(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

We review recent advances in laser cell surgery, and investigate the working mechanisms of femtosecond laser nanoprocessing in biomaterials with oscillator pulses of 80-MHz repetition rate and with amplified pulses of 1-kHz repetition rate. Plasma formation in water, the evolution of the temperature distribution, thermoelastic stress generation, and stress-induced bubble formation are numerically simulated for NA=1.3, and the outcome is compared to experimental results. Mechanisms and the spatial resolution of femtosecond laser surgery are then compared to the features of continuous-wave (cw) microbeams. We find that free electrons are produced in a fairly large irradiance range below the optical breakdown threshold, with a deterministic relationship between free-electron density and irradiance. This provides a large ‘tuning range’ for the creation of spatially extremely confined chemical, thermal, and mechanical effects via free-electron generation. Dissection at 80-MHz repetition rate is performed in the low-density plasma regime at pulse energies well below the optical breakdown threshold and only slightly higher than used for nonlinear imaging. It is mediated by free-electron-induced chemical decomposition (bond breaking) in conjunction with multiphoton-induced chemistry, and hardly related to heating or thermoelastic stresses. When the energy is raised, accumulative heating occurs and long-lasting bubbles are produced by tissue dissociation into volatile fragments, which is usually unwanted. By contrast, dissection at 1-kHz repetition rate is performed using more than 10-fold larger pulse energies and relies on thermoelastically induced formation of minute transient cavities with lifetimes <100 ns. Both modes of femtosecond laser nanoprocessing can achieve a 2–3 fold better precision than cell surgery using cw irradiation, and enable manipulation at arbitrary locations.

Mechanisms of femtosecond laser nanosurgery of cells and tissues

This article reviews acoustic microfiuidics: the use of acoustic fields, principally ultrasonics, for application in microfiuidics. Although acoustics is a classical field, its promising, and indeed perplexing, capabilities in powerfully manipulating both fluids and particles within those fluids on the microscale to nanoscale has revived interest in it. The bewildering state of the literature and ample jargon from decades of research is reorganized and presented in the context of models derived from first principles. This hopefully will make the area accessible for researchers with experience in materials science, fluid mechanics, or dynamics. The abundance of interesting phenomena arising from nonlinear interactions in ultrasound that easily appear at these small scales is considered, especially in surface acoustic wave devices that are simple to fabricate with planar lithography techniques common in microfluidics, along with the many applications in microfluidics and nanofluidics that appear through the literature.

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Microscale acoustofluidics: Microfluidics driven via acoustics and ultrasonics

Driven by functionality and purity demand for applications of inorganic nanoparticle colloids in optics, biology, and energy, their surface chemistry has become a topic of intensive research interest. Consequently, ligand-free colloids are ideal reference materials for evaluating the effects of surface adsorbates from the initial state for application-oriented nanointegration purposes. After two decades of development, laser synthesis and processing of colloids (LSPC) has emerged as a convenient and scalable technique for the synthesis of ligand-free nanomaterials in sealed environments. In addition to the high-purity surface of LSPC-generated nanoparticles, other strengths of LSPC include its high throughput, convenience for preparing alloys or series of doped nanomaterials, and its continuous operation mode, suitable for downstream processing. Unscreened surface charge of LSPC-synthesized colloids is the key to achieving colloidal stability and high affinity to biomolecules as well as support materials,...

Laser Synthesis and Processing of Colloids: Fundamentals and Applications

High intensity ultrasound can be used for the production of novel materials and provides an unusual route to known materials without bulk high temperatures, high pressures, or long reaction times. Several phenomena are responsible for sonochemistry and specifically the production or modification of nanomaterials during ultrasonic irradiation. The most notable effects are consequences of acoustic cavitation (the formation, growth, and implosive collapse of bubbles), and can be categorized as primary sonochemistry (gas-phase chemistry occurring inside collapsing bubbles), secondary sonochemistry (solution-phase chemistry occurring outside the bubbles), and physical modifications (caused by high-speed jets or shock waves derived from bubble collapse). This tutorial review provides examples of how the chemical and physical effects of high intensity ultrasound can be exploited for the preparation or modification of a wide range of nanostructured materials.

Sonochemical synthesis of nanomaterials

Bubbles in liquids, soft and squeezy objects made of gas and vapour, yet so strong as to destroy any material and so mysterious as at times turning into tiny light bulbs, are the topic of the present report. Bubbles respond to pressure forces and reveal their full potential when periodically driven by sound waves. The basic equations for nonlinear bubble oscillation in sound fields are given, together with a survey of typical solutions. A bubble in a liquid can be considered as a representative example from nonlinear dynamical systems theory with its resonances, multiple attractors with their basins, bifurcations to chaos and not yet fully describable behaviour due to infinite complexity. Three stability conditions are treated for stable trapping of bubbles in standing sound fields: positional, spherical and diffusional stability. Chemical reactions may become important in that respect, when reacting gases fill the bubble, but the chemistry of bubbles is just touched upon and is beyond the scope of the present report. Bubble collapse, the runaway shrinking of a bubble, is presented in its current state of knowledge. Pressures and temperatures that are reached at this occasion are discussed, as well as the light emission in the form of short flashes. Aspherical bubble collapse, as for instance enforced by boundaries nearby, mitigates most of the phenomena encountered in spherical collapse, but introduces a new effect: jet formation, the self-piercing of a bubble with a high velocity liquid jet. Examples of this phenomenon are given from light induced bubbles. Two oscillating bubbles attract or repel each other, depending on their oscillations and their distance. Upon approaching, attraction may change to repulsion and vice versa. When being close, they also shoot self-piercing jets at each other. Systems of bubbles are treated as they appear after shock wave passage through a liquid and with their branched filaments that they attain in standing sound fields. The N-bubble problem is formulated in the spirit of the n-body problem of astrophysics, but with more complicated interaction forces. Simulations are compared with three-dimensional bubble dynamics obtained by stereoscopic high speed digital videography.

Physics of bubble oscillations

Sound and light emission by bubbles is studied experimentally. Single bubbles kept in a bubble trap and single lasergenerated bubbles are investigated using ultrafast and highspeed photography in c...

Bubble dynamics, shock waves and sonoluminescence

Experimental and theoretical bubble dynamics

Acoustic cavitation, bubble dynamics and sonoluminescence.

1. History of Optics.- 2. The Main Areas of Optics.- 3. Fundamentals of Wave Optics.- 4. Coherence.- 5. Multiple-Beam Interference.- 6. Speckles.- 7. Holography.- 8. Interferometry.- 9. Fourier Optics.- 10. The Laser.- 11. Ultrafast Optics.- 12. Nonlinear Optics.- 13. Fiber Optics.- A. The Fourier Transform.- A.1 One-Dimensional Fourier Transform.- A.2 Two-Dimensional Fourier Transform.- A.3 Convolution and Autocorrelation.- A.4 Properties of the Fourier Transform.- A.5 Selected Functions and Their Fourier Transforms.- Problems.- B. Solutions of Problems.- References.

Thomas Kurz

Papers

Physics of bubble oscillations

Bubble dynamics, shock waves and sonoluminescence

Experimental and theoretical bubble dynamics

Acoustic cavitation, bubble dynamics and sonoluminescence.

Coherent Optics: Fundamentals and Applications