Andrew C. Millard

Optical second harmonic generation (SHG) is a second-order process that has found application in the imaging of intrinsic (typically non-resonant) SHG in a variety of biological tissues. With the application of resonance-enhanced SHG to study specific molecules in biological membranes, it is possible to image physiological indicator dyes bound to cellular membranes. We have extended this line of research in order to directly determine the sensitivity of SHG to the membrane potential of individual cells. We use styryl dyes that have been developed in our laboratory because these dyes readily insert into cell membranes and respond to changes in membrane potential by a fast, electrochromic mechanism. Furthermore, the same molecular features — particularly the donor-acceptor pair on a conjugated backbone — that enable electrochromism also permit significant SHG by these dyes.

We have imaged voltage-clamped neuroblastoma cells stained with such dyes over a range of excitation wavelengths. We find that we can readily detect significant changes in SHG with membrane potential, generally to greater sensitivity than that of the “one-photon” fluorescence techniques for which these dyes were designed. We have, for instance, found conditions that yield sensitivities of up to 43% per 100mV, four times better than fluorescence. We find that the sensitivity depends on the chemical structure of the dye molecule outside of the ANEP chromophore itself, but for each dye there is a wavelength dependence consistent with a “two-photon resonance” at approximately twice the wavelength of the one-photon absorption band. Our apparatus and method have now been optimised for the screening of new dyes and dye constructs, but our results to date already demonstrate that SHG provides a new technique for the optical determination of membrane potential that promises considerable improvements over existing fluorescence methods.

This talk was given on 9th October 2003 at the Annual Meeting of the Optical Society of America in Tucson, AZ. It will be given on 15th February 2004 at the Annual Meeting of the Biophysical Society in Baltimore, MD.

Second harmonic generation (SHG) is a non-linear optical process that takes place in ultrafast-laser microscopy, offering an alternative to two-photon fluorescence (2PF) for imaging in a modality we have called SHIM. While 2PF involves the excitation of a fluorophore by absorption of two photons, followed by relaxation and non-coherent emission, SHG is a non-absorptive process in which two photons are converted into a single photon of twice the energy, emitted coherently. SHG is confined to loci lacking a center of symmetry, a constraint that is readily satisfied by cellular membranes with only one leaflet stained by a dye. Furthermore, the molecular features employed in the design of our fluorescent, membrane-staining, electrochromic styryl dyes are precisely those that contribute to large non-linear optical responses. In this report, we extend our earlier observations that SHIM of these dyes is sensitive to membrane potential by imaging voltage-clamped neuroblastoma cells. Our experimental setup also allows for monitoring of 2PF, permitting us to directly compare the sensitivities of the two modalities. We find that SHG is modulated by membrane potential with greater sensitivity than that of fluorescence, and that the sensitivity is dependent on excitation wavelength.

This talk was given on 3rd March 2003 at Annual Meeting of the Biophysical Society in San Antonio, TX.

Second harmonic generation (SHG) microscopy is a useful new technique for biological imaging, with many advantages over existing one-photon fluorescence techniques. Many structural proteins show intrinsic SHG, complementing other methods of imaging. Using a microscope that allows simultaneous patch-clamping and non-linear imaging of cells, we find that SHG from membrane-bound dyes is a sensitive probe of trans-membrane potential.

This talk was given on 14th December 2002 at the Annual Meeting of the American Society for Cell Biology in San Francisco, CA.

Second harmonic generation (SHG) is a non-linear optical process which can take place in a microscope using ultrafast (near-infrared) laser light. While two-photon fluorescence involves the near-simultaneous absorption of two photons to excite a fluorophore, followed by relaxation and non-coherent emission, SHG is a nearly instantaneous process in which two photons are converted into a single photon of twice the energy, emitted coherently. Furthermore, SHG is confined to loci lacking a center of symmetry; this constraint is readily satisfied at cellular membranes in which one leaflet has been stained, making SHG microscopy suitable for the imaging of membranes. Since it is a non-linear process, SHG can be confined to the region of greatest power density at the focus of the microscope, resulting in intrinsic three-dimensional sectioning and greatly reducing out-of-plane photobleaching and phototoxicity. We report on our work to quantify SHG from cellular membranes that have been stained with voltage-sensing styryl dyes. With the goal of measuring membrane potential using SHG microscopy, we discuss in particular the necessary step of establishing the relationship between SHG signal and the concentration of dye in the membrane.

This talk was given on 26th February 2002 at the Annual Meeting of the Biophysical Society in San Francisco, CA.

Optical third harmonic generation (THG) is strongly localised to interfaces between materials with different susceptibilities. Third harmonics are produced by tightly focused femtosecond laser pulses if the susceptibility changes along the focal volume. Conversely, if the focus lies in region of uniform susceptibility, THG is inhibited. Since the susceptibility of many biomolecules changes according to their electrochemical state, THG provides a minimally invasive technique with which to probe molecular activity. Having imaged whole blood and finding substantial enhancement of THG by erythrocytes, we examined the relative THG in a model system using haemoglobin solutions at physiological concentrations of ~2mM, excited using 100fs pulses with wavelengths ranging from 900 to 1005nm. We found that THG in haemoglobin is approximately 4% that in equimolar fluorescein. Preliminary data show that there are significant differences between THG in deoxy- versus oxyhæmoglobin.

Optical sectioning studies of blood flow in capillaries in the brain involve the injection of fluorescein into the blood stream so that erythrocytes are seen as dark objects on a bright background of blood plasma under two-photon imaging. Since erythrocytes enhance THG, however, they may be imaged directly using this technique, without the need for exogenous markers. Furthermore, THG measurements may yield information about the oxygen content of erythrocytes, and thus serve as a novel tool for studies of hæmodynamics.

This talk was given on 23rd January 2001 at SPIE’s Photonics West in San José, CA. Further developments were presented on 26th February 2002 at the Annual Meeting of the Biophysical Society in “Evidence for Resonances in the Third Harmonic Spectra of Hæmoglobin as a Function of Ligand Binding State” by Omar G. R. Clay.

Support for the work presented in this talk was provided by La Jolla Interfaces in Science and the Burroughs Wellcome Fund.

Recently Barad et al. * have shown that the third harmonic generation (THG) of light at the interface of a transparent sample can be used to map the surface of optical glass fibers in index matching fluid. In this talk we extend the demonstrated principle of the technique and show the potential of three dimensional THG imaging of live biological specimens. THG imaging is significant for a variety of reasons.

1. It is a background free imaging technique requiring no additional staining.
2. It is generally non-fading in nature.
3. It can be used with specimens having only low (phase) contrast.

Due to the localisation of the THG at interfaces where there is a change in refractive index or non-linear susceptibility, the technique as applied to microscopy inherently produces optically sectioned images. This allows three dimensional reconstruction as in traditional confocal microscopy. The following figure is a three dimensional image of spiral algae reconstructed from THG image sections.

In this talk, we report on the first (to our knowledge) demonstration of the dynamical imaging of live specimens, under both moderate and high numerical aperture (0.6 and 1.3 respectively). While significant work remains to fully develop THG microscopy as applied to biological systems, this first demonstration is critical in that it begins to help establish the relevance of the technique to living specimens.

The slides for this talk (PDF, 991k) are available. The talk was given on

• 25th May 1999 at OSA’s CLEO/QELS ’99 in Baltimore, MD.
• 15th October 1999 to the Warren Group of the Department of Chemistry at Princeton University.
• 19th October 1999 to the Instrumentation Division of Brookhaven National Laboratory.
• 14th February 2000 at the Annual Meeting of the Biophysical Society in New Orleans, LA.
• 2nd October 2000 to the Center for Biomedical Imaging Technology at the University of Connecticut Health Center.

Support for some of the work presented in this talk was provided by La Jolla Interfaces in Science and the Burroughs Wellcome Fund.

* See Y. Barad, H. Eisenberg, M. Horowitz and Y. Silberberg, “Non-linear Scanning Laser Microscopy by Third Harmonic Generation” Appl. Phys. Lett. 70 922 (1997) as well as J. A. Squier, M. Müller, G. J. Brakenhoff and K. R. Wilson, “Third Harmonic Generation Microscopy” Opt. Expr. 3 315 (1998). A more recent paper is also available.

Third harmonic light is produced by a laser beam that is tightly focused at an interface. It has been recently demonstrate that it is possible to image both biological and non-biological specimens in optical sections using this light.

