Draft:Fluorescence upconversion

• Comment: needs many references Ozzie10aaaa (talk) 14:12, 17 June 2025 (UTC)

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Fluorescence upconversion (FU) is an ultrafast laser spectroscopic technique. It is a variant of sum-frequency generation (of which the Second-harmonic generation (SHG) is a special case) but applied to the detection of the incoherent fluorescence. It is therefore closely related to the Optical Kerr Gating (OKG) technique. There is, however, some confusion about the term "fluorescence upconversion". Historically, it relates to a non-linear optical technique, which is used to detect transient fluorescence with a very high time-resolution. More recently, the term has been used to describe the sequential absorption of two (or more) photons in a material leading to the emission of light at a shorter wavelength than the excitation wavelength (Photon upconversion). Although related, the two applications should not be confused. Here only the first one will be discussed.

Description

Fluorescence upconversion (FU) is a time-resolved spectroscopic technique which relies on the use of ultrashort laser pulses, typically a hundred femtoseconds or less. It is a pump-probe technique with the two pulses separated in time by a controllable time-delay. The most striking characteristic of FU is that the time resolution is only limited by the laser pulse duration, which today easily is < 100 femtoseconds. Two early technical reviews, written by Jagdeep Shah and Paul Barbara respectively, describe the FU technique in detail Some more recent reviews also describe the technique.

Simplified scheme of a fluorescence upconversion setup

Briefly, a fairly strong pump pulse excites the sample, generating the fluorescence (at a frequency ν_F) which is collected and focused in a nonlinear optical crystal. In parallel, an intense probe pulse (also called gate pulse, at a frequency ν_G) is focused and superposed with the fluorescence in the crystal. The instantaneous interaction of the fluorescence and the probe pulse in the crystal allows the generation of sum-frequency light at a frequency ν_S = ν_G + ν_F (where ν is the frequency). It is important that the fluorescence and the probe pulses arrive simultaneously (or nearly) in the crystal - to this purpose the probe pulse is directed through a controllable optical delay stage.

Simply speaking, the probe (gate) pulse represents a "time window" during which the fluorescence is detected. An important advantage of this technique is that the intensity of the detected signal (the sum frequency light) is directly proportional to the intensity of the fluorescence. Since the sum frequency light appears at shorter wavelengths than the fluorescence, a monochromator or an optical filter can be used to suppress both fluorescence and diffused laser light, allowing for a high signal-to-noise ratio when detected, for example, by a photo-multiplier.

Technical considerations

The laser and the pump and probe pulses

Today, the most common femtosecond laser by far is the Ti:S laser which comes either as a single oscillator or as an amplified system. In both cases , the laser provides < 100 femtosecond pulses with high stability and high average powers (several Watts). While the former work at high repetition rates (80-100 MHz) and are broadly tunable (700-1000 nm), the latter run at a few kHz and are in most cases set at a given wavelength (around 800 nm). The pulse energies are also very different; a few tens of nJ for an oscillator while an amplified system can provide pulses of several mJ.

The fundamental wavelength around 800 nm, which may not be ideal for excitation but frequency doubling into the near UV (around 400 nm) may be more adapted for many samples. Due to the very high stability of Ti:S lasers, efficient frequency tripling is also possible, opening up the possibility to excite around 267 nm, a wavelength very well suited for biological systems.

Recently, there has been a rapid development of Ytterbium fiber lasers, providing infrared pulses of a few 100 femtoseconds at repetition rates of a few 100 kHz. Amplification produces very high average powers of several tens of Watts. The wavelength is 1.06 micrometers, but frequency-doubling or -tripling generates visible of near-UV pulses suitable for excitation.

The optical delay

A variable optical delay is used to vary the path length of the probe pulse. Such an optical delay stage uses a retroreflector (two mirrors or a cube-corner) mounted on a mechanical translation stage aligned along the optical axis of the probe pulse. Moving the translation stage with the retroreflector corresponds to an adjustment of the path length and consequently the time at which the gate pulse arrive in the crystal relative to the fluorescence.

