Spectral Noise Correlations of an Ultrafast Frequency Comb

Abstract

Cavity-based noise detection schemes are combined with ultrafast pulse shaping as a means to diagnose the spectral correlations of both the amplitude and phase noise of an ultrafast frequency comb. The comb is divided into ten spectral regions, and the distribution of noise as well as the correlations between all pairs of spectral regions are measured against the quantum limit. These correlations are then represented in the form of classical noise matrices, which furnish a complete description of the underlying comb dynamics. Their eigendecomposition reveals a set of theoretically predicted, decoupled noise modes that govern the dynamics of the comb. These matrices also contain the information necessary to deduce macroscopic noise properties of the comb.

Modal analysis for noise characterization and propagation in a femtosecond oscillator

“…This indicates that the spectral noise correlations within the analyzed sideband frequencies are predominantly governed by mode-locking dynamics of the OFC. To reveal the underlying physical process behind OFC noise dynamics, one approach is eigendecomposing the noise matrices and finding the independent noise modes as introduced in [16]. This provides three significant phase modes and two dominant amplitude modes in our OFC that reasonably reproduces the theoretical modes [6].…”

Direct temporal mode measurement of photon pairs by stimulated emission

“…Similarly, for an input at the idler port of |{β(ω)} , the output at the signal field is â out s (ω) = dω 2 F (ω, ω 2 )β * (ω 2 ) ≡ α out (ω). (19) Notice that with a singular value decomposition in Eq. (3) for F (ω 1 , ω 2 ) and decomposition of Eq.…”

“…However, our simulation is based on Eqs. (18,19) without the knowledge of the decomposition in Eq.(3). We will use the cross-feedback method discussed in Sect.III to find the converged functions β c out (ω) and α c out (ω).…”

“…To maintain the size, we normalize the mode functions β(ω) and α(ω) after each step of application of Eqs. (18,19). So the results are independent of F , which is then set to 1 in the simulation.…”

Spectral Methods for Determining the Stability and Noise Performance of Passively Modelocked Lasers

“…As a result, the amplitudes of the eigenmodes will be correlated. This issue was a source of confusion in a recent experiment that found the eigenmodes of a modelocked laser [70].…”