Method for minimizing sample damage during the ablation of material using a focused ultrashort pulsed beam

In one aspect the invention provides a method for laser induced breakdown of a material with a pulsed laser beam where the material is characterized by a relationship of fluence breakdown threshold (Fth) versus laser beam pulse width (T) that exhibits an abrupt, rapid, and distinct change or at least a clearly detectable and distinct change in slope at a predetermined laser pulse width value. The method comprises generating a beam of laser pulses in which each pulse has a pulse width equal to or less than the predetermined laser pulse width value. The beam is focused above the surface of a material where laser induced breakdown is desired. The region of least confusion (minimum beam waist or average spot size) is above the surface of the material in which laser induced breakdown is desired since the intensity of the beam falls off in the forward direction, preferably the region of the beam at or within the surface is between the region of least confusion and sufficient to remove material and the minimum intensity necessary for laser induced breakdown of the material to be removed, most preferably the region of minimum intensity is disposed at the surface of the material to be removed. The beam may be used in combination with a mask in the beam path. The beam or mask may be moved in the x, y, and Z directions to produce desired features. The technique can produce features smaller than the spot size and Rayleigh range due to enhanced damage threshold accuracy in the short pulse regime.

FIELD OF THE INVENTION
 This invention relates generally to methods utilizing lasers for modifying
 internal and external surfaces of material such as by ablation or changing
 properties in structure of materials. This invention may be used for a
 variety of materials.
 BACKGROUND OF THE INVENTION
 Laser induced breakdown of a material causes chemical and physical changes,
 chemical and physical breakdown, disintegration, ablation, and
 vaporization. Lasers provide good control for procedures which require
 precision such as inscribing a micro pattern. Pulsed rather than
 continuous beams are more effective for many procedures, including medical
 procedures. A pulsed laser beam comprises bursts or pulses of light which
 are of very short duration, for example, on the order of 10 nanoseconds in
 duration or less. Typically, these pulses are separated by periods of
 quiescence. The peak power of each pulse is relatively high often on the
 order of gigawatts and capable of intensity on the order of 1013 w/cm2.
 Although the laser beam is focused onto an area having a selected
 diameter, the effect of the beam extends beyond the focused area or spot
 to adversely affect peripheral areas adjacent to the spot. Sometimes the
 peripheral area affected is several times greater than the spot itself.
 This presents a problem, particularly where tissue is affected in a
 medical procedure. In the field of laser machining, current lasers using
 nanosecond pulses cannot produce features with a high degree of precision
 and control, particularly when nonabsorptive wavelengths are used.
 It is a general object to provide a method to localize laser induced
 breakdown. Another object is to provide a method to induce breakdown in a
 preselected pattern in a material or on a material. U.S. Pat. No.
 5,656,186 to Mourou et al. is directed to a method for laser-induced
 breakdown. The teaching of Mourou et al. requires that the laser beam be
 focused to a point at or beneath the surface from which material is to be
 removed. Applicants have discovered that it is undesirable to focus at or
 beneath the surface since this results in undesired damage beneath the
 surface, in particular to the substrate (or underlayer) on which the
 material that is to be removed is disposed. This is particularly a problem
 where the underlayer is very sensitive to the laser light and/or can be
 easily damaged by the laser light. Applicants have unexpectedly discovered
 that the light source should be focused above the surface to be removed
 toward this undesired change.
 SUMMARY OF THE INVENTION
 In one aspect the invention provides a method for laser induced breakdown
 of a material with a pulsed laser beam where the material is characterized
 by a relationship of fluence breakdown threshold (Fth) versus laser beam
 pulse width (T) that exhibits an abrupt, rapid, and distinct change or at
 least a clearly detectable and distinct change in slope at a predetermined
 laser pulse width value. The method generating a beam of laser pulses in
 which each pulse has a pulse width equal to or less than the predetermined
 laser pulse width value. The beam is focused to a point above the surface
 of a material where laser induced breakdown is desired. The beam is
 focused to have the region of least confusion above the surface of a
 material where laser-induced breakdown is desired.
 In one aspect, the invention may be understood by further defining the
 predetermined laser pulse width as follows: the relationship between
 fluence breakdown threshold and laser pulse defines a curve having a first
 portion spanning a range of relatively long (high) pulse width where
 fluence breakdown threshold (Fth) varies with the square root of pulse
 width (T1/2). The curve has a second portion spanning a range of short
 (low) pulse width relative to the first portion. The proportionality
 between fluence breakdown threshold and pulse width differ in the first
 and second portions of the curve and the predetermined pulse width is that
 point along the curve between its first and second portions. In other
 words, the predetermined pulse width is the point where the Fth versus
 .tau.p relationship no longer applies, and, of course, it does not apply
 for pulse widths shorter than the predetermined pulse width.
 The scaling of fluence breakdown threshold (Fth) as a function of pulse
 width (T) is expressed as Fth proportional to the square root of T1/2) is
 demonstrated in the pulse width regime to the nanosecond range. The
 invention provides methods for operating in pulse widths to the picosecond
 and femtosecond regime where we have found that the breakdown threshold
 (Fth) does not vary with the square root of pulse width (T1/2).
 Pulse width duration from nanosecond down to the femtosecond range is
 accomplished by generating a short optical pulse having a predetermined
 duration from an optical oscillator. Next the short optical pulse is
 stretched in time by a factor of between about 500 and 10,000 to produce a
 timed stretched optical pulse to be amplified. Then, the time stretched
 optical pulse is amplified in a solid state amplifying media. This
 includes combining the time stretched optical pulse with an optical pulse
 generated by a second laser used to pump the solid state amplifying media.
 The amplified pulse is then recompressed back to its original pulse
 duration.
 In one embodiment, a laser oscillator generates a very short pulse on the
 order of 10 to 100 femtoseconds at a relatively low energy, on the order
 of 0.001 to 10 nanojoules. Then, it is stretched to approximately 100
 picoseconds to 1 nanosecond and 0.001 to 10 nanojoules. Then, it is
 amplified to typically on the order of 0.001 to 1,000 millijoules and 100
 picoseconds to 1 nanosecond and then recompressed. In its final state it
 is 10 to 200 femtoseconds and 0.001 to 1,000 millijoules. Although the
 system for generating the pulse may vary, it is preferred that the laser
 medium be sapphire which includes a titanium impurity responsible for the
 lasing action.
 In one aspect, the method of the invention provides a laser beam which
 defines a spot that has a lateral gaussian profile characterized in that
 fluence at or near the center of the beam spot is greater than the
 threshold fluence whereby the laser induced breakdown is ablation of an
 area within the spot. The maximum intensity is at the very center of the
 beam waist. The beam waist is the point in the beam where wave-front
 becomes a perfect plane; that is, its radius of curvature is infinite.
 This center is at radius R=0 in the x-y axis and along the Z axis, Z=0.
 This makes it possible to damage material in a very small volume Z=0, R=0.
 Thus it is possible to make features smaller than spot size in the x-y
 focal plane and smaller than the Rayleigh range (depth of focus) in the Z
 axis. It is preferred that the pulse width duration be in the femtosecond
 range although pulse duration of higher value may be used so long as the
 value is less than the pulse width defined by an abrupt or discernable
 change in slope of fluence breakdown threshold versus laser beam pulse
 width.
 In another aspect, a diaphragm, disk, or mask is placed in the path of the
 beam to block at least a portion of the beam to cause the beam to assume a
 desired geometric configuration. In still further aspects, desired beam
 configurations are achieved by varying beam spot size or through Fourier
 Transform (FT) pulse shaping to cause a special frequency distribution to
 provide a geometric shape.
 It is preferred that the beam have an energy in the range of 10 nJ
 (nanojoules) to 1 millijoule and that the beam have a fluence in the range
 of 0.1 J/cm2 to 100 J/cm2 (joules per centimeter square). It is preferred
 that the wavelength be in a range of 200 nm (nanometers) to 1 .mu.m
 (micron).
 Advantageously, the invention provides a new method for determining the
 optimum pulse width duration regime for a specific material and a
 procedure for using such regime to produce a precisely configured cut or
 void in or on a material. For a given material the regime is reproducible
 by the method of the invention. Advantageously, very high intensity
 results from the method with a modest amount of energy and the spot size
 can be very small. Damage to adjoining area is minimized which is
 particularly important to human and animal tissue.
 These and other object features and advantages of the invention will be
 become apparent from the following description of the preferred
 embodiments, claims, and accompanying drawings.

DETAILED DESCRIPTION
 Pulses of light emitted by a laser are capable of removing material from a
 sample. Typically, the light is focused onto the surface of the sample to
 both 1) increase the intensity of the light and 2) localize the region of
 material removal. We have found that it is particularly advantageous to
 focus the laser beam above the surface of the material to be ablated,
 rather than focusing at or below the surface. In any situation where
 material must be removed from the surface without risking damage or
 ablation of the underlying substrate, our focusing technique is crucial.
 By focusing above the surface, the maximum intensity of laser light occurs
 away from the sample. The light intensity then decreases monotonically as
 the laser beam moves toward and into the sample (see FIG. 14a). This
 procedure ensures that the laser intensity inside the sample is always
 less than the intensity at the surface of the material to be ablated.
 Since it is often necessary to confine ablation and potential damage to
 the surface of the sample, focusing above the plane of the sample and then
 adjusting the intensity of the light to the minimum necessary for ablation
 ensures that no region beneath the surface of the sample will be ablated
 or damaged.
 Our focusing technique is particularly critical when ultrashort (&lt;10
 psec) pulsed lasers are utilized for ablation. Since ultrashort pulsed
 laser ablation is non-thermal, the ablated region is limited to the
 spatial extent of the focused laser light. Therefore, to eliminate
 ablation and damage to the underlying substrate, it is essential to ensure
 that the peak light intensity occurs outside the sample. Our method
 ensures this. Our technique contrasts significantly with laser ablation in
 which the objective is to remove large quantities of material without
 regard to inflicting damage to the underlying substrate. In this case, by
 focusing the laser beam at or below the surface the laser intensity peaks
 inside the material (see FIG. 14b). This results in the maximum ablation
 efficiency, a desirable characteristic when drilling a simple hole without
 regard to substrate damage.