An optical delay line consists of a retroreflector on a translation stage. The axis of motion of the translation stage must be aligned with the optical axis (in this case a laser beam).

Since the speed of light c is constant, it is very easy to calculate the change in delay time Δt caused by a change in position Δx of the mechanical stage:

Δt = 2*Δx / c

The factor of two comes from the back and forth passage through the delay stage of the gate pulse.

Polarizations

The relative polarizations of the three light-waves (the laser gate pulse, the fluorescence and the sumfrequency light) involved in the fluorescence upconversion process play an important role. Laser light in itself is polarized and the phase-matching condition (see below) of the nonlinear crystal constitute a polarisation-selection. Note that the fluorescence from a disordered sample, such as molecules in a solution, is unpolarized.

Without going into details, for a given geometry and orientation of the crystal, only certain polarisations of the gate pulse and the fluorescence will interact. The crystal acts as a polarizer, selecting the component of the fluorescence that will interact with the gate pulse.

This opens up the possibility to make polarisation-dependent measurements by simply changing the polarization of the excitation pulse with regards to the polarization detected by the crystal.

By recording both parallell and perpendicular signals, one can calculate the time-evolution of the Fluorescence anisotropy.

The nonlinear optical crystal

In the past, different nonlinear crystals have been used, such as KDP, LiIO₃ and urea. Today, the by far most widely used crystal is BBO, a uniaxial crystal. This means that for light polarized along the x- and y-axes the propagation is governed by the ordinary refraction index ${n_{o}}$ while for light polarized along the z axis the propagation is governed by the extraordinary refraction index ${n_{e}}$. Moreover, BBO is a negative uniaxial crystal in the sense that ${n_{e}}$ < ${n_{o}}$.

Only the case of a BBO-like crystals, that is, negative uniaxial crystals will be considered in the following.

The detection

The upconverted light is normally situated in the near-UV spectral region, which makes it possible to isolate it from both the IR probe pulse and the fluorescence by using a combination of optical filters and a monochromator. The filtered upconversion light is then easily detected by a UV-sensitive photo-multiplier (pm).

Here one should distinguish between a setup using a laser oscillator or a an amplified laser system. As mentioned above, the former runs at a high repetition rate, providing a low pulse energy while the latter runs at a low repetition rate and provides a much higher pulse energy. For these reasons, it is favorable to use the single photon counting technique with an oscillator while a direct analog integrating technique is prefereable when using an amplified system. More preciesely, in the former case, the weak signal from the pm is measured with a photon-counter, the output of which is directly recorded by computer. In the latter case, the analog signal from the pm can be measured with lock-in techniques combined with boxcar integration. Storage oscilloscopes have also been used.

Conditions

The fluorescence upconversion process is active under the conditions that:

• The probe pulse and the fluorescence are temporally overlapping in the crystal.
• The probe pulse and the fluorescence are spatially overlapping, i.e. they are superposed in the crystal.
• phase-matching conditions are respected (${\bar {k}}$_S = ${\bar {k}}$_G + ${\bar {k}}$_F where ${\bar {k}}_{i}$ are the wave vectors for the sumfrequency light, the gate pulse and the fluorescence respectively).

The technique relies thus on two fundamental physical principles:

• the conservation of energy : hν_S = hν_G + hν_F
• the conservation of momentum : ${\bar {k}}$_S = ${\bar {k}}$_G + ${\bar {k}}$_F

The conservation of the momentum can also be written:

${n_{S} \over \lambda _{S}}{\hat {e}}$_S = ${n_{G} \over \lambda _{G}}{\hat {e}}$_G + ${n_{F} \over \lambda _{F}}{\hat {e}}$_F

where $\lambda _{S}$ is the wavelength of the sumfrequency light, $\lambda _{G}$ the wavelength of the gate pulse and $\lambda _{F}$ the wavelength of the fluorescence. ${\hat {e}}$_i (i= S,G,F) are the unit vectors. Note that this is a vector relation and the relative orientations of the three vectors in order to satisfy it depend on the properties of the nonlinear optical crystal. In the colinear case this vector expression reduces to a scalar condition

