Ultra-Short-Pulse Laser Technology and Applications: Lecture 5

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Lectures on

Ultra-Short-Pulse Laser Technology and Applications Fifth Lecture

Applications: materials processing, dental lasers, optical coherence tomography, nonlinear microscopy, rapid-prototyping

5.1 Three general aspects of applications

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5.2 High temporal resolution by optical pump-probe experiments

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5.3 Material ablation by ultra-short pulses

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5.4 Medical applications of ultra-short pulses 5.4.1 5.4.2 5.4.3 5.4.4 5.4.5

Applications to hard-tissue ablation in dentistry Applications to soft-tissue ablation: examples Optical coherence tomography using ultra-short pulses Three-dimensional resolution by non-linear interactions within the focus of ultra-short pulses Advanced applications in optical communications

References (Lecture 5)

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5.1 Three general aspects of applications Modern applications of ultra-short (i.e. picosecond and femtosecond) laser pulses represent a fascinating wealth of new options becoming more and more mature, also for commercial use. One may divide them into three categories according to the dominant feature for the specific type of application, some of them being already discussed above: •

Ultra-short time duration

•

Ultra-broad spectral bandwidth

•

High-average power

Ultra-short laser pulses of even modest average power in the tens of mW regime permit outstanding temporal resolution reaching down to the sub-fs time domain. Amplified pulses of shortest duration (i.e. nowadays few-cycle duration) allow the most efficient generation of ultra-short wavelengths in the XUV and X-ray regime, especially when carrier-envelope phase-stabilized, as was shown earlier in chapter 4.3. Ultra-high intensities can be attained with setups of table size giving the opportunity to discover a new regime of non-linear optics associated with much higher photon energies than in the visible, also explained in detail in chapter 4. Another aspect of application is quite new, whereby the ultra-short laser is only a tool for the generation of extremely broad spectra organized in well-defined and equally spaced frequencies represented by the longitudinal modes. On this basis, optical frequency standards have been revolutionized, as was explained in chapter 4.1. In case of solely taking advantage of the short coherence length associated with ultrashort pulses, optical coherence tomography (OCT) allows unprecedented threedimensional imaging. This aspect of application will be discussed below. Even ultra-broadband communication takes advantage of the high number of well-defined longitudinal modes in ultra-short pulse lasers. High-average power systems represent a new tool for efficient and precise manufacturing of even hardest materials without the necessity of resonantly absorbed wavelengths creating negligible damage to the surrounding and remaining material which can be of anorganic or biological nature. Taking advantage of non-linear

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processes confined to the focus of a mode-locked train of ultra-short pulses yields the possibility of three-dimensional resolution, being well-known in non-linear microscopy since some time, but representing an innovative solution to three-dimensional structuring within the context of rapid-prototyping. 5.2 High temporal resolution by optical pump-probe experiments Fig.5.1 shows an example of a pump-probe experiment (compare the lecture notes “ultra-short light pulses”, chapter 7 Applications) for the measurement of absorption

Fig.5.1: Optical pump-probe experiment of the absorption dynamics as an example for the application of ultra-short pulses for time-resolved measurements in the 20 ps-regime. PR prism, RR retroreflector, PM photomultiplier, PO polarizer

dynamics in a semiconductor performed by the author [1]. The experiment involved an actively mode-locked Nd:YAG laser emitting ~80 ps pulses whose repetition rate in the order of 80 MHz was reduced by a modulator. The pulse duration was controlled simultaneously by a specially designed autocorrelator for long delays of more than 1 ns [2]. In a beam splitter about 90% of the power was separated to form the pump beam propagating along the path through a λ/2-plate and a chopper to become recombined with the probe beam which travelled via a folded delay stage to become collinear with the pump again in second beam splitter. Both beams, being orthogonally polarized with respect to each other, were focused onto the sample. The pump beam increased the carrier density by becoming absorbed, but very shortly after, bleaching started to be effective by absorption saturation. The probe beam transmitted through the sample (its contribution to absorption was considered to be negligible) which could be delayed by up to 1 ns, allowed to measure the amount of bleaching being effective at any time within the measurement time span. For this purpose, a

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polarizer filtered out the transmitted pump light and, additionally for the increase of measurement accuracy, a lock-in technique in association with the chopper was employed. The time resolution of this experiment was ∼20 ps being not outstanding but sufficient for the problem. Fig.5.2 exhibits the typical result of such a measurement: the graphs collected at different intensities represent the evolution of bleaching in a sample of GaAs. From this finding, via a rather complicated numerical iterative evaluation procedure, based on the basic formula for the lifetime of carriers decaying by three different processes given in the figure, the Auger recombination

coefficient

could be derived. This was a quite important problem at that

time

when

attempts

were made to explain the much stronger time-dependFig.5.2: Bleaching of the absorption in GaAs depending on carrier density. Full lines, measuement data, dotted lines, numerical simulation in order to yield parameters A (Auger), B (bimolecular) and C (normal recombination)

ence of the threshhold current in quaternary semiconductor lasers (of the type GaInAsP employed in

the communication business) with respect to GaAs diode lasers. The answer yielded by such experiments to the question which became widely known as T0-problem was the much higher Auger recombination efficiency represented by the coefficient A being a material property [3]. It could only become reduced by lowering the carrier density at threshold by chosing semiconductor media of higher gain like quantum wells. Fig.5.3 depicts another type of time-resolving measurement technique: the crosscorrelation method. In this case, the effect of two ultra-short pulse laser beams on a sample is studied under a varying temporal delay relative to each other. The signal

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Ultra-Short-Pulse Laser Technology and Applications: Lecture 5 yielded by the consecutive or cumulative effect of the beams is taken and accordingly evaluated. In the case of this figure, the correlation signal of

luminescence

in

two

GaInAs samples, one being undamaged and the other after He+ bombardement, was studied with respect to time delay. The laser employed was a CPM dye laser with λ ≈ 620 nm and a pulse duration τ = 100 fs. The resulting time resolution in this case is in the order of ∼10 fs [4]. A record temporal resolution at the time this work has Fig.5.3: Time-resolving measurement of luminescence in GaInAs by cross-correlation of 100 fs pulses of a CPM dye laser with λ ≈ 620 nm. The achievable time resolution is around 10 fs.