 The following are examples which illustrate the benefit of focusing the
 laser beam above the surface of the sample to avoid sample damage. In the
 course of developing a tool to ablate chromium defects on a quartz
 photomask, we focused a femtosecond pulsed laser beam onto the surface of
 the chromium. We found that it was difficult to avoid damaging the
 underlying quartz substrate using this approach, since the normal
 variation in focus which typically occurred would often cause the laser
 beam to be focused inside the quartz. When the beam focus occurred in the
 quartz, the laser intensity was sufficient to damage the quartz rendering
 the photomask unusable. However, by focusing the laser beam above the
 chromium surface, we could adjust the laser intensity so that the Cr was
 ablated while the quartz was unaffected. Similarly, in removing unwanted
 biological tissue such as a tumor from an organ, focusing the laser beam
 above the surface of the tumor results in its removal without damaging the
 underlying tissue. Consider a tumor attached to the retina of the eye.
 Focusing a pulsed laser at or below the surface of the tumor can result in
 a maximum laser intensity in the retina rather than the tumor. As the
 tumor is slowly ablated by the laser beam, the laser intensity at or below
 the retina will be greater than the laser intensity at the tumor if the
 laser is focused at or below the surface of the tumor. Focusing above the
 surface of the tumor ensures that the laser intensity is as small as
 possible at the retina and decreases with increasing depth into the
 retina. This minimizes inadvertent damage to the retina.
 There are numerous methods of controlling the focal position of the laser
 beam which will ensure that the maximum intensity occurs above the surface
 of the material to be ablated. FIG. 2 shows a schematic diagram of the
 optical system for repairing chromium defects on a photomask. An objective
 lens forms an image of the mask on a video camera such as a CCD array. By
 adjusting the distance (F) between the mask and the objective, the image
 can be brought into a sharp focus. The optimal distance provides a high
 quality image of the mask with excellent spatial resolution. This optimal
 distance can be determined by visually inspecting the sharpness of the
 image on the CCD array as the distance is varied, using either a computer
 to perform an analysis of the mask image or manually determining the best
 focused image. Alternatively, a height sensor can be used to maintain the
 optimum distance between the mask and the objective lens. The laser beam
 shown in FIG. 15 illuminates an aperture, which in turn is imaged onto the
 mask using the relay lens and the mirror. We intentionally adjust the
 position of the relay lens to ensure that the image of the aperture is
 focused somewhat above the plane of the mask when the objective lens is
 adjusted to the optimal imaging distance. Since the objective lens has a
 large numerical aperture, small variations in the distance between the
 mask and objective can result in large changes in the effective optical
 intensity at or below the mask surface. Typically, the uncertainty in the
 distance F shown in FIG. 15 is comparable to the depth of focus of the
 optical system. The depth of focus (D) is related to the wavelength of the
 light (W) and the numerical aperture of the objective lens (NA), and is
 given approximately by:
EQU D.about.W/(2*(NA).sup.2)
 We adjust the position of relay lens to form an image of the aperture a
 distance slightly greater than D above the plane of the mask, with the
 mask image at best focus. For the mask repair tool we constructed, the
 numerical aperture is approximately 0.95 and the wavelength of light is
 400 nm. Using the method described above, we would typically form an image
 of the aperture approximately 300 nm above the plane of the mask. This
 ensures that the peak optical intensity from the laser beam occurs above
 the mask rather than at or below the surface of the mask, even in cases
 where the mask image is slightly out of focus (due to the typical
 uncertainty in determining the optimum focus). The slight defocus in the
 aperture image at the mask plane has a negligible effect on the spatial
 resolution of the ablated region.
 A more general optical approach is shown in FIG. 16. As in the case
 described above, the distance (F) between the objective lens and the
 sample is adjusted to bring the image of the sample to the best focus
 (highest spatial resolution image). However, in this case the laser beam
 does not illuminate an aperture. Rather, the entire beam enters the
 objective lens and is focused to a gaussian spot. By adjusting the
 convergence angle of the laser beam, either through internal adjustments
 in the laser or through the use of a weak external lens system, the laser
 beam is brought to a focus slightly above the surface of the sample. The
 laser intensity is adjusted independently (using filters or a combination
 of a waveplate and frequency doubling crystal) to a value such that
 ablation just occurs at the sample surface. Since the peak laser intensity
 occurs above the surface of the sample rather than inside the sample, the
 possibility of ablation or damage to the underlying material in the
 substrate is minimized.
 In both cases described above, the focus of the laser beam above the
 surface of the sample can be maintained by 1) establishing a fixed offset
 in the relative focus of the sample image and the laser beam, and 2)
 maintaining the sample at the optimal distance from the objective by
 monitoring the sample image and/or a height sensor. If a significant depth
 of material must be removed (e.g. greater than the depth of focus of the
 optical system), then the distance between the sample and the objective
 lens can be continuously varied by monitoring the depth of the ablated
 material and moving either the objective or the sample in the Z direction.
 DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
 Referring to FIG. 1 there is shown an apparatus for performing tests to
 determine the laser induced breakdown threshold as a function of laser
 pulse width in the nanosecond to femtosecond range using a chirped-pulse
 amplification (CPA) laser system. The basic configuration of such a CPA
 system is described in U.S. Pat. No. 5,235,606 which is assigned to the
 assignee of the present invention and which has inventors in common with
 this present application. U.S. Pat. No. 5,235,606 is incorporated herein
 by reference in its entirety.
 Chirped-pulse amplification systems have been described by Jeffrey Squier
 and Gerard Mourou, two of the joint inventors in the present application,
 in a publication entitled Laser Focus World published by Pennwell in June
 of 1992. It is described that CPA systems can be roughly divided into four
 categories. The first includes the high energy low repetition systems such
 as ND glass lasers with outputs of several joules but they may fire less
 than 1 shot per minute. A second category are lasers that have an output
 of approximately 1 joule and repetition rates from 1 to 20 hertz. The
 third group consists of millijoule level lasers that operate at rates
 ranging from 1 to 10 kilohertz. A fourth group of lasers operates at 250
 to 350 kilohertz and produces a 1 to 2 microjoules per pulse. In U.S. Pat.
 No. 5,235,606 several solid state amplifying materials are identified and
 the invention of U.S. Pat. No. 5,235,606 is illustrated using the
 Alexandrite. The examples below use Ti:Sapphire and generally follow the
 basic process of U.S. Pat. No. 5,235,606 with some variations as described
 below.
 The illustrative examples described below generally pertain to pulse
 energies less than a microjoule and often in the nanojoule range with
 pulse duration in the range of hundreds of picoseconds or less and the
 frequency on the order of 1 kilohertz. But these examples are merely
 illustrative and the invention is not limited thereby.
 In a basic scheme for CPA, first a short pulse is generated. Ideally the
 pulse from the oscillator is sufficiently short so that further pulse
 compression is not necessary. After the pulse is produced it is stretched
 by a grating pair arranged to provide positive group velocity dispersion.
 The amount the pulse is stretched depends on the amount of amplification.
 Below a millijoule, tens of picoseconds are usually sufficient. A first
 stage of amplification typically takes place in either a regenerative or a
 multipass amplifier. In one configuration this consists of an optical
 resonator that contains the gain media, a Pockels cell, and a thin film
 polarizer. After the regenerative amplification stage the pulse can either
 be recompressed or further amplified. The compressor consists of a grating
 or grating pair arranged to provide negative group velocity dispersion.
 Gratings are used in the compressor to correspond to those in the
 stretching stage. More particulars of a typical system are described in
 U.S. Pat. No. 5,235,606, previously incorporated herein by reference.
 An important aspect of the invention is the development of a characteristic
 curve of fluence breakdown threshold Fth as a function of laser pulse
 width specific to a material. Then identify on such curve, the point at
 which there is an abrupt, or distinct and rapid change or at least a
 discernable change in slope characteristic of the material. In general it
 is more desirable to operate past this point because of the more precise
 control of the laser induced breakdown (LIB) or ablation threshold.
 EXAMPLE 1
 Opaque Material
 FIG. 1 shows an experimental setup for determining threshold fluence by
 determining scattered energy versus incident fluence and by determining
 threshold fluence versus pulse width. The system includes means for
 generating a pulsed laser beam as described earlier, and means, typically
 a lens, for collecting emission from the target to a photomultiplier tube.
 Change of transmission through a transparent sample is measured with an
 energy meter.
 FIG. 2 shows a plot of data obtained from an absorbing medium which is gold
 using 150 fs pulse and FIG. 3 shows threshold fluence pulse width. The
 arrow in FIG. 3 identifies the point at which the relationship between the
 threshold fluence and pulse width varies dramatically.
 In experimental conditions with wavelength of 800 nm and 200 fs pulses on
 gold (FIG. 3), the absorption depth is 275 A with a diffusion of 50 A. In
 the case of nanosecond pulses the diffusion length, which is on the order
 of 10 .mu.m (micron) in diameter, is much longer than the absorption
 depth, resulting in thermal diffusion being the limiting factor in feature
 size resolution. Empirical evidence for the existence of these two regimes
 is as exhibited in FIG. 3. Here both experimental and theoretical ablation
 thresholds are plotted as a function of pulse width. An arrow at
 approximately 7 picoseconds pulse width (designated herein as T or .tau.p)
 delineates the point (or region closely bounding that point) at which the
 thermal diffusion length (lth) is equal to the absorption depth (1/a). It
 is clear that for a smaller size spot a shorter (smaller) pulse is
 necessary. For spot size on the order of 1000 .ANG. or less, pulse width
 on the order of 100 femtoseconds or less will be needed. It is clear from
 the figure that this is the point at which the ablation threshold
 transitions from a slowly varying or nearly constant value as a function
 of pulse width to one that is dramatically dependent on pulse time. This
 result is surprising. It has been that the electron thermalization time
 for laser deposited energy in gold is on the order of, or less than, 500
 fs and the electron-lattice interaction time is 1 ps. The consequences of
 this for ultrafast laser pulses is that the energy is contained within the
 beam spot. In fact for energies at or near the threshold for ablation, the
 spatial profile of the laser beam will determine the size and shape of the
 region being ablated (FIGS. 4 and 5).
