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中文摘要：
构造出了有限维Hilbert空间Roy型奇偶非线性相干态。讨论了它们的正交归一完备性和振幅平方压缩效应．研究表明，在此空间中Roy型奇偶非线性相干态是归一完备的。但不具有正交性；当复参数相位角口满足一定条件时它们存在振幅平方压缩效应，同时导出了压缩条件与参数s,r以及函数f（n）之间的关系。最后借助于数值计算，发现对于5维（或7维）Hilbert空间中Roy型偶（或奇）非线性相干态，当参数日和Lamb-Dike参数η取某一给定值时，在参数，变化的不同取值范围内，它们均可以呈现振幅平方压缩效应。
英文摘要：
The Roy-type even and odd nonlinear coherent states in a finite-dimensional Hilbert space are constructed. Their amplitudesquared squeezing effect, orthonormalized property, unitary property and completeness relations are discussed. The results reveal the existence of unitary property, completeness relations and non-orthonormalized property. There exists the amplitude-squared squeezing effect for the Roy-type even and odd nonlinear coherent states when the phase θ of parameter β meets the fixed condition. The relations between conditions of squeezing effect and parameters s, r and function f（n） are given. Finally using the numerical method, it is found that in some different ranges of r, the amplitude-squared squeezing effect exists in Roy-type even and odd nonlinear coherent states field in a finite-dimensional Hilbert space when the parameters s, θ and Lamb-Dike parameter η are given as the fixed value.
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