Third Harmonic Generation (THG) takes place under a very restrictive condition: the axial focal symmetry must be broken by a change in material properties. The localised production of third harmonic light at such boundaries provides inherent optical sectioning; thus it is possible to produce three dimensional reconstructions of microscopic systems by imaging THG from different planes perpendicular to the axis of beam propagation. Notably, in contrast to most applications of more traditional single or multi-photon laser fluorescence microscopy, no exogenous fluorophore is used to label the specimen: certain naturally occurring material property boundaries automatically serve as the “label”.

As well as traditional laser systems, we report here on the use of a compact, diode-pumped, femtosecond fiber laser for THG microscopy. We discuss the technical issues involved in using the fiber laser for THG microscopy, and demonstrate a new imaging technique that using THG as a local light source.

This talk was given

• on 3rd April 1999 at the 1999 LJIS Symposium at the University of California, San Diego.
• on 6th September 1999 at EPS-11: Trends in Physics in London, UK. (The accompanying poster (PDF, 964k) is available.)

Support for some of the work presented in this talk was provided by La Jolla Interfaces in Science and the Burroughs Wellcome Fund.

As ultrafast multiphoton microscopes become more useful for biological imaging, a major challenge for researchers is to determine the exposure conditions that provide the best combination of image resolution, contrast and specimen viability. To do this requires an accurate understanding of the spatial and temporal evolution of ultrashort pulses at the focus produced by a microscope objective. The objective itself, however, can significantly alter the pulses. Some effects, such as the broadening of pulses due to group delay dispersion in materials along the path, are understood and partial compensation for them can be made. Other effects, such as radial variations in the propagation time and variations in the pulse width, are less well understood. In this work, we investigate the radially dependent propagation and focusing of ultrashort pulses through a Zeiss CP-Achromat 100x, 1.25 NA, infinity-corrected, oil immersion microscope objective. We also extend to this high numerical aperture case the technique of collinear type II second harmonic generation frequency-resolved optical gating which has previously been used to measure the temporal intensity and phase of ultrashort pulses at the focus of air objectives with lower numerical aperture.

The proceedings manuscript for this talk is available. The talk was given on 29th January 1999 at SPIE’s Photonics West in San José, CA.

After a brief mathematical introduction to this material, I shall demonstrate how this extension of vector calculus may be applied with considerably utility to classical physics, including special relativity and electromagnetism. I shall then revisit the mathematics to ascertain how spinors fit within this framework, and discuss the matrix representations for general dimensionalities. Returning to physics, I shall show that the appearance of the Pauli sigma matrices when considering non-relativistic three-space is as expected. However, it will be seen that usual forms of the Dirac gamma matrices are at odds with the expected dimensionality of space-time. Furthermore, I shall rederive the Dirac equation using Ryder’s argument * and, with the requirement that phases be complex, arrive instead at an extended Dirac equation; this describes both a lepton and a lepton-neutrino and incorporates electroweak transformations via a Kaluza–Klein-like scheme.

This talk was given on 31st March 1998 at the Institute for Advanced Study.

* See chapter two of Quantum Field Theory (Cambridge University Press, 1996) by L. H. Ryder for his derivation of the Dirac equation from Pauli spinors and Lorentz transformations.

Non-commutativity appears in physics almost hand-in-hand with quantum mechanics. Non-commuting operators corresponding to observables lead to Heisenberg’s Uncertainty Principle, which is often used as a prime example of how quantum mechanics transcends “common sense”, while the operators that generate a symmetry group are usually given in terms of their commutation relations. This talk discusses the motivation for taking physics beyond the usual stopping point of non-commuting quantities as matrices with complex elements, and investigates the possible impact and experimental consequences of such a course of action. To illustrate the discussion, the talk uses a number of recent developments to highlight such points as the possibilities for using more general algebras than the complex numbers, taking some examples from the successful generalisation to quaternionic quantum mechanics, and the potential of Adler’s trace dynamics * as a tool for dealing with non-commuting quantities in applying the Principle of Least Action.

It is intended that this talk will concentrate more on the motivation and experimental aspects of the material, rather than on the mathematics and theory — on the “why” rather than the “how”.

The text of this talk is available. This talk was given on

• 22nd April 1997 in the Department of Physics at Princeton University.
• 5th June 1997 at Schlumberger–Doll Research in Ridgefield CT.
• 20th February 1998 to the Wilson Group of the Department of Chemistry and Biochemistry at the University of California, San Diego.

* For a review of the foundations of trace dynamics (also known as generalised quantum dynamics), see Quaternionic Quantum Mechanics and Quantum Fields by S. L. Adler. A more recent result is also available.