Apparatus and method for cavity-enhanced ultrafast two-dimensional spectroscopy

1. An apparatus for two-dimensional (2D) spectroscopy, the apparatus comprising:

at least one cavity configured to contain a sample; and

a controller configured to control

a pump excitation using at least two frequency combs resonantly enhanced in at least one transverse mode of the at least one cavity,

a probe excitation using at least one frequency comb resonantly enhanced in at least one transverse mode of the at least one cavity, and

generating a resonantly enhanced signal frequency comb via a nonlinear-optical response of the sample,

wherein pump pulses and probe pulses circulate about the at least one cavity to acquire intracavity round trip phase shifts.

2. The apparatus of claim 1 wherein the intracavity round trip phase shifts are based on differing carrier envelope offset frequencies of the at least two frequency combs of the pump excitation.

3. The apparatus of claim 1 wherein the intracavity round trip phase shifts are based on a round trip Gouy phase of an Hermite-Gaussian mode.

4. An apparatus for two-dimensional (2D) spectroscopy, the apparatus comprising:

at least one cavity configured to contain a sample; and

a controller configured to control

a pump excitation using at least two frequency combs resonantly enhanced in at least one transverse mode of the at least one cavity,

a probe excitation using at least one frequency comb resonantly enhanced in at least one transverse mode of the at least one cavity, and

generating a resonantly enhanced signal frequency comb via a nonlinear-optical response of the sample,

further comprising an interferometer that includes at least one acousto-optic modulator (AOM) configured to generate the at least two frequency combs of the pump excitation and the at least one frequency comb of the probe excitation.

5. The apparatus of claim 4 , wherein cavity-enhanced 2D spectroscopy is performed using only one frequency comb generator, with additional phase-cycling frequency combs produced using the at least one AOM.

6. The apparatus of claim 5 , wherein the frequency comb generator is a mode-locked laser.

7. An apparatus for two-dimensional (2D) spectroscopy, the apparatus comprising:

at least one cavity configured to contain a sample; and

a controller configured to control

a pump excitation using at least two frequency combs resonantly enhanced in at least one transverse mode of the at least one cavity,

a probe excitation using at least one frequency comb resonantly enhanced in at least one transverse mode of the at least one cavity, and

generating a resonantly enhanced signal frequency comb via a nonlinear-optical response of the sample,

wherein a combination of spatial mode discrimination, frequency discrimination, and temporal discrimination suppresses undesired signals from a 2D spectroscopy signal.

8. The apparatus of claim 7 , wherein the 2D spectroscopy signal is isolated using heterodyne detection with a local oscillator comb.

9. An apparatus for performing optical spectroscopy, the apparatus comprising:

at least two cavities; and

a controller configured to control

a pump excitation using at least two frequency combs resonantly enhanced in at least one transverse mode of a pump cavity of the at least two cavities,

a probe excitation using at least one frequency comb resonantly enhanced in at least one transverse mode of a probe cavity of the at least two cavities, and

generating a resonantly enhanced signal frequency comb via a nonlinear-optical response of the sample,

further comprising at least one point of overlap of the pump excitation and the probe excitation in the at least two cavities.

10. An apparatus for performing optical spectroscopy, the apparatus comprising:

at least two cavities; and

a controller configured to control

a pump excitation using at least two frequency combs resonantly enhanced in at least one transverse mode of a pump cavity of the at least two cavities,

a probe excitation using at least one frequency comb resonantly enhanced in at least one transverse mode of a probe cavity of the at least two cavities, and

generating a resonantly enhanced signal frequency comb via a nonlinear-optical response of the sample,

wherein the at least two cavities provide a non-collinear geometry.

11. The apparatus of claim 10 , wherein the controller is further configured to isolate a 2D spectroscopy signal in the non-collinear geometry by demodulating a signal that appears as an amplitude modulation on light transmitted in the probe cavity.

12. The apparatus of claim 11 , wherein the controller is further configured to control recording of the 2D spectroscopy signal using demodulation of the light transmitted in the probe cavity at a demodulation frequency of carrier-envelope offset differences of the at least two frequency combs of the pump excitation.

13. A method for performing two-dimensional (2D) spectroscopy, comprising:

generating a pump excitation using at least two frequency combs;

generating a probe excitation using at least one frequency comb; and

generating resonantly enhanced signal frequency combs via a nonlinear optical response of a sample,

wherein the at least two pump frequency combs and the at least one probe frequency are resonant with at least one transverse mode of at least one cavity in which a sample is positioned for performing 2D spectroscopy.

14. The method of claim 13 , wherein the resonantly enhanced signal frequency combs enhance the 2D spectroscopy of the sample.

15. The method of claim 13 , wherein the at least two pump frequency combs and the at least one probe frequency comb are coupled to at least one transverse mode of the at least one cavity.

16. The method of claim 13 , wherein probe pulses acquire phase shifts in each round trip of the at least one cavity, with the acquired phase shifts based on a round trip Gouy phase of an Hermite-Gaussian mode.

17. The method of claim 13 , wherein circulating pump pulses acquire phase shifts in each round trip of the at least one cavity.

18. The method of claim 17 , wherein the acquired phase shifts of the circulating pump pulses are based on a round trip Gouy phase of an Hermite-Gaussian mode.