Why does shot noise rise with frequency in LIGO sensitivity? In plots of the sensitivity of the LIGO interferometer, photon shot noise is the dominant noise source at the high frequency end, e.g. this graphic:

It appears to rise roughly in linear proportion with frequency. In contrast, the wikipedia article on shot noise mentions that shot noise has a uniform spectral distribution.
How to understand this seeming contradiction ?
 A: The shot noise is actually frequency-independent.
What changes is the response of the interferometer at high frequencies.
At low frequencies you can treat the phase of the gravitational wave (GW) as fixed whilst the laser light traverses the arms of the interferometer.
At higher frequencies this approximation will breakdown. One has to take into account that the phase of the gravitational wave may change, or even reverse, whilst light traverses the arms.
For a standard Michelson set up, the GW phase will reverse and the response will start to fall if $\lambda_{\rm GW}/2 < 2L$, where $\lambda_{\rm GW} = c/f$ is the GW wavelength and $L$ is the length of the arms. Thus we expect a fall in response when
$$ f > \frac{c}{4L} $$
In the more usual Fabry-Perot resonator set-up used by aLIGO, then something similar will happen, but now the laser light effectively travels backwards and forwards a number of times roughly equal to the finesse (actually $\sqrt{F}$ times, where $F$ is the coefficient of finesse). This means that the fall in sensitivity occurs at lower frequencies, approximately
$$ f > \frac{c}{4L\sqrt{F}}\ . $$
A more rigorous treatment (an answer to How is the phase gain of a Fabry-Perot resonator for gravitational wave detection derived? is still required...) shows that the "phase gain" of the interferometer falls by a factor of $[1 + F(2\pi fL/c)^2]^{1/2}$ beyond this and so goes as $\sim f^{-1}$ at high frequencies.
Since the signal-to-noise ratio is proportional to this phase gain, then this means that the minimum detectable strain amplitude increases as $f$.
For aLIGO, $\sqrt{F} \sim 250$, $L=4$ km, so we expect a fall in response for $f> 75$ Hz (see your blue dashed curve - but note that although the interferometer response curve is flat at lower frequencies, the shape of the sensitivity curve also rises at lower frequencies due to radiation pressure noise and the shape can also be modified somewhat by "squeezing" the light  - solid purple curve.).
When your plot labels the curve with "shot noise" it simply means that it is shot noise that determines the "height" of the curve at those frequencies (not the slope). For example, the shot noise is proportional to the square root of the laser power, so if you quadruple the laser power, the minimum detectable strain falls by a factor of 2 if shot noise dominates. This is the difference between the dashed curves and the solid curves at high frequencies.
A: Shot noise operating on the readout of the interferometer is indeed frequency independent.
However, gravitational waves don't directly act on the readout of the interferometer. Assuming a linear response (which is approximately true at least for this question), gravitational wave with frequency $f$ creates an oscillating response with frequency $f$ in the interferometer's readout, but the amplitude and phase are related by a transfer function $\tilde{T}(f)$
\begin{equation}
\tilde{o}(f) = \tilde{T}(f) \tilde{h}(f)
\end{equation}
where $\tilde{h}(f)$ is the gravitational wave, $\tilde{o}(f)$ is the readout of the interferometer, and $\tilde{T}(f)$ is the transfer function (all expressed in the frequency domain, or if you want you could view this equation as being true for a gravitational wave with a single frequency).
The transfer function encodes how the interferometer responds to a passing gravitational wave. For us there are two main important features. The first is that at low frequencies, the transfer function is approximately constant. This corresponds to the limit where the gravitational wavelength is much larger than the size of the detector$^\star$. The second is that at high frequencies, the transfer function falls off as $1/f$. Roughly speaking, without getting into the math, the reason for this is that when the gravitational wavelength is smaller than the size of the detector, each arm is stretched and squeezed multiple times along its length, and these stretches and squeezes tend to cancel out so the full length of the arms doesn't change very much. So the interferometer responds less and less to gravitational waves of shorter and shorter wavelengths (higher and higher frequencies), once the wavelength is less than the size of the interferometer.
In order to be able to compare the noise properties with gravitational-wave sources, one constructs the noise amplitude spectral density curve (which I'll call $\tilde{N}(f)$ for noise amplitude spectral density) by dividing the noise in the interferometer readout by the transfer function
\begin{equation}
\tilde{N}(f) \propto \left| \frac{\tilde{o}(f)}{\tilde{T}(f)} \right|
\end{equation}
where I've left out a few normalization factors that aren't important for this question. If you didn't do this, then you would need to multiply the gravitational wave $\tilde{h}(f)$ by the transfer function to be able to compare the signal strength and the noise strength. Since $\tilde{T}(f)$ depends on the instrument, it is more common to "propagate the noise to the input". Then theorists can compute the gravitational wave strength for a given source once, and different experimentalists working on different instruments can compute their $\tilde{N}(f)$ once, and both sides can make a comparison and compute the expected signal-to-noise ratio.
Since $\tilde{T}(f) \sim 1/f$ at large frequencies (where shot noise dominates), and since shot noise is frequency-independent, the gravitational-wave noise curve $\tilde{N}(f)$ grows like $f$.

$^\star$ Really the gravitational wavelength has to be larger than the photon path length through the interferometer, which is larger than the physical size of the detector because LIGO/Virgo are Fabry-Perot interferometers and the photons bounce inside the arms something like 100 times before exiting. A more precise way to phrase the condition is that the response of the interferometer is approximately constant with frequency below the pole frequency of the interferometer, which for LIGO and Virgo is around a few hundred Hz.