 Additional experiments were performed to measure the amount of
 recombination light produced as a function of the fluence impinging on a
 gold film. The technique involved is based upon the experimental setup
 previously described. A basic assumption is that the intensity of the
 light is proportional to the amount of material ablated. In FIG. 4, the
 material removed is plotted as a function of fluence. A well defined
 threshold fluence is observed at which material removal is initiated. By
 having only a small fraction of the gaussian beam where the fluence is
 greater than the threshold, the ablated region can be restricted to this
 small area. In FIG. 4, Ra is the radial position on the beam where the
 fluence is at threshold. Ablation, then, occurs only within a radius Ra.
 It is evident that by properly choosing the incident fluence, the ablated
 spot or hole can in principle be smaller than the spot size, Rs. This
 concept is shown schematically in FIG. 5. Although the data for a 150 fs
 pulse is shown in FIG. 4, this threshold behavior is exhibited in a wide
 range of pulse widths. However, sub spot size ablation is not possible in
 the longer pulse regimes, due to the dominance of thermal diffusion as
 will be described below.
 Additional experiments on opaque materials used a 800 nm Ti:Sapphire
 oscillator whose pulses were stretched by a grating pair, amplified in a
 regenerative amplifier operating at 1 kHz, and finally recompressed by
 another grating pair. Pulse widths from 7 ns to 100 fs were obtained. The
 beam was focused with a 10.times. objective, implying a theoretical spot
 size of 3.0 .mu.m in diameter. A SEM photo-micrograph of ablated holes
 obtained in a silver film on glass, using a pulse width of 200 fs and a
 pulse energy of 30 nJ (fluence of 0.4 J/cm2) produced two holes of
 diameter approximately 0.3 .mu.m in diameter. Similar results have been
 obtained in aluminum.
 These results suggest that by, producing a smaller spot size which is a
 function of numerical aperture and wavelength, even smaller holes can be
 machined. We have demonstrated the ability to generate the fourth harmonic
 (200 nm) using a nonlinear crystal. Thus by using a stronger objective
 lens along with the 200 nm light, holes with diameters of 200 angstroms
 could in principle be formed.
 These examples show that by using femtosecond pulses the spatial resolution
 of the ablation/machining process can be considerably less than the
 wavelength of the laser radiation used to produce it. The ablated holes
 have an area or diameter less than the area or diameter of the spot size.
 In the special case of diffraction limited spot size, the ablated hole has
 a size (diameter) less than the fundamental wavelength size. We have
 produced laser ablated holes with diameters less than the spot diameter
 and with diameters 10% or less of the laser beam spot size.
 For ultrafast pulses in metals the thermal diffusion length, lth=(Dt)1/2
 (where D is the thermal diffiusivity and t the pulse time), is
 significantly smaller than the absorption depth (1/a), where a is the
 absorption coefficient for the radiation.
 Those skilled in the art will understand that the basic method of the
 invention may be utilized in alternative embodiments depending on desired
 configurations of the induced breakdown. Examples include, but are not
 limited to using a mask in the beam path, varying spot size, adjusting
 focus position by moving the lens, adjusting laser cavity design, Fourier
 Transform (FT) shaping, using a laser operating other than TEMoo, and
 adjusting the Rayleigh range, the depth of focus or beam waist.
 The use of a mask is illustrated in FIGS. 6A and B. The basic method
 consists of placing a mask in the beam path or on the target itself. If is
 desired to block a portion of the beam, the mask should be made of an
 opaque material and be suspended in the beam path (FIG. 6A), the mask may
 be placed on the target and be absorptive so as to contour the target to
 the shape of the mask (FIG. 6B).
 The varying spot size is accomplished by varying the laster f/#, i.e.,
 varying the focal length of the lens or input beam size to the lens as
 adjustable diaphragm in other than the TEMoo mode means that higher order
 transverse modes could be used. This affects the beam and material as
 follows: the beam need not be circular or gaussian in intensity. The
 material will be ablated corresponding to the beam shape.
 The Rayleigh range (Z axis) may be adjusted by varying the beam diameter,
 where the focal plane is in the x-y axis.
 EXAMPLE 2
 Transparent Material
 A series of tests were performed on an SiO2 (glass) sample to determine the
 laser induced breakdown (LIB) threshold as a function of pulse width
 between 150 fs-7 ns, using a CPA laser system. The short pulse laser used
 was a 10 Hz Ti:Sapphire oscillator amplifier system based on the CPA
 technique. The laser pulse was focused by an f=25 cm lens inside the SiO2
 sample. The Rayleigh length of the beam is .about.2 mm. The focused spot
 size was measured in-situ by a microscope objective lens. The measured
 spot size FWHM (full at half max) was 26 .mu.m in diameter in a gaussian
 mode. The fused silica samples were made from Corning 7940, with a
 thickness of 0.15 mm. They were optically polished on both sides with a
 scratch/dig of 20-10. Each sample was cleaned by methanol before the. Thin
 samples were used in order to avoid the complications of self-focusing of
 the laser pulses in the bulk. The SiO2 sample mounted on a computer
 controlled motorized X-Y translation stage. Each location on the sample
 was illuminated by the laser only once.
