It looks very cool.

Sure. Just for the logs, ContourPlot[] must not be used where it does not fit

Clear[h, h1, h1r]
h[x_, y_, w_] := Cos[2 \[Pi] (x^2 + y^2)/(2 5 w)]^2
h1[x_, y_] := h[x, y, 17.]
h1r[r_] := Cos[2 \[Pi] r^2/170.]^2

combine three different 2D graphics into one plot

Show[{ContourPlot[h1[x, y], {x, -15, 15}, {y, -15, 15},
   Contours -> 10, 
   ColorFunction -> "Pastel",
   PlotLegends -> Automatic,
   DisplayFunction -> Identity],
  ParametricPlot[(# {Cos[\[Phi]], Sin[\[Phi]]}) & /@ 
    Sqrt[85. Range[5]], {\[Phi], 0, 2 \[Pi]},
   PlotStyle -> {Black, Dashed},
   DisplayFunction -> Identity], 
  Graphics[{Black, Point[{0, 0}],
    DisplayFunction -> Identity}]},
 DisplayFunction -> $DisplayFunction]

as

Contour Plot -- Not Displaying

because one has to deliver variables in the plot functions which relate to the variables given in the domain specification of the plot. For all explicit plot functions the variables must be the same, so

Clear[h, h1]
h[x_, y_, w_] := Cos[2 \[Pi] (x^2 + y^2)/(2 5 w)]^2
h1[x_, y_] := h[x, y, 17.]

then still you don't see an output with

ContourPlot[h1[x, y]==1, {x, -15, 15}, {y, -15, 15},GridLines -> Automatic]

despite

In[54]:= FindInstance[1/170 (x^2 + y^2) == 1, {x, y}, Reals, 3] // N
Out[54]= {{x -> 9.5, y -> 8.93029}, {x -> -10.3333, y -> -7.95124}, {x -> 3.25, y -> 12.6269}}

the request has a meaningful domain. If you mouse over

ContourPlot[h1[x, y], {x, -15, 15}, {y, -15, 15}, Contours -> 10]

you see value 1 is not caught. In the manual ContourPlot is a hint

Contours  for functions f(x,y) = 0 where f(x,y) >= 0 are always poorly detected

This is the case here (for h1[x,y]==1 where h1[x,y]<=1).

This works

Plot3D[h1[x, y], {x, -15, 15}, {y, -15, 15}, PlotPoints -> {31, 39}]

Your commands above do not seem to hang together as a complete set. You define h, which is not then used (did you mean h1?).

In the next line, you have h1 u1 = ...

Are h1 and u1 supposed to be multiplied together? If so, why are you then assigning to them (with a single = sign) as though they were a variable? What does this mean?

You seem to be using h1 as a function, taking parameters x and y. But in that case, should you not define it by, say

h1[x_, y_] := Cos[(2[Pi] ((x)^2 + (y)^2)/(25 w))]^2

From what I can tell, you seem to have a number of confusions. I suggest you look at some examples of ContourPlot and gradually adapt them towards what you want.