Second harmonic helicity and Faraday rotation in gated single-layer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn><mml:mi>T</mml:mi><mml:mo>?</mml:mo><mml:mtext>?</mml:mtext><mml:msub><mml:mrow><mml:mi>WTe</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:math>

Single-layer of 1T$'$ phase WTe$_2$ provides a rich platform for exotic physical properties such as nonlinear Hall effect and high-temperature quantum spin hall transport. Utilizing continuum model diagrammatic method, we calculate the second harmonic conductivity monolayer 1T$'$-WTe$_2$ modulated by an external vertical electric field electron doping. We obtain finite helicity Faraday rotation signal in response to linearly polarized incident light presence time-reversal symmetry. The signal's is highly controllable altering bias potential serves optical indicator current. Our study motivates future experimental investigation spectroscopy two dimensional materials.