Vapor-phase nonlinear optics is undergoing a renaissance, driven in large part by electromagnetically induced transparency (EIT). EIT increases conversion efficiencies, eliminates the need for phase matching, and reduces optical intensities for pump beams from gigawatts to megawatts per square centimeter. The technology offers the prospect of a new class of efficient light sources operating at wavelengths that are unobtainable from existing coherent laser sources and solid-state nonlinear devices.
EIT is a technique for eliminating the effect of a medium on a propagating beam of electromagnetic radiation. It can improve the transmission of laser beams through media that otherwise would absorb the incident radiation or distort its phase profile via self-phase modulation (self-focusing) or density inhomogeneties (turbulence).1 At the same time, EIT generates a macroscopic population of coherently driven, uniformly phased atoms, which enhances the nonlinear optical conversion efficiency.
Consider a low-intensity, pulsed probe laser beam that propagates through a collection of two-level atoms (ground and first excited state). A plot of optical transmission as a function of laser frequency shows that when the beam is off the atomic energy resonance, it transmits through the medium without loss. As the laser frequency sweeps through resonance, however, the transmission drops to zero; the atomic distribution is opaque to resonant radiation and strongly absorbs the laser energy (see figure 1).
Figure 1. Optical transmission as a function of laser frequency shows that transmission drops to zero as the laser beam approaches resonance with the medium (top). If a second, resonant beam illuminates the material, the absorption profile for the first beam now shows a transmission peak on resonance (bottom). Each data point corresponds to a single laser pulse at a particular detuning.
If we simultaneously expose the material to a second, coherent coupling beam whose frequency is resonant between the same upper level and a new level, we can dramatically alter the absorption profile for the probe beam. Instead of reaching a minimum when the probe beam is on resonance, the absorption profile now shows a transmission peak. The effect occurs because the two electromagnetic fields exert equal and oppositely phased forces on the electrons, thus freezing the motion of the electron at the frequencies of the applied lasers. If there is no electron motion, then there is no polarization and no dielectric constant. The medium is in a state of electromagnetically induced transparency.
This material excitation is termed atomic coherence and propagates through the atomic medium with the laser pulses. If we were able to image the entire atomic distribution, we'd see the atoms oscillating in phase with one another. This new state of matter has been dubbed "phaseonium" by Marlan Scully and his colleagues at Texas A&M University (College Station, TX).
The effect also works to decouple the propagation of intense laser fields from the collection of two-level atoms. We started with an aperture covered with a wire grid and illuminated by a probe beam at 283 nm. The beam propagated through a cell filled with atomic lead vapor and was imaged by a charge-coupled-device (CCD) camera. We detuned the laser 20 cm-1 above resonance to obtain nearly complete weak-probe transmission that suffered neither attenuation nor self-phase modulation (see figure 2). When we increased the intensity of the probe laser to approximately 10 MW/cm2, self-focusing effects scrambled the phase profile of the propagating wave, severely distorting the transmitted image quality. When we applied the beam from a 406-nm coupling laser, with an intensity roughly 8 MW/cm2, the EIT effect restored image clarity.
Figure 2. Illuminating the cell filled with Pb vapor by a probe beam at 283 nm produces a clear image (top). Increasing the beam intensity distorts the image (middle). Triggering EIT with a second beam at 406-nm restores image clarity (bottom).enhanced nonlinear optics
In four-wave-mixing, three laser fields (probe (P), coupling (C), and mixing (M)) are applied to a medium to generate a fourth output. The standard perturbation-theory equation describing the growth of the generated field in the nonlinear medium is
where EP , E*C , and EM are the electric fields of the interacting fields, Δk represents phase mismatch information, and deff is an effective nonlinearity, which, for atomic media, takes the form
where N is the atomic density and the Δω terms represent the detunings of the probe, coupling, and mixing lasers from their respective transitions. The three applied fields combine to create a forcing polarization wave, which is just a material excitation oscillating at the frequency of the generated field. From Maxwell's equations, this forcing polarization generates a new, "free" electromagnetic field: the output beam.
In general, material dispersion causes a phase velocity mismatch for arbitrary nonlinear optical processes. If the phase velocities of the free and forcing waves are unequal, then destructive interference from free-wave components generated in different parts of the nonlinear medium will severely limit the attainable conversion efficiency. Phase matching is the process of equating these two phase velocities.
