A standard laser beam has photon degeneracy, or coherence,
C, of at most
8μ2, where
μ is the number of photons in the laser itself. Even quantum-engineered lasers, if required to produce a beam with the standard statistical properties, have limited coherence, scaling as
μ4. Moreover, such lasers (still unrealised) require very unconventional gain and output-coupling mechanisms. Here, we propose a different path to increasing
C: cascaded linear amplifiers, with conventional couplings. By dropping the requirement on the beam's properties, this approach can, in theory, achieve
C scaling exponentially in
μ. Here
μ is the total source excitation number, across all the amplifiers. Two amplifiers suffice to surpass the standard
μ2 scaling.
Properties of light sources based on amplified spontaneous emission (ASE) are similar to the properties of lasers in many regards. However, even though ASE has been widely studied, its photon statistics have not been settled. There are no reliable theoretical estimates or unambiguous experimental data for the second-order coherence function of photons that characterizes the coherence properties of a light source. Our computer simulation clearly establishes that, independently of pump power, the light produced by ASE is similar to that of a thermal source. This result lays bare the fundamental difference between ASE radiation and laser radiation.