${n_{S} \over \lambda _{S}}$ = ${n_{G} \over \lambda _{G}}$+${n_{F} \over \lambda _{F}}$

Quantum efficiency

The quantum efficiency ${\eta _{q}}$ of the fluorescence upconversion process is the ratio of generated sum-frequency photons ${N_{S}}$ over the total number of incoming fluorescence photons ${N_{F}}$. Under the condition that only a minor part of the incoming fluoresence is upconverted the quantum efficiency for a uniaxial Type I crystal is given by

${\eta _{q}}$ = ${N_{S} \over N_{F}}$ = ${2{\pi }^{2}d_{eff}^{2}L^{2}(P_{G}/A) \over c{\epsilon }_{0}^{3}\lambda _{F}\lambda _{S}n_{o,F}n_{o,G}n_{S}(\theta _{m})}$

where $d_{eff}^{2}$ is the "effective" nonlinear coefficient of the crystal, $L$ is the crystal length (provided the interaction length of the gate pulse and the focused fluorescence is much longer than $L$), $P_{G}$ is the power of the gate beam, $A$ is the area of the focused and overlapping fluorescence and gate beam, $c$ the speed of light, ${\epsilon }_{0}$ the vacuum permittivity. ${n_{o,F}}$ and ${n_{o,G}}$ are the ordinary refraction indices of the crystal at the wavelengths of the fluorescence and the gate pulse respectively. ${n_{S}(\theta _{m})}$ is the effective refraction index at the wavelength of the sumfrequency light. Note that for a the polarisation of the sumfrequency light is perpendicular to that of the fluorescence and the gate pulse.

The above equation is not easy to apply quantitatively but it allows some general observations: the FU efficiency is proportional to the gate power $P_{G}$ and inversely proportional to the area of the focused and overlapping fluorescence and gate beam $A$. The FU efficiency also goes with the square of the crystal length $L^{2}$ but, as explained below, increasing the crystal length will decrease the time-resolution. Therefore, there is a trade-off between signal and time-resolution when chosing the crystal thickness. Mahr and coworkers estimated a possible 30% quantum efficiency, but the actual observed values are orders of magnitude lower. Note that in this equation the spatial overlap of the gate beam and the fluorescence is supposed to be close to perfect.

Quantum efficiency and signal intensity

It is important to distinguish between the quantum efficiency and the signal intensity. The quantum efficiency is a relative number - the ratio of generated sum-frequency photons over the "total number" of incoming fluorescence photons. It is important to better describe this "total number" which depends on several factors.

• the spatial part of the totally emitted fluorescence that is collected by the optics and focussed in the crystal
• the spectral part of the focussed fluorescence that is actually convertable, i.e. respects phase matching conditions
• the temporal part of the fluorescence decay that is temporally overlapping with the gating pulse (see comment below)
• the quantum efficiency of the crystal

comment about the signal and the fluorescence lifetime

For a given configuration the calculated efficiency may be very high, but the actual signal intensity very low if the fluorescence lifetime is long (several nanoseconds) and the gating pulse very short (100 fs). There are just not enough fluorescence photons coinciding with the gating pulse.

It is misleading to think that a compound with a high fluorescence quantum yield should give a high FU signal. If the fluorescence lifetime is very long, the FU signal will be very low. Conversely, a compound with a low fluorescence quantum yield but very short the DNA nucleobases for example). It is actually more relevant to consider the radiative fluorescence lifetime than the fluorescence quantum yield.

