4C1 - Nonlinear effects in an NMR experiment

We have studied multiple-photon transition in a low-field nuclear magnetic resonance (NMR) experiment. It is well known that a saturation of the NMR occurs when using a sufficiently high alternating magnetic field which induces multiple-photons transitions. We show theoretically that these multiphoton transitions are accompanied by an harmonic generation. For a
n
-photon transition, this generation occurs mostly on the
n
th and (
n \pm 1
)th harmonic. For an irradiating field
2H_{1} \cos \omega
t of pulsation ω such that
n\omega= \gamma H_{0}=\omega_{0}
where H
0
is the steady field and θ is the angle between H
0
and H
1
the amplitudes
S\min{n}\max{n}
and
S\min{n}\max{n+1}
of these components are given by
S\min{n}\max{n} = f_{n}(\theta) (H_{1})^{n}
,
S\min{n}\max{n+1} = \cos \theta f_{n}(\theta) (H_{1})^{n+1}
. We have verified these equations in a low-field NMR experiment (
H_{0} = 0.7
Gs/s), polarizing first a flowing liquid in a high magnetic field. The liquid then flows in a modified Bloch spectrometer. The receiving coil is still perpendicular to the steady field but it is possible to adjust the angle θ between the axis of the emission coils (H
1
field) and the steady-field H
0
. Using a synchronous detection at the output of the receiving coil on the pulsation
(n - 1) \omega, n\omega
, or
(n + 1) \omega
, we have directly detected multiphoton transistions. The above equations have been verified for
n = 2
to
n = 5
. There are slight discrepancies at high excitation which may be explained taking into account a large saturation.