been carried out, is illustrated in Fig.5.4. It reveals the setup of a measurement of the “tunnelling time” of op-

tical pulses through multilayer dielectric mirrors (1D photonic bandgaps) [5]. In this case, being easily understandable with respect to the measurement procedure, the accuracy was better than 0.3 fs demonstrating the capacity of sub-femtosecond resolution for ultrafast spectroscopy. The result demanding the propagation of a pulse faster than the speed of light has been a very hot Fig.5.4: Pump-probe measurement of the „tunneling time“ of optical pulses through multilayer dielectric mirrors yielding an accuracy better than 0.3 fs

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topic for a certain time. The explanation is centered on the fact that the pulse is attenuated by about 100 times in an asymmetric way so that shifts of the pulse center contribute to the speed of propagation. 5.3 Material ablation by ultra-short pulses Ablation, i.e. vaporization of material without substantial heating of the bulk, was successfully tested with all kinds of matter so far. Hence this method allows to shape metals, semiconductors and insulators as well as biological substance leading to interesting aspects for commercial applicability. This aspect puts several limiting requirements onto the source of the ultra-short pulses, i.e. the mode-locked laser. 1.

Compactness: e.g. 40 × 40 × 30 cm3

2.

Moderate cost: e.g. ≤ 50 000 €

3.

Design: simple, robust, stable

4.

Relevant specifications: • pulse length • wavelength • average power • repetition rate • pulse quality and stability

Besides important aspects of laser oscillator and amplifier design, as they have been discussed in detail in the previous chapters, the price of diode laser optical pump power is a major limitation. This is illustrated in Fig.5.5 following data and estimations by D. Scifres of Spectra Diode Labs (SDL) [6]: the price of diode pump power is plotted versus the year indicating a decrease in $/Watt of 60% per year. This allows a very optimistic extrapolation of 1 $/W to be reached around 2005. It might be a question of precision for such a forecast, but there is no question that such values are Fig.5.5: Price of diode laser optical power versus year (extrapolation for 2005)

going to be reached. Unfortunately,

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prices for diode-pumped solid-state laser like Nd:YAG of today are still higher than for flashlamp-pumped ones. For many industrial fabrication processes the shaping of metals is of great importance. A very impressive comparison between the effect of femtosecond pulses drilling holes in steel and nanosecond pulses of even higher energy is depicted in Fig.5.6a und b [7]. The main advantage of the ultra-short pulse application can be recognized very easily: it is the regularly

shaped

crater

rims with no trace of damage in the surrounding material.

In

more

scientific

terms, there is no evidence of thermal or shock-wave collateral damage. The lower figure illustrating the impact of the ns pulses demonstrates just the contrary. Nevertheless, there is still discussion on this issue facing the experimental result that under specific circumstances even ns pulses may yield smooth craters and surrounded

by

absolutely

unmolten material, as shown in Fig.5.7 [8].In general, subpicosecond pulses are the ones of choice for achieving the best results in case that Fig.5.6: Femtosecond ablation of metals by (a, top) femtosecond and (b, bottom) nanosecond pulses according to Momma et al. [7].

the fluence onto the focal area is selected carefully not overheating

the

material

leading to heat diffusion by hot carriers into the surroundings. Fig.5.8 representing a result of Laser Zentrum Hannover (by S. Nolte and B.N. Chichkov) demonstrates the

Ultra-Short-Pulse Laser Technology and Applications: Lecture 5

Fig.5.7: Laser ablated nozzle plate comprising an array of 500 nm diameter slant holes at 20° to surface. τp = 20 - 40 ns, kHz repetition rate (Knowles et al. [8])

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Fig.5.8: Microstructuring of tungsten by laser ablation with pulses of τp = 100 fs, Ep ≈1mJ, kHz rep. rate, λ=780 nm (Courtesy S. Nolte, B.N. Chichkov, Laser-Zentrum Hannover, Germany)

capability of 100 fs pulses with Ep ≈ 1mJ for microstructuring of even hardest metals like tungsten in this case. The following set of SEM pictures in Fig.5.9 illustrates the effect of laser pulses of different duration from 3 ps down to 5 fs on a high-bandgap dielectric like silica cre-

Fig.5.9: Multishot damage in fused silica by N=80 ultra-short pulses of different duration and fluence at λ=780nm yielding various depths as indicated in the figure. Fotos courtesy M. Lenzner, presently at BAM, Berlin, Germany

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ating multi-shot damage [9]. The different shapes of the ablation craters depicted in the four micrographs can be clearly seen. Picosecond ablation yields a very irregular hole, while shorter and shorter pulses give rise to eventually completely smooth holes as the last photograph shows being created by the shortest 5 fs pulses. Laser-induced breakdown resulting in damage to dielectrics has been subject of extensive experimental and theoretical investigations since powerful lasers became available [10,11,12]. It has been described in terms of three major processes: (i) the excitation of electrons in the conduction band by impact and multiphoton ionization (MPI), (ii) heating of the conduction-band (hencefourth free) electrons by the radiation, and (iii) transfer of the plasma energy to the lattice. For pulses of a few picoseconds or shorter, heat diffusion is “frozen” during the interaction [13] and the shock-like energy deposition leads to ablation. Experiments being the background for Fig.5.9 by Lenzner et al. were carried out at Photonics Institute a few years ago [9] as a comparison of two isotropic dielectrics, fused silica (FS, Corning 7940), and barium aluminium borosilicate (BBS, Corning 7059). The surfaces of the samples were formed by a direct drawing process from the melt; resulting in a residual surface roughness of < 13 nm. The bandgap energies of the two materials are Eg ≈ 9 eV and Eg ≈ 4 eV, respectively. For a quantitative evaluation of ablation, the samples were investigated by light and scanning electron microscopy. In order to make the ablated volume per pulse Va and the ablation depth da accurately measurable, each site was exposed to 50 pulses at a given fluence. As an example, Fig.5.10 depicts Va versus on-axis fluence F for two different pulse durations in FS. The linearity of Va(F) is striking and found to be a general feature for the entire pulse width regime studied. This characteristic can be utilized for determining the damage threshold fluence Fth by extrapolating the regression line of Va on F to Va = 0. Fig.5.11 shows Fth determined in such a way for pulse durations between 5 ps and 5 fs in FS and BBS. The error bars depict relative (random) errors, the absolute (systematic) error of the measurements was less than ±15%. Figs.5.12 and 5.13 show the accumulated ablation depth as a function of the number of laser shots for FS and BBS, respectively, revealing important differences (A) and similarities (B) in the behavior of the two materials. (A) The comparable slopes of the regression lines in Fig.5.12 yield ablation depths da that exhibit hardly any dependence on

