Method and apparatus for high precision variable rate material removal and modification

A method and apparatus is disclosed for fast precise material processing and modification which minimizes collateral damage. Utilizing optimized, pulsed electromagnetic energy parameters leads to an interaction regime which minimizes residual energy deposition. Advantageously, removal of cumulative pulse train residual energy is further maximized through the rapid progression of the ablation front which move faster than the thermal energy diffusion front, thus ensuring substantial removal of residual energy to further minimize collateral thermal damage.

FIELD OF THE INVENTION 
The present invention is generally related to the field of pulsed 
electromagnetic energy source systems suitable for material and biological 
tissue modification processing and removal and is more particularly 
related to a material removal and modification method and apparatus in 
which pulsed electromagnetic sources of high ablation-to-deposition depth 
ratios are operable at pulse repetition rates ranging up to approximately 
several hundreds of thousands of pulses per second so as to efficiently 
and precisely remove substantial material volumes while substantially 
eliminating collateral damage. 
BACKGROUND OF THE INVENTION 
The past three decades have brought increased interest in the use of lasers 
in material processing applications. Early procedures for material 
processing and cutting involved optical drilling using continuous wave or 
relatively long pulse (e.g., 50 to 350 .mu.s) lasers such as C02, ruby and 
ND:YAG (Neodymium doped Yittrium Aluminum Garnet). These systems, however, 
required relatively high radiant exposure and resulted in significant 
alterations to surrounding tissue. As a consequence, lasers could become 
an effective cutting tool only in areas which did not require high degree 
of precision or control. 
Optical drilling with ER:YAG (Erbium doped YAG) lasers yielded encouraging 
results in the late 1980s, and has demonstrated its capability to perform 
as an efficient drill while incurring only relatively low levels of 
collateral damage to surrounding tissue, provided that no more than one to 
three pulses per second were applied to the target material. The success 
of ER:YAG systems, operating in the microsecond pulse duration regime and 
minimizing thermal damage has also been observed in several areas of 
applications in material processing and medicine, and can be attributed to 
the high absorption coefficient of these materials at the particular 
wavelengths characteristic of the Er:YAG system (2900 nm), when used in 
combination with the relatively short pulse durations and at low pulse 
repetition rates. 
Laser systems adapted to hard tissue processing, such as dentin and enamel 
removal in dental applications are disclosed in: 1. Hibst R, Kelly U. 
Experimental studies of the application of the Er:YAG laser on dental hard 
substances: I. Measurement of the Ablation Rate. Laser Surgery and 
Medicine 1989, 9:352-7; and, 2. Keller U, Hibst R. Experimental studies of 
the application of the Er:YAG laser on dental hard substances: II. Light 
microscopy and SEM investigations. Lasers in Surgery and Medicine 1989; 
9:345-351.) 
Both pulsed CO2 and Er:YAG are disclosed in: Walsh, J. T., Flotte, T. J., 
Anderson, R. R., Deutsch, T. F., "Pulsed CO.sub.2 Laser Tissue Ablation: 
Effect of Tissue Type and Pulse Duration on Thermal Damage, "Lasers in 
Surgery and Medicine, Vol. 8, pp.108-118, 1988; Walsh, J. T., Flotte, T. 
J., Deutsch, T. F., "Er:YAG Laser Ablation of Tissue: Effect of Pulse 
Duration and Tissue Type on Thermal Damage, "Lasers in Surgery and 
Medicine, Vol. 9, No. 4, pp. 314, 1989; and Walsh, J. T., Deutsch, T. F., 
"Er:YAG Laser Ablation of Tissue: Measurement of Ablation Rates, "Lasers 
in Surgery and Medicine, Vol. 9 No. 4, pp. 327, 1989. 
A Ho:YSGG laser system is disclosed in Joseph Neev, Kevin Pham, Jon P. Lee, 
Joel M. White, "Dentin Ablation with Three Infrared Lasers," Lasers in 
Surgery and Medicine, 18:121-128 (1996). 
The laser systems disclosed (Er:YSGG, HO:YSGG, and Pulsed CO2) all operate 
in the IR region of the electromagnetic spectrum and are pulsed in two 
different regimes: about 250 microsecond pulse durations for the ER:YSGG 
and HO:YSGG lasers, and about 150 microsecond pulse durations for the CO2 
system. 
While the disclosed removal rate is in the range of approximately tens of 
micrometers per pulse, the disclosed laser systems exhibit wavelength 
dependent absorption and result in high removal rates by operating at 
pulse energies in excess of 30 millijoules per pulse and often on the 
order of a few hundreds of .mu.J per pulse. Enhancing material removal by 
increasing laser power is, however, accompanied by increased photothermal 
and photomechanical effects which causes collateral damage in adjacent 
material. In addition, increasing power leads to plasma de coupling of the 
beam, e.g., incident laser energy is wasted in heating the ambient in 
front of the target. High intensity pulses additionally cause very loud 
acoustic snaps, when the laser pulse interacts with tissue. These snaps or 
pops include a large high frequency component which is very objectionable 
to a user or, in the case of a medical application, to a patient. In 
addition to the psychological impact of such noise, these high frequency 
snaps are able to cause hearing loss in clinicians when repeated over a 
period of time. 
