(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

Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

Rayleigh, Brillouin and Raman scatterings in fibers result from the interaction of photons with local material characteristic features like density, temperature and strain. For example an acoustic/mechanical wave generates a dynamic density variation; such a variation may be affected by local temperature, strain, vibration and birefringence. By detecting changes in the amplitude, frequency and phase of light scattered along a fiber, one can realize a distributed fiber sensor for measuring localized temperature, strain, vibration and birefringence over lengths ranging from meters to one hundred kilometers. Such a measurement can be made in the time domain or frequency domain to resolve location information. With coherent detection of the scattered light one can observe changes in birefringence and beat length for fibers and devices. The progress on state of the art technology for sensing performance, in terms of spatial resolution and limitations on sensing length is reviewed. These distributed sensors can be used for disaster prevention in the civil structural monitoring of pipelines, bridges, dams and railroads. A sensor with centimeter spatial resolution and high precision measurement of temperature, strain, vibration and birefringence can find applications in aerospace smart structures, material processing, and the characterization of optical materials and devices.

Recent progress in distributed fiber optic sensors.

By incorporating a section of large positive-dispersion fiber in an all-fiber erbium ring laser, we obtain high-energy pulses with spectral widths of 56 nm. The chirp on these pulses is highly linear and can be compensated for with dispersion in the output coupling fiber lead. The result is a fully self-starting source of 77-fs pulse with 90 pJ of energy and greater than 1 kW of peak power at a 45-MHz repetition rate.

77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser

Optical Waveguide Theory

Nonlinear birefringence effects in a fibre ring laser cavity have been exploited to produce selfstarting, passive mode-locking to give 1.5 ps soliton pulses.

/pdf/selfstarting-passively-mode-locked-fibre-ring-soliton-laser-53e2713c5z.pdf

Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation

A distributed optical fibre sensor is introduced which is capable of quantifying multiple dynamic strain perturbations along 1 km of a sensing fibre simultaneously using a standard telecommunication single-mode optical fibre The technique is based on measuring the phase between the Rayleigh scattered light from two sections of the fibre which define the gauge length The phase is spatially determined along the entire length of the fibre with a single pulse This allows multiple moving strain perturbation to be tracked and quantified along the entire length of the fibre The demonstrated setup has a spatial resolution of 2 m with a frequency range of 500-5000 Hz The minimum detectable strain perturbation of the sensor was measured to be 80 ne

/pdf/a-distributed-optical-fibre-dynamic-strain-sensor-based-on-45vhw4ppc7.pdf

A distributed optical fibre dynamic strain sensor based on phase-OTDR

Extensive research on Brillouin- and Raman-based distributed optical fibre sensors over the past two decades has resulted in the commercialization of distributed sensors capable of measuring static and quasi-static phenomena such as temperature and strain. Recently, the focus has been shifted towards developing distributed sensors for measurement of dynamic phenomena such as dynamic strain and sound waves. This article reviews the current state of the art distributed optical fibre sensors capable of quantifying dynamic vibrations. The most important aspect of Rayleigh and Brillouin scattering processes which have been used for distributed dynamic measurement are studied. The principle of the sensing techniques used to measure dynamic perturbations are analyzed followed by a case study of the most recent advances in this field. It is shown that the Rayleigh-based sensors have longer sensing range and higher frequency range, but their spatial resolution is limited to 1 m. On the other hand, the Brillouin-based sensors have shown a higher spatial resolution, but relatively lower frequency and sensing ranges.

/pdf/contributed-review-distributed-optical-fibre-dynamic-strain-1dcmqm9ye6.pdf

Contributed Review: Distributed optical fibre dynamic strain sensing.

We report an extended range distributed temperature sensor based on coherent detection of the frequency shift of the spontaneous Brillouin backscatter combined with Raman amplification. The Raman amplification was achieved within the sensing fibre using either co- or counter-propagating Raman pump with respect to the probe pulse and experiments were conducted to investigate the optimum pump and probe power combination. With a co-propagating Raman pump a temperature resolution of 0.8C was achieved at a sensing range of 150km with 50m spatial resolution.

150-km-range distributed temperature sensor based on coherent detection of spontaneous Brillouin backscatter and in-line Raman amplification

Simultaneous optical fibre distributed strain and temperature measurements have been obtained, by measuring the spontaneous Brillouin intensity and frequency shift, using the technique of microwave heterodyne detection. The enhanced stability from using a single coherent source combined with optical preamplification results in a highly accurate sensor. Using this sensor, distributed temperature sensing at 57 km and simultaneous distributed strain and temperature sensing at 30 km were achieved, the longest reported sensing lengths to date for these measurements. As a simultaneous strain and temperature sensor, a strain resolution of 100 μe and temperature resolution of 4 C were achieved.

Trevor P. Newson

Papers

Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation

A distributed optical fibre dynamic strain sensor based on phase-OTDR

Contributed Review: Distributed optical fibre dynamic strain sensing.

150-km-range distributed temperature sensor based on coherent detection of spontaneous Brillouin backscatter and in-line Raman amplification

Simultaneous distributed fibre temperature and strain sensor using microwave coherent detection of spontaneous Brillouin backscatter