Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arbitrary optical wave evolution with Fourier transforms and phase masks   A large number of applications in classical and quantum photonics require the
capability of implementing arbitrary linear unitary transformations on a set of
optical modes. In a seminal work by Reck et al. it was shown how to build such
multiport universal interferometers with a mesh of beam splitters and phase
shifters, and this design became the basis for most experimental
implementations in the last decades. However, the design of Reck et al. is
difficult to scale up to a large number of modes, which would be required for
many applications. Here we present a constructive proof that it is possible to
realize a multiport universal interferometer on N modes with a succession of 6N
Fourier transforms and 6N+1 phase masks, for any even integer N. Furthermore,
we provide an algorithm to find the correct succesion of Fourier transforms and
phase masks to realize a given arbitrary unitary transformation. Since Fourier
transforms and phase masks are routinely implemented in several optical setups
and they do not suffer from the scalability issues associated with building
extensive meshes of beam splitters, we believe that our design can be useful
for many applications in photonics.

25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess