Phase control for double-nested quadrature modulator

A double-nested quadrature modulator, comprising:

• an outer Mach-Zehnder (MZ) interferometer including an in-phase (I) branch and a quadrature (Q) branch,
• the I branch including a first inner MZ interferometer having a first left branch and a first right branch,
• the Q branch including a second inner MZ interferometer having a second left branch arm and a second right branch,
• a phase between the first inner MZ interferometer and the second inner MZ interferometer being 90 degrees or −90 degrees;
• the double-nested quadrature modulator being configured to:
• receive a set of phase dithers at the first inner MZ interferometer and at the second inner MZ interferometer, the set of phase dithers including one or more in-phase dither states and one or more anti-phase dither states;
• and
• receive an adjustment to the outer MZ interferometer, wherein sub-branches of the I branch and the Q branch are adjusted differentially without a direct dither being applied to the outer MZ interferometer.

A double-nested quadrature modulator, comprising:

• an outer Mach-Zehnder (MZ) interferometer including an in-phase (I) branch and a quadrature (Q) branch,
• the I branch including a first inner MZ interferometer having a first left branch and a first right branch,
• the Q branch including a second inner MZ interferometer having a second left branch arm and a second right branch,
• a phase between the first inner MZ interferometer and the second inner MZ interferometer being approximately 90 degrees or −90 degrees;
• and
• a controller configured to:
• apply a set of phase dithers to the first inner MZ interferometer and the second inner MZ interferometer,
• the set of phase dithers including:
• a first dither state [I+δθ°, Q+δθ°],
• a second dither state [I+δθ°, Q−δθ°],
• a third dither state [I−δθ°, Q−δθ° ], and
• a fourth dither state [I−δθ°, Q+δθ° ],
• wherein δθ represents a phase dither applied to one or more branches of the first inner MZ interferometer or the second inner MZ interferometer,
• determine an initial error term based at least in part on the set of phase dithers;
• and
• adjust, based on the initial error term, the outer MZ interferometer to a target error term, wherein branches of the I branch and the Q branch are adjusted differentially without a direct dither applied to the outer MZ interferometer.