Systems, apparatus, and methods of nonlinear terahertz (THz) magnetic resonance measurement
A nonlinear terahertz (THz) spectroscopy technique uses a sample illuminated by two THz pulses separately. The illumination generates two signals B A and B B , corresponding to the first and second THz pulse, respectively, after interaction with the sample. The interaction includes excitation of at least one ESR transition in the sample. The sample is also illuminated by the two THz pulses together, with an inter-pulse delay τ, generating a third signal B AB . A nonlinear signal BNL is then derived via B NL =B AB −B A −B B . This nonlinear signal B NL can be then processed (e.g., Fourier transform) to study the properties of the sample.
1. An apparatus for nonlinear terahertz (THz) spectroscopy, the apparatus comprising:
a THz radiation source to illuminate a sample with a plurality of THz pulses, the plurality of THz pulses comprising:
a first copy of a first THz pulse;
a first copy of a second THz pulse; and
a pulse train including a second copy of the first THz pulse and a second copy of the second THz pulse separated by an inter-pulse delay τ, the pulse train inducing an electron spin resonance (ESR) in the sample;
a detector, in optical communication with the sample, to generate:
a first signal B A representing a response of the sample to the first copy of the first THz pulse;
a second signal B B representing a response of the sample to the first copy of the second THz pulse; and
a third signal B AB representing a response of the sample to the pulse train; and
a processor, operably coupled to the detector, to estimate a nonlinear ESR response B NL of the sample to the pulse train based on the first signal B A , the second signal B B , and the third signal B AB .
2. The apparatus of claim 1 , wherein the plurality of THz pulses has a wavelength of about 0.1 THz to about 20 THz.
3. The apparatus of claim 1 , wherein the inter-pulse delay τ is about 0 ps to about 100 ps.
4. The apparatus of claim 1 , wherein the THz radiation source comprises:
a laser to emit a plurality of optical pulses; and
a nonlinear crystal, in optical communication with the laser, to generate the plurality of THz pulses by optically rectifying the plurality of optical pulses.
5. The apparatus of claim 4 , wherein the THz radiation source further comprises:
at least one delay stage, in optical communication with the laser, to delay a first optical pulse in the plurality of optical pulses with respect to a second optical pulse in the plurality of optical pulses so as to generate the inter-pulse delay τ.
6. The apparatus of claim 4 , wherein the nonlinear crystal comprises LiNbO 3 .
7. The apparatus of claim 1 , wherein the detector comprises:
an electro-optic crystal to receive the plurality of THz pulses, the plurality of THz pulses generating a time-dependent birefringence in the electro-optical crystal; and
an optical detector, in optical communication with the electro-optical crystal, to detect a plurality of optical probe pulses transmitted through the electro-optical crystal, the plurality of optical probe pulses having polarizations that vary in response to the time-dependent birefringence.
8. The apparatus of claim 7 , wherein the electro-optical crystal comprises a GaP crystal.
9. The apparatus of claim 1 , wherein the processor is configured to estimate at least one of a zero-field splitting (ZFS) or a spin-spin interaction strength of the sample based on the nonlinear ESR response BNL.
10. The apparatus of claim 9 , wherein the processor is configured to estimate the at least one of the ZFS or the spin-spin interaction strength of the sample based on the nonlinear ESR response BNL.
11. The apparatus of claim 1 , wherein the THz radiation source is configured to change the inter-pulse delay τ so as to generate a two dimensional (2D) nonlinear ESR signal BNL(t, τ), where t is time, and wherein the processor is configured to perform a two-dimensional (2D) Fourier transform of the 2D nonlinear ESR signal B NL (t, τ) with respect to the time t and the inter-pulse delay τ.
