Tunable cascaded Mach-Zehnder interferometer structures
Cascaded Mach-Zehnder Interferometer (CMZI) structures comprising electrically resistive heaters provisioned across the stages so as to enable improved filter wavelength control. In embodiments, CMZI heater power supply control is made a linear function by scaling the number of heater elements between the stages in proportion with the magnitude of the arm differential (e.g., ΔL, 2ΔL) for the corresponding stage.
1 . An apparatus comprising:
a first Mach-Zehnder interferometer (MZI) structure having a first arm length differential;
a second MZI structure having a second arm length differential that is a multiple of the first arm length differential;
a first number of electrically resistive heater elements proximal to an arm of the first MZI structure, wherein the first number of electrically resistive heater elements are to dissipate power through Joule heating to modulate a phase difference associated with the first arm length differential through the thermo-optic effect;
a second number of electrically resistive heater elements proximal to an arm of the second MZI structure, wherein the second number of electrically resistive heater elements are to dissipate power through Joule heating to modulate a phase difference associated with the second arm length differential through the thermo-optic effect, wherein the second number of heater elements is approximately equal to the first number of heater elements times the multiple, and wherein individual ones of the first and second number of resistive heater elements all have substantially the same resistance value.
2 . The apparatus of claim 1 , wherein individual ones of the first and second number of heater elements are all connected in electrical parallel across a first heater power supply rail and a second heater supply rail.
3 . The apparatus of claim 2 , further comprising a voltage source coupled to the first heater supply rail.
4 . The apparatus of claim 1 , wherein individual ones of the first and second number of heater elements all have substantially the same composition and substantially the same length.
5 . The apparatus of claim 1 , wherein the multiple of the arm length differential is two, the first number of heater elements is one, and the second number of heater elements is two.
6 . The apparatus of claim 1 , wherein the second MZI structure is in a serial cascade with the first MZI structure.
7 . A cascaded Mach-Zehnder interferometer (CMZI) structure, wherein the CMZI structure comprises:
a first Mach-Zehnder interferometer (MZI) structure comprising:
a first pair of optical waveguides with an optical path length difference of ΔL; and
a plurality of first electrical resistors, wherein one or more of the first resistors, each having a first resistance, are adjacent to each of the first pair of optical waveguides and are to dissipate power through Joule heating to modulate a phase difference associated with the optical path length difference of the first pair of optical waveguides through the thermo-optic effect; and
a second MZI structure comprising:
a second pair of optical waveguides with an optical path length difference of twice ΔL; and
a plurality of second electrical resistors, wherein two or more of the second resistors, each having approximately the first resistance, are adjacent to each of the second pair of optical waveguides and are to dissipate power through Joule heating to modulate a phase difference associated with the optical path length difference of the second pair of optical waveguides through the thermo-optic effect.
8 . The CMZI structure of claim 7 , wherein all of the first resistors are electrically coupled across a common supply rail and one of a second supply rail or a third supply rail.
9 . The CMZI structure of claim 8 , wherein all of the second resistors are electrically coupled across the common supply rail and one of the second supply rail or the third supply rail.
10 . The CMZI structure of claim 8 , wherein the second resistors comprise two pairs of second resistors, each pair of the second resistors adjacent to a corresponding one of the second pair of optical waveguides.
11 . The CMZI structure of claim 10 , wherein each of the second resistors in each of the pairs of second resistors has approximately the first resistance.
12 . The CMZI structure of claim 10 , wherein a first pair of the second resistors adjacent to a longer one of the second waveguides are electrically coupled in parallel across the common supply rail and the second supply rail, and wherein a second pair of the second resistors adjacent to a shorter one of the second waveguides are electrically coupled in parallel across the common supply rail and the third supply rail.
13 . The CMZI structure of claim 12 , further comprising a third stage, wherein the third stage comprises:
a third pair of optical waveguides with an optical path length difference of twice ΔL summed with π/2; and
a plurality of third electrical resistors, wherein two or more of the third resistors, each having approximately the first resistance, are adjacent to each of the third pair of optical waveguides.
14 . The CMZI structure of claim 13 , wherein a first pair of the third resistors adjacent to a shorter one of the third waveguides are coupled in electrical parallel across the common supply rail and the second supply rail, and wherein a second pair of the third resistors adjacent to a longer one of the third waveguides are coupled in electrical parallel across the common supply rail and the third supply rail.
15 . The CMZI structure of claim 14 , wherein each of the second resistors and the third resistors has a length approximately equal to a length of each of the first resistors.