The Cationminus signpi Interaction.

(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

Sources and systems for far-infrared or terahertz (1 THz = 10(12) Hz) radiation have received extensive attention in recent years, with applications in sensing, imaging and spectroscopy. Terahertz radiation bridges the gap between the microwave and optical regimes, and offers significant scientific and technological potential in many fields. However, waveguiding in this intermediate spectral region still remains a challenge. Neither conventional metal waveguides for microwave radiation, nor dielectric fibres for visible and near-infrared radiation can be used to guide terahertz waves over a long distance, owing to the high loss from the finite conductivity of metals or the high absorption coefficient of dielectric materials in this spectral range. Furthermore, the extensive use of broadband pulses in the terahertz regime imposes an additional constraint of low dispersion, which is necessary for compatibility with spectroscopic applications. Here we show how a simple waveguide, namely a bare metal wire, can be used to transport terahertz pulses with virtually no dispersion, low attenuation, and with remarkable structural simplicity. As an example of this new waveguiding structure, we demonstrate an endoscope for terahertz pulses.

Metal wires for terahertz wave guiding

Molecular recognition of protein-ligand complexes : applications to drug design

A broadband, compact, all-electrically driven mid-infrared frequency comb based on a quantum cascade laser widens the scope of application of combs in this frequency range beyond that of sources which depend on a chain of optical components. Optical frequency combs are light sources that produce a comb-like spectrum, with sharp equidistant frequency modes, and have many uses in metrology and spectroscopy applications. The mid-infrared regime is particularly important for molecular fingerprinting, but so far the comb sources in this wavelength regime are bulky and rely on a chain of optical components. For wide practical applications, an electrically injected, compact scheme is desired. Andreas Hugi et al. now demonstrate a mid-infrared frequency comb generator based on a semiconductor device, a continuous-wave quantum cascade laser. Optical frequency combs1 act as rulers in the frequency domain and have opened new avenues in many fields such as fundamental time metrology, spectroscopy and frequency synthesis. In particular, spectroscopy by means of optical frequency combs has surpassed the precision and speed of Fourier spectrometers. Such a spectroscopy technique is especially relevant for the mid-infrared range, where the fundamental rotational–vibrational bands of most light molecules are found2. Most mid-infrared comb sources are based on down-conversion of near-infrared, mode-locked, ultrafast lasers using nonlinear crystals3. Their use in frequency comb spectroscopy applications has resulted in an unequalled combination of spectral coverage, resolution and sensitivity4,5,6,7. Another means of comb generation is pumping an ultrahigh-quality factor microresonator with a continuous-wave laser8,9,10. However, these combs depend on a chain of optical components, which limits their use. Therefore, to widen the spectroscopic applications of such mid-infrared combs, a more direct and compact generation scheme, using electrical injection, is preferable. Here we present a compact, broadband, semiconductor frequency comb generator that operates in the mid-infrared. We demonstrate that the modes of a continuous-wave, free-running, broadband quantum cascade laser11 are phase-locked. Combining mode proliferation based on four-wave mixing with gain provided by the quantum cascade laser leads to a phase relation similar to that of a frequency-modulated laser. The comb centre carrier wavelength is 7 micrometres. We identify a narrow drive current range with intermode beat linewidths narrower than 10 hertz. We find comb bandwidths of 4.4 per cent with an intermode stability of less than or equal to 200 hertz. The intermode beat can be varied over a frequency range of 65 kilohertz by radio-frequency injection. The large gain bandwidth and independent control over the carrier frequency offset and the mode spacing open the way to broadband, compact, all-solid-state mid-infrared spectrometers.

/pdf/mid-infrared-frequency-comb-based-on-a-quantum-cascade-laser-1a0a174joi.pdf

Mid-infrared frequency comb based on a quantum cascade laser

Second-order optical nonlinearities in materials are of paramount importance for optical wavelength conversion techniques, which are the basis of new high-resolution spectroscopic tools. Semiconductor technology now makes it possible to design and fabricate artificially asymmetric quantum structures in which optical nonlinearities can be calculated and optimized from first principles. Extremely large second-order susceptibilities can be obtained in these asymmetric quantum wells. Moreover, properties such as double resonance enhancement or electric field control will open the way to new devices, such as fully solid-state optical parametric oscillators.

https://science.sciencemag.org/content/sci/271/5246/168.full.pdf

Quantum Engineering of Optical Nonlinearities

We report the first experimental evidence of a nonlinear optical effect due to intersubband transitions in compositionally asymmetrical multiquantum wells. The effect is detected as an optical rectification signal appearing at the structure terminals when irradiated by a continuous 10.6 μm CO2 laser. The net electro‐optical coefficient of the structure is found to be 7.2 nm/V which is more than three orders of magnitude higher than for bulk GaAs. The results are in good agreement with theoretical predictions.

Observation of nonlinear optical rectification at 10.6 μm in compositionally asymmetrical AlGaAs multiquantum wells

We report the first experimental evidence of second harmonic generation due to inter-subband transitions in compositionally asymmetrical multiquantum wells using a continuous CO2 laser. The extremely large value of the second-order susceptibility (χ(2)2ω ~ 7.6×10−7m/V) is ingood agreement with theoretical predictions.

Second harmonic generation by intersub-band transitions in compositionally asymmetrical MQWs

We report on the observation of resonant intersubband second‐harmonic generation in asymmetric GaAs/AlGaAs quantum wells using a cw or Q‐switched tunable CO2 laser as the pumping source. The dependence of the second‐harmonic intensity with the pump photon wavelength is presented for the first time. A Lorentzian‐like second‐harmonic line shape is found with a maximum at 10.9 μm and a linewidth of 0.4 μm (4.1 meV). These results are in good agreement with theoretical predictions. The expected quadratic dependence of the second‐harmonic conversion efficiency with pump intensity is well verified for intensities up to 150 kW/cm2. The calibrated second‐harmonic power reaches 0.13 μW for a cw pump power of 0.8 W. The value of 7.2×10−7 m/V deduced for the second‐order nonlinear susceptibility is about 1900 times greater than that found in bulk GaAs.

Detailed analysis of second‐harmonic generation near 10.6 μm in GaAs/AlGaAs asymmetric quantum wells

We report giant, nonlinear optical rectification in asymmetric quantum wells weakly coupled by an intermediate potential barrier. This phenomenon originates from (i) macroscopic displacements (30 nm) of carriers during optical transitions and (ii) large storage times of excited electrons because of a slow transfer mechanism between the wells (≊6 ps at 77 K). The resulting rectification coefficient is 1.62×10−3 m/V per well, more than six orders of magnitude higher than in bulk GaAs. These structures really behave as giant ‘‘quasimolecules’’ optimized for infrared optical nonlinearities and their use may be envisioned for a new class of infrared detectors.

P. Bois

Papers

Quantum Engineering of Optical Nonlinearities

Observation of nonlinear optical rectification at 10.6 μm in compositionally asymmetrical AlGaAs multiquantum wells

Second harmonic generation by intersub-band transitions in compositionally asymmetrical MQWs

Detailed analysis of second‐harmonic generation near 10.6 μm in GaAs/AlGaAs asymmetric quantum wells

Giant nonlinear optical rectification at 8–12 μm in asymmetric coupled quantum wells