Farey tree and devil’s staircase of a modulated external-cavity semiconductor laser

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Abstract
We report frequency locking at Farey fractions of an electrically modulated semiconductor laser within an external cavity. The winding numbers as a function of the ratio of the modulation frequency to inverse resonator round trip time show the hierarchy of a Farey tree and the structure of a devil’s staircase. The dimension of the set complementary to the stairs is determined to be 0.89. This demonstrates that the external-cavity semiconductor laser exhibits the universal properties characteristic for nonlinear systems driven by two competing frequencies.