Time-resolution and group-velocity dispersion

The time-resolution of a FU setup can in principle be said to be limited by the cross-correlation between the pump and probe (gate) pulses, but this is without taking into account the effects of the Group-velocity dispersion, that is, the wavelength-dependent propagation of the two pulses as well as the fluorescence. Briefly, different wavelengths propagate with different velocities in optically dense media. This has several consequences. Firstly, the pump (excitation) pulse travels more slowly than the fluorescence in the sample. Secondly, the probe (gate) pulse travels faster than the fluorescence which itself travels faster than the sum-frequency light in the nonlinear crystal. Both these effects will produce a temporal broadening of the detected signal meaning that the efective time-resolution will be less than expected from the cross-correlation signal. Clearly, it is of interest to reduce as much as possible the pathlengths through all optically dense media. For example, it is useful to use reflective instead of refractive optics. Likewise, it is useful to use as thin as possible filters and crystals.

In addition, for a broad fluorescence spectrum, the long wavelength components travel faster than the short wavelength components in all optically dense medium, such as the sample, the cell walls and the crystal, but also any lenses and filters used. This produces a "distortion" of the spectrum in the sense that the for a given position of the optical delay the corresponding time-delay is not constant; it depends on the fluorescence wavelength. This has important consequences when trying to make spectral recordings (see below).

All the broadening effects described above involve the difference in propagation time between two waves of different wavelengths ${\lambda _{1}}$ and ${\lambda _{2}}$ through an optically dense material of length $L$. This difference can be written as

${\Delta t}$ = $L[{1 \over {v}_{g,\lambda _{1}}}-{1 \over {v}_{g,\lambda _{2}}}]$

where ${v}_{g,\lambda _{1}}$ and ${v}_{g,\lambda _{2}}$ are the respective group velocities. It follows that the time-resolution decreases with the length of the material. The wavelength-dependent group velocities for most materials (solvents, crystals) can be calculated from their wavelength-dependent refraction indices which in turn are given by the Sellmeier equation.

explicit example

To give an explicit example, consider an excitation pulse at 400 nm moving through a 1 mm sample generating fluorescence peaking at 600 nm. If the group velocities are ${v}_{g,400}=1.88x10^{8}ms^{-1}$ and ${v}_{g,600}=1.99x10^{8}ms^{-1}$

${\Delta t}$ = $1.00x10^{-3}m[{1 \over 1.88x10^{8}ms^{-1}}-{1 \over 1.99x10^{8}ms^{-1}}]$ = $2.94x10^{-13}ms^{-1}$

That is, the group velocity difference between the excitation pulse and the fluorescence wavelengths generates an increasing mismatch between the fluorescence emitted from different positions along the propagation path. The excitation pulse lags behind the already generated fluroescence.

This corresponds to an effective broadening of the response function of about 300 fs, which is about a factor of three more than the typical cross-correlation function of about 100 fs mentioned above.

Kinetic recordings

By scanning the optical delay (see above) between the fluorescence (i.e. the excitation pulse) and the gating pulse, kinetic traces of the fluorescence at a given wavelength can be obtained. This is the most straight-forward application of fluorescence upconversion. Typically, a mechanical delay stage controlled by a step-motor can be positioned by 1 micrometer steps. Using the formula given above it is easy to show that this corresponds to 6.67 femtoseconds.

Spectral recordings

In general, the FU technique provides a limited spectral bandwidth (<10 nm), much less than that of the probed fluorescence (> 100 nm). In order to monitor the time-evolution of the full fluorescence spectrum several approaches are used.

The most widely used method is to reconstruct the time-resolved fluorescence spectrum a posteriori from a number of individual kinetic traces recorded at different wavelengths.

The major problem for making a direct recording of a broad fluorescence spectrum is the group-velocity dispersion; different wavelengths propagate with different velocities through the optical components (filters, lenses, crystal,..). The difference in arrival time in the crystal of the "blue" and "red" components of the fluorescence spectrum may amount to several hundreds of femtoseconds.

A step-wise scanning approach has been developed, where the monochromator is positioned in wavelength while the phase-matching angle is optimized and the optical delay adjusted for the group-velocity difference for each wavelength.

