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Gdansk Lecture: materials for optics. P. Audebert. Where we are :. ECOLE NORMALE SUPERIEURE DE CACHAN (Paris area) Main goal: Train future university and high school teachers. 1320 students “normaliens” 760 other students 300 foreign students (China, US, Canada, Poland, India) 260 PhD

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## P. Audebert

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**Gdansk Lecture: materials for optics**P. Audebert**ECOLE NORMALE SUPERIEURE DE CACHAN**(Paris area) Main goal: Train future university and high school teachers • 1320 students “normaliens” • 760 other students • 300 foreign students (China, US, • Canada, Poland, India) • 260 PhD • 345 professors and assistant professors • 70 Post-docs • 238 technical staff • 17 departments • 12 laboratories • 3 institutes • More than 100 international programs**Outline**• Introduction • Basics on light and matter • Fluorescent molecules and materials. • What is fluorescence-theory • Fluorescent molecules • Fluorescent materials • Plasmon resonnance and sensing • Applications • Molecules and materials for NLO • Second order • Third order • Non-linear absorption • Molecules and materials for NLO • Figures of merit and influence of size. • Conclusion**INTRODUCTION:**Recalling what light is.**Wavelengths of “Light”**nm: for near UV, visible, and near IR light mm: for IR and far IR light (sometimes wavenumbers preferred, n = 10000/l if n in cm-1 and l in mm) Å: for x-ray. But in this regime people usually use photon energy in eV. Typical range of IR spectra recording We have**Light Wave**• Plane electromagnetic wave • k: propagation constant or wave number • w: angular frequency • Phase of the wave (wt –kz+f0) • Wave front : A surface over which the phase of a wave is constant. • Optical field : refers to the electrical field Ex. Traveling wave along Z**Propagation of Light**Light is a kind of electro-magnetic wave. In the general case the field varies with all space ordinates (in addition to time) A: amplitude vector. f: phase.**Wave Vector and Wave number**Wave Vector, k: Use to indicate the direction of propagation. The vector whose direction is normal to the wavefront, and magnitude is k = 2p/l. For a plane wave, A is constant, and k The magnitude of k, k = 2p/l, is also called the wave number.**Phase velocity**• The relationship between time and space for a given phase, f, that corresponds to a maximum field, can be described by: • So, during a time interval dt, this constant phase (max. field) moves a distance dz. From the relation above it comes : • Therfore it defines the phase velocity of this wave as:**What happens to molecules upon photoexcitation?**Fluorescence deals with light reemission after absorption; It competes with plenty of other phenomena that can also occur after a photon absorption. Absorption is a linear process, which occurs when the incident photon energy matches a molecule/atom orbital gap + some additionnal conditions…**Optical absorption basics: What are the possible transitions**in a simple molecule? Not all transitions are allowed (there are symetry rules) and some of them, eg the np* are associated to a partial charge transfer (results in a increase of the transition dipole).**Singlet and triplet states**From Hund’s rule, the triplet state lies always below the singlet state. Conversion is sometimes possible, but not always.**Transmittance and absorbance; the Beer-Lambert law.**Experimentally, the eﬃciency of light absorption at a wavelength l by an absorbing medium is characterized by the absorbance A(l) or the transmittance T(l) , deﬁned as In a (very) large majority of case, the absorption of a solution is given by the Beer-Lambert law below. The unit of e is therefore L.mol-1.cm-1**Absorption coefficients and cross section**We can define the decadic absorption coefficient: And the Naperian absorption coefficient: Which allows to introduce in turn the molecular absorption cross-section:**Relation between s and e**This is exactly the Beer-Lambert law with e = (1/2.3)Nas**Examples of e values**The molar absorption coefficient is a very widespread value to estimate the absorption efficiency of a given compound. Here are reported the values for classical organic chemicals and dyes (at maximum).**Origin of emission from a molecule : The Perrin-Jablonski**diagram.**Emission (or non-emission) from a molecule : The time scale**for the processes.**Absorption and emission from a molecule : The fine**structure. Molecules can be in different vibrational states; the relative proportion of molecules in the different states is given by the Boltzmann law: N0/N1 = exp[-(E1-E0)/kT] This can induce a fine structure in the spectrum, if the vibrationnal levels have enough spacing. In the case of anthracene, the spacing is around 1400 cm-1, which comes to 2.8 10-20 J, and has the consiquence that virtually all molecules are in the ground state (N0/N1 = 0.001). In this case the spectrum has the shape represented on the left. In the general case, the levels are tighter spaced (quasi continuum) which leads to overlap between absorption and fluorescence spectrum)**Summary of all the possibilities for desactivation of a**molecule. Each process can be favoured according to the position of the different energy levels and the molecular structure (presence of heavy atoms favour intersystem crossing.**Fluorescence life-times**Once a molecule has been excited by absorption of a photon, to its excited state that we will call A*, it has therefore several paths of deactivation, fluorescence being one of them. This is quite well exemplified in the scheme below: We can call knr the constant summarizing all the non radiative processes, against kr which summarizes the radiative ones (mainly fluorescence). The disparition of A* follows a classical 1rst order kinetics, and its life-time can be measured.