Cavity-Enhanced Two-Photon Double Resonance Spectroscopy

Cavity-enhanced two-photon double-resonance spectroscopy for the study of molecular dark states

Dark states, notwithstanding their critical roles in molecular physics, are inaccessible with single-photon excitations from the ground electronic and vibrational state because these transitions are forbidden or extremely weak. For example, the electric-dipole transition from a singlet ground state (S₀) to a triplet state (T) is forbidden because they have different spin multiplicities. Transitions to certain vibronic states may be forbidden for symmetry reasons or as a result of vanishing Franck-Condon (FC) factors. Therefore, dark states are often the missing links in molecular spectroscopy and dynamics on multiple potential energy surfaces (PESs). Two-photon spectroscopic techniques can be employed to approach a dark state (|2>) from the ground state (|0>) via an intermediate state (|1>). In one possible excitation scheme, the dark state is accessed by two-photon double-resonance (DR) excitation (|2>←|1>←|0>, Fig. 1a), in which both |2>←|1> and |1>←|0> transitions are allowed. Another important spectroscopic technique for approaching dark states is stimulated-emission pumping (SEP, Fig. 1b), which uses a “pump-dump” scheme involving a three-level Λ-type system. In conventional SEP, molecules are pumped from the ground state (|0>) using a pulsed laser to an excited state (|1>). Another pulsed laser, whose frequency is scanned, is used to dump the |1>-state population to lower states. When the dump laser frequency is in resonance with a downward transition |1>→|2>, where |2> is between |0> and |1> in energy, sideways fluorescence following the |1>←|0> excitation decreases. The SEP spectrum is recorded as depletion of the sideways LIF from the |1> state as a function of the dump laser frequency.

In general, the combined probability of multi-photon excitation is low. Therefore, conventional two-photon spectroscopy techniques typically use nanosecond tunable lasers (dye lasers or optical parametric oscillators, OPOs) to improve the overall S/N. The spectral resolution is hence limited by the linewidth of the laser sources. Moreover, SEP using pulsed lasers has limited sensitivity because it is not a background-free technique. The maximum degree of depletion of the LIF signal is 50% assuming that |1> and |2> form a two-level system. The maximum S/N of SEP is therefore determined by the stability of the LIF signal, which is in turn limited by the stabilities of the pump laser output and concentration of molecules.

Recently, our group has started developing two cavity-ring-down (CRD)-based two-photon spectroscopic techniques using continuous (CW) laser sources: double-resonance cavity ring-down (DR-CRD) and stimulated-emission pumping cavity ring-up (SEP-CRU). They combine the advantages of two-photon excitation in circumventing forbidding selection rules and the high sensitivity of CRD to investigate molecular dark states.

In the CRD-based two-photon spectroscopy measurements, the ground-state (|0>) population is pumped to an intermediate state (|1>) (Figs. 1a and 1b). The excited-state population will be detected in a CRD fashion. CRD measurement requires a steady population of the initial state – in this case, the excited state |1>. Therefore, it is necessary to use a CW laser as the pump laser for the |1>←|0> excitation. A high-finesse optical cavity is locked to the pump laser using a PZT actuator to enhance the absorption (Fig. 2a). Alternatively, the pump laser can be locked to the cavity, albeit much more difficult. The second optical cavity for the ring-down (or “ring-up”) laser beam forms a small angle with the pump-beam cavity (Fig. 2a). In the DR-CRD experiment (Fig. 1a), excited molecules in the intermediate state (|1>) are further excited by a second “repump” laser to the target dark state higher in energy (|2>). In SEP-CRU spectroscopy (Fig. 1b), the second laser is used to stimulate down, i.e., “dump”, the intermediate-state (|1>) population to a target dark state (|2>) that is lower in energy.

In both DR-CRD and SEP-CRU experiments, the frequency of the first (pump) laser is fixed to a judiciously chosen transition that circumvents forbidding selection rules or unfavorable FC factors. The frequency of the second (repump or dump) laser is scanned, and its transmission through the cavity is monitored to map out the energy level structure of the target state. Compared to the non-resonance case, the ring-down time of the second laser decreases when its frequency is in resonance with an upward (|2>←|1>) transition and increases when its frequency is in resonance with a downward (|1>→|2>) transition – hence the term “ring-up”. (See Fig. 1c.)

We assume that: (i) the |1>←|0> transition is highly saturated due to cavity enhancement, and the repump/dump laser can be treated as a perturbation. The population of the intermediate |1> state, therefore, remains steady in the presence of the repumping/dumping; (ii) the dark state (|2>) is not thermally populated; and (iii) lifetime of the dark state, although relatively long compared to bright states, is still significantly shorter than the repetition rate of the ring-down or ring-up measurement. Under these assumptions, the ring-down time of a repump laser can be described as:

where σ₁₂ is the absorption cross section of the |2>←|1> transition, N₁ is the population of the |1> state, and l is the absorption length. For a dump laser:

where g₁₂ is the gain due to |1>→|2> stimulated emission. (See Fig. 1c.)

At each frequency of the repump/dump laser, the pump laser beam is blocked and unblocked alternately with an AOM or an optical chopper. Ring-down times of the repump/dump laser with and without the pump laser are compared to determine the direction (upward or downward) and the intensity of the |2>←|1> or |1>→|2> transition. A decrease (increase) in the ring-down time when the pump laser beam is unblocked indicates an upward (downward) transition, i.e., an absorption (stimulated emission), from the |1> state. (See Fig. 1d.) We are constructing a room-temperature CRD-based two-photon spectroscopy apparatus using an X-shaped dual-cavity CRD cell (Fig. 2a. Also, see Fig. 2b for a photo of the cell).

As a proof-of-principle experiment, we will use the CW-OPO as the pump laser to excite transitions to the υ₃=1 level of CH₄, and use the Ti:Sapphire ring laser to repump the υ₃=7<--1 transitions. A detailed diagram of the experimental setup can be found in Fig. 3. The OPO is locked to a Doppler-free saturated absorption line of CH₄. The υ₃=7<--1 transitions are detected by CW-CRD spectroscopy. Two experimental configurations will be used: In the first experiment, the mid-IR laser beam from the OPO and the near-IR beam from the Ti:Sapphire ring laser are overlapped in a single cavity using dichroic mirrors. In the second experiment using the X-shaped cavity, the repump/dump-beam cavity is locked to the OPO.

A jet-cooled cavity-enhanced two-photon spectroscopy apparatus is also under construction. In this experiment, a supersonic jet expansion is collimated with a skimmer and then intercepted perpendicularly by both the pump and the repump/dump beams (Fig. 2c). A pinhole nozzle is preferred to a slit-jet nozzle in the future two-photon experiment because of lower vibrational and rotational temperatures that can be reached in the jet expansion.

Compared to traditional DR or SEP spectroscopy, the two-photon techniques described here have significantly higher S/N thanks mainly to cavity enhancement. Sub-Doppler resolution can be achieved with narrow-linewidth lasers. The rotational and fine structure of the target molecules can be resolved in future two-photon spectroscopy measurements. The spectra are expected to be significantly simplified because only a single intermediate state is populated. Finally, the two-photon spectroscopic techniques are molecular and conformational selectivity.