1 Basics of Femtosecond Technology

Georg Schüle

Keywords: Laser-tissue interaction, femtosecond laser, plasma formation, cavitation bubble

1.1 Laser–Tissue Interaction

Only a short time after the practical demonstration of the laser, its unique properties have found use in medicine. The first medical application was in ophthalmology, the eye being the only optically transparent organ of the human body. Understanding and utilization of the basic laser–tissue interaction is essential to tailor the laser parameters to the specific requirements of the medical need. In general, there are four fundamentally different laser–tissue interaction mechanisms. They vary depending on the duration of the light exposure (the laser pulse duration) as well as the irradiance, which is the power per unit area delivered. ▶ Fig. 1.1 gives the overview.

These four different interactions are applicable for general photoinduced tissue effects and can be generated with other light sources as long as the boundary conditions of irradiance as well as pulse duration are maintained.

1.1.1 Photochemical Effects

Starting with long exposure times of seconds or longer as well as low-irradiance photochemical interaction is the leading interaction mechanism. This is typically used in combination with UV (ultraviolet) wavelengths given the single photon energy needs to be energetic enough to cause direct interaction with the tissue. The photon energy is directly absorbed, leading to photochemical alterations of molecular bonds. The energy of molecular bonds ranges from 3 to 9 eV (electron volt). This equals the energy of single photons with 410 to 138 nm wavelength. Typical examples of photochemical effects are skin sunburns where the sun’s UV light of low irradiance in combination with long exposures leads to erythema. In ophthalmology, corneal crosslinking ¹ utilizes photochemical interaction using the UV LED (light-emitting diode) light of several mW/cm² along with a photosynthesizer to achieve a chemical reaction and with that the desired tissue effect. But, also photodynamic therapy for the treatment of neovascularization ² is another example utilizing a red laser wavelength to induce photochemical changes.

1.1.2 Photocoagulation

Photocoagulation ³ refers to heating and thermal modification of the tissue due to linear absorption of the incident light. Exposure durations in the second down to sub-milliseconds along with low irradiance levels in range of 10 W/cm² are required. The laser-induced heating will lead to temperature-induced protein denaturation of the tissue. The main light absorbers of tissue are water (in the infrared region), melanin (broadband absorber), and hemoglobin (distinct spectral peaks in the visible range) as well as general protein absorption in the far UV. Depending on the selected target chromophore, specific wavelengths can be selected to achieve the desired optical absorption depth and with that the desired specific depth location of the generated heat. An important factor is the rate at which the laser energy will be absorbed by the tissue. This will allow to control the lateral spread of the heat and with that define the denaturation extend beyond the illuminated area. Examples for photocoagulation are retinal photocoagulation, argon laser trabeculoplasty, ⁴ and laser thermal keratoplasty. ⁵

1.1.3 Photoablation

The mechanism of photoablation is referred to when the laser pulse duration is shorter or within the thermal relaxation time T_r of the irradiated tissue. The thermal relaxation time T_r is the time required for the peak temperature to diffuse over the distance of the optical penetration depth µ_a of the laser light. It is defined as

where   is the thermal diffusivity of the tissue.

A special case of photoablation is the excimer ablation for photorefractive keratectomy (PRK). ⁶ The laser with a wavelength of 193 nm and the single photon energy of 6.4 eV leads to a photodecomposition of single molecules. However, additionally, the disintegrated structure is ejected, driven by the kinetic energy provided by the absorbed photons. The fact that the single pulse ablation depth is deeper than just the optical penetration depth is a good indicator that mechanical spallation is also a contributing factor. At moderate irradiance levels, this will lead to localized heating and thermal expansion of the tissue and the generation of mechanical forces due to the thermal expansion of the heated compared to the unheated tissue. These force gradients will lead to a mechanical ablation of the tissue. This leads to a highly precise ablation of the tissue structure with minimal damage to adjacent tissue. This is why, it is used in PRK and LASIK (laser-assisted in situ keratomileusis).

1.2 Plasma-Induced Ablation

The previously described three laser–tissue interactions of photochemical, photocoagulation, and photoablation strictly rely on the linear absorption of the laser light by a tissue-intrinsic chromophore. If the tissue would be transparent, no effect would be achieved. This is the clear separation to the plasma-induced ablation in which the laser light generates its own localized absorber by nonlinear absorption. This nonlinear absorption is a multistep process.