Researchers have tried to increase the effective nonlinearity by tuning the probe and coupling lasers closer to material resonances to minimize Δω, but the resultant absorption and self-phase modulation destroyed the beam profiles. The large detunings and high optical intensities required for workable vapor-phase nonlinear systems limited the degree of material excitation and overall nonlinearity. Small nonlinearities require long interaction lengths and precise phase-matching measures, which often are difficult or impossible to implement. All of these factors have conspired to prevent vapor-phase nonlinear devices from becoming practical light sources.
Now, using EIT techniques, intense interacting lasers can be tuned right into resonance without loss or "beam blow-up," significantly enhancing the nonlinear process. Looking at frequency converters in the frequency domain, the probe and coupling lasers establish a local oscillator (the atomic coherence) that beats against a third applied field to generate sum and difference frequencies. Properly tuned, the probe and coupling lasers initiate EIT in the medium and can significantly increase the atomic coherence, which leads to a strong nonlinearity.
In a material with maximum coherence, a near-complete conversion from the mixing field to the generated field occurs in the same density-length product that would normally cause a 180° phase-slip between the free and forcing waves (one uncompensated coherence length). The introduction of EIT thus minimizes phase-matching requirements, eliminating the need for external phase-matching agents.
The nonlinear generation occurs collinearly (on-axis). The power densities required for preparation of the maximal coherence condition are several orders of magnitude lower than those previously used, well below damage thresholds of both the materials and the dielectric coatings. The price of EIT is that it requires high-quality laser sources, but advances in high-power, compact, pulsed pump-laser technology continue to benefit this field. living in the real world
In Steve Harris's group at the Stanford University E. L. Ginzton Laboratory (Palo Alto, CA), we demonstrated these principles in a series of experiments. We used the frequency-doubled and -tripled outputs of a trio of titanium-doped sapphire (Ti: sapphire) regenerative amplifiers to generate the three interacting laser fields.2 Each amplifier operated in a single-longitudinal mode to deliver 10 to 15 ns pulses with Fourier-transform-limited (FTL) bandwidths. The pulses overlapped spatially and temporally and propagated through a distribution of Pb atoms in a heat pipe maintained at 1100° C.
A 283-nm probe laser field (up to 3 mJ per pulse) and a 406-nm coupling laser (up to 20 mJ per pulse) established EIT in a cylindrical region of Pb atoms several millimeters wide. The material excitation mixed with a third 233-nm mixing laser field (up to 1 mJ per pulse) to generate a VUV field at 186 nm. Intensities of the probe and coupling lasers inside the Pb vapor were 10 MW/cm2 and 15 MW/cm2, respectively. A Pellin-Broca prism at the exit of the cell disperses the beams.
At a mixing laser detuning ΔωM of 40 cm-1, small-signal energy conversion efficiencies exceeded 70% (figure 3). The VUV light was generated in a collinear beam with a peak power of 30 kW, in a Gaussian spatial profile with near-diffraction-limited divergence. Overall optical energy reached conversion efficiency reaches about 1%.
Figure 3. At a mixing-laser detuning ΔωM of 40 cm-1, small-signal energy conversion efficiencies exceed 70%. The inset shows the applied (a) and depleted (b) 233-nm mixing field temporal waveforms and the generated (c) 186-nm VUV radiation.
Last year, Harris's group teamed with Lene Hau's group at Harvard University (Cambridge, MA) to investigate EIT in a Bose-Einstein condensate of sodium atoms, which culminated in the remarkable demonstration of optical group velocities of 38 mph.3 At Stanford University, Alexei Sokolov has begun a program of EIT in molecular deuterium. A promising result is the generation of a wide (in excess of 50,000 cm-1) spectral comb;4 if this comb can be phased properly, it may be used to synthesize subfemtosecond pulses.
Our understanding of EIT continues to evolve, and this knowledge will facilitate the construction of practical light sources operating in otherwise inaccessible regions of the spectrum. oe References
1. S. Harris, Phys. Today 50, p. 36 (1997).
2. A. Merriam, S. Sharpe, et al., IEEE J. Sel. Top. Quant. Elect. 5 (1999).
3. L. Hau, S. Harris, et al., Nature 397, p. 594 (1999).
4. A. Sokolov, et al., Phys. Rev. Lett. 85, p. 562 (2000).
Andrew Merriam is an atomic physicist and engineering consultant, formerly with Steve Harris's group at Stanford University.