Ultra-Short-Pulse Laser Technology and Applications: Lecture 5

Fig.5.10: Volume Va of fused silica ablated by one laser pulse versus energy fluence F for two different pulse durations

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Fig.5.11: Threshold fluence in FS and BBS versus τ at λ = 780 nm. Each site was irradiated by 50 laser pulses [9]

the pulse duration in FS. In strong contrast, such a τ invariance is limited to the subpicosecond regime in BBS (Fig.5.13), whereas da rapidly decreases for decreasing pulse durations as τ approaches the 10 fs regime. The reproducibility of ablation is, in both materials, substantially higher in the 10 fs regime than in the subpicosecond regime. A few years ago, Stuart et al. [14] derived a simple rate equation for the evolution of a free electron density n(t) in a dielectric medium exposed to intense laser radiation,

dn/dt = αI(t)n(t) + σkIk,

(1)

where I(t) is the intensity of the laser pulse, α is the avalanche coefficient, and σk is the k-photon absorption cross-section with the smallest k satisfying kћω ≥ Eg, where

ω is the laser angular frequency. The energy of the free electrons heated by the laser is subsequently transferred to the lattice. This energy transfer leads to the ablation of the heated zone, which is the major manifestation of femtosecond optical breakdown. The experimental observations could be consistently interpreted in terms of Eq. (1).

Fth can be predicted by postulating a threshold electron density nth associated with the onset of permanent damage and solving the rate equation. In strong contrast with long-pulse damage, the density of seed electrons for the avalanche does not have to be postulated because it no longer relies on thermal excitation of impurity states, but

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Fig.5.12: Ablation depth in fused silica FS for increasing number of pulses and different pulse durations, measured at fluence levels of 5±J/cm2 [9].

Fig.5.13: Ablation depth in barium aluminum borosilicate BBS for increasing number of pulses and different pulse durations at fluence levels of 6.2±0.7 J/cm2 [9].

can be produced by MPI with rapidly increasing efficiency for decreasing pulse duration. The dramatically increased reproducibility of ablation in the 10 fs regime reportted above is a direct consequence of the strongly increased deterministic seed electron production for the avalanche (Fig.5.9 basically illustrates this finding in a two-dimensional way). Another interesting finding derived from theory applies just for 5 fs pulses, where photoionization is dominated by tunnelling as the breakdown threshold is approached at this pulse duration. Quantitative prediction of the penetration depth of the incident radiation, and hence that of da, would call for solving the coupled rate and wave equations for n(t,z) and E(z,t). Nevertheless, the influence of the pulse duration on da, which is expected to scale inversely proportional to the free electron density, can be qualitatively assessed by inspecting rate Eq. (1). For a regime in which carrier generation is dominated by impact ionization, Eq. (1) predicts an electron density, and hence da, that is independent of τ at a fixed fluence. By contrast, in an MPI-dominated regime, da is expected to rapidly decrease for decreasing pulse durations (at F is constant). The theoretically accessible values of the avalanche and MPI coefficients allow predicting the qualitative behavior of da (τ) and its comparison with the data in Figs.5.12 and 5.13. The fraction of the critical density produced by photoionization at F = Fth is calculated as

np(500 fs)/nth ≈ 4×10-8 and np(50 fs)/nth ≈ 1.5×10-4 for FS, and

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np(500 fs)/nth ≈ 0.09 and np(50 fs)/nth ≈ 0.35 for BBS. These data suggest that optical breakdown in fused silica is dominated by the avalanche process down to the 10 fs regime, whereas in BBS having much smaller bandgap, multiphoton ionization takes over for pulse durations below 100 fs. This finding is conclusively confirmed by the data in Figs.5.12 and 5.13. As a matter of fact, da is virtually independent of pulse duration for FS in the entire femtosecond regime. In BBS, this applies only to the subpicosecond regime, with da becoming subject to a rapid decrease with decreasing pulse duration for τ approaching the 10 fs regime. These results show that, even for a bandgap as large as ∼9 eV, MPI produces some 10 orders of magnitude higher seed electron density in the 10 fs regime than available in thermal equilibrium. As a result, sub-10 fs laser ablation can be accomplished with a precision corresponding to a few tens of atomic layers. Maybe this will allow precise microstructuring in the future also for dielectrics by applying 10 fs pulses in the mJ regime. The comparison of ablation results for metals and dielectrics given above clearly reveals the fact that the former are much easier to shape by ablation as sufficient densities of free electrons to be heated are around. For a quantitative treatment, there exist a number of theories of different comFig.5.14: Scheme of interaction of laser pulses with a metal exciting first the electron gas which is coupled to the lattice in a delayed fashion

plexity to describe the relevant parameters. In the following, a simple two-temperature model [7] is presented by its basic aspects. Fig.5.14

schematically depicts the situation where laser radiation penetrates a solid thereby first heating the electrons. The hot electron gas is coupled (via a coupling coefficient γ) to the lattice transferring thermal energy there. Of course, the electron gas may also loose heat via diffusion, especially via hot electrons. Eventually, the lattice undergoes ablation as soon as the temperature exceeds the boiling point, and hence atoms being expelled off the surface. The table in Fig.5.15 contains the coupled rate equations for electron temperature Te and lattice temperature Ti based on the heat balance in the electron gas (1) and the lattice (2). All the symbols used are ex

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plained in the figure. There exist two special solutions of these coupled differential equations: in the first case, the characteristic diffusion length of electrons l is much

Fig.5.15: Metal ablation: Theoretical description by a simple two-temperature model [7]

smaller than the optical penetration depth δ. In the second case l is much larger than δ. This fact yields different ablation efficiencies as depicted in Fig.5.16. Calculations

Fig.5.16: Ablation depth per pulse versus fluence for Ti:sapphire laser pulses with λ = 780 nm and τp = 150 fs. The lines represent the best fits to the corresponding equations in Fig.5.15 indicating two ablation thresholds and efficiencies.

