Adiabatic decoupling sidebands.

Abstract

An analytical solution is given for amplitudes and phases of adiabatic decoupling sidebands as a function of spin inversion time tau. Since all the adiabatic decoupling phases theta(t, tau) refocus at two periods (2T) of the decoupling pulse, the sidebands are located at n/2T rather than at n/T as observed in other decoupling schemes. The real (R(n)(tau)) and imaginary (I(n)(tau)) amplitudes of the sidebands have symmetry R(n)(tau) = R(-n)(tau) and I(n)(tau) = -I(-n)(tau), forming a mirror image between the counterparts of the sidebands. When frequency sweep changes direction all I(n)(tau) are inverted while all R(n)(tau) remain unchanged, leading to pure absorption sidebands with two accumulations as demonstrated by Kupce and Freeman, and to an exchange of sidebands between counterparts. The sum of the real parts for sidebands n = 1 and 2 is almost a constant near on-resonance decoupling, and it increases substantially for large decoupling offsets. The phase defocusing can be minimized for all decoupling offsets by inserting an initial decoupling period with T(ini) = T/2, eliminating all sidebands located at n/2T (n = +/-1, +/-3, +/-5, ...).