305:, and are not sensitive to interfaces deeper in the probed medium. SHG measurements allow the incident laser beam to pass without interaction through higher level materials to the target interface where the second harmonic signal is generated. In cases where the transmitting materials do interact with the beam, these contributions to the second harmonic signal can be resolved in other experiments and subtracted out. The resulting measured second harmonic signal contains the second harmonic component from the buried interface alone. This type of measurement is useful for determining the surface structure of the interface. As an example, Cheikh-Rouhou et al. demonstrated this process to resolve interface structures of 5 layer systems.
334:. As CO coverage approached 1 monolayer, the SHG intensity leveled off. Larger molecules like dyes often can form multilayers on a surface, and this can be measured in situ using SHG. As the first monolayer forms, the intensity can often be seen to increase to a maximum until a uniform distribution of particles is obtained (Figure 3). As additional particles adsorb and the second monolayer begins to form, the SHG signal decreases until it reaches a minimum at the completion of the second monolayer. This alternating behavior can typically be seen for the growth of monolayers. As additional layers form, the SHG response of the substrate is screened by the adsorbate and eventually, the SHG signal levels off.
251:
electronic structures. There are two major changes that occur at the interface: 1) the interplanar distances of the top layers change and 2) the atoms redistribute themselves to a completely new packing structure. While symmetry is maintained in the surface planes, the break in symmetry out-of-plane modifies the second-order susceptibility tensor Ο, giving rise to optical second harmonic generation. Typical measurements of SHG from crystalline surfaces structures are performed by rotating the sample in an incident beam (Figure 1). The second harmonic signal will vary with the
40:
layer of a system, properties of the second harmonic signal then provide information about the surface atomic or molecular layers only. Surface SHG is possible even for materials which do not exhibit SHG in the bulk. Although in many situations the dominant second harmonic signal arises from the broken symmetry at the surface, the signal in fact always has contributions from both the surface and bulk. Thus, the most sensitive experiments typically involve modification of a surface and study of the subsequent modification of the harmonic generation properties.
243:
314:
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molecular orientation experiments. The beam is incident on the sample in a total internal reflection geometry which improves the second harmonic signal because as the wave propagates along the interface, additional second harmonic photons are generated, By rotating either the polarizer or the analyzer, the s- and p-
350:
As molecular layers adsorb to surfaces it is often useful to know the molecular orientation of the adsorbed molecules. Molecular orientation can be probed by observing the polarization of the second harmonic signal, generated from a polarized beam. Figure 4 shows a typical experimental geometry for
325:
Surface SHG is useful for monitoring the growth of monolayers on a surface. As particles adsorb, the SHG signal is altered. Two common applications in surface science are the adsorption of small gas molecules onto a surface and the adsorption of dissolved dye molecules in a liquid to a surface.
1660:
is the surface number density of the adsorbed molecules, ΞΈ and Ξ¨ are orientational angles relating the molecular coordinate system to the laboratory coordinate system, and <x> represents the average value of x. In many cases, only one or two of the molecular hyperpolarizability tensor are
39:
media. Surface second harmonic generation is a special case of SHG where the second beam is generated because of a break of symmetry caused by an interface. Since centrosymmetric symmetry in centrosymmetric media is only disrupted in the first (occasionally second and third) atomic or molecular
250:
It may seem paradoxical at first that surface SHG which relies on a break in symmetry is possible in crystals which have an inherent symmetric structure. At a crystalline interface half of the atomic forces experienced in the bulk crystal are not present which causes changes in the atomic and
216:
to hold under this final condition, both terms must be 0. The four independent terms are material dependent properties and can vary as the external conditions change. These four terms give rise to the second harmonic signal, and allow for calculation of material properties such as electronic
1669:
In addition to these applications, surface SHG is used to probe other effects. In surface spectroscopy, where either the fundamental or second harmonic are resonant with electronic transitions in the surface atoms, details can be determined about the electronic structure and band gaps. In
355:
signals are measured which allow for the calculation of the second-order susceptibility tensor Ο. Simpson's research group has studied this phenomenon in depth. The molecular orientation can differ from the laboratory axis in three directions, corresponding to three angles. Typically, SHG
108:Ο. While the Ο tensor contains 27 elements, many of these elements are reduced by symmetry arguments. The exact nature of these arguments depends on the application. When determining molecular orientation, it is assumed that Ο is rotationally invariant around the
235:
807:
The second-order susceptibility tensor, Ο, is the parameter which can be measured in second order experiments, but it does not explicitly provide insight to the molecular orientation of surface molecules. To determine molecular orientation, the second-order
60:, a centrosymmetric crystal which is only capable of SHG in the bulk in the presence of an applied electric field which would break the symmetry of the electronic structure, surprisingly also produced a second harmonic signal in the absence of an external
530:
524:
255:
angle of the sample due to the symmetry of the atomic and electronic structure (Figure 2). As a result, surface SHG theory is highly dependent on geometry of the superstructure. Since electron interactions are responsible for the SHG response, the
273:
in the 2Γ1 construction and 3 mirror planes in the 7Γ7 construction thereby providing new information to the bonding structure of the surface atoms. Since then, surface SHG has been used to probe many other metallic surfaces such as reconstructed
824:
where β terms denote the molecular coordinate system as opposed to the laboratory coordinate system. Ξ² can be related to Ο through orientational averages. As an example, in an isotropic distribution on the surface, Ο elements are given by.