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based on the formulae derived above show the following corresponding results for two cases of different laser specifications:

Ablation Depth in Metals Pulse energy 10 µJ, repetition rate 1 MHz, average power 10 W Focal diameter d ∼ 10 µm per pulse per ms Al 320 nm 0.32 nm Au 310 nm 0.31 nm Cu 270 nm 0.27 nm

d ∼ 50 µm per pulse per ms 43 nm 43 µm 36 nm 36 µm 13 nm 13 µm

Pulse energy 1 mJ, repetition rate 10 kHz, average power 10 W Focal diameter d ∼ 10 µm per pulse per ms Al 710 nm 7.1 µm Au 700 nm 7.0 µm Cu 640 nm 6.4 µm

d ∼ 50 µm per pulse 430 nm 430 nm 380 nm

per ms 4.3 µm 4.3 µm 3.8 µm

In case the average power is kept constant, the results suggest to employ rather higher repetition rates and smaller pulse energies to achieve the best ablation efficiency. Of course, the repetition rate is limited by the time, the ablated plasma plume needs to leave the area of laser irradiation yielding an upper limit for repetition in the regime between 100 kHz and 1 MHz. Fig.5.17a and b shows two other examples of high-precision ultra-short pulse machining of metals, in this case of copper: (a) represents a scanning electron micrograph of a micro-gear wheel out of Cu. (b) demonstrates the reproducibility of ablation by femtosecond pulses.

Fig.5.17: Femtosecond ablation of copper: (a, left) scanning electron micrograph of a micro-gear wheel. (b, right). Array of holes in order to demonstrate the reproducibility. λ = 390 nm, τp = 120 fs, F = 0.8 J/cm2, number of pulses N = 5000 [7]

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5.4 Medical applications of ultra-short pulses 5.4.1 Applications to hard-tissue ablation in dentistry Already shortly after the first demonstration of the laser in the year 1960, first attempts to ablate dental hard-tissue were undertaken. As soon as in 1967, however, it became evident that ruby, Nd:YAG and CO2 lasers are not suitable for such applications because by their interaction a damaging temperature rise within the pulp occurred. Hence, only dental technologic applications (prosthesis etc.) of these lasers could be successfully carried out. The critical limit for a reversible temperature rise within the pulp lies around 5°C above body temperature. If this limit is exceeded irreversible damage is caused [15]. The Ho:YAG and the Er:YAG became the next candidates for dental lasers. Because of the danger of overheating the pulp they are only used in a pulsed mode mostly under application of a cooling water spray onto the location of treatment on the tooth. The pulse durations thereby are in a range between 4 µs and several 100 µs and the repetition rates typically are around 1-20 Hz. While the laser energy in case of the Erlaser predominantly is coupled in via absorption of water within the dental hard tissue, in case of the Ho-laser due to the weaker coupling of radiation to water absorption mostly thermal ablation takes place. Therefore, already in 1993 this type of laser was considered to be not suited for the treatment of dental hard tissue. The wavelength of the Er-laser is located close to an absorption maximum of water thus allowing to couple energy into the dental tissue very effectively. Thereby, via immediate heating and vaporization of the water content within the focus on a tooth, micro-explosions take place blowing out pieces of tissue [16]. By this approach, ablation rates become feasible which allow practical application of this technology. Associated with this mechanism of ablation, however, micro-cracks within the dental hard-tissue occur penetrating down to 0.3 mm depth within the tooth. Conventional turbine based cavity preparation, for comparison, only causes cracks up to 0.02 mm depth. Already at the beginning of the 1990s, investigations on ablating dental hard tissue (enamel and dentine) were carried out with ultra-short pulses [17,18,19] involving pulse durations around 30 ps. The results achieved with respect to shape of faces,

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quality of the crater rims and absence of damage within the remaining material (key issues: free of cracks as well as of molten, re-solidified zones along rims and faces of cavities) were clearly superior to conventional IR laser systems. In case of suitably selected parameters even complete absence of damage could be achieved. The reason for this improvement can be seen in plasma-induced ablation, whereby dental tissue is not removed by sudden vaporization of water as described for the case of conventional IR laser systems, but via direct plasma formation and the consecutive expulsion of material. The associated shock waves and the thermal load are significantly smaller than in conventional laser cavity preparation. The mechanisms of plasma-induced ablation are as follows: at power densities >1011 W/cm² obtainable routinely with ultra-short pulses of sufficient pulse energy at suitable focusing conditions, an electric field of >107 V/cm is generated at the focus spot. A micro-plasma is induced with an absorption coefficient much higher than that of enamel. Consequently, the laser beam is absorbed totally by the plasma. The ablation itself is caused by the ionization of the enamel and the shock wave generated by this. The validity of this model was proven by numerous publications and consequently elaborated for the regimes of femto-, sub-pico- and picosecond pulse durations. In comprehensive studies the interaction of ultra-short pulses with dental tissue and the ideal parameters for ablation were investigated. Thereby, out of reasons of system availability, predominantly results covering the time interval between 120 fs and a few ps as well as above 20-25 ps were reported. Spatial scanning over the area to be treated, having been employed by some research groups right from the beginning on in order to make handling for the dentist more efficient as opposed to small focal areas, was soon also requested out of more scientific reasons, because laser shots impacting repetitively onto the same spots yield unfavorable heat distribution and cavity shapes [20] being undesirable in practical applications. The details of ultra-short pulse tissue interaction are as follows: i) Plasma formation by the impact of ultra-short pulses The incident electromagnetic field of the laser radiation causes an avalanche-like generation of free electrons. The laser energy is absorbed that rapidly within the material so that at pulse durations of ∼10 ps and less hardly any thermal or hydrodynamic response can take place. The value of the fluence leading to the formation of a plasma depends on several factors, like the wavelength, pulse duration, physical

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tissue parameters and defect density [21]. Models to calculate the relevant quantities in case of dental hard tissue follow quite exact calculations performed on silica assuming a situation matching to an insulator in many respects. Fig.5.18 gives relevant data on damage threshold for fused silica at λ = 1053 nm and 825 nm as well as for Fig.5.18: Observed values of damage threshold for fused silica at λ = 1053 nm (full circles) and 825 nm (full triangles), and CaF2 at λ = 1053 nm (full squares). Solid lines are τ1/2 fits to long pulse results. Estimated absolute error in data is ± 15% [22]. calcium fluoride CaF2 at λ = 1053 nm [22]. The trigger for the plasma formation is the high intensity I of the incident radiation (starting at ∼0.1-10 TW/cm²). At such values multi-photon absorption (MPA) is very likely to occur. A valence electron can gain enough energy by the absorption of several photons (e.g. 8 for fused silica, 6 for water @ λ = 1 µm) resulting in an effectively free electron. The probability for the simultaneous absorption of m photons scales as Im also making the process quite confined. The free electron faces additional acceleration in the electromagnetic field of the laser pulse creating a hot electron. Collisions with the surrounding atoms lead to impact ionization causing an avalanche process to start. Even transparent media become highly absorbing in this way. In general, an initial electron concentration n0 is present in all materials, especially in dental hard tissue. It can be easily shown (similarly to description above)[23] that n0 is unimportant if it is small compared to the ratio of the MPA source term to the avalanche rate. This is always the case due to the high nonlinearity if I is sufficiently high. The electric conductivity can be derived in a simplified model by assumptions on the electron-phonon coupling and hence on the mobility of electrons being comparable in silica and dental enamel. According to the Wiedemann-Franz law the thermal and the electric conductivity are mutually proportional thus allowing to approximate the thermal diffusivity. Quantitative results of the model thus are: the thermal diffusion length for heat induced by a 1 ps pulse is on the order ~0.01 µm in biological tissue. Hence no heat conduction for pulses with

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durations < 1 ps may be assumed (for comparison the mean-free path of an electron in Si is ~1000 times larger, hence the corresponding diffusion length ~1 µm).

ii) Ultra-short pulse propagation in dental material The propagation of an ultra-short laser pulse within a material in this context is governed by absorption and reflection at the layer of plasma generated by the pulse itself. Absorption is described in this case (when neglecting reflection as a first step) by the dissipated energy per time employed for the generation of free electrons. Measurements like the ones depicted in Fig.5.19 for fluences 10% above the ablation threshold show that the values of absorption throughout the whole range of depths within tissue do not differ significantly for pulse durations between 0.5 ps and 10 ps. For all pulse durations within this regime nearly the whole energy is deposited within a layer of ∼1 µm thickness [24]. Fig.5.19: Distribution of the absorbed laser energy density in direction of the beam for 4 different pulse durations in dental hard-tissue. The fluences were assumed to be 10% above ablation threshold. Nearly all the energy is deposited within a layer of 1 µm (λ = 1053 nm, µa linear absorption coefficient)

Fig.5.20: Generation of free electrons (a) solely via MPA (dotted line) and (b) via MPA and impact ionization together (full line). The incident laser pulse is shown by the broken line for reference [23].

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Fig.5.20 describes the evolution of electron density at the material surface for a pulse close to ablation threshold. From the quasi-parallel onsets of curve (a) and (b) within the rising part of the pulse it becomes evident that MPA within the ultra-short pulse temporal regime is the most important initiation effect for the increase of carrier density. Because of its strong intensity dependence, in fact, it ends very soon after the peak of the pulse indicated by horizontal part of curve (a) [23]. After MPA impact ionization dominates based on the acceleration of electrons in the electric field of the laser leading to stochastic collisions of those electrons with atoms giving rise to avalanche multiplication effects. The incident radiation is most effectively absorbed in the vicinity of the critical electron density nc (see below). Radiation being not absorbed on its way towards this layer having nc is reflected there [21]. As soon as the material within the surface layer is completely ionized, the additional incident radiation acts predominantly towards the increase of electron energy. The reflection over the temporal span of the incident pulse, however, is rather incomplete as it is graphically demonstrated in Fig.5.21.

Fig.5.21: The generation of high electron densities yields reflection of the laser pulse by the plasma. The full line depicts the intensity transmitted into the tissue underneath the plasma layer. The dotted line represents the shape of the incident pulse for reference [21].

Generally, the reflection increases proportional to the plasma density, i.e. the penetration depth decreases with the generation of the plasma. If the electron density in the material reaches the critical value nc being defined as

mω 0 nc = 4π e 2

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the plasma becomes highly reflective for the incident radiation (ω0 being the angular frequency of the laser light). Thus, a dependence of the critical electron density

nc ∝ 1/λ² on the wavelength λ follows representing the well-known shielding effect. The higher the intensity within the pulse, the earlier reflection occurs, i.e. strong absorption of radiation happens at such electron densities n within a very thin layer whose thickness is proportional to √n. After nc is reached, the penetration depth is not reduced any further. As soon as total ionization has taken place, additional input energy is used for heating the electrons causing a rather fast drop of absorption and an increase of reflection. This leads to the conclusion that intensities being higher than necessary for plasma formation are not useful. Hence, the existence of an optimum fluence for ultra-short pulse ablation can be derived. Reflection plays only a minor role for fs pulses as due to their short duration only a fraction of the trailing pulse edge can be reflected. For ps pulses stronger interaction takes place because a substantial part of the pulse propagates into the plasma formed by the leading section of the pulse, i.e. a larger fraction of the energy is employed for the heating of the plasma or reflected. Process of ablation The ablation process proper happens after the end of the impacting laser pulse. As all the absorbed energy is concentrated in a very thin layer, an energy density occurs far above the binding energy per atom. Consecutively, the energy of the electrons is transferred to the ions, a process lasting some tens of ps. The largest fraction of the energy within the plasma is not used to overcome the binding energy but for acceleration of the material to be expelled [20]. The plasmafied material is thrown out according to hydrodynamic laws whereby the layer thickness and the velocity of expulsion can be calculated according to the deposited energy. Ablation depths are around ∼1 µm. An increase of pulse energy does not lead linearly to an increase of penetration depth, due to the rising reflectivity of the plasma. The typical duration of the expulsion process lies within a few ns [20]. The processes of material expulsion and crater formation are to a large amount independent of the structure and molecular composition of the tissue. Behind the layer of thickness δ a shock wave propagates into the material, heating up and removing also deeper lying layers. The transfer of input energy into heat, however, is limited to ∼15 %. The expanding expelled

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plasma cools down and recombines within a time duration of ~100 ps. Thereby the exiting plasma wave undergoes a transition into a wave of evaporation. This evaporation process of the irradiated tissue goes on until the temperature falls below the evaporation point.

Effects on the surrounding tissue Only a small amount of energy stays in the surrounding material while most of it is removed together with the ablated matter. Via the dissipation of the shock wave energy a rise of pressure and temperature is caused in deeper lying layers. Thus 3 zones may be distinguished within the material: 1. Ablated zone (< 0.32 µm): the material is completely removed (1 - 30 ps after the end of the pulse). In this case, the penetration of MPA amounts to ∼0.1 µm, up to 0.18 µm depth plasma is generated by the electron avalanche. Between 0.18 µm and ∼0.32 µm, i.e. within a layer where no plasma is built up, ablation is caused by impact heating. The shock wave penetrating into the tissue still deposits sufficient energy to enable ablation there (i.e. evaporation). 2. Zone of irreversible physical modifications: shock heating, however with no ablation (> 0.32 µm). 3. Zone influenced by mechanical and thermal interaction where reversible effects take place with no indication for physical modifications. Zones 1 and 2 together may have a thickness of < 5 µm in reality in case of certain fluences [25]. Caused by high pressures on the surface of the material during the ablation process (plasma expansion) a pressure wave penetrates into the material propagating at a velocity of ∼5 µm/ns (slightly faster than the speed of sound at room temperature). According to simulations, the pressure peaks reach up to ∼10 kbar and decay exponentially towards larger material depths. The simulations also report on tensile stresses allowing to assume that ablation also may happen via splintering off processes. The shock wave of the entering pressure wave has extremely high frequency (1-10 GHz). Due to this, however, it cannot penetrate deeply into the tissue and is absorbed in a very shallow layer under the surface (< 1 µm). The amplitude of recoil pressure caused by the evaporation process is defined by the product of expelled mass times the expulsion velocity. The duration of this recoil pulse depends on

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the temperature distribution within the irradiated medium. As the fraction of energy contained within the high-frequency components of the recoil wave is much higher in case of ultra-short pulses than in case of longer laser pulses (e.g. sub-ns pulses) the shock wave of the former is damped significantly more. A shock wave in the kbar regime can damage the tissue persistently. The steeper the rising slope of the wave amplitude the higher the damage. Via nonlinear propagation of acoustic waves of high amplitude their velocity can exceed the speed of sound thereby generating very steep rising slopes. When comparing shock waves caused by 350 ps pulses with corresponding ones originating from 350 fs pulses, the former cause more substantial damage as the major part of their frequency spectrum contains lower frequencies intruding into tissue with higher pressures. In comparison, 350 fs shock waves have only ¼ of the recoil amplitude and half of the gradient depth of the 350 ps waves. Heat conduction is another very critical issue on the surrounding tissue and has to be discussed also. The thermal relaxation time τrel is the characteristic time heat needs to penetrate deeper into the material in order to reduce the local temperature by a factor of 2. If the pulse duration is substantially shorter than τrel the heat input depends only on the incident laser radiation and not on the heat conduction properties of the tissue. In order to avoid linear absorption and the associated strong heating, the laser pulses should have a risetime as short as possible to generate plasma as early as possible. The trailing edge is much less critical as its energy is mostly reflected by the plasma. Out of all these findings one can derive the following conclusion: sub-picosecond pulses cause a lower heat input into the surrounding tissue, although in no case picosecond pulses were declared to be incapable for the ablation of dental hard tissue. As a conclusion of this subsection, 3 electron micrographs (Fig.5.22a,b,c) are presented showing examples of successful dental enamel processing by femtosecond pulses (A. Kasenbacher in cooperation with Laser-Zentrum Hannover). These results have been acquired with a commercial laser system of rather great complexity comparable to the setup depicted in Fig.5.23 not allowing commercial application of

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this technique without the availability of a totally different new ultra-short pulse laser design, maybe following one of the concepts presented in Lecture 2.

Fig.5.22: Examples of successful femtosecond ablation of dental enamel. The micrograph on the left bottom shows a detail of the larger section on the left top. The parameters are: depth d=321 µm, λ=780 nm, energy per pulse Ep=50µJ, τp=130 fs, fluence F= 4.2 J/cm2, Ipeak=3.23×1013 W/cm2, frep= 1kHz Courtesy A.Kasenbacher, Germany

Fig.5.23: Typical setup and parameters of a standard femtosecond Ti:sapphire laser system with amplifier: λ=750-850 nm, τp=100 fs – 5 ns, Ep=1 mJ (350 µJ), fr=1kHz (5kHz), beam quality 6 times diffraction limited.

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5.4.2 Applications to soft-tissue ablation: examples Soft-tissue can be ablated by ultrashort pulses very effectively, as the example on bovine brain tissue given in Fig.5.24 [26] shows. The precision of the cut and the complete absence of thermal collateral damage are intriguing. The laser operation data are mentioned in the figure caption. Fig.5.24: Optical photomicrograph showing a 550 µm deep excision in bovine brain tissue. τp=140 fs, Ep=11 µJ, λ=800 nm, spot size dspot=20 µm, excision volume by ablation Va=0.37 mm3, number of applied pulses N=36000. Va/pulse=10.3×103 µm3. The sample was stained with HE.

