(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

The quest for all-optical signal processing is generally deemed to be impractical because optical nonlinearities are usually weak. The emerging field of nonlinear photonic crystals seems destined to change this view dramatically. Theoretical considerations show that all-optical devices using photonic crystal designs promise to be smaller than the wavelength of light, and to operate with bandwidths that are very difficult to achieve electronically. When created in commonly used materials, these devices could operate at powers of only a few milliwatts. Moreover, if these designs are combined with materials and systems that support electromagnetically induced transparency, operation at single-photon power levels could be feasible.

Enhancement of nonlinear effects using photonic crystals.

Quantum cascade (`QC') lasers are reviewed. These are semiconductor injection lasers based on intersubband transitions in a multiple-quantum-well (QW) heterostructure, designed by means of band-structure engineering and grown by molecular beam epitaxy. The intersubband nature of the optical transition has several key advantages. First, the emission wavelength is primarily a function of the QW thickness. This characteristic allows choosing well-understood and reliable semiconductors for the generation of light in a wavelength range unrelated to the material's energy bandgap. Second, a cascade process in which multiple - often several tens of - photons are generated per electron becomes feasible, as the electron remains inside the conduction band throughout its traversal of the active region. This cascading process is behind the intrinsic high-power capabilities of the lasers. Finally, intersubband transitions are characterized through an ultrafast carrier dynamics and the absence of the linewidth enhancement factor, with both features being expected to have significant impact on laser performance. The first experimental demonstration by Faist et al in 1994 described a QC-laser emitting at 4.3 µm wavelength at cryogenic temperatures only. Since then, the lasers' performance has greatly improved, including operation spanning the mid- to far-infrared wavelength range from 3.5 to 24 µm, peak power levels in the Watt range and above-room-temperature (RT) pulsed operation for wavelengths from 4.5 to 16 µm. Three distinct designs of the active region, the so-called `vertical' and `diagonal' transition as well as the `superlattice' active regions, respectively, have emerged, and are used either with conventional dielectric or surface-plasmon waveguides. Fabricated as distributed feedback lasers they provide continuously tunable single-mode emission in the mid-infrared wavelength range. This feature together with the high optical peak power and RT operation makes QC-lasers a prime choice for narrow-band light sources in mid-infrared trace gas sensing applications. Finally, a manifestation of the high-speed capabilities can be seen in actively and passively mode-locked QC-lasers, where pulses as short as a few picoseconds with a repetition rate around 10 GHz have been measured.

https://iopscience.iop.org/article/10.1088/0034-4885/64/11/204/pdf

Recent progress in quantum cascade lasers and applications

Materials chemistry and the pursuit of new compounds through exploratory synthesis are having a strong impact in many technological fields. The field of nonlinear optics is directly impacted by the availability of enabling materials with high performance. Nonlinear optical (NLO) phenomena such as second harmonic and difference frequency generation (SHG and DFG, respectively) are effective at producing a coherent laser beam in difficult to reach frequency regions of the electromagnetic spectrum. Such regions include the infrared (IR), far-infrared, and terahertz frequencies. High performance NLO crystals are critical for applications utilizing these coherent light sources, and new materials are continuously sought for better conversion efficiency and performance. The class of metal chalcogenides is the most promising source of potential NLO materials with desirable properties particularly in the IR region where most classes of materials face various fundamental challenges. We review the recent developments...

Metal Chalcogenides: A Rich Source of Nonlinear Optical Materials

Frequency conversion in nonlinear optical crystals1,2 is an effective means of generating coherent light at frequencies where lasers perform poorly or are unavailable. For efficient conversion, it is necessary to compensate for optical dispersion, which results in different phase velocities for light of different frequencies. In anisotropic birefringent crystals such as LiNbO3 or KH2PO4 (‘KDP’), phase matching can be achieved between electromagnetic waves having different polarizations. But this is not possible for optically isotropic materials, and as a result, cubic materials such as GaAs (which otherwise have attractive nonlinear optical properties) have been little exploited for frequency conversion applications. Quasi-phase-matching schemes1,3, which have achieved considerable success in LiNbO3 (ref. 4), provide a route to circumventing this problem5,6, but the difficulty of producing the required pattern of nonlinear properties in isotropic materials, particularly semiconductors, has limited the practical utility of such approaches. Here we demonstrate a different route to phase matching — based on a concept proposed by Van der Ziel 22 years ago7 — which exploits the artificial birefringence of multilayer composites of GaAs and oxidised AlAs. As GaAs is the material of choice for semiconductor lasers, such optical sources could be integrated in the core of frequency converters based on these composite structures.

Phase matching using an isotropic nonlinear optical material

We demonstrate phase-matched second-harmonic generation from a λ=16 μm pump in a GaAs-based waveguide Phase matching is obtained by using the form birefringence in an AlGaAs/Al2O3 multilayer obtained by selective wet oxidation

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Second-harmonic generation at l=1.6 micro m in AlGaAs/Al2O3 waveguides using birefringence phase matching

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.

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

We present a two-color (956 and 985 nm) InGaAs/AlGaAs laser structure epitaxially stacked through a low-resistance (10−5–10−4 Ω cm2) Esaki junction, exhibiting two threshold characteristics. It is shown that this structure can be considered as a bipolar cascade laser.

Epitaxially stacked lasers with Esaki junctions: A bipolar cascade laser

Selective wet oxidation of AlAs was used to obtain huge birefringence in GaAs/AlAs optical waveguides. A single polarization waveguide was obtained by oxidizing an AlAs layer buried in a GaAs guiding layer. The TM mode is below cutoff due to the high index contrast between the layers. Applications to phase matching in nonlinear optical conversion are envisaged.

/pdf/huge-birefringence-in-selectively-oxidized-gaas-alas-optical-afa4hy6d8q.pdf

J. Nagle

Papers

Phase matching using an isotropic nonlinear optical material

Second-harmonic generation at l=1.6 micro m in AlGaAs/Al2O3 waveguides using birefringence phase matching

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

Epitaxially stacked lasers with Esaki junctions: A bipolar cascade laser

Huge birefringence in selectively oxidized GaAs/AlAs optical waveguides