260:
model is usually numerically solved using
Density Functional Theory to predict the SHG response of a given surface. SHG sensitivity to surface structure approach was effectively demonstrated by Heinz, Loy, and Thompson, working for
1674:
the second harmonic signal is magnified and surface features are imaged with a resolution on the order of a wavelength. Surface SHG can also be used to monitor chemical reactions at a surface with picosecond resolution.
217:
structure, atomic organization, and molecular orientation. Detailed analysis of the second harmonic generation from surfaces and interfaces, as well as the ability to detect monolayers and sub-monolayers, may be found in
269:(111) surface would alter its behavior as the temperature was raised and the superstructure changed from a 2Γ1 structure to the 7Γ7 structure. Noting the change in signal, they were able to verify the existence of one
92:. During the 70s and 80s, most of the research in this field focused on understanding the electronic response, particularly in metals. In 1981, Chen et al. showed that SHG could be used to detect individual
84:
et al. showed that the second harmonic signal was generated from the surface. Interest in this field waned during the 1970s and only a handful of research groups investigated surface SHG, most notably
1646:
1349:
164:. Second Harmonic Generation further restricts the independent terms by requiring the tensor is symmetric in the last two indices reducing the number of independent tensor terms to 4: Ο
2074:
Bourguignon, Bernard; Zheng, Wanquan; Carrez, Serge; Fournier, FrΓ©dΓ©ric; Gaillard, Michel L.; Dubost, Henri (2002). "On the anisotropy and CO coverage dependence of SHG from Pd(111)".
781:{\displaystyle \mathrm {I} _{p}^{2\omega }(\gamma )=C|s_{5}\chi _{zxx}+\cos ^{2}{\gamma }\ {(s_{2}\chi _{xxz}+s_{3}\chi _{zxx}+s_{4}\chi _{zzz}-s_{5}\chi {zxx})}|^{2}(I^{\omega })^{2}}
2217:
Simpson, Garth J.; Westerbuhr, Sarah G.; Rowlen, Kathy L. (2000). "Molecular
Orientation and Angular Distribution Probed by Angle-Resolved Absorbance and Second Harmonic Generation".
394:
2306:
Simpson, Garth J.; Rowlen, Kathy L. (2000). "Orientation-Insensitive
Methodology for Second Harmonic Generation. 2. Application to Adsorption Isotherm and Kinetics Measurements".
1052:
2012:
Heinz, T. F.; Loy, M. M. T.; Thompson, W. A. (1985-01-07). "Study of Si(111) Surfaces by
Optical Second-Harmonic Generation: Reconstruction and Surface Phase Transformation".
2182:
Kikteva, Tanya; Star, Dmitry; Leach, Gary W. (2000). "Optical Second
Harmonic Generation Study of Malachite Green Orientation and Order at the Fused-Silica/Air Interface".
56:. Prior to Terhune's discovery, it was believed that crystals could only exhibit second harmonic generation if the crystal was noncentrosymmetric. Terhune observed that
368:
distribution of the molecules, resulting in x- and y- coordinate terms to be interchangeable. When analyzing the second-order susceptibility tensor Ο, the quantities Ο
800:
terms depend on the experimental geometry are functions of the total internal reflection angles of the incident and second harmonic beams and the linear and nonlinear
1697:
Bloembergen, N.; Chang, R. K.; Jha, S. S.; Lee, C. H. (1968-10-15). "Optical Second-Harmonic
Generation in Reflection from Media with Inversion Symmetry".