Also applications in ophthalmology have been successfully tested. Corneal shaping usually is well-known in the context of application of excimer laser radiation. Fig.5.25 depicts a series of 4

scanning electron micrographs of in-vitro intrastromal cutting in a primate eye (i.e. a cut achieved in the interior of the cornea by a two-dimensional series of optical breakdowns) [27]. The first row allows a comparison between (a, left) a successfully

Fig.5.25: Corneal ultra-accurate surgery by femtosecond laser pulses: (top row) SEMs of in-vitro intrastromal cutting in primate eye, (a) successful by femtosecond and (b) unsatisfactory by 60ps pulses. (bottom row) Intraoperative and 1-week post-operative view of rabbit eye treated with femtosecond laser pulses in a spiral pattern.

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lifted corneal flap and extracted lenticule, generated by a femtosecond laser, and (b, right) unsatisfactory dissection when using longer 60 ps pulses. The background of this procedure is the idea to keep an epithel layer of the cornea intact and remove only internal layers. The second row in Fig.5.25 shows the interoperative (a, left) and 1-week post-operative (b, right) view of rabbit eye treated with femtosecond laser pulses in a spiral pattern. Strong scattering at the cavitation bubbles is observed in (a). Transparency returns to normal at approximately 3 days (b). Ultra-short pulses have been applied for myocardium drilling as shown in Fig.5.26a depicting a comparison between the results achieved by excimer laser (top) and ultra-short pulse laser (bottom). The former approach is characterized by extensive thermal damage surrounding the hole while the latter shows a smooth-sided hole free of thermal damage to surrounding tissue (source U.S. Department of Energy, Medical Technology Program Livermore National Laboratory). In Fig.5.26b the luminescence

Fig.5.26: (a,left) Histological section of pig myocardium drilled by excimer (top) and USPL (bottom), illustrating extensive thermal damage or smooth-side holes, respectively. (b,right) Luminescence signal for bone and spinal cord. The prominent Ca peaks allow the distinction between bone and spinal cord or other soft tissue. (bottom,left) 1 ns ablation of enamel showing extensive thermal damage and cracking. (bottom, right) Smooth hole in enamel with no thermal damage after drilling with a USPL.

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signals of different tissue sections are identified by their spectroscopic lines. This idea also has a great potential for identification feedback when ablating dental tissue. 5.4.3 Optical coherence tomography using ultra-short pulses A very challenging rather new field of application of shortest femtosecond pulses is optical coherence tomography [28] which was advertised in recent years in many publications, e.g. in the trade journal Biophotonics (October 1999) on the front page (Fig.5.27). This method originally involved superluminescent diodes having a rather short coherence length defining the resolution of measurement [29], originally of distances between optically different layers in the eye, like the thickness of the cornea or the depth of the eye down to the retina [30]. Soon, two-dimensional scanning of the background of the eye was achieved and, furthermore, this method was applied to a variety of scattering biological media like skin tissue or dental tissue [31]. A major step forward was made by taking advantage of the short coherence length of femtosecond pulses which is in the µm regime and hence about one order of magnitude shorter than the one of superluFig.5.27: Optical coherence tomography filling headlines of journals: tomogram of Xenopus laevis (African frog) with subcellular resolution.

minescent diodes but associated with excellent brightness of laser sources. As a definition, optical coherence to-

mography allows non-invasive images of cross-sections (tomograms) in scattering media, especially in biological tissue. Imaging through scattering media was an issue since long time, i.e. since the early das of laser development. Fig.5.28 schematically shows the propagation of a laser pulse through scattering media. The unscattered photons are faster, but fewer and under normal conditions completely overwhelmed by the scattered photons arriving later. If it is possible to establish a temporal gate

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Fig.5.28: Scheme for imaging through scattering media (a) by employing a fast optical gate switch allowing just few unscattered but faster photons to reach the detection system generating the image while the larger numbers of scattered photons are shut off (b). switch to select only the unscattered photons, imaging becomes possible. This was achieved by non-linear fast optical switches which, however, are very inefficient and require large laser power. In the concept of OCT, the gate is realized as a coherence gate. Fig.5.29 exhibits a very simplified scheme of a modern fiber-based optical coherence

tomograph

[32].

It

seems to be worth mentioning that it is no problem or even

contradiction

when

considering ∼10 fs pulses with a bandwidth of about 120 nm propagating through non-negligible

lengths

of

optical fiber associated with a lot of dispersion. It is the Fig.5.29: (upper half) Scheme of a fiber-optic Michelson interferometer for optical coherence tomography consisting of measurement (S) and reference (R) arms. (lower half) Tomographic cross sections through an onion, taken (a) by highresolution Ti:S OCT or (b) superluminescence diode OCTsystems [32].

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coherence length and bandwidth remaining unchanged even if the originally bandwidth limited pulses out of the laser are torn apart by dispersion. A compensator within the reference arm should provide approximately equal dispersion conditions in both, the measurement and the reference arm. Fig.5.30 allows a comparison of bandwidth and coherence length for superluminescent diodes and femtosecond laser pulses being more or less self-explaining. Thus, superluminescence diodes yield ∼20 µm longitudinal resolution while femtosecond lasers achieve one order of magnitude smaller values, i.e. ≥2 µm. In this way, a resolution of ∼2 µm in the longitudinal direction is achieved as it can be seen in Fig.5.31 showing subcellular details of African frog tissue (xenopus laevis [33,34]) with a lateral resolution of 3 µm. This most modern version of OCT, although so far only performed by Ti:sapphire pulses around 800 nm penetrating about 1 mm into normal tissue, seems to be ideally suited for the application of diode-pumped femtosecond lasers like Cr3+:LiSAF or LiSGaF as they can be directly diode-pumped and hence are Fig.5.30: Comparison of bandwidth (top) and coherence length (bottom) for superluminescent diodes and femtosecond laser pulses

substantially simpler and potentially cheaper. Their penetration depth is also somewhat deeper due to the center wavelength being about 100 nm

longer. The average power needed for OCT lies in the sub-10mW regime, usually it is 3-5 mW, representing a rather modest requirement in general. For ophtalmological applications only 300 µW are needed and only ∼1mW would be permissible for safety reasons [35]. The implementation of OCT together with compact and moderately priced femtosecond laser sources in several wavelength regimes would be highly desirable: there are absorption windows around 950 nm, 1300 nm (yielding approximately 4 mm penetration depth) and 2200 nm. If taking also advantage of secondary

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information like spatially resolved dispersion and absorption (compare Fig.5.32 [36]) this will revolutionize in-vivo non-destructive medical diagnosis being applicable to many areas of interest via endoscopic methods.

