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In this Letter we study the evolution of the higher-order squeezing, namely,$n$th-order single-mode squeezing, sum- and difference-squeezing for thecodirectional Kerr nonlinear coupler. We show that the amount of squeezingdecreases when $n$, i.e. the squeezing order, increases. For specific values ofthe interaction parameters squeezing factors exhibit a series ofrevival-collapse phenomena, which become more pronounced when the value of $n$increases. Sum-squeezing can provide amounts of squeezing greater than thoseproduced by the $n$th higher-order ($n\geq 2$) squeezing for the same values ofinteraction parameters and can map onto amplitude-squared squeezing. Further,we prove that the difference-squeezing is not relevant measure for obtaininginformation about squeezing from this device.

Higher-order squeezing for the codirectional Kerr nonlinear coupler