(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

The various arguments for introducing optical interconnections to silicon CMOS chips are summarized, and the challenges for optical, optoelectronic, and integration technologies are discussed. Optics could solve many physical problems of interconnects, including precise clock distribution, system synchronization (allowing larger synchronous zones, both on-chip and between chips), bandwidth and density of long interconnections, and reduction of power dissipation. Optics may relieve a broad range of design problems, such as crosstalk, voltage isolation, wave reflection, impedence matching, and pin inductance. It may allow continued scaling of existing architectures and enable novel highly interconnected or high-bandwidth architectures. No physical breakthrough is required to implement dense optical interconnects to silicon chips, though substantial technological work remains. Cost is a significant barrier to practical introduction, though revolutionary approaches exist that might achieve economies of scale. An Appendix analyzes scaling of on-chop global electrical interconnects, including line inductance and the skin effect, both of which impose significant additional constraints on future interconnects.

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Rationale and challenges for optical interconnects to electronic chips

We review the family of optoelectronic devices whose performance is enhanced by placing the active device structure inside a Fabry‐Perot resonantmicrocavity. Such resonantcavity enhanced (RCE) devices benefit from the wavelength selectivity and the large increase of the resonant optical field introduced by the cavity. The increased optical field allows RCE photodetector structures to be thinner and therefore faster, while simultaneously increasing the quantum efficiency at the resonant wavelengths. Off‐resonance wavelengths are rejected by the cavity making RCE photodetectors promising for low crosstalk wavelength division multiplexing(WDM) applications. RCE optical modulators require fewer quantum wells so are capable of reduced voltage operation. The spontaneous emission spectrum of RCE light emitting diodes(LED) is drastically altered, improving the spectral purity and directivity. RCE devices are also highly suitable for integrated detectors and emitters with applications as in optical logic and in communication networks. This review attempts an encyclopedic overview of RCE photonicdevices and systems. Considerable attention is devoted to the theoretical formulation and calculation of important RCE device parameters. Materials criteria are outlined and the suitability of common heteroepitaxial systems for RCE devices is examined. Arguments for the improved bandwidth in RCE detectors are presented intuitively, and results from advanced numerical simulations confirming the simple model are provided. An overview of experimental results on discrete RCE photodiodes, phototransistors, modulators, and LEDs is given. Work aimed at integrated RCE devices,optical logic and WDM systems is also covered. We conclude by speculating what remains to be accomplished to implement a practical RCE WDM system.

Resonant cavity enhanced photonic devices

Data are presented characterizing a new process for fabrication of vertical‐cavity surface‐emitting lasers based on the selective conversion of high Al composition epitaxial AlGaAs to a stable native oxide using ‘‘wet oxidation.’’ The native oxide is used to form a ring contact to the laser active region. The resulting laser active regions have dimensions of 8, 4, and 2 μm. The lowest threshold laser is achieved with the 8‐μm active region, with a minimum threshold current of 225‐μA continuous wave at room temperature.

Native-Oxide Defined Ring Contact for Low Threshold Vertical-Cavity Lasers

We address the long-standing issue of extracting light as efficiently as possible from a high-index material, n/spl ges/2, where as little as 2%-10% of light not suffering total internal reflection is extracted at standard plane faces due to the small critical angle /spl sim/1/n. Using a planar microcavity to redirect spontaneous emission toward the surface, constructive interferences can bring 15%-50% of the light out, enhancing brightness and efficiency. In this first of two papers, an approximate approach is used showing the importance of small cavity order m/sub c/ and of the m/sub c//n/sup 2/ ratio. We define a condition for microcavity regime as m/sub c/<2n/sup 2/. It is shown that most of light extraction is usually attained for moderate mirror reflectivities /spl sim/1-m/sub c//n/sup 2/ typically below 90%, and without strong directionality. Balance between emission directionality, radiance (brightness), and spectral narrowing is discussed. We define a brightness enhancement factor B given by Bm/sub c//spl Delta//spl Omega/=4/spl pi/ where /spl Delta//spl Omega/ is the largest internal solid angle of either the cavity mode or that deduced from the material emission linewidth. Design rules are applied to distributed dielectric mirrors yielding an optimal number of periods. The underlying physical competition between emission into guided modes, Fabry-Perot modes and the so-called "leaky modes" is analyzed.

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Impact of planar microcavity effects on light extraction-Part I: basic concepts and analytical trends

Data are presented demonstrating a strong influence of a closely spaced AlAs/GaAs distributed Bragg reflector on the spontaneous emission characteristics of an InGaAs‐GaAs quantum well. The mirror to quantum well spacings on different crystal samples correspond to optical path lengths of either 1/4, 1/2, or 3/4 of the emission wavelength. The samples are characterized using photoluminescence, electroluminescence, and reflectivity measurements. Spontaneous emission is found to be greatly enhanced for a 1/2 wavelength spacing, while 1/4 and 3/4 spacings suppress the spontaneous emission by a factor of ≳1000.

Effect of an AlAs/GaAs mirror on the spontaneous emission of an InGaAs‐GaAs quantum well

Data are presented showing that it is possible to optically couple a semiconductor quantum well to a mirror, and thus influence its spontaneous emission lifetime, for mirror to quantum well spacings of less than an optical wavelength. Light emitting diodes with various mirror to quantum well spacings corresponding to quantum well placement at either interference nodes or antinodes are characterised in terms of light output efficiency and frequency response.

Optically-coupled mirror-quantum well InGaAs-GaAs light emitting diode

Data are presented characterizing the transverse mode behavior of AlAs/GaAs/InGaAs vertical‐cavity surface‐emitting lasers fabricated using a native‐oxide process. The native‐oxide process results in laser diodes with active regions defined to be 10, 8, and 4 μm squares. We show that the transverse lasing mode is influenced by mirror reflectivity, with significant mode changes occurring with drive current for 8–10 μm devices in the ranges of one to four times threshold. In smaller devices of 4 μm square dimension, the transverse mode at threshold appears as a lowest order mode.

Transverse mode behavior in native-oxide-defined low threshold vertical-cavity lasers

Data are presented on an electron‐beam evaporated ZnSe/CaF2 distributed Bragg reflector for use on a vertical‐cavity surface‐emitting laser operating at a wavelength ∼0.98 μm. Mirror characteristics are measured using optical transmission and reflectivity for quarter‐wave structures with varying numbers of pairs from one to five. The optical characteristics of the ZnSe/CaF2 quarter‐wave stack is compared to similar structures of electron‐beam evaporated Si/SiO2 reflectors. The ZnSe/CaF2 mirror is found to be superior to the Si/SiO2 mirror in terms of both higher reflectivity and lower optical loss for all structures investigated. Comparison is also made between ZnSe/CaF2 and Si/SiO2 mirrors in the continuous‐wave performance of AlAs‐GaAs‐InGaAs quantum‐well vertical‐cavity surface‐emitting lasers. Superior laser performance is achieved with the ZnSe/CaF2 mirror in terms of threshold current and lasing efficiency.

T. J. Rogers

Papers

Native-Oxide Defined Ring Contact for Low Threshold Vertical-Cavity Lasers

Effect of an AlAs/GaAs mirror on the spontaneous emission of an InGaAs‐GaAs quantum well

Optically-coupled mirror-quantum well InGaAs-GaAs light emitting diode

Transverse mode behavior in native-oxide-defined low threshold vertical-cavity lasers

ZnSe/CaF2 quarter‐wave Bragg reflector for the vertical‐cavity surface‐emitting laser