Draft:Fluorescence upconversion

Introductory Remarks

Fluorescence upconversion is a variant of sum-frequency generation and closely related to Second-harmonic generation. There is 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 technique, which relies on the use of temporally short 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 means < 100 femtoseconds. Two early technical reviews describe the FU technique in detail. Some more recent reviews also describe the technique.

Simplified scheme of a fluorescence upconversion setup

Basically, 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 an outgoing sum-frequency photon (at a frequency ν_S = ν_G + ν_F where ν is the frequency). It is important that the fluorescence and the probe pulse arrive simultaneously (or nearly) in the crystal - to this purpose the probe pulse is directed through a controllable optical delay stage (see below).

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.

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.

The nonlinear crystal

Historically, several different crystals have been used, such as KDP, LiIO₃ and urea. Today, the by far most widely used cystal is BBO.

Polarizations

Polarization of light is a very important aspect of the fluorescence upconversion process. Laser light is polarized and the nonlinear crystal is in itself polarisation-selective. Note that the fluorescence from a disordered sample (such as molecules in a solution) is not necessarily polarized in itself, but have a distribution of polarizations (it may of course be fully isotropic). 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 part of the fluorescence that will interact with the gate pulse. A crystal can be defined as Type I or type II in the sense that the gate pulse and the detected fluorescence have the same or perpendicular polarisations. This opens up the possibility to make polarisation-dependent measurements by simply changing the polarisation of the excitation beam with regards to the polarization detected by the crystal.

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 ($\overline{k}$_S = $\overline{k}$_G + $\overline{k}$_F where $\overline{k}$ is the wave vector). This depends on the properties of the nonlinear optical crystal.

The technique relies thus on two fundamental physical principles:

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

The conservation of the momentum can also be written:

$\frac{n_S}{{\lambda }_S}\hat{e}$_S = $\frac{n_G}{{\lambda }_G}\hat{e}$_G + $\frac{n_F}{{\lambda }_F}\hat{e}$_F

where $\hat{e}$_i (i= S,G,F) are the unit vectors.

In the colinear case this vector expression reduces to a scalar condition

$\frac{n_S}{{\lambda }_S}$ = $\frac{n_G}{{\lambda }_G}$+$\frac{n_F}{{\lambda }_F}$

Quantum efficiency

The quantum efficiency of the upconversion process is the ratio of sum-frequency photons over the total number of incoming fluorescence photons

${\eta }_q$ = $\frac{N_S}{N_F}$ = $\frac{8{\pi }^2{d}_{eff}^2{L}^2(P_L/A)}{c{ϵ}_0^3{\lambda }_F{\lambda }_S{n}_{o,F}{n}_{o,G}{n}_S(\theta )}$

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.

Applications

Here we list a few noteworthy examples where FU has been used to study ultrafast processes in photophysics and photochemistry.

The first physicochemical study using this technique was reported by Mahr and Hirsch in 1975. 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).

FU has been used to study the ultrafast conformational dynamics of oligothiophenes.

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

Commercial instruments

Several commercial apparatuses based on this technique can also be found on the market.

Since more than 20 years CDP Systems provides the FOG100 apparatus.

Ultrafast Systems proposes the Halcyone apparatus.

IB Photonics proposes the FluoMax apparatus. It comes in two version, either for oscillators (1-100 MHz, SC version) or Ti:S or Yb regenerative amplifiers (0.1-10 kHz, MP version).

The company LIOPTEC proposes a broadband FU setup FLUPS.

Cautionary remark

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.