fancyhdr : vertical alignment of left header

Question

I am trying to reproduce the following without the comments in green and blue :

The LaTeX code I am using is as follows :

\documentclass[11pt, letterpaper]{letter}

\usepackage[includeheadfoot,margin=0.5in]{geometry}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{bm} %for boldface math
\usepackage{braket}
\usepackage[colorlinks,citecolor=red,urlcolor=blue,bookmarks=false,hypertexnames=true]{hyperref}


\usepackage{fancyhdr}
\pagestyle{fancy}
 \fancyhf{}
 \fancyhead[L]{\fontsize{40}{40} \selectfont \textsc{Franklin Lee}}
 \renewcommand\headrule{\vskip-0.7\baselineskip\makebox[\textwidth]{\shadowfill}}
\newcommand\shadowfill{%
  \leavevmode\leaders\hbox{\ooalign{%
  \vrule height 1pt depth 0pt width 1pt\cr%
  \textcolor{cyan}{\vrule height 0pt depth 1pt width 1pt}}%
  }\hskip\fill\kern0pt%
  }

  % Left Header alignment gone wrong 

 \fancyhead[R]{Address Line 1, \\ Address Line 2, \\ Mobile No \\ Email}


\begin{document}

\vspace{2in} % Does not work

Hello 



\end{document}

But this produces :

I would like to adjust the following things :

1. Put some space between the header text and the header line
2. Align the left header text as being vertical centre with respect to the right header text
3. Put some space between the header line and the following text
4. Extend the header line so that it covers more horizontal space than the following text

Can someone please help me out here?

Answer 1

For your query 1, 3

\documentclass[11pt, letterpaper]{letter}

\usepackage[includeheadfoot,margin=0.5in]{geometry}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{bm} %for boldface math
\usepackage{braket}
\usepackage[colorlinks,citecolor=red,urlcolor=blue,bookmarks=false,hypertexnames=true]{hyperref}


\usepackage{fancyhdr}
\pagestyle{fancy}
 \fancyhf{}
 \fancyhead[L]{\fontsize{40}{40} \selectfont \textsc{Franklin Lee}}
 \renewcommand\headrule{\vskip-0.1\baselineskip\makebox[\textwidth]{\shadowfill}}
\newcommand\shadowfill{%<----------------------change amount of baseline skip
  \leavevmode\leaders\hbox{\ooalign{%
  \vrule height 1pt depth 0pt width 1pt\cr%
  \textcolor{cyan}{\vrule height 0pt depth 1pt width 1pt}}%
  }\hskip\fill\kern0pt%
  }

  % Left Header alignment gone wrong 

 \fancyhead[R]{Address Line 1, \\ Address Line 2, \\ Mobile No \\ Email}


\begin{document}

\vspace*{2in} % change

Hello 



\end{document}

EDITFor serial no 2

For more space under Franklin Lee add a blank line under it

\fontsize{14}{14} \selectfont \textsc{}

--the size of the blank line is controlled by the fontsize{14}{14}-- you can make it {10}{10} or {20}{20}

MWE

\documentclass[11pt, letterpaper]{letter}
usepackage[includeheadfoot,margin=0.5in]{geometry}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{bm} %for boldface math
\usepackage{braket}
 \usesepackage[colorlinks,citecolor=red,urlcolor=blue,bookmarks=false,hypertexnames=true]{hyperref}


\usepackage{fancyhdr}
\pagestyle{fancy}
 \fancyhf{}
 \fancyhead[L]{\fontsize{40}{40} \selectfont \textsc{Franklin 
  Lee}\\\fontsize{14}{14} \selectfont \textsc{}}
 \renewcommand\headrule{\vskip-0.1\baselineskip\makebox[\textwidth] 
 {\shadowfill}}
  \newcommand\shadowfill{%
  \leavevmode\leaders\hbox{\ooalign{%
  \vrule height 1pt depth 0pt width 1pt\cr%
  \textcolor{cyan}{\vrule height 0pt depth 1pt width 1pt}}%
  }\hskip\fill\kern0pt%
  }

  % Left Header alignment gone wrong 

 \fancyhead[R]{Address Line 1, \\ Address Line 2, \\ Mobile No \\ Email}
\begin{document}
\vspace*{2in} % Does not work
Hello 
\end{document}

Serial No 4

If you want the right side of header line to be increased in length

\hskip\fill\kern0pt%

change the 0pt to -8pt or positive 8pt for shortening the line--this also depends on the margin set in the geometry