本文在文献２０的基础上进一步提出了多模辐射场的Ｎ－Ｙ最小测不准态、Ｎ－Ｈ最小测不准态、Ｎ－Ｙ压缩最小测不准态以及Ｎ－Ｈ压缩最小测不准态等的定义．构造了由多模（ｑ模）相干态｜｛Ｚｊ｝＞ｑ及其相反态｜｛－Ｚｊ｝＞ｑ的线性叠加所组成的第Ⅰ类两态叠加多模叠加态光场｜ψ（２）１＞ｑ，利用文献２０新近提出的有关多模辐射场的两种非线性高阶压缩的定义，首次对态｜ψ（２）１＞ｑ的Ｎ次方Ｙ压缩及Ｎ次方Ｈ压缩效应进行了详细研究．结果表明，１）当Ｎ为偶数时，态｜ψ（２）１＞ｑ恒处于Ｎ－Ｙ最小测不准态；当Ｎ为奇数时，态｜ψ（２）１＞ｑ在一定条件下可呈现出周期性变化的、任意阶的Ｎ次方Ｙ压缩效应．２）当ｑ·Ｎ为偶数时，态｜ψ（２）１＞ｑ恒处于Ｎ－Ｈ最小测不准态；当ｑ·Ｎ为奇数时，在另外的条件下，态｜ψ（２）１＞ｑ则可呈现出周期性变化的、任意阶的Ｎ次方Ｈ压缩效应．３）Ｎ次方Ｙ压缩及Ｎ次方Ｈ压缩效应的压缩深度与腔模总数ｑ、压缩参数Ｒｊ以及压缩阶数Ｎ等非线性相关，后者与上述参量的非线性关联程度要比前者的更强． Based on the literature 20, we further propose the minimum N-Y Uncertainty state, the N-H Uncertainty state, the N-Y Uncertainty state, and the N-H compression minimization problem Quasi-state definition. The first kind of superposition multimode superposition state field | ψ (2) consisting of multi-mode (q-mode) coherent state | {Zj}> q and its opposite state | {-Zj}> q is constructed ) 1> q. Using the definitions of two nonlinear higher-order compressions recently proposed in Document 20 for multimode radiation fields, the N-th power Y-compression and the N-th power H-compression for the first time | ψ (2) 1> q Effect has been studied in detail. The results show that 1) when | N | is an even number, the state | ψ (2) 1> q is always in the N-Y minimum uncertainty state. When N is odd, the state | ψ (2) 1> q is under certain conditions The Nth-ary Y-compression effect of any order can be presented with periodic changes. 2) when q · N is even, the state | ψ (2) 1> q is always in the N-H minimum undetermined state; when q · N is odd, the state | ψ (2) 1> q can exhibit a cyclical variation of any order of N-th power H compression. 3) The compressive depth of N-th power Y-compression and N-th power H-compression effect is nonlinearly correlated with the total number of cavity modes q, the compressive parameters Rj and the compressive order N, which are more nonlinearly related to the above parameters Stronger