We investigated the influence of polarization and apodization on laser induced optical breakdown threshold in transparent and diffuse media using linearly and radially polarized light. We demonstrate a lower irradiance threshold for optical breakdown using radially polarized light. The dominance of radial polarization in higher-order multiphoton ionization has important medical applications where a lower irradiance threshold may allow reaching deeper layers inside the skin with less risk of collateral damage and thereby improving safety and efficacy of treatment.
©2013 Optical Society of America
Laser induced optical breakdown (LIOB) is a non-linear absorption process leading to plasma formation at locations where the irradiance threshold for breakdown is surpassed. Optical breakdown occurs when a critical free electron density (ρc) of 1018-1020/cm3 is reached and significant optical absorption begins to occur in the plasma [1–3]. LIOB can occur by pure multiphoton ionization, by avalanche ionization or a combination of the two . The irradiance threshold to create breakdown is a function of both medium characteristics, such as ionization energy and impurity level, and the beam characteristics, such as wavelength, pulsewidth, spot size, and polarization. When a strongly focused high power laser beam interacts with matter, as in multiphoton absorption processes, the incoming optical field and the medium form a combined quantized system  and therefore to couple efficiently to small quantum systems such as single atoms or molecules, the incoming field must be well matched in both its amplitude and phase, but also in its polarization properties . Even though the influence of polarization in multiphoton absorption processes has been the subject of several theoretical as well as experimental studies [6–9], to the best of our knowledge, the investigation has so far concentrated predominantly on beams with uniform states of polarization, and space variant polarization states have received less attention. However, new effects and phenomena have been recently predicted and observed for spatially inhomogeneous states of polarization due to their unique properties and symmetry [10–15]. The unique properties of radially polarized laser beams to produce strong longitudinal electric and magnetic fields at the focus under tight focusing conditions are exploited in a great variety of applications, ranging from microscopy and material processing to optical trapping and particle acceleration [8–13].
When reaching to the limit, it has been shown theoretically and experimentally that focusing of radially polarized light yields the smallest possible focal spot [15–18]. However, the advantage of radially polarized light over the linearly polarized light for spot size reduction application is evident only for specific combinations of high NA and annular illumination [16,17]. Creating a tighter focus generally implies that multiple photons are present in a confined volume (temporal coherence) with overlapping space functions (spatial coherence) and thereby reducing the pulse energy for creating optical breakdown. However, strong focusing of homogeneously polarized light results in scrambling of the polarization state in the focus , thus reducing the number of photons with same polarization required for higher-order multiphoton ionization. Radially polarized light provides the additional advantage of preserving the polarization in the focus due to its total rotational symmetry that perfectly matches the focusing optics and therefore the degree of spatial and temporal coherence is not affected due to focusing. Thus the use of radially polarized light may offer advantages and additional possibilities in creating optical breakdown for biomedical applications such as ophthalmic surgery, lithotripsy, cell surgery, angioplasty and skin rejuvenation [20,21].
In this manuscript, we investigate the influence of polarization and apodization on breakdown threshold in aqueous transparent and calibrated scattering phantoms made from water suspensions of polystyrene microspheres using linearly and radially polarized light. We demonstrate that radially polarized light yields a lower irradiance threshold for creating optical breakdown.
2. Materials and methods
The experimental setup used for optical breakdown threshold measurements comprises a pulsed laser source, beam shaping optics and mirrors to guide the laser beam via the articulated arm and an aspheric focusing lens (NA = 0.67, f = 2.84 mm, AR: 1050-1620 nm). The laser source is a flash lamp pumped SLM TEM00 Nd: YAG laser which delivers 200 ps laser pulses of 1064 nm with maximum pulse energy of less than 1 mJ. The pulse energy was controlled using a polarization beam splitter and a half lambda wave-plate. To create annular illumination, we introduced in the beam path glass slides with a dark spot of diameter 1 and 2 mm (NA ratio = 0.3 and 0.6). NA ratio = 0 corresponds to the condition of clear aperture, without the glass slides. Radially polarized light is generated by transforming the linearly polarized beam using a commercially available polarization converter (ARCoptix, Switzerland) . The laser power is initially set below threshold and is then increased until a visible flash and an audible sound are detected, which testify that LIOB has occurred.