U.S. Pat. No. 5,342,198, to Vassiliadis, et al. discloses an ER:YAG IR 
laser system suitable for the removal of dentin in dental applications. 
The laser produces a pulsed output having a beam with a pulse duration in 
the range of several tens of picoseconds to about several milliseconds. 
Although disclosed as being efficient in the removal of dentin and dental 
enamel, the mechanism by which material removal is effected is not 
understood. Significantly, however, the only laser systems disclosed as 
suitable for the process are those which operate at wavelengths (1.5 to 
3.5 microns) that have proven to be generally effective for enamel 
interaction. Thus, the absorption characteristics of the material target 
are of primary concern to the removal rate. In addition, high energy 
levels are required to remove enamel and dentin, leading to the problem of 
thermal damage and acoustic noise. 
Additional possibilities for the application of lasers to the field of 
dentistry in particular, and to hard tissue ablation in general, have been 
proposed by the use of excimer lasers that emit high intensity pulses of 
ultraviolet (UV) light. 
Several such pulsed UV excimer laser systems, typically with pulse 
durations in the approximately 1 to 125 nanosecond range are disclosed in: 
1. Neev J, Stabholz A., Liaw L. L, Torabinejad M, Fujishige J. T., Ho P. H, 
Berns M. W., "Scanning Electron Microscopy and Thermal characteristics of 
Dentin ablated by a short-pulse XeCl Laser", Lasers in Surgery and 
Medicine; 
2. Neev J, Liaw L, Raney D, Fujishige J, Ho P, Berns M. Selectivity and 
efficiency in the ablation of hard Dental tissue with ArF pulsed excimer 
lasers. Lasers Surgery and Medicine 1991; 11:499-510; 
3. Neev J, Raney D, Whalen W, Fujishige J, Ho P, McGrann J, Berns M. 
Ablation of hard dental tissue with 193 nm pulsed laser radiation: A 
photophysical study. Spie proceedings, January 1991; and 
4. Neev J, Raney D, Whalen W, Fujishige J, Ho P, McGrann J, Berns M. Dentin 
ablation with two excimer lasers: A comparative study of physical 
characteristics. Lasers Life Sci 1992; 4(3):1-25. Both the short 
wavelengths and nanosecond range pulse durations used by excimer lasers 
contribute to define a different regime of laser-tissue-interaction. Short 
wavelength ultraviolet photons are energetic enough to directly break 
chemical bonds in organic molecules. As a consequence, UV excimer lasers 
can often vaporize a material target with minimal thermal energy transfer 
to adjacent tissue. The resultant gas (the vaporization product) is 
ejected away from the target surface, leaving the target relatively free 
from melt, recast, or other evidence of thermal damage. 
Another important characteristic of UV excimer lasers is that materials 
which are transparent to light in the visible or near infra-red portions 
of the electromagnetic spectrum often begin to exhibit strong absorption 
in the UV region of the spectrum. It is well established that the stronger 
a materials absorption at a particular wavelength, the shallower the 
penetration achieved by a laser pulse having that wavelength. Thus, in 
many types of materials, a pulse typically only penetrates to a depth in 
the range of from about 10 to about 100 micrometers. By simply counting 
pulses, great precision can be achieved in defining removal depths. In 
addition, organic tissue is strongly absorbent in the UV wavelengths (193 
nm for ArF, for example) therefore allowing the laser-tissue interaction 
region to be controlled with great precision. 
Notwithstanding the relatively damage free material removal characteristics 
of UV excimer lasers, these systems suffer from several disadvantages 
which limit their applicability to biological tissue processing. The 
reports of damage free tissue removal result from evaluations performed on 
single pulses, or on pulses with a very low repetition rate (typically 
about 1 to 10 Hertz). Because of the low volumetric removal per pulse of 
excimer systems (material removed per unit time is poor), efficient 
material removal can only be accomplished by high pulse repetition rates. 
However, when the pulse repetition rate exceeds about 3 to 5 Hertz, 
considerable thermal and mechanical collateral damage is observed. While 
UV photons are sufficiently energetic to directly break chemical bonds, 
they are also sufficiently energetic to promote mutagenic effects in 
tissue irradiated at UV wavelengths, raising concerns about the long term 
safety and health of a system operator. The scattered light produced by 
excimer lasers also presents a significant threat to the clinician and/or 
the patient. Even low intensity scattered radiation, with wavelengths 
below 300 nanometers, is able to interact with the ambient environment to 
produce atomic oxygen and other free radicals. These can, in turn, react 
with the lens and cornea of the eye, producing cataracts, and produce 
burns on the skin equivalent to sun burns. As a consequence, excimer laser 
systems have been found to be most suitable for inorganic material 
processing applications, such as thin coating patterning or dielectric or 
semiconductor material etching. 