2144:
Cheikh-Rouhou, W.; Sampaio, L.C.; Bartenlian, B.; Beauvillain, P.; Brun, A.; et al. (2002). "SHG anisotropy in Au/Co/Au/Cu/vicinal Si(111)".
289:
Perhaps one of the most powerful uses of surface SHG is the probing of surface structure of buried interfaces. Traditional surface tools such as
812:
tensor Ξ², must be calculated. For adsorbed molecules in a uniaxial distribution, the only independent hyperpolarizability tensor terms are Ξ²
356:
measurements of this type are only able to extract a single parameter, namely the molecular orientation with respect to the surface normal.
89:
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dominant. In these cases, the relationships between Ο and Ξ² can be simplified. Bernhard Dick presents several of these simplifications.
2402:
1828:
1917:
Guyot-Sionnest, P.; Chen, C. K., Shen, Y. R. General considerations on optical second-harmonic generation from surfaces and interfaces
1788:
1671:
96:, and since then, much research has gone into using and understanding SHG as surface probe of molecular adsorption and orientation.
2263:
Simpson, Garth J.; Rowlen, Kathy L. (2000). "Orientation-Insensitive
Methodology for Second Harmonic Generation. 1. Theory".
294:
112:-axis (normal to the surface). The number of tensor elements reduces from 27 to the following 7 independent quantities: Ο
1357:
1060:
2109:
Jakobsen, C.; Podenas, D.; Pedersen, K. (1994). "Optical second-harmonic generation from vicinal Al(100) crystals".
1969:
Weber, M.; Liebsch, A. (1987-05-15). "Density-functional approach to second-harmonic generation at metal surfaces".
20:
2397:
1934:
Lohner, F.P.; Villaeys, A.A. (1998). "Anisotropy analysis of the SHG intensity by surfaces of simple metals".
519:{\displaystyle \mathrm {I} _{s}^{2\omega }(\gamma )=C|s_{1}\sin {2\gamma }\ \chi _{xxz}|^{2}(I^{\omega })^{2}}
388:. The intensities of the s and p polarizations in the second harmonic are given by following relationships:
290:
218:
804:
respectively which relate the electric field components at the interface to incident and detected fields.
2351:"Irreducible tensor analysis of sum- and difference-frequency generation in partially oriented samples"
831:
352:
298:
81:
809:
104:
Just as bulk second harmonic generation, surface SHG arises out of the second-order susceptibility
48:
Second harmonic generation from a surface was first observed by
Terhune, Maker, and Savage at the
49:
1786:
Shen, Y. R. (1986). "Surface Second
Harmonic Generation: A New Technique for Surface Studies".
330:
is adsorbed onto a Pd(111) surface, the SHG signal decreased exponentially as predicted by the
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Terhune, R. W.; Maker, P. D.; Savage, C. M. (1962). "Optical
Harmonic Generation in Calcite".
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in 1962, one year after Franken et al. first discovered second harmonic generation in bulk
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Guyot-Sionnest, P.; Shen, Y.R.;"Bulk contribution in surface second-harmonic generation".
327:
36:
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1801:
61:
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where Ξ³ is the polarization angle with Ξ³ = 0 corresponding to p-polarized light. The
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64:. During the 1960s, SHG was observed for many other centrosymmetric media including
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Figure 2: Polar crystal surface SHG response (arbitrary units) (adapted from )
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When dealing with adsorbed molecules on a surface, it is typical to find a
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1865:"Detection of Molecular Monolayers by Optical Second-Harmonic Generation"
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is a method for probing interfaces in atomic and molecular systems. In
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Shen, Y R (1989). "Optical Second Harmonic Generation at Interfaces".
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23:(SHG), the light frequency is doubled, essentially converting two
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Chen, C. K.; Heinz, T. F.; Ricard, D.; Shen, Y. R. (1981-04-13).
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in 1985. They showed that the SHG signal from a freshly cleaved
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must be 0 and only three independent tensor terms remain: Ο
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Figure 4: Total internal reflection geometry of surface SHG
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2314:(15). American Chemical Society (ACS): 3407β3411.
2271:(15). American Chemical Society (ACS): 3399β3406.
2190:(13). American Chemical Society (ACS): 2860β2867.
