How to prepare publication-quality plots and use calligraphic fonts in Gnuplot?

I use Gnuplot for most of my plots and save the plots as a png. But the resolution of the plots are not so good to put in research papers. So, I need help regarding the following two things:

1. How to prepare publication-quality plots (eps) in Gnuplot?

2. How to use calligraphic fonts in the plot, like those written using \mathcal{} in latex?

I searched on the internet regarding these two things, but could not get any ideas.

Thanks in advance.

Since you are stating LaTeX code in your question, I suppose that a solution including LaTeX is suitable for you. I am using gnuplot for producing publication-quality plots (and even TOC-figures!) too, and for me the most convenient method is to use the cairolatex standalone terminal, use LaTeX syntax (e.g. \mathcal{}) in the labels, plot titles and so on, and to compile the figures with pdfLaTeX. Often enough, journals accept figures not only in .eps, but also in .pdf format. If a journal was to refuse .pdf, I would simply convert the figure in the end (i.e. right before submission) to .eps, .png or whatever.