We employed Fourier transform spectroscopy to record the excitation spectrum of WSe$_{\text{2}}$, the general setup is shown in Figure \ref{Fig}. To obtain the spectra, the broadband pulses of an \textit{NKT SuperK} laser were spectrally separated using a 300 lines/mm grating and collimated onto a Spatial Light Modulator (SLM). The frequency components of the pulse were modulated according to the scheme laid out in section 2 at a resolution of $\sim$0.66 nm/pixel. After modulation, the pulses were recombined on the grating and directed into a microscope via galvo mirrors for scanning the beam. The illuminating objective was a 40x, 0.6 NA long working distance \textit{Olympus} objective focused to a 750 nm spot. The sample was mounted on a chip carrier with a hole underneath the chip to enable imaging in transmission.

A further long working distance 36x, 0.52 NA reflective objective was used to capture the fluorescence of the WSe$_{\text{2}}$. The background laser light was blocked with a 785 nm longpass filter and the remaining fluorescence imaged with a photon counting \textit{Hamamatsu ORCA-Quest qCMOS} camera.

The WSe$_{\text{2}}$ flake was prepared via exfoliation and mounted across two gold electrodes that were printed via lithography 5\,$\mu$m apart on a sapphire substrate and then encapsulated in a hBN layer ($\sim$ 40\,nm). The source-drain voltage was controlled using the same Lock-In amplifier as used in the detection, sharing a common ground.

For each illumination point, the PC and PL response of the WSe$\text{2}$ were simultaneously measured. The PC is measured by maintaining a constant source-drain voltage across the two electrodes. In doing so, a built-in field is generated at the forward electrode that yields charge separation. The non-uniform potential landscape resulting from an applied lateral field across a high-impedance TMD-electrode contact is well established \cite{li2013surface,singh2021analytical}. The dark current resistance for the device used here is measured at 10\,G$\Omega$. The built-in potential barrier allows the WSe$\text{2}$ contact to be viewed as a point of charge separation. Consequently, PC is only detected for excitons that diffuse to the active electrode. The current detection was carried out using a home-built printed circuit board, that fed current to a \textit{Stanford Instruments SR830 DSP} Lock-In Amplifier. The laser was modulated with a chopper at 167 Hz as a reference signal to separate the photocurrent response of the flake from the dark current. The value of source-drain voltage was chosen based upon a potential sweep that was carried out prior to the spectral measurement which can be seen in Figure 2 along with the fluence dependence of the photoresponse of the device. In both cases the values for measurement were chosen to maximise the current response to illumination, while staying under the saturation (non-linear) conditions for the device. All of the data presented in the main text was measured at -0.5\,V. The direction was chosen to utilise the electrode that had the best contact with all parts of the flake, however photocurrent maps at different source-drain potentials and directions are available in Figure 3. \