Optical breakdown was created in distilled water (sample 1) and scattering phantoms. Water suspensions of Polystyrene microspheres (Polysciences, Inc) with diameters of ϕ0.75 μm (anisotropy factor, g = 0.85) were used to make calibrated scattering phantoms with reduced scattering coefficients (µs’) of 5.3 (sample 2) and 7.1 cm−1 (sample 3), based on scattering cross sections following from Mie theory calculations, taking into account the wavelength of the laser light and the refractive index of water.
The focal spot size was experimentally measured using the knife-edge method. The setup comprises a sliding blade, two photodiodes, an oscilloscope, two motorized-stages, and a computer. The motors are controlled by the computer via a LabVIEW program, which allows scanning the focal area in the x and z direction with nanometer accuracy. The step sizes are set to 0.15 μm and 0.3 μm, respectively. A second photodiode positioned inside the optical system is used as the reference signal to the oscilloscope for background noise reduction. The recorded signal is post-processed for calculating the beam waist using LabVIEW.
The pulse energy corresponding to optical breakdown threshold measured in distilled water and diffuse media using linearly and radially polarized light is shown in Fig. 1. The error bars indicate the standard deviation of three measurements. As expected, the pulse energy required to create breakdown increases with the increasing scattering properties of the medium because of the path length dependent scattering losses of the photons as it propagates through the medium, regardless of the incident polarization state. We observe that higher incident power is required for radial polarization than for linear polarization, while it is comparable in sample 3 for higher NA ratios. This is probably due to the increased polarization scrambling in the focus for linearly polarized light as the mask is introduced. The higher incident power required to create breakdown with radially polarized light is a consequence of the larger focal spot obtained in this case. This is further confirmed by the spot-size measurements performed using the knife edge method and is shown in Table 1.
For the experimental settings that we used in this study (NA = 0.67), the circularly/linearly polarized beam is expected to be preferred over the radial polarization for the purpose of spot size reduction [16,17]. This is because, in the case of radially polarized light, there is a significant contribution from plane waves that are barely tilted, which have a small longitudinal field component compared with their transverse field component. Therefore, focusing of radially polarized beam will include a non-localized donut component at the focal plane, resulting from the transverse polarization, which prevents the spot size from being reduced beyond that obtained with linearly polarized incident field.
The performances of the two states of polarization are different in all samples when analyzed in terms of irradiance threshold, as shown in Fig. 2. To calculate the irradiance threshold, the measured pulse energy is normalized by laser pulse width and the experimentally calculated spot size. We have measured higher irradiance threshold of 5.43 x 1012, 4.31 x 1012 and 5.89 x 1012 W/cm2 in water due to the relatively smaller spot sizes (3.31, 4.27 and 5.37 μm). In previous report , the irradiance threshold measured for 200 ps laser pulses (spot size of 30 μm) in water was 1x1011 W/cm2. We found that radially polarized light yields a lower irradiance threshold in all samples. Furthermore, we observe that the ratio of the irradiance required to create breakdown with linear over radial polarization Ithlin/Ithrad, increases as the scattering coefficient of the medium increases. The irradiance ratio is 1.4 in water (µs’ = 0 cm−1), 1.9 in sample 2 (µs’ = 5.3 cm−1), and 2.3 in sample 3 (µs’ = 7.1 cm−1). This implies that when radially polarized light propagate through diffuse media like skin, the depolarization of photons resulting from multiple scattering is weak compared to linearly polarized light.
We have performed numerical simulations to investigate how the focusing lens affects the structure of the electric field in the focus for NAmax = 0.67 and for NA ratio = 0, 0.3 and 0.6. Numerical simulations were performed in MATLAB based on the analytic solution of the diffraction integral described at any point P (r, θ, ϕ) in the image space for linearly  and radially  polarized input beam. Annular illumination is simulated using an apodizing filter constituted by a circular shading mask (mask diameter = 0, 1 mm and 2 mm). In the case of clear aperture the transverse component of the linearly polarized beam has a circular intensity distribution located at the center of the focal region, the orthogonal-transverse component shows a four leaf clover intensity distribution, and the longitudinal component is calculated to have an intensity distribution shaped as two off-axis lobes (Fig. 3). When a radially polarized beam is employed, the transverse component is shaped as a ring around the focus, the longitudinal component is a circle centered in the focus and the orthogonal transverse field is identically zero (Fig. 3). As a result, the polarization in the focus is always oriented along the radial direction and its orientation depends only on the azimuthal angle, in exactly the same manner as the input beam. Therefore a radially polarized beam holds the additional property of maintaining the polarization pattern in the focus, regardless of the focusing conditions. We also examined the polarization of the wave front in the focal plane in case of NA = 0.67 with and without annular aperture. The appearance of an orthogonal-transverse component causes the partial rotation of the electric field vector, hence the scrambling of the state of polarization at certain locations in the focal volume. For a linearly polarized input beam, the contribution of the orthogonal-transverse component can be always considered negligible when integrated over the whole focal plane, but there are single locations at which its amplitude is not negligible and causes the rotation of the electric field.