In addition, the operational parameters of excimer laser systems are such 
that material removal remains a wavelength and beam energy dependent 
process (although weakly dependent on wavelength). Even when pulsed in the 
tens of nanoseconds pulse duration regime, excimer lasers are configured 
to deliver energy in the range of from about 10 to about 1000 millijoules 
per pulse. At the higher energies, excimer lasers suffer from the same 
problems caused by plasma decoupling and pulse to pulse interaction as IR 
lasers. Additionally, as pulse energy increases, so too does the intensity 
of the associated acoustic snap. 
Neev et al. (University of California Case No. 95-313-1) U.S. patent 
application Ser. No. 08/584,522 described a Selective material removal 
processing Ultra Short Pulse Lasers (USPL) system in combination with a 
feedback system and with higher pulse repetition rates. This invention is 
directed to a system for efficient biological tissue removal using ultra 
short pulses. Such pulse durations are shorter than the characteristics 
electron-phonon energy transfer time, thus minimizing collateral thermal 
damage. The method also requires that plasma is formed and decayed so that 
a thin layer portion of the material is removed. The plasma formation step 
is then repeated at a pulse repetition rate greater than 10 pulses per 
second until a sufficient depth of material has been removed with little 
transfer of thermal or mechanical energy into the remaining material due 
to the shortness of the pulse duration. The preferred wavelength for that 
invention is in the range of 200-2500 nm. The laser specified in that 
patent application is a Chirped Pulse Amplifier (CPA) Solid-state laser. 
That patent further specified that the laser system is comprised of a 
feedback means for analyzing material characteristics in response to 
interaction between the laser pulses. The envisioned feedback means 
comprises a spectrograph to evaluate the plasma formed by each pulse. The 
feedback means is operatively coupled to the laser. The laser operatively 
responds to the control signal such that the laser ceases operation upon 
receipt of the control signal. The feedback means also comprises an 
optical tomograph which optically evaluates the amount of target material 
removed by each pulse. 
This invention should work well in many applications. Unfortunately, the 
equipment for the ultrashort pulse duration is very expensive (currently, 
over $100,000 and often two or three times that amount) and still requires 
many components and careful maintenance. The systems are also very large 
and delicate and require large volume for storage and expert maintenance 
at this stage of the technology. Also the interaction is not very 
selective nor highly sensitive to the targeted material type but rather 
ablate most materials. This, in turn, effects some risk of over ablating 
or removal of unintended structures. The highly interactive nature of the 
ultrashort pulse process possess additional problems to attempts to 
deliver the ultrashort pulse beam to the target. Most optical fibers as 
well as mirror and lenses could easily be damaged if ablation threshold is 
exceeded (either through narrowing of the beam spot size, an increase in 
pulse energy, or compression of the pulse duration). Thus ultrashort 
pulses are hard to deliver through most conventional delivery systems. 
An additional problem is that ultrashort pulse lasers are currently 
achieved principally in the near IR region of the electromagnetic 
spectrum. This is a highly transparent region for most biotissue material. 
Consequently, some portion of the radiation propagates linearly into the 
material and is not confined to the surface. This additional energy 
propagating into the target may then encounter more absorbing structures 
(for example the blood vessels in the retina) and will then result in a 
secondary--unintended--ablative interaction, posing risk to the patients 
or to the material being processed. 
U.S. Pat. No. 4,907,586 issued to Bille and Brown for "METHOD FOR RESHAPING 
THE EYE", disclosed a method for modifying tissue with a quasi-continuous 
laser beam to change the optical properties of the eye which comprises 
controllably setting the volumetric power density of the beam and 
selecting a desired wavelength for the beam. Tissue modification is 
accomplished by focusing the beam at a preselected start point in the 
tissue and moving the beam's focal point in a predetermined manner 
relative to the start point throughout a specified volume of the tissue or 
along a specified path in the tissue. 
More particularly, the method describes a sequence of uninterrupted 
emissions of at least one thousand pulses lasting for at least one second. 
The pulses were specified lasting approximately one picosecond (1 ps) in 
duration and of less than 30 micro joules (30 .mu.J). 
The invention disclosed in U.S. Pat. No. 4,907,586 should work well for 
reshaping the eye, but is confined to the region of 1 ps and thus also 
involves the generation of ultrashort pulses and their relative low 
thermal and mechanical deposition of energy during the single pulse 
interaction. This device thus requires the use of expensive ultrashort 
pulses with all the specified limitations mentioned above. In addition, 
this invