Second harmonic generation microscopy with tightly focused linearly and radially polarized beams

SECOND HARMONIC GENERATION MICROSCOPY WITH TIGHTLY FOCUSED LINEARLY AND RADIALLY POLARIZED BEAMS Yew Yan Seng Elijah A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY GRADUATE PROGRAMME IN BIOENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2008 Contents Introduction 1.1 Motivation . . . . . . . . . . . . . . . . . . 1.2 Overview . . . . . . . . . . . . . . . . . . . 1.3 Nonlinear interaction of light with matter 1.4 The nonlinear susceptibility tensor . . . . 1.5 Factors affecting SHG efficiency . . . . . . 1.6 Focusing with high NA objectives . . . . . 1.6.1 Linearly polarized beams . . . . . . 1.6.2 Radially polarized beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 12 13 15 Literature review 2.1 SHG . . . . . . . . . . . . . . . . . . . . . . 2.1.1 SHG from biological materials . . . . 2.1.2 Collagen and myosin . . . . . . . . . 2.1.3 Nonlinear microscopy . . . . . . . . . 2.2 Polarization and focusing of light . . . . . . 2.2.1 Radial polarization . . . . . . . . . . 2.2.2 Linearly to radially polarized beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 19 20 22 27 30 31 33 . . . . . . . 38 38 41 46 49 50 54 54 Theory of SHG with tight focusing 3.1 Tensorial nature of SHG . . . . . . . . . . . . 3.1.1 Effects of focusing on SHG . . . . . . . 3.2 SHG far-field radiation . . . . . . . . . . . . . 3.3 Induced SHG polarization with tight focusing 3.3.1 Induced SHG polarization . . . . . . . 3.4 Far field radiation of SHG . . . . . . . . . . . 3.4.1 Linear objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Materials and methods 64 4.1 Preparation of samples . . . . . . . . . . . . . . . . . . . . . . 64 4.2 SHG and TPF microscopy . . . . . . . . . . . . . . . . . . . . 65 i 4.3 4.4 4.5 4.6 Back aperture of objective . . . . . . Filters and imaging . . . . . . . . . . Generation of radial polarization . . Pupil functions for radial polarization . . . . . . . . . . . . . . . . . . . . . . . . Results and discussion 5.1 SHG and TPF microscopy of skin . . . . . . . . 5.2 SHG with radially and linearly polarized beams 5.3 Longitudinally sectioned collagen . . . . . . . . 5.3.1 Low NA focusing . . . . . . . . . . . . . 5.3.2 High NA focusing . . . . . . . . . . . . . 5.3.3 Resolution of SHG . . . . . . . . . . . . 5.4 Transversely sectioned collagen . . . . . . . . . 5.4.1 Low and high NA focusing . . . . . . . . 5.4.2 High NA with radially polarized beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 71 73 82 . . . . . . . . . 91 91 95 97 97 101 104 108 108 110 Recommendations 121 Conclusion 124 List of publications 127 References 130 Appendix: Accepted publications 143 ii List of Figures 1.1 1.2 1.3 1.4 1.5 Two-photon excitation and SHG . . . . . . . . . . Phase matching factor against confocal parameter Vectorial effects of tight focusing . . . . . . . . . Electric field of a tightly focused linearly polarized Linearly and radially polarized beams . . . . . . . . . . . . 12 14 16 17 2.1 2.2 Illustration of a sarcomere . . . . . . . . . . . . . . . . . . . . Cross-section of a sarcomere . . . . . . . . . . . . . . . . . . . 25 26 3.1 3.2 3.3 43 49 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 Schematic of the illumination scheme . . . . . . . . . Dipole array of SHG scatterers . . . . . . . . . . . . . Induced SHG polarization from collagen for a tightly linearly polarized beam . . . . . . . . . . . . . . . . Induced SHG polarization from collagen for a tightly radially polarized beam . . . . . . . . . . . . . . . . Induced SHG polarization from myosin for a tightly linearly polarized beam . . . . . . . . . . . . . . . . Induced SHG polarization from myosin for a tightly radially polarized beam . . . . . . . . . . . . . . . . Far-field radiation of SHG (A) . . . . . . . . . . . . . Far-field radiation of SHG (A) . . . . . . . . . . . . . Far-field radiation of SHG (B) . . . . . . . . . . . . . Far-field radiation of SHG (B) . . . . . . . . . . . . . Far-field radiation of SHG (A) . . . . . . . . . . . . . Far-field radiation of SHG (A) . . . . . . . . . . . . . Far-field radiation of SHG (B) . . . . . . . . . . . . . Far-field radiation of SHG (B) . . . . . . . . . . . . . 4.1 4.2 4.3 4.4 General layout of a SHG microscope . . . . . . . . . . . . Beam path through the scan unit and microscope . . . . . Schematic setup of spatial light modulator mode converter Phase patterns for radial polarization . . . . . . . . . . . . 3.4 3.5 3.6 iii . . . . . . . . . . . . beam . . . . . . . . . . . . . . . . . . . . . . . . focused . . . . . focused . . . . . focused . . . . . focused . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 53 55 56 58 58 59 60 61 61 62 63 66 69 74 77 4.5 4.6 4.7 4.8 4.9 4.10 spatial light modulator generated radial polarization . Profile of the radially polarized beam . . . . . . . . . Bessel-Gauss and Gaussian beam pupil functions . . . Ratio of |Ez2 |/|Ex2 | for different pupil functions . . . . Intensity profiles . . . . . . . . . . . . . . . . . . . . The variation of |Ez2 |/|Ex2| with increasing annulus . . . . . . . . 79 81 84 86 88 89 SHG and autofluorescence TPF images of skin . . . . . . . . . SHG and autofluorescence TPF images of normal skin . . . . . SHG and autofluorescence TPF images of normal skin . . . . . SHG image of collagen with low NA objective (I) . . . . . . . SHG image of collagen with low NA objective (II) . . . . . . . SHG image of collagen with high NA objective . . . . . . . . . Polarization analyzed images of SHG images of collagen . . . . Resolution obtained with a 60x NA 1.4 oil immersion objective SHG images with low and high NA objective . . . . . . . . . . Hollow-tubed structure of collagen fibres . . . . . . . . . . . . SHG imaging with azimuthal, radial polarized beams on transversely sectioned tendon . . . . . . . . . . . . . . . . . . . . . 5.12 High NA SHG images with radially polarized light . . . . . . . 5.13 Polarization analysis of SHG signals . . . . . . . . . . . . . . . 5.14 SHG images with an analyzer . . . . . . . . . . . . . . . . . . 93 94 96 98 100 102 105 107 111 112 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 iv . . . . . . . . . . . . . . . . . . . . . . . . 113 115 117 119 List of Tables 4.1 Back focal plane diameters . . . . . . . . . . . . . . . . . . . . 5.1 Theoretical and experimental FWHM from SHG . . . . . . . . 108 v 71 List of Abbreviations The following is a list of abbreviations used in this thesis. SHG NA NIR TPF PAL-SLM LC-SLM SLM = = = = = = = Second-harmonic generation Numerical aperture Near infra-red Two-photon fluorescence Parallel-aligned spatial light modulator Liquid-crystal spatial light modulator Spatial light modulator vi Acknowledgements This thesis is the result of a long journey first undertaken in 2002. Many problems have I met and yet many more people who were kind and helpful. I would like to thank: Prof. Sheppard for his kind guidance and his incredible patience. He has been a veritable store of information and always ready to explain concepts, even basic ones with care and detail. I also appreciate and value the impromptu discussions we have had even when he had a full schedule. Prof. Malini for her guidance and support as my co-supervisor on this project. She has made her time and resources available to me and I am grateful for that. Prof. Raghunath for his support and guidance. He has allowed me easy access to materials and resources that I would otherwise have had to travel far and wide to obtain. My parents as they have encouraged me in every way, always ready to sacrifice that one bit more for me to pursue my dream. My heartfelt thanks to them for having given me the grounding and the foundations of loving books. My wife, Karen, for her steadfast belief in me all these years. You have been supportive of me all this while, never rushing me nor pushing me though you could have had so much more (and those yellow fluff balls that insist on inhabiting my bed). Last but not least, I also thank God for His unfailing love for me. Where I have fallen and despaired, He has always provided a way for me. I feel glad now that this journey has come to a close. But like the traveller in Frost’s poem I may not tarry long for: “The woods are lonely, dark and deep,/ But I have promises to keep,/ And miles to go before I sleep,/ And miles to go before I sleep.” vii Abstract The polarization dependence of second-harmonic generation (SHG) as a result of focusing linearly and radially polarized beams with objectives of high and low numerical apertures (NA) has been investigated. It was found that the axial and transverse components of the electric field present in a tightly focused beam interact through the nonlinear susceptibility tensor resulting in SHG signals that have different polarizations. In particular SHG from rat-tail tendons sectioned transverse to the long axis of the tendon was imaged with tightly focused linearly and radially polarized beams. It was found that an x or y polarized beam generated SHG signals that had a cos2 or sin2 dependency on the orientation of the analyzer. It was also found that a tightly focused radially polarized fundamental beam generated radially polarized SHG that was not dependent on the orientation of the analyzer. A scalar approximation that assumed a homogeneous electric field at the focus did not explain the observed SHG polarization qualitatively. Rather the vectorial nature of the electric field at the focus had to be assumed so as to explain the experimental observations qualitatively. It was also observed that a higher NA objective gives better resolution in general and that the resolution was better for a linearly polarized beam compared to a radially polarized beam. Resolution was also dependent on the pupil function. For a tightly focused linearly and radially polarized beam with a Gaussian and Bessel-Gauss pupil function respectively, the resolution (the FWHM) of the SHG image was found to be 220 nm and 350 nm respectively and matches the calculated value of 270 nm and 370 nm. The ability of tightly focused light of different polarizations to excite the different tensor components as well as the dependency of the SHG polarization on the tensor indicates that it is possible to identify different types of collagen through SHG imaging. The use of radially and linearly polarized beams therefore provides a novel way of exciting SHG efficiently when it is not possible to orient the sample to the position for effective SHG. This is a likely situation in a clinical setting manipulating the polarization of the beam rather than the patient is easier. This will have implications in the use of SHG and nonlinear optical methods in clinical diagnostics since the polarization state of SHG is dependent upon the χ(2) tensor, minor changes in the tensor can be analyzed and detected thereby extending the use and functionality of SHG. Chapter Introduction 1.1 Motivation As medicine and health services improve so the general health and life span improve for the general population. At the same time the increased lifespan and growing population lead to a burdening of the health system. At some point preventive medicine becomes important as well as continual management of individuals who are or have suffered an illness. New techniques and technology then become important to serve this growing sector. While there are many diseases worthy of attention two diseases- hepatitis infection and myocardial infarction- in the Asia region stand out. The first because hepatitis is endemic to Asia and many are infected with the hepatitis B virus (HBV). Infection with the hepatitis virus can lead to a hardening (cirrhosis) of the liver where it eventually loses its function. 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Express, 14:1167–1174, 2006 (doi:10.1364/OE.14.001167) NeuroImage, 29:38–45, 2005 (doi:10.1016/j.neuroimage.2005.07.019) [...]... like spokes in a bicycle wheel as shown in figure 1.5 Figure 1.5: (a) Shows a linearly polarized beam, (b) shows the radially polarized beam, and (c) shows an azimuthally polarized beam The focused radially polarized beam has a strong axial component when tightly focused as seen in figure 1.3 (d) The electric fields in the radial and 17 axial directions are given by equation (1.15) [22]: α cos1/2 θ sin θ... infarct or progression of cirrhosis in the liver 1.2 Overview This thesis investigates the effects of focusing linearly and radially polarized beams with high numerical aperture (NA) objectives on second- harmonic generation (SHG) Among the nonlinear optical methods utilized in microscopy, SHG and two-photon fluorescence are among the most advantageous This 3 is because these methods offer the advantage... Ω, then for linearly polarized illumination (x polarized) and an axially symmetric aplanatic system, the electric field in the x , y and z directions are thus given in equation (1.13): Ex (u, v) = −i(I0 + I2 cos 2φ), (1.13a) Ey (u, v) = −iI2 sin 2φ, (1.13b) Ez (u, v) = −2I1 cos φ, (1.13c) 13 Figure 1.3: Effects of focusing in the paraxial limit on (a) linearly, and (b) radially polarized beams The low... serve to hold the thick and thin filaments in position or to regulate the contractile motion of the muscle The sarcomere therefore has a characteristic ‘banded’ pattern that is visible in polarized light microscopy as a result of the mixture of thick and thin filaments as shown in 2.1 The banding that occurs in a sarcomere can be categorized in dark (A-bands) and light (I-bands) The A-band itself is subdivided... sarcomere and consists of proteins that stabilize and join thick filaments together; the H-zone, which consists only of thick filaments and the zone of overlap, which contains both thick and thin filaments The I-band contains only thin filaments and no thick filaments, and overlaps with the adjacent sarcomere 24 as shown in figure 2.1 Thin filaments are 5-6 nm in diameter and about 1 micron in length, and are... of the electric field other than the dominant one as they are able to interact through the second- order nonlinear susceptibility tensor (χ(2) ) We investigate this through the use of tightly focused linearly and radially polarized beams on a common biological sample, collagen 1.3 Nonlinear interaction of light with matter Shine red light through a piece of glass or, if you have it, quartz or some exotic... as the polarization before the lens Effects of high NA focusing for (c) linearly, and (d) radially polarized beams For a high numerical aperture lens, the rays (especially the outer rays) bend over a large angle resulting in significant axial and transverse components (blue arrows) Away from the axis of propagation, the linearly polarized beam has an axial component that is π out of phase on either side... Radially polarized beams The presence of a significant electric field component in the axial direction can be utilized as a means of observing molecular orientation both in fluorescence as well as in SHG [16–21] The vectorial nature of high NA focusing as seen in figure 1.4 indicates 15 Figure 1.4: The electric field (normalized) at the focal plane for a focused x polarized ( (a) to (c) ) and radially polarized. .. lasers has made multi-photon and harmonic generation microscopy accessible for imaging applications With the invention of the laser other nonlinear optical phenomenon were quickly verified It was not possible to explain all the phenomena through equation (1.1) and it was observed that higher order terms had to be added to equation (1.1) that would describe the second, third and higher order 6 Figure 1.1:... quartz crystal and recorded the first SHG signal Early theoretical treatments dealt mainly with the interaction in large crystals or interfaces [11, 25, 26] These early experiments utilized CW lasers together with long crystals [9, 12, 27–30] Often these early experiments were limited to low efficiency in the second- harmonic as a result of dispersion within the crystals so that the second- harmonic ‘walked . SECOND HARMONIC GENERATION MICROSCOPY WITH TIGHTLY FOCUSED LINEARLY AND RADIALLY POLARIZED BEAMS Yew Yan Seng Elijah. focusing linearly and radially polarized beams with high numerical aperture (NA) objectives on second- harmonic gen- eration (SHG). Among the nonlinear optical methods utilized in microscopy, SHG and. transverse to the long axis of the tendon was imaged with tightly focused linearly and radially polarized beams. It was found tha t an x or y polarized beam generated SHG signals that had a cos 2 or