Line-breaking two equations within equation array

eqnarrayequations

I have the code

\begin{eqnarray}
    &&\nonumber
    \left.\begin{array}{l}
        & \textbf{E}_{\textrm{tr}}  (x,y,z)= \left(\ts \textbf{s} + \tp \textbf{p}_+\right) \, \exp\lec{i   {\ko} \les\left({x\cos\psi+y\sin\psi}\right)\sin\theta_{\rm inc}+(z-N  P )   \cos \theta_{\rm inc}\ris }\ric
        \\[5pt]
        \textbf{H}_{\textrm{tr}} (x,y,z) = 
        \eta_0^{-1}\left(\ts \textbf{p}_+ - \tp \textbf{s}\right)
        \, \exp\lec{i   {\ko} \les\left({x\cos\psi+y\sin\psi}\right)\sin\theta_{\rm inc} +(z-N P)   \cos \theta_{\rm inc}\ris
        }\ric
    \end{array}\right\}\,,
    \\[5pt]
    &&
    \qquad\qquad\qquad z>N P \,.
\end{eqnarray}

which produces the output

enter image description here

No matter what I try, I cannot get this to render more nicely. I would like for each equation to break after the plus sign, and for the equation number to appear to the right of the bracket.

Best Answer

In order to make your code compilable, I had to come up with emergency definitions of \ts, \tp, \ko, \ric, \ris, \lec, and \les.

I've also simplified your code by replacing the eqnarray environment with a far more flexible aligned environment and by getting rid of all interior \left and \right sizing directives. (Hint: they do nothing except mess up the horizontal spacing.) Next, I replaced the 4 instances of \textbf with \mathbf. Finally, I would state z>N P in ordinary, i.e., inline, math on a line following the displayed equations.

enter image description here

\documentclass{article}
\usepackage{amsmath} % for 'aligned' environment
%% check if the following definitions are appropriate
\providecommand\ts{t_s}
\providecommand\tp{t_p}
\providecommand\ko{k_0}
\providecommand\lec{\bigl\{}
\providecommand\ric{\bigr\}}
\providecommand\les{\bigl[}
\providecommand\ris{\bigr]}
\newcommand\minc{{\mathrm{inc}}}
\newcommand\mtr{{\mathrm{tr}}}

\begin{document}
\begin{equation}
\left.\begin{array}{@{}l}
\begin{aligned}
\textbf{E}_\mtr (x,y,z)
    &= (\ts \mathbf{s} + \tp \mathbf{p}_+)  
      \exp\lec i \ko \les({x\cos\psi+y\sin\psi})\sin\theta_\minc \\
    &\qquad+(z-N P ) \cos \theta_\minc\ris \ric
    \\[\jot]
\textbf{H}_\mtr (x,y,z) 
    &= \eta_0^{-1}(\ts \mathbf{p}_+ - \tp \mathbf{s})
      \exp\lec i \ko \les({x\cos\psi+y\sin\psi})\sin\theta_\minc \\
    &\qquad+(z-N P) \cos \theta_\minc\ris\ric
\end{aligned}
\end{array}\right\}
\end{equation} 
and $z>N P$.
\end{document}
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