frequency component; wherein the first waveguide has first and second arrays of openings (118a, 118b) extending therethrough and into the first gap, the openings of the first and second arrays running along the optical axis of the first waveguide on respective opposite first and second sides of the optical axis, the first and second arrays of openings defining first and second arrays of supporting fingers (119a,119b), respectively, for supporting the first waveguide over the first gap, wherein the first and second arrays of supporting fingers extend between the optical axis and the first and second support bars, respectively, wherein positions of the supporting fingers along the optical axis are coordinated with positions of the modulation crests and valleys along the optical axis, whereby, when heat is applied by the first resistive heater to the first waveguide, spatial refractive index variations, caused by spatial temperature variations along the optical axis due to heat flow through the supporting fingers to the first and second support bars, are spatially coordinated with the modulation crests and valleys, and wherein the openings of the first and second arrays of openings each have a length along the optical axis, and the lengths of the first and last openings of each of the first and second arrays of openings are larger than the length of any other opening of the first and second arrays of openings. a first substrate section; first and second spaced apart support bars extending upwardly from the first substrate section; a first waveguide for guiding light therein, wherein the first waveguide has an optical axis and is supported by the first and second support bars above the first substrate section so that a first gap exists between the first substrate section and the first waveguide, wherein an effective refractive index of the first waveguide is spatially modulated along the optical axis, forming a grating for reflecting an optical frequency component of the light guided by the first waveguide to propagate back therein, wherein at least one of phase or amplitude of the spatial modulation of the effective refractive index is varying along the optical axis, forming modulation crests and valleys, wherein the crests are spaced apart at a first spatial frequency along the optical axis; and a first resistive heater disposed on the first waveguide, for heating the first waveguide for tuning an optical frequency of the reflected optical frequency component; wherein the first waveguide has first and second arrays of openings (118a, 118b) extending therethrough and into the first gap, the openings of the first and second arrays running along the optical axis of the first waveguide on respective opposite first and second sides of the optical axis, the first and second arrays of openings defining first and second arrays of supporting fingers (119a,119b), respectively, for supporting the first waveguide over the first gap, wherein the first and second arrays of supporting fingers extend between the optical axis and the first and second support bars, respectively, wherein positions of the supporting fingers along the optical axis are coordinated with positions of the modulation crests and valleys along the optical axis, whereby, when heat is applied by the first resistive heater to the first waveguide, spatial refractive index variations, caused by spatial temperature variations along the optical axis due to heat flow through the supporting fingers to the first and second support bars, are spatially coordinated with the modulation crests and valleys, and wherein the openings of the first and second arrays of openings each have a length along the optical axis, and the lengths of the first and last openings of each of the first and second arrays of openings are larger than the length of any other opening of the first and second arrays of openings.