| CPC G02F 1/212 (2021.01) | 20 Claims |

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16. 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.
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