Apply from the filter gallery "Halftone pattern > Line". Use high contrast setting. Your photo needs nothing special, the effect works with normal RGB images, but
- the background is good to be removed before if you do not want "engraved" background.
- it's useful to mix the image to BW with Image > Adjustments > Black and white to get wide and smooth greyscale.
The lines are unfortunately horizontal, but you can rotate the image temporarily with expanded canvas size. See an example:
You see that some of the lines are grey, not black. You can make them black with Image > Adjustments > Treshold.
You must have very high resolution image (thousands of pixels) to get smooth lines. You can also apply median filtering to smooth the result. The benefit is not big because Photoshop's filter is well done.
More smoothing is available if you simplify the greyscale image with Cutout filter before applying the halftoning. Just in my image it resulted unpleasant lack of symmetry, because right and left eyes, altough nearly as bright, were left to different sides of brightness step treshold.
I have got best results in vector domain. See this link:
Create engraving in GIMP/Inkscape
The story is quite wide discussion of engraving lookalike effects.
Vector domain approach uses tracings at different greyshade tresholds. The tracing results are used as clipping masks for different line widths.
It uses freeware instead of Photoshop. Inkscape is quite easy for this job.