1977:(14). American Physical Society (APS): 7411β7416.
1875:(15). American Physical Society (APS): 1010β1012.
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1343:
1046:
780:
518:
2225:(5). American Chemical Society (ACS): 887β898.
1705:(3). American Physical Society (APS): 813β822.
1641:{\displaystyle \chi _{XXZ}={\frac {1}{2}}N_{s}}
1344:{\displaystyle \chi _{ZXX}={\frac {1}{2}}N_{s}}
317:Figure 3: Surface SHG Adsorption Isotherm for
2056:Shinku/Journal of the Vacuum Society of Japan
2020:(1). American Physical Society (APS): 63β66.
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2146:Journal of Magnetism and Magnetic Materials
1906:Nonlinear Surface Electromagnetic Phenomena
1908:; North-Holland: New York, 1991; Chapter 5
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360:Calculation of molecular orientation
100:Excitation of second harmonic signal
90:University of California at Berkeley
2184:The Journal of Physical Chemistry B
1842:10.1146/annurev.pc.40.100189.001551
1829:Annual Review of Physical Chemistry
1802:10.1146/annurev.ms.16.080186.000441
238:Figure 1: Crystal surface SHG setup
1789:Annual Review of Materials Science
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536:
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326:Bourguignon et al. showed that as
17:Surface second harmonic generation
14:
1047:{\displaystyle \chi _{ZZZ}=N_{s}}
31:into a single photon of energy 2
27:of the original beam of energy
2054:Iwai, Tetsuya; Mizutani, Goro
1836:(1). Annual Reviews: 327β350.
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2158:10.1016/s0304-8853(01)00840-x
2152:(1β3). Elsevier BV: 532β535.
2088:10.1016/s0039-6028(02)02000-9
2082:(2β3). Elsevier BV: 567β574.
1948:10.1016/s0030-4018(98)00314-9
1921:, 33, 12, 1986 pp 8254β8263.
295:scanning tunneling microscopy
2370:10.1016/0301-0104(85)85085-0
2123:10.1016/0039-6028(94)90021-3
1796:(1). Annual Reviews: 69β86.
1735:, 38, 12, 1988 p 7985-7989.
2364:(2). Elsevier BV: 199β215.
1942:(4). Elsevier BV: 217β224.
1881:10.1103/physrevlett.46.1010
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2403:Second-harmonic generation
21:second harmonic generation
2117:(1β2). Elsevier BV: 1β7.
2026:10.1103/physrevlett.54.63
1762:10.1103/PhysRevLett.8.404
297:as well as many forms of
1983:10.1103/physrevb.35.7411
301:must be conducted under
2349:Dick, Bernhard (1985).
2014:Physical Review Letters
1869:Physical Review Letters
1750:Physical Review Letters
1711:10.1103/physrev.174.813
1665:Additional applications
309:Adsorption measurements
291:atomic force microscopy
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2219:Analytical Chemistry
1672:monolayer microscopy
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810:hyperpolarizability
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230:Interface structure
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208:). In order for Ο
50:Ford Motor Company
37:noncentrosymmetric
2320:10.1021/ac000347k
2277:10.1021/ac000346s
2231:10.1021/ac9912956
2196:10.1021/jp992728b
1971:Physical Review B
1919:Physical Review B
1733:Physical Review B
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321:6G (adapted from
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219:Guyot-Sionnest
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70:semiconductors
62:electric field
45:
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271:mirror plane
249:
225:Applications
109:
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86:Y. R. Shen's
80:. In 1968,
47:
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28:
16:
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282:(111), and
82:Bloembergen
2392:Categories
1679:References
94:monolayers
2378:0301-0104
2328:0003-2700
2285:0003-2700
2239:0003-2700
2204:1520-6106
2166:0304-8853
2131:0039-6028
2096:0039-6028
2034:0031-9007
1991:0163-1829
1956:0030-4018
1889:0031-9007
1850:0066-426X
1810:0084-6600
1770:0031-9007
1719:0031-899X
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366:uniaxial
278:(110),
54:crystals
1999:9941043
820:, and Ξ²
384:, and Ο
286:(100).
258:jellium
253:azimuth
221:et al.
78:liquids
58:calcite
44:History
25:photons
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106:tensor
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66:metals
2354:(PDF)
2374:ISSN
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293:and
276:gold
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204:, βΟ
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176:), Ο
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2366:doi
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2227:doi
2192:doi
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