**Fluorescence intensity**The fluorescence intensity is directly linked to the amount of excited molecules still remaining inside the solution, and the radiative rate constant: Most of the time the decay is monoexponential, and parallels what is observed in radioactive decay, although with much faster decay rates!**Quantum yields**A very important property for a fluorescent molecule is the radiative quantum yield, that is, the proportion of reemitted light against the absorbed light. The fluorescence yield is therefore nothing else than the ratio of the radiative rate constant against the sum of the deexcitation constants. Or otherwise: It is also possible, on the same basis, to define the yield for the intersystem crossing (isc) and the phosphorescence, which are usually lower than for fluorescence.**Some values for classical fluorophores**Aromatic hydrocarbons are usually good fluorophores, here are some examples with life-times and quantum yields.**Emission spectra and Stokes shift**Since the quantum yield concerns all photons emitted from a molecule, it can also be described from the integral of the emission spectrum. The Stokes shift is a very important parameter, which describes the energy gap (often expressed in nm) between the absorption and the emission spectra.**Examples of Stokes shift**Examples of a large and small Stokes shift in two classical dyes, a benzoazinone and a rhodamine.**Heavy atom effect**The presence of heavy atoms in fluorescent molecules has huge effects on the intersystem crossing, and favors the phosphorescence at the expense of fluoresence, especially with bromine and iodine, as exemplified with the naphtalene derivatives below.**Fluorescence quenching**The excited state of a molecule can react with several type of substrates, exchanging energy, electrons or chemical species (mainly protons) leading to fluorescence quenching. The kinetic analysis is very similar to deactivation processes, except that it is now a bimolecular rate! (which can comes to a 1rst order kinetics in case of quencher excess)**Fluorescence quenching : Main paths**Summary of all possible deactivation paths:**Fluorescence quenching : Three main situations, relatively**to the process. • The excited state of a molecule can react immediately with quencher in large excess (interactions already exist between the quencher and the fluorophore): We have extinction of part of the fluorophores. Two life times can be distinguished according to the association of the quencher with the fluorophore or not. • 2) The quencher is not in larger excess, but the life-time of the fluorophore is short enough and long-range interactions (eg energy transfer) can occur. Again, part of the fluorophore that are in the vicinity of the quencher are extinct, while others are not. This case is kinetically analogous to 1) for part of the fluorophores, and again two life times can be distinguished according to the presence or not of the quencher in the vicinity of the fluorophore. In the two above cases, the response are concentration dependent. • These cases are called : Static quenching. • 3) The quencher is not in large excess, and transport can occur during the quenching process (long life-time and/or fast diffusion). Then the pseudo first order may not applies any longer. This case may be more complex. • This last case is called « dynamic quenching » and the apparent rate constant sometimes change with time.**Fluorescence quenching : Calculation of the two cases of**static quenching In the first case (sphere of effective quenching) the quenching efficiency is related to the number of quenchers, equal to Na Q Vq , where Q is the quencher concentration, Vq the sphere volume, and Na the Avogadro number. It can be shown that: In the second case (preequilibrium) there is an equilibrium M + Q = [MQ]. MQ does not fluoresce while the fluorescence of M is unaffected. Therefore: And, at steady state:**Dynamic fluorescence quenching : Stern-Volmer kinetics**This is what happens in cases 1) or 2) (for selected fluorophores), let be M the fluorophore, and Q the quencher, we have: It comes to: Since the fluorescence intensity is proportionnal to the M* concentration:**Fluorescence quenching : Stern-Volmer kinetics (2)**Since the fluorescence intensity decay is therefore a single exponential, whose characteristic time comes from the factor inside the exponential: And therefore we have the relation, known as the Stern-Vomer law: For quantum yields we have :**Fluorescence quenching : Stern-Volmer kinetics (3)**Under steady-state illumination, we have: Where I0 and I are the steady-state fluorescence intensities in the absence and presence of quencher respectively, and KSV = kq t0 Q, proportionnal to the quenching rate, is called the Stern-Volmer constant. The relation is called the Stern-Volmer relation.**Fluorescence quenching : Summary, including life-time**dependance. The table below shows the different I/Q and lg(I)/t curves that can be expected from the various mechanisms previously detailed.**Very classical fluorescent laser dyes (1)**Rhodamine Rhodamine 6G Coumarines (coumarine and umbelliferone) Tétracene Malachite green**Classical laser dyes (2)**Acridine orange Acridine yellow Pyrilium dye Cyanine Fluorol Phenoxazine dye Cresyl violet**Other fluorescent dyes**Flavanthrone quinophtalone isoindolinone isoindoline**Classical fluorescent dyes: Metal complexes and analogues.**Fluorophore Anchoring group BODIPY TR-X Magnesium tetraphenylporphyrin Iridium complex Zinc octaethylporphyrin Magnesium phtalocyanin**Fluorescein: pH sensing**2 excitation ex1 ex2, 1 emission em**Rhodamin synthesis and activation**Synthesis of the core Functionnalisation**Synthesis of indolium dyes (1)**Fischer indole synthesis**Synthesis of indolium dyes (2)**Near infrared dye

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