 Two diagnostics were used to determine the breakdown threshold Fth. First,
 the plasma emission from the focal region was collected by a lens to a
 photomultiplier tube with appropriate filters. Second, the change of
 transmission through the sample was measured with an energy meter. (See
 FIG. 1) Visual inspection was performed to confirm the breakdown at a
 nanosecond pulse duration. FIG. 7 shows typical plasma emission and
 transmitted light signal versus incident laser energy plots, at a laser
 pulse width of .tau.p=300 fs. It is worth noting that the transmission
 changed slowly at around Fth. This can be explained by the temporal and
 spatial behavior of the breakdown with ultrashort pulses. Due to the
 spatial variation of the intensity, the breakdown will reach threshold at
 the center of the focus, and because of the short pulse duration, the
 generated plasma will stay localized. The decrease in transmitted light is
 due to the reflection, scattering, and absorption by the plasma. By
 assuming a gaussian profile in both time and space for the laser
 intensity, and further assuming that the avalanche takes the entire pulse
 duration to reach threshold, one can show that the transmitted laser
 energy Ut as a function of the input energy U is given by
EQU Ut=kU, U&lt;=Uth
EQU Ut=kUth[1+ln(U/Uth)], U&gt;Uth
 where k is the linear transmission coefficient. The solid curve in FIG. 7
 is plotted using Eq. (1), with Uth as a fitting parameter. In contrast,
 breakdown caused by nanosecond laser pulses cuts off the transmitted beam
 near the peak of the pulses, indicating a different temporal and spatial
 behavior.
 FIG. 8 shows the fluence breakdown threshold Fth as a function of laser
 pulse width. From 7 ns to about 10 ps, the breakdown threshold the scaling
 in the relatively long pulse width regime (triangles and squares) are also
 shown as a comparison--it can be seen that the present data is consistent
 with earlier work only in the higher pulse width portion of the curve.
 When the pulse width becomes shorter than a few picoseconds, the threshold
 starts to increase. As noted earlier with respect to opaque material
 (metal), this increased precision at shorter pulse widths is surprising. A
 large increase in damage threshold accuracy is observed, consistent with
 the multiphoton avalanche breakdown theory. (See FIGS. 8 and 9.) It is
 possible to make features smaller than spot size in the x-y focal plane
 and smaller than the Rayleigh range (depth of focus) in the longitudinal
 direction or Z axis. These elements are essential to making features
 smaller than spot size or Rayleigh range.
 EXAMPLE 3
 Tissue
 A series of experiments was performed to determine the breakdown threshold
 of cornea as a function of laser pulse width between 150 ns, using a CPA
 laser system. As noted earlier, in this CPA laser system, laser pulse
 width can be varied while all other experimental parameters (spot size,
 wavelength, energy, etc.) remain unchanged. The laser was focused to a
 spot size (FWHM) of 26 .mu.m in diameter. The plasma emission was recorded
 as a function of pulse energy in order to determine the tissue damage
 threshold. Histologic damage was also assessed.
 Breakdown thresholds calculated from plasma emission data revealed
 deviations from the scaling law, Fth .alpha. T1/2, as in the case of and
 glass. As shown in FIG. 9, the scaling law of the fluence threshold is
 true to about 10 ps, and fail when the pulse shortens to less than a few
 picoseconds. As shown in FIGS. 10 and 11, the ablation or LIB threshold
 varies dramatically at high (long) pulse width. It is very precise at
 short pulse width. These results were obtained at 770 nm wavelengths. The
 standard deviation of breakdown threshold measurements decreased markedly
 with shorter pulses. Analysis also revealed less adjacent histological
 damage with pulses less than 10 ps.
 The breakdown threshold for ultrashort pulses (&lt;10 ps) is less than
 longer pulses and has smaller standard deviations. Reduced adjacent
 histological damage to tissue results from the ultrashort laser pulses.
 In summary, it has been demonstrated that sub-wavelength holes can be
 machined into metal surfaces using femtosecond laser pulses. The effect is
 physically understood in terms of the thermal diffusion length, over the
 time period of the pulse deposition, being less than the absorption depth
 of the incident radiation. The interpretation is further based on the hole
 diameter being determined by the lateral gaussian distribution of the
 pulse in relation to the threshold for vaporization and ablation.