12. A method of nonlinear terahertz (THz) spectroscopy, the method comprising:
illuminating a sample with a first copy of a first THz pulse;
generating a first signal BA representing a response of the sample to the first copy of the first THz pulse;
illuminating the sample with a first copy of a second THz pulse;
generating a second signal BB representing a response of the sample to the first copy of the second THz pulse;
illuminating the sample with a pulse train including the a second copy of the first THz pulse and a second copy of the second THz pulse, separated by an inter-pulse delay r, the pulse train inducing an electron spin resonance (ESR) in the sample;
generating a third signal BAs representing a response of the sample to the pulse train; and
estimating a nonlinear ESR signal BNL based on the first signal BA, the second signal BB, and the third signal BAs.
13. The method of claim 12 , wherein illuminating the sample with the first copy of the first THz pulse comprises transmitting the first copy of the first THz pulse at a wavelength of about 0.1 THz to about 10 THz.
14. The method of claim 12 , wherein illuminating the sample with the pulse train comprises transmitting the second copy of the second THz pulse about 0 ps to about 100 ps after transmitting the second copy of the first THz pulse.
15. The method of claim 12 , wherein illuminating the sample with the first copy of the first THz pulse comprises illuminating at least one of a transition metal ion or a rare earth ion.
16. The method of claim 12 , wherein illuminating the sample with the first copy of the first THz pulse comprises illuminating glycated hemoglobin.
17. The method of claim 12 , further comprising generating the first copy of the first THz pulse by transmitting an optical pulse through a nonlinear crystal via optical rectification.
18. The method of claim 17 , wherein transmitting the optical pulse comprises transmitting the optical pulse through a LiNbO 3 crystal.
19. The method of claim 12 , wherein generating the first signal comprises:
transmitting the first THz pulse through an electro-optical crystal to generate a time-dependent birefringence in the electro-optical crystal; and
detecting an optical probe pulse transmitted through the electro-optical crystal so as to generate the first signal B A .
20. The method of claim 12 , further comprising:
estimating at least one of a zero-field splitting (ZFS) or a spin-spin interaction strength of the sample based on the nonlinear ESR signal B NL .
21. The method of claim 20 , wherein estimating the at least one of the ZFS or the spin-spin interaction strength of the sample comprises performing a Fourier transform of the nonlinear ESR signal BNL.
22. The method of claim 12 , further comprising: changing the inter-pulse delay τ so as to generate a two-dimensional ( 2 D) nonlinear ESR signal BNL(t, τ), where τ is time; and performing a two-dimensional ( 2 D) Fourier transform of the 2 D nonlinear ESR signal Bnl(t, τ) with respect to the time t and the intcr-pulse delay τ.
23. A system for nonlinear terahertz (THz) spectroscopy, the system comprising:
a THz radiation source illuminate a sample with a plurality of THz pulses, the plurality of THz pulses comprising a plurality of THz pulse groups and an ith THz pulse group in the plurality of THz pulse groups comprising:
a first copy of a first THz pulse;
a first copy of a second THz pulse; and
a pulse train including a second copy of the first THz pulse and a second copy of the second THz pulse separated by an inter-pulse delay τ i , where i is a positive integer, the pulse train inducing an electron spin resonance (ESR) in the sample;
a detector in optical communication with the sample, for the ith THz pulse group in the plurality of THz pulse groups, the detector generating:
a first signal B A (t, τ i ) representing a response of the sample to the first copy of the first THz pulse, where t is time;
a second signal B B (t, τ i ) representing a response of the sample to the first copy of the second THz pulse; and
a third signal B AB (t, τ i ) representing a response of the sample to the pulse train; and
a processor, operably coupled to the detector, to estimate a nonlinear ESR signal BNL for the ith THz pulse group based on the first signal B A (t, τ i ), the second signal B B (t, τ i ), and the third signal B AB (t, τ i ), the processor further performing a 2D Fourier transform to the nonlinear ESR signal B NL (t, τ i ) with respect to the time t and the inter-pulse delay τ i so as to estimate at least one of a zero-field splitting (ZFS) or a spin-spin interaction strength of the sample.