Broadband detection of the upconversion signal can in principle be obtained with a spectrograph equipped with a CCD camera. However, as mentioned above, the limited bandwidth of the crystal does not allow to cover the whole fluorescence spectrum. An elegant approach to overcome is to rapidly rotate the crystal during the measuring time. The broad spectrum recorded for a given delay time must however be corrected for the group velocity dispersion.

A much more advanced approach has been developed by Ernsting and coll. who adjust the wavelength-dependent angular dispersion of the focused fluorescence in order to fulfill phase-matching conditions over a wide spectral range.

FU imaging

Femtosecond Lifetime Imaging using FU has been reported. Space-resolved fluorescence decays of different tryptophan residues in a fluorescent protein were recorded on the picosecond timescale.

History

The first demonstration of the FU technique was reported by Mahr and Hirsch in 1975. They used FU to characterize the temporal shape of the pulses emitted from a Rhodamine 6G dye laser pumped by a mode-locked Argon laser. They also examined the incoherent luminescence emitted from the excited dye jet and found that it contained a long tail extending to several nanoseconds. This corresponds to the spontaneous emission (fluorescence) of the excited dye. Soon after, Mahr, Hirsch and coworkers applied the FU technique to bacteriorhodopsin. Using a picosecond mode-locked dye laser, they measured the emission lifetime of bacteriorhodopsin at physiological temperatures to be 15 +/- 3 ps.

Since then the number of articles using this technique increases steadily every year and today more than 1200 scientific papers can be found (Web of Science 2025, but this is certainly an underestimation).

Among the first applications of FU with sub-picosecond time resolution was the study of polar solvation dynamics. Indeed, the solvent influences the solubility of a solute, the stability of a solution and even the reaction rates of different compounds in solution. The understanding of such solvent effects is fundamental in chemistry. Their equally important dynamics are called solvation dynamics. Briefly, solvation dynamics can in principle be studied by using an "inert" fluorescent probe molecule and follow the evolution of the fluorescence spectrum in time i.e. the Time-Dependent Fluorescence Stokes Shift (TDFSS). With "inert" probe molecule it is understood a molecule that does not undergo any other relaxation processes than solvation, which is far from trivial. Other possible processes that may affect the fluorescence spectrum are, for example vibrational relaxation, photoisomerization, conformational change or charge transfer processes, all of which have also been studied by FU .

Hallidy and Topp were the first to study solvation dynamics using FU. They characterized the temperature-dependence of the evolution of the fluorescence spectrum in terms of interpreted in terms of independent re!axation processes: solvation dynamics and solvent-assisted fluorescence quenching. Already this early example highlights the eifficulty to assign observations to a specific well-defined process.

Graham Fleming and coworkers pursued the characterization of the Time-Dependent Fluorescence Stokes Shift of chosen fluorescent probe molecules in various low-viscous solvents at room-temperature. They distinguished various solvation processes, from slower long-range diffusional processes to ultrafast inertial effects in the first solvation shell.

Another possible origin of the observed Stokes shift is intramolecular vibrational relaxation. The group of Wolfgang Kaiser used FU to study vibrational relaxation processes in polyatomic molecules. The group of Paul Barbara used FU to study solvation dynamics and vibrational relaxation but also excited-state intramolecular proton transfer in various organic molecules.

The polarisation sensitivity of FU (see above) was used by several groups to record the time-dependent fluorescence anisotropy and thereby study the rotational relaxation dynamics of dyes in solution.

FU in the ultraviolet region has been used to study various biomolecules such as proteins. and the very shortlived intrinsic fluorescence of DNA constituents.

Caution

As mentioned in the beginning fluorescence upconversion should not be confused with photon upconversion, sometimes called upconversion fluorescence. While FU is an instantaneous interaction between the fluorescence, the probe-pulse and the sum-frequency light in the nonlinear crystal, photon upconversion is based on the sequential absorption of two (or more) photons in an optical material leading to light emission at shorter wavelength than the excitation light but at a (much) later time.

References

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