 Laser induced optical breakdown dielectrics consists of three general
 steps: free electron generation and multiplication, plasma heating and
 material deformation or breakdown. Avalanche ionization and multiphoton
 ionization are the two processes responsible for the breakdown. The laser
 induced breakdown threshold in dielectric material depends on the pulse
 width of the laser pulses. An empirical scaling law of the fluence
 breakdown threshold as a function of the pulse width is given by Fth
 .alpha. .sqroot..tau.p, or alternatively, the intensity breakdown
 threshold, Ith=Fth/.tau.p. Although this scaling law applies in the pulse
 width regime from nanosecond to tens of picoseconds, the invention takes
 advantage of the heretofore unknown regime where breakdown threshold does
 not follow the scaling law when suitably short laser pulses are used, such
 as shorter than 7 picoseconds for gold and 10 picoseconds for SiO2.
 While not wishing to be held to any particular theory, it is thought that
 the ionization process of a solid dielectric illuminated by an intense
 laser pulse can be described by the general equation
EQU dne(t)/dt=.eta.(E)ne(t)+(dne(t)/dt)PI-(dne(t)/dt)loss
 where ne (t) is the free electron (plasma) density, .eta.(E) is the
 avalanche coefficient, and E is the electric field strength. The second
 term on the right hand side is the photoionization contribution, and the
 third term is the loss due to electron diffusion, recombination, etc. When
 the pulse width is in the picosecond regime, the loss of the electron is
 negligible during the duration of the short pulse.
 Photoionization contribution can be estimated by the tunneling rate. For
 short pulses, E.about.108 V/cm, the tunneling rate is estimated to be
 w.about.4.times.109 sec-1, which is small compared to that of avalanche,
 which is derived below. However, photoionization can provide the initial
 electrons needed for the avalanche processes at short pulse widths. For
 example, the data shows at 1 ps, the rms field threshold is about
 5.times.107 V/cm. The field will reach a value of 3.5.times.107 V/cm (rms)
 at 0.5 ps before the peak of the pulse, and w.about.100 sec-1. During a
 DELTA.t.about.100 fs period the electron density can reach ne.about.nt
 [1-exp(-w.DELTA.t)].about.1011 cm-3, where nt.about.1022 is the total
 initial valence band electron density.
 Neglecting the last two terms there is the case of an electron avalanche
 process, with impact ionization by primary electrons driven by the laser
 field. The electron density is then given by ne (t)=no.times.exp(n(E)t),
 where no is the initial free electron density. These initial electrons may
 be generated through thermal ionization of shallow traps or
 photoionization. When assisted by photoionization at short pulse regime,
 the breakdown is more statistical. According to the condition that
 breakdown occurs when the electron density exceeds nth .congruent.1018
 cm-3 and an initial density of no .congruent. 1010 cm-3, the breakdown
 condition is then given by .eta..tau.p .congruent.18. For the experiment,
 it is more appropriate to use nth .congruent.1.6.times.1021 cm-3, the
 plasma critical density, hence the threshold is reached when eta..tau.p
 .congruent.30. There is some arbitrariness in the definition of plasma
 density relating to the breakdown threshold. However, the particular
 choice of plasma density does not change the dependence of threshold as
 function of pulse duration (the scaling law).
 In the experiment, the applied electric field is on the order of a few tens
 of MV/cm and higher. Under such a high field, the electrons have an
 average energy of .about.5 eV, and the electron collision time is less
 than 0.4 fs for electrons with energy U.gtoreq.gt;=5-6 eV. Electrons will
 make more than one collision during one period of the electric
 oscillation. Hence the electric field is essentially a dc field to those
 high energy electrons. The breakdown field at optical frequencies has been
 shown to correspond to dc breakdown field by the relationship Erm.kappa.th
 (w)=Edcth (1+w2 .tau.2)1/2, where w is the optical frequency and .tau. is
 the collision time.
 In dc breakdown, the ionization rate per unit length, .alpha., is used to
 describe the avalanche process, with .eta.=.alpha.(E)vdrift, where vdrift
 is the drift velocity of electrons. When the electric field is as high as
 a few MV/cm, the drift velocity of free electrons is saturated and
 independent of the laser electric field, vdrift .congruent.2.times.107
 cm/s.
 The ionization rate per unit length of an electron is just eE/Ui times the
 probability, P(E), that the electron has an energy .gtoreq.gt;=Ui, or
 .alpha.(E)=(eE/Ui)P(E). Denoting EkT,E p, and Ei as threshold fields for
 electrons to overcome the decelerating effects of thermal, phonon, and
 ionization scattering, respectively. Then the electric field is
 negligible, EkT, so the distribution is essentially thermal, P(E) is
 simply exp(-Ui/kT). It has been suggested: P(E).about.exp(-const/E) for
 EkT p; P(E).about.exp(-const/E2) at higher fields (E&gt;Ep). Combining the
 three cases the expression that satisfies both low and high field limits:
EQU .alpha.(E)=(eE/Ui)exp(-Ei/(E(1+E/Ep)+EKT).
 This leads to Fth .alpha. E2 .tau.p.about.1/.tau.p, i.e., the fluence
 threshold will increase for ultrashort laser pulses when E&gt;.sqroot.Ep
 Ei is satisfied.
 FIG. 12 is a plot of .alpha. as a function of the electric field, E. From
 experimental data, calculated according to .eta..tau.p=30 and
 eta.=avdrift. The solid curve is calculated from the above equation, using
 Ei=30 MV/cm, Ep=3.2 MV/cm, and EkT=0.01 MV/cm.