1.2.1 Plasma Formation

The process of laser plasma formation essentially consists of the generation of quasi-free electrons due to an interplay of photoionization and avalanche ionization. ⁷ This is illustrated in ▶ Fig. 1.2. The availability of high peak powers of nanosecond down to femtosecond lasers in combination with tight focusing allows a high-enough photon density to pump the valence electrons to the conduction band. The minimal energy of 6.5 eV to get a valence electron to the conduction band requires the simultaneous absorption of multiple photons at the same time, given the energy of a 1,064-nm photon is only 1.17 eV. For this wavelength, the simultaneous absorption of more than six photons is required. Once in the valence band, the now free electron will absorb more photons until it reaches the critical energy at about 1.5 times the valence band energy, and inverse bremsstrahlung absorption will lead to the reduction in energy but at the same time the impact ionization will pump a second electron to the conduction band. Now two free electrons are available, which again will absorb photons and be pumped up to the critical energy. This will continue as long as photons are available, and an avalanche chain reaction will take place until so many free electrons are available that, at the critical density, a plasma is formed. Once a plasma is formed, the probability of absorbing other photons is extremely high. Due to the high density of photons, the laser generated its own absorber even in a transparent medium (▶ Fig. 1.2).

This cascading ensures the plasma generation to start at the location with highest photon density, the laser focus. The pulse energy required to reach the plasma formation threshold depends on the pulse duration as well as laser focus size. For nanosecond lasers, the threshold is typically in the millijoule (mJ) range—as used in posterior capsulotomy ⁸—and lowers to tens of microjoule (µJ) for picosecond and sub-microjoule for femtosecond laser pulses as used in corneal refractive surgery. ⁹

1.2.2 Shock Waves and Cavitation Bubbles

After the laser pulse ends, the plasma starts to transfer its absorbed energy into the tissue. As the focus is the highly localized heat source and the heat conduction is slow compared to the laser pulse duration, all heat is highly localized, which results in an overheating of the tissue. Additionally, the plasma expands at supersonic velocities, which results in the emission of high-pressure shock waves. The shock waves with high tensile stresses beyond the tensile strength of the tissue lead to the formation of cavitation bubbles. The size of the cavitation bubble strongly depends on the energy stored in the plasma. As the plasma threshold energy ranges from mJ for ns pulses to sub-µJ for fs pulses, the cavitation bubble size also greatly varies. For ns laser, the associated bubble size is 1 to 2 mm (at 1 mJ) and reduces to 200 to 500 μm for ps down to smaller than 30 μm for fs laser pulses. It is important to note that the size of the cavitation bubble typically limits the precision of the laser-induced effect and not the size of the plasma.

The event sequence as well as the generated dimensions for different pulse durations is illustrated in ▶ Fig. 1.3.

Depending on the precision requirement of the specific application, one can choose a laser which has cavitation bubbles small enough to fulfill the medical need. The disruption of tissue with these short pulses enables one to place fine and highly localized cuts without collateral damage to adjacent tissue. Additionally, the cavitation bubble can assist further tissue separation by cleaving layered structures such as corneal tissue. Placing adjacent spots in tissue generates a cut, and moving the focus in a planar fashion generates a planar cut. If a system is configured to move the laser focus in all three dimensions, the system can create cuts in any shape. In order to keep incision time to a limit, high repetition rate laser systems are desirable.

For posterior capsulotomy ⁸ using an ns laser is done manually and with that only single pulses are emitted from the laser, modern fs lasers work in the 100 kHz up to several MHz repetition rate with multiple millions of pulses applied for processing.

1.3 System Considerations

1.3.1 Laser Safety

There are many technical limitations which can limit the speed of a system, but if one overcomes these technical challenges, one is ultimately limited by the laser safety. It is important to realize that not all laser energy is absorbed in the focus even in the ideal case and some is still transmitted to the tissue behind the target structure. Also, there is a chance that the laser light has to transmit through scattering tissue and is not able to focus well enough to generate a plasma in the first place. In this case all light will be transmitted to the tissue behind the target structure. For ophthalmic applications, the retinal as well as iris or corneal safety limits are most relevant. The limits are governed by ISO 15004, IEC 60825, and ANSI Z136, and all systems need to conform to them.

1.3.2 Numerical Aperture

Besides pulse duration, the focusing spot size also plays an important role because it affects not only the plasma threshold energy and with that the cavitation size and effect precision but also the aspect ratio of the focal spot. These are variables one needs to consider and optimize for each application. The parameter defining the laser spot size is the optical systems numerical aperture (NA). This is a dimensionless number that characterizes the angle over which the optics focuses the light. The NA is defined as

in which n is the refractive index of the medium in which the laser gets focused and the θ is the half-angle of the maximum cone of light. For laser light, one can approximate the laser focus size as

in which λ is the laser wavelength and D is the laser focus spot size representing the diameter in which the intensity of the laser is reduced to 13.5% of its peak intensity.

The axial extension of the focus is termed the Rayleigh range b. This represents the axial length of the focus in which the intensity is decreased by 50%. It can be calculated as:

For a 1-µm laser source (which nearly all fs lasers are), the actual dimensions for D and b are depicted in ▶ Fig. 1.4.

1.3.3 Beam Aspect Ratio

Highly different beam aspect ratio can be generated by varying the NA. ▶ Fig. 1.5 shows the calculated aspect ratio as a function of the NA, as well as a graphical representation of the beam shapes. Highly elongated beams with aspect ratio of 30 can be generated, as well as nearly spherical beam shapes with an aspect ratio of about 1.

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