Fig.5.31: Optical coherence tomograms of African frog tadpole (Xenopus laevis) yielded by a Ti:sapphire femtosecond laser having τp=5.4 fs and 250 nm bandwidth revealing sub-cellular resolution. The image is 0.83 × 1 mm large, 1800 × 1000 pixels. On the left picture, the olefactory tube (OT) and mitosis of 2 cell pairs (arrows) are shown. Courtesy of W. Drexler.

Optical coherence tomography is also, as mentioned above, used for dental applications: Fig.5.33 illustrates this approach and its results in an impressive way allowing to distinguish the various features of a tooth, aiding diagnosis (source U.S Department of Energy, UCRL-MI129402).

Fig.5.32: Comparison of high-resolution (top) and spectroscopic (bottom) femtosecond OCT. By exploiting linear optical properties like dispersion and absorption, additional contrast can be yielded which usually is depicted in false colors as the bar below the pictures indicates [36].

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Fig.5.33: Optical coherence tomography for dental applications. (left) Cross sectional images taken with OCT can be combined to give a 3-dimensional representation. (right) In the OCT image (right part) the various features of a tooth can be easily distinguished, aiding diagnosis. 5.4.4 Three-dimensional resolution by non-linear interactions within the focus of ultra-short pulses Ultra-short pulses having sufficient single pulse energy and repetition rates in the MHz regime allow the application of high peak powers to the focal spots reaching intensities as required for various non-linear processes without destroying the sample necessarily, together with sufficient speed for e.g. sampling or scanning purposes. Multiphoton non-linear microscopy (e.g. [37]) takes advantage of this aspect allowing three-dimensional resolution via two- and three-photon fluorescence excitation or second and third harmonic generation. In this case, the requirements with respect to short pulse durFig.5.34: Example of multi-photon nonlinear microscopy depicting two-photon fluorescence of leukaemia cells of rats [37]

ation or high-average power are not very stringent. Therefore, this technique has been started to be employed

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already a number of years ago. Fig.5.34 represents a very successful example depicting two-photon fluorescence of leukaemia cells of rats [37]. The development of compact diode-pumped sources might contribute to the wide spread of this technique in an innovative way as well as the availability of a wide spectral range of ultra-short pulses. Related to this concept, with respect to localized non-linear intra-focal interaction, but demanding for much more average power is a rather novel approach to rapidprototyping with polymers. Traditionally, two-dimensional computer controlled exposition of monomers to UV cw laser radiation allows to solidify them to polymeric structures. They have to be created layer by layer eventually yielding a sizable three-dimensional body. Typical commercial exposition times for 30 cm sized figures are of the order of 50 hours limited by UV laser power on the one hand, but also by many mechanical steps like immersion into the liquid monomer, wiping off the excess liquid, linear sequential exposition by a scanned focus and so forth. Fig.5.35 illustrates how Fig.5.35: Classical steps of rapidprototyping employing monomers to become UV-hardened: first a calculated CAD-model is computer-decomposed into layers. In each of the layers laser-assisted generation of cured rasin structures is carried out, which consecutively form the real 3D model. The fabrication of the single solidified layers involves a number of mechanical steps of motion like dipping in and wiping off, so that the overall process is rather time consuming. this technique works. 3D-prototyping, however, makes use of three-dimensional confinement of non-linear interactions within the focus of an ultra-short pulse train. Two- or three-photon absorption can expose a monomer [38,39] and create a hard structure within the volume of the liquid [40] starting from a substrate. There are no mechanical motions required any more, and therefore the process is potentially much

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faster than the traditional one depending basically on the average power of the ultrashort pulse source. Laser-Zentrum Hannover so far is one of the first institutions publically demonstrating the method for rather small structures (1 cm dimension) [41].

Fig.5.36: Example for stereo lithography for medical applications generated by polymer rapid-prototyping. The commercial fabrication process takes around 50 hours representing a potential for shortening by more advanced methods like 3D ultra-short pulse rapid-prototyping.

In the field of integrated optics, higher and higher densities of package are necessary and realized involving waveguide writing in three dimensions. Recently, some work on photonic device fabrication in glass using non-linear materials processsing with a femtosecond laser oscillator was completed successfully at M.I.T. having the potential for revolutionizing the integrated device fabrication [42]. A crosssection of the three-dimensi-

Writing beam

onally written waveguides by

Top surface

ultra-short pulses is depicted 60µ µm

10µ µm

Guided, coupled beams Writing progression

in Fig.5.37. Fig.5.37: Scheme of 3D-writing of waveguides by ultra-short pulses incident from the top on the 60 µm thick wafer. The vertical separation of the guides is 60 µm.

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5.4.5 Advanced applications in optical communications Also in the field of optical communication femtosecond pulses become more and more important and get used for wavelength division multiplexing (WDM) and demultiplexing. Fig.5.38 illustrates a 206-channel chirped-pulse WDM transmitter as published by Nuss, Knox and collaborators at Bell Laboratories about 4 years ago [43]. This represented a record for the number of channels, using a single femtosecond laser (τp < 100 fs, fr =36.7 MHz @1.55 µm) and a single time-division multiplexed electro-absorption modulator. The channel spacing is ∼37 GHz (0.3 nm), and the bit rate in each channel is 36.7 Mbit/s. In the meantime, this approach has been dramatically improved to a 1021 channel WDM system [44]. Very recently, 80 Gbit/s demultiplexing via a semiconductor optical amplifier in an ultra-fast nonlinear interferometer using two mode-locked fiber lasers (@ 1550 nm and 1545 nm) yielding a 5 ps switching window has been achieved at M.I.T. Lincoln Laboratory [45].

9.94 GHz

Ext. Clock

9.94 Gb/s Data

st

271 RF harm.

Pulse Pattern Generator

4 km DCF (-340ps/nm)

(*) Dynamic bias adjustment

fs Fiber Laser 36.7 MHz

Tx Output

InGaAsP Modulator