In this paper we have presented the influence of polarization and apodization on laser induced breakdown threshold in transparent and scattering media. Based on the pulse parameters and laser wavelength used in this study, the expected mechanism by which optical breakdown occurs is multiphoton initiated avalanche ionization . The multiphoton ionization probability is expressed by the following formula :
The dependence of multiphoton absorption (MPA) on input light polarization is usually more explicitly expressed in terms of cross section σN which is a measurable parameter that characterizes the average N-photon absorbability of the medium. Several studies report on the influence of polarization in MPA processes, but the investigation has been limited so far to linear and circular polarization. Furthermore, theoretical as well as experimental conclusions are contradictory. Theoretically, while Klarsfeld and Maquet  found an analytical expression for the ratio σNcirc/ σNlin between the cross sections for circular and linear polarization which demonstrates the dominance of circular polarization, whereas Reiss  showed that linearly polarized is preferred for higher order multiphoton processes. The situation is not less controversial from an experimental point of view. Experiments in Cesium found a better efficiency for circular polarization, while the dominance of linear polarization was qualitatively observed in high-order multiphoton ionization of nitric oxide . More recently, experiments on sapphire and fused silica demonstrated a superiority of linear polarization with a threshold irradiance ratio Ithlin/Ithcirc of 1.23 and 1.13 respectively .
This makes our experimental results very valuable in the road towards a deeper understanding of the role of polarization in multiphoton absorption processes. Here we showed that radially polarized light dominates over linearly polarized in three samples of different scattering properties. The obtained results give a further confirmation of the dependence of MPA processes on input polarization and on the coherence of the laser light and also suggest that the degree of coherence in the focus is higher for radially polarized light than for linearly polarized light. The propagation of polarized light through biological tissue causes the polarization status of photons to change due to tissue birefringence and tissue scattering. The polarization state of light after a single scattering event depends on the scatterer, direction of scatter, and incident polarization state. Because each scattering event can modify the incident polarization state differently, the scrambling effect of single scattering events accumulates, until finally the polarization state is completely random, i.e. uncorrelated with the incident polarization state. Previous studies on the propagation of polarized light trough scattering media have shown that linearly polarized light depolarizes quicker or slower than circularly polarized light depending on the medium properties (type, size and concentration of scattering particles) [26,27]. Most tissues, like the skin, have a preferential scattering in the forward direction with a scattering anisotropy (g) between 0.7 and 0.9 . Here we demonstrated that radially polarized light performs better than linearly polarized light while propagating through tissue phantoms in scattering phantoms with an anisotropy factor g = 0.85.
The results presented in this manuscript on the influence of polarization and apodization on laser induced optical breakdown has potential applications in the fields of fundamental as well as applied research in obtaining desired photomechanical effects with lower irradiance [20,21,29,30]. The results obtained are expressed in terms of pulse energy and irradiance to demonstrate the differences in benefits that could be obtained for different applications while using linearly and radially polarized light for optical breakdown. Linearly polarized light is attractive in terms of better availability of laser sources with less critical requirements on pulse energy and in reducing the cost price of ultra-short lasers and laser based skin treatment devices. The lower intensity threshold obtained with radially polarized light offers the benefits of creating deeper lesions inside the skin leading to precise and well-localized tissue effects with less risk of collateral damage, and thereby improving safety and efficacy of treatment.
In this manuscript, we report for the first time, the effects of polarization and apodization on laser induced optical breakdown threshold using linearly and radially polarized light. The irradiance threshold for optical breakdown was experimentally measured for different conditions of polarization and apodization in transparent and scattering phantoms. We found that optical breakdown can be created with lower irradiance threshold by exploiting the properties of radially polarized light. Moreover, the benefits of radially polarized light over linearly polarized light in preserving the degree of coherence in the focus increases as the scattering properties of the medium is increased. Lower irradiance threshold may allow deeper layers of tissue to be reached, resulting in higher efficacy of treatment and since a lower power is delivered over the same target area, the risks of collateral damage can also be reduced. This has important implications for optical breakdown based biological applications where desired photomechanical effects can be obtained with lower irradiance.
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