This window opens if you press the **Generate Amplitudes...** button of
the **Node Prior-Info.** window when its focus node is a valid Beam-Splitter.
The window allows you to specify certain parameters that characterize a
beam-splitter.

Even if the focus node is a beam-splitter, when you press the **Generate
Amplitudes...** button, the computer will refuse to open the above window
unless:

- the focus node has exactly two parent nodes,
- Both parent nodes are scalar-field nodes OR both parent nodes are vector-field nodes.

In the scalar-field case, M_{2}, M_{1}, N_{1} and
N_{2 }are the numbers of photons that pass through the two incoming
and the two outgoing ports. Quantum Fog gives names of the form
(N_{1},N_{2}) to the states of the beam-splitter.

In the vector-field case, M_{2}, M_{1}, N_{1} and
N_{2 } also correspond in a 1-1 fashion to the incoming and
outgoing ports, but instead of being non-negative integers, they
are 2-component vectors. For example, M_{1} = (M_{1x},
M_{1y}), where M_{1x} and M_{1y} are non-negative
integers. Quantum Fog gives names of the form ((N_{1x},
N_{1y}), (N_{2x}, N_{2y})) to the states of the
beam-splitter.

*t* and *r* , satisfying |*t* |^{2}
+ |*r* |^{2} = 1, are the complex transmission and reflection
coefficients of the beam-splitter. You must enter into the first 3 editable
boxes the magnitude squared of *t* , phase of *t* and
phase of *r* . These 3 parameters completely specify the complex
numbers *t* and *r* .

Consider the scalar-field case. Frequently, nets which contain a beam-splitter
node are such that we know what is the maximum number of photons that will
ever enter the beam-splitter. For example, suppose that a net starts
with 2 photons in its root nodes, and that for one of the input states
(M_{1}, M_{2}) of the beam-splitter, M_{1} +
M_{2} = 3. Then the list of states of the beam-splitter node would
be forced to include all states with N_{1} + N_{2} = 3. Or
would it? Clearly, such states would never occur in any of the possible stories
of the net. So if we were to exclude such states from the list of states
of the beam-splitter node, the physical predictions of the net (that is,
the results reported in the **Node Probs.**, **Bi-node Probs.** and
**Stories** windows) would still be valid. That's where the **Max. Output
Number **editable field comes in. Quantum Fog lists those and only those
states (N_{1}, N_{2}) for which N_{1} + N_{2}
is smaller or equal to the value specified in the **Max. Output Number**
box. In our example, we could set the **Max. Output Number** to 2 and
thus exclude states with N_{1} + N_{2} = 3. Of course, excluding
some states would cause the **Total Probability** button of the **Node
Prior-Info.** window to give a result different from 1. But the physical
predictions of the net would not change, and we would save memory by excluding
unused baggage from the transition matrix.

In the vector-field case, Quantum Fog lists those and only those states
((N_{1x}, N_{1y}), (N_{2x}, N_{2y})) for
which N_{1x} + N_{1y}+ N_{2x}+ N_{2y} is
smaller or equal to the value specified in the **Max. Output Number **box.

More information about Beam-Splitters can be found in the document entitled "Quantum Fog Library Of Essays" that accompanies this manual.