 These parameters are calculated from U=eEl, where U is the appropriate
 thermal, phonon, and ionization energy, and l is the correspondent energy
 relation length (lkT=lp.about.5 .ANG., the atomic spacing, and li
 .congruent.30 .ANG.). It shows the same saturation as the experimental
 data. The dashed line is corrected by a factor of 1.7, which results in an
 excellent fit with the experimental data. This factor of 1.7 is of
 relatively minor importance, as it can be due to a systematic correction,
 or because breakdown occurred on the surface first, which could have a
 lower threshold. The uncertainty of the saturation value of vdrift also
 can be a factor. The most important aspect is that the shape (slope) of
 the curve given by the equation provides excellent agreement with the
 experimental data. Thus, the mechanism of laser induced breakdown in fused
 silica (Example 2), using pulses as short as 150 fs and wavelength at 780
 nm, is likely still dominated by the avalanche process.
 Opaque and transparent materials have common characteristics in the curves
 of FIGS. 3, 8, and 9 each begins with Fth versus T1/2 behavior but then
 distinct change from that behavior is evident. From the point of
 deviation, each curve is not necessarily the same since the materials
 differ. The physical characteristics of each material differ requiring a
 material specific analysis. In the case of SiO2 FIG. 8) the energy
 deposition mechanism is by dielectric breakdown. The optical radiation is
 releasing electrons by multiphoton ionization (M PI) that are tightly
 bound and then accelerating them to higher energies by high field of the
 laser. It is thought that only a small amount of relatively high energy
 electrons exist prior to the laser action. The electrons in turn collide
 with other bound electrons and release them in the avalanching process. In
 the case of metal, free electrons are available and instantly absorbing
 and redistributing energy. For any material, as the pulses get shorter
 laser induced breakdown (LIB) or ablation occurs only in the area where
 the laser intensity exceeds LIB or ablation threshold. There is
 essentially insufficient time for the surrounding area to react thermally.
 As pulses get shorter, vapor from the ablated material comes off after the
 deposition of the pulse, rather than during deposition, because the pulse
 duration is so short. In summary, by the method of the invention, laser
 induced breakdown of a material causes thermal-physical changes through
 ionization, free electron multiplication, dielectric breakdown, plasma
 formation, other thermal-physical changes in state, such as melting and
 vaporization, leading to an irreversible change in the material. It was
 also observed that the laser intensity also varies along the propagation
 axis (FIG. 13). The beam intensity as a function of R and Z expressed as:
EQU I((Z, R)=Io/(1+Z/ZR)2 .multidot.exp(-2R2/W2z)
 where ZR is the Rayleigh range and is equal to [Figure] Wo is the beam size
 at the waist (Z=0).
 We can see that the highest value of the field is at Z=R=0 at the center of
 the waist. If the threshold is precisely defined it is possible to damage
 the material precisely at the waist and have a damaged volume representing
 only a fraction of the waist in the R direction or in the Z direction. It
 is very important to control precisely the damage threshold or the laser
 intensity fluctuation.
 For example, if the damage threshold or the laser fluctuations known within
 10% that means that on the axis (R=0) I(0,Z)/Io=1/(1=(Z/ZR)2=0.9 damaged
 volume can be produced at a distance ZR/3 where ZR again is the Rayleigh
 range. For a beam waist of Wo=.lambda. then Figure] and the d distance
 between hole can [Figure] as shown in FIG. 13.
 The maximum intensity is exactly at the center of the beam waist (Z=0,
 R=0). For a sharp threshold it is possible to damage transparent,
 dielectric material in a small volume centered around the origin point
 (Z=0, R=0). The damage would be much smaller than the beam waist in the R
 direction. Small cavities, holes, or damage can have dimensions smaller
 than the Rayleigh range (ZR) in the volume of the transparent, dielectric
 material. In another variation, the lens can be moved to increase the size
 of the hole or cavity in the Z dimension. In this case, the focal point is
 essentially moved along the Z axis to increase the longitudinal dimension
 of the hole or cavity. These features are important to the applications
 described above and to related applications such as micro machining,
 integrated circuit manufacture, and encoding data in data storage media.
 Advantageously, the invention identifies the regime where breakdown
 threshold fluence does not follow the scaling law and makes use of such
 regime to provide greater precision of laser induced breakdown, and to
 induce breakdown in a preselected pattern in a material or on a material.
 The invention makes it possible to operate the laser where the breakdown
 or ablation threshold becomes essentially accurate. The accuracy can be
 clearly seen by the I-bars along the curves of FIGS. 8 and 9. The I-bars
 consistently show lesser deviation and correspondingly greater accuracy in
 the regime at or below the predetermined pulse width.
 While this invention has been described in terms of certain embodiment
 thereof, it is not intended that it be limited to the above description,
 but rather only to the extent set forth in the following claims. The
 embodiments of the invention in which an exclusive property or privilege
 is claimed are defined in the appended claims.
 The teaching of the following references are incorporated herein by
 reference:
 Foreign References