This detector type allows one to integrate the yield of photoelectrons emerging from the material irradiated by electromagnetic field. We assume that the yield is proportional to the electromagnetic absorbed energy \(W\) times the probabilty of an electron to reach the surface of the material.

\[ Y \sim \int W({\bf r})*p_s({\bf r})d{\bf r} \]

This probability may be approximated by the exponent:

\[ p_s({\bf r})=\exp(-|{\bf r}-{\bf r}_s|/\lambda_{ee}) \]

where \({\bf r}\) is a location inside material, \({\bf r}_s\) – the closest point on the surface of the photo emitting material, \(\lambda_{ee}\) – mean electron-electron scattering path. The above expression assumes that the electron escape probability is governed by electron-electron collisions within material.

The actual evaluation of the integral is performed by a set of frequency type detectors (see uiExperiment::AddDetectorSet) that should be placed inside photo-emitting material. The detectors provide frequency-dependent fields and the integration is performed over space. Below is an example of adding photo electron integrating detectors. In this 1D example the material extends from 1.5 to 1.7 in Z and the field is incident in the positive Z direction:

task.AddObject(M,GetPlate(Vector_3(0,0,1),Vector_3(0,0,1.5f),1),1);
task.AddDetectorSet("idi", Vector_3(0, 0, 1.5f), Vector_3(0, 0, 1.7f), Vector_3(-1, -1, -0.5), DET_F);
task.GetDetectorSet("idi")->SetUpdateRange(10, .3f, 1.f);
 
valtype lambda_ee = 0.005f;
task.GetDetectorSet("idi")->SetIntegration(new emPhotoElectrons(lambda_ee, M, task.GetRayTracer(), 0, true, dx, 100), argr);

The electromagnetic field in the material decreases exponentially with the distance to the surface:

\[ E(\omega) \sim \exp(-|{\bf r}-{\bf r}_s|/s_{skin}(\omega)) \\ W(\omega) \sim \exp(-2|{\bf r}-{\bf r}_s|/s_{skin}(\omega)), \]

where \(s(\omega)_{skin}\) is the skin depth of the material at a given frequency \(\omega\). The electroin yield is thus proportional to

\[ Y(\omega) \sim \int \exp(-|{\bf r}-{\bf r}_s|(2/s_{skin}(\omega)+1/\lambda_{ee}))d{\bf r} \]

The integrating detectors should extend deep enough inside the material to cover 2-3 skin depths. The skin depth of the material may be obtained by calling emMedium::get_skin or in table form using uiExperiment::DumpMedium function. The integration is performed by adding integrands as functions of interpolated fields at the detectors, so the detectors should be placed with sufficient dencity, often more than one detector per mesh step. In the above example we use 2 detectrors per mesh step \(dx\), see the fourth parameter of uiExperiment::AddDetectorSet.

Also, since the integrand in \(Y(\omega)\) decreases exponentially the most significant contribution to the integral is from the detectors close to the surface. The interpolated fields in EMTL are linear combination from fields at the closest mesh cells, so there may be a contribution of the fields outside the material when we integrate close to the surface. To reduce the effect of these incorrect fields the actual integration may be performed outside certain limiting distance \(x_0\) from the surface. This distance is controlled by the 6th parameter of emPhotoElectrons::emPhotoElectrons, which we set the same as the mesh step \(x_0 = dx\) in the example.

If this minimal distance \(x_0\) is set, then the integrands of yield are corrected to analytically account for the missing regions close to the surface. This correction is made under the assumption of the exponential growth of the field toward the surface. The corrected values are calculated as follows.

\[ Y_{corr}(\omega) = Y_1(\omega)\exp(-2x_0/s_{skin}(\omega))+ 2W_1(\omega) (1-\exp(-x_0/s_w(\omega)) ) s_w/s_{skin}(\omega), \]

where integrals are evaluated outside the distance \(x_0\) from the surface:

\[ Y_1(\omega) \sim \int_{|{\bf r}-{\bf r}_s|>x_0} \exp(-|{\bf r}-{\bf r}_s|/s_w(\omega)))d{\bf r} \\ W_1(\omega) \sim \int_{|{\bf r}-{\bf r}_s|>x_0} \exp(-2|{\bf r}-{\bf r}_s|/s_{skin}(\omega))d{\bf r}. \]

Here \(s_w(\omega) = 2s_{skin}(\omega)\lambda_{ee}/(2s_{skin}(\omega)+\lambda_{ee})\).

The integrals \(Y_{corr}(\omega)\), \(W_1(\omega)\) and \(Y_1(\omega)\) are output as the second, third and fifth columns respectively of the file produced by the integration procedure ("idi.d" in the above example).