Measurement and characterization of nonlinear phase shifts
View Patent ↗Temporal phase shifts induced by cross-phase modulation in an optical fiber are directly characterized with a spectral equivalent of the Foucault technique used to spatially resolve wavefronts. The temporal phase induced by a high power pulsed pump on a monochromatic probe via cross-phase modulation is converted in a temporal intensity modulation via spectral filtering. A measurement of the modulated instantaneous power of the filtered signal allows to directly determine the time-resolved nonlinear phase shift. Additionally, an equivalent of the transport-of-intensity equation, which links the evolution of the instantaneous power of the electric field in a dispersive medium to the instantaneous values of the power and phase of the field. This derivation permits the measurement of temporal phase shifts using only intensity information in a direct, non-interferometric manner.
1. A method for determining a phase shift of an optical signal, said method comprising the steps of:
inducing, a temporal phase shift into the optical signal;
converting, the phase modulation of the optical signal into an intensity modulation;
measuring, the intensity modulated signal; and
determining, the phase shift of the optical signal from the intensity measurement(s).
2. The method of claim 1 , wherein said inducing step further comprises the step(s) of:
interacting nonlinearly, a pump signal with the optical signal in a nonlinear medium.
3. The method of claim 2 , further comprising the steps of:
determining, the instantaneous power of the pump signal; and
determining, a nonlinear property of the nonlinear medium.
4. The method of claim 1 , wherein said converting step comprises the step of:
filtering, the phase modulated optical signal with a filter having a known set of characteristics; and said phase shift determining step uses the known set of filter characteristics.
5. The method of claim 4 , wherein said known set of filter characteristics includes spectral amplitude and phase of the transmission of the filter.
6. The method of claim 1 wherein said converting step comprises the step of:
propagating the optical signal in a dispersive medium having a known set of dispersive characteristics; and said phase shift determining step uses the known dispersive characteristics.
7. The method according to claim 1 , wherein said inducing step further comprises the steps of:
propagating nonlinearly, the optical signal in a nonlinear medium; and
said converting step further comprises the steps of:
propagating the optical signal in a dispersive medium having a known set of dispersive characteristics and said phase shift determining step uses the known dispersive characteristics.
8. The method according to claim 1 , wherein said phase shift determining step proceeds according to the following relationship:
∂
I
∂
φ
(
2
)
(
t
,
0
)
=
∂
∂
t
[
I
(
t
)
·
∂
ψ
∂
t
]
where
I is the intensity of the optical signal;
ψ is the phase of the optical signal;
φ (2) is the second order dispersion of the medium; and
is the time.
9. The method of claim 1 , wherein the phase shift determining step proceeds according to the following relationship:
P ′( t )= P 0 ·|τ(0)| 2 ·[1−2 Im[φ τ ( t )]/τ(0)]
where
P′ is the measured power after the filter
P 0 is the average power
τ ( 0 ) is a characteristic of the filter
{tilde over (φ)} is the Fourier transform of the phase modulation φ
φ τ is the Fourier transform of {tilde over (φ)}·τ
τ is the complex spectral transmission of the filter
t is the time variable.