## 2 Experimental Setup
We find a rapid decrease of the observed \(g^{(2)}(\tau)\) values with increasing wavelength separation with a FWHM of \(2.6\,\mathrm{nm}\) assuming a Gaussian shape. The \(g^{(2)}(\tau=0)\) values are going down to \(1.10\) in the wings at wavelengths far off by more than \(4\,\mathrm{nm}\) with respect to the center. The characteristic FWHM of the \(g^{(2)}(\tau=0,\lambda)\) values is nearly equal to the convolution of the FWHM of the used interference filters. Therefore, we are convinced that the observed characteristic wavelength-wavelength correlation decay values and thus the GS resolution are not intrinsic to the exploited ASE but are actually due to the FWHM of the chosen interference filters used for the selection of the wavelengths. A theoretical description of spectral photon bunching in ASE is currently still not available [33; 50; 51]. For the GS experiments with the acetylene sample, the light in the object arm has been also additionally spectrally narrowed by a fiber-based spectral filter with a FWHM of \(2.5\,\mathrm{nm}\) in order to restrict the rather broad ASE spectrum as already shown in the inset of Figure 3 for three different optical pump power conditions. The realization of a requested higher spectral resolution in the reference arm (see discussion above) has been achieved by an Echelette grating with \(600\,\mathrm{grooves/mm}\) and a blaze wavelength of \(\lambda_{\mathrm{Blaze}}=1.6\,\mathrm{\SIUnitSymbolMicro m}\) (Thorlabs GR25-0616). The beam incident onto the grating has been enlarged by two cylinder lenses with focal length of \(f_{1}=5\,\mathrm{cm}\) and \(f_{2}=9\,\mathrm{cm}\) in order to achieve a higher spectral resolution by increasing the number of illuminated grating grooves yielding finally a variable Gaussian-like wavelength reference spectrum with medium \(FWHM=0.49\pm 0.02\,\mathrm{nm}\). In accordance with the analogy between GI and GS, we define and exploit a GS detection protocol for our experimental GS setup by starting with the GI terminology and replacing the spatial coordinate \(x\) by the spectral variable \(\lambda\), such that the intensity cross-correlation coefficients are now a function of the reference-arm wavelength. By varying this reference-arm wavelength, the wavelength-dependent  
Figure 3: Measured wavelength-wavelength correlations of light emitted by the EDFA: The full optical spectrum of the EDFA (magenta solid line) has been measured by a standard optical spectrum analyzer. The selected wavelength band is also depicted (green solid line) for direct comparison with the second-order correlation data (red crosses with a dashed line based on a Gaussian fit). The error bars correspond to the standard deviation for a set of 5 measurements. The inset shows the unfiltered EDFA spectrum for three different optical pump conditions of the EDFA. intensity correlations, thus the ghost spectrum has been determined according to Equation (2) in the framework of a detection protocol based on GI terminology. \[g^{(2)}(\tau=0,\lambda_{\text{ref}})=\frac{\langle I_{\text{ref}}(t,\lambda_{ \text{ref}})I_{\text{obj}}(t+\tau)\rangle_{t}}{\langle I_{\text{ref}}(t,\lambda_ {\text{ref}})\rangle_{t}\langle I_{\text{obj}}(t+\tau)\rangle_{t}} \tag{2}\]  
We note that this detection protocol is based on the classical definition of the second-order Glauber correlation function which represents the most basic GI signal detection modality, now adapted in full analogy of GI towards GS. Figure 4 (left) shows the ghost spectrum in terms of \(g^{(2)}(\tau=0,\lambda_{\text{ref}})\) (red data points) together with a standard absorption spectrum of acetylene (in blue). The standard spectrum as measured by a grating spectrometer (MS9710C OSA, Anritsu, Atsugi, Kanagawa Prefecture, Japan) clearly shows the central absorption feature of acetylene at \(\lambda_{\text{C}}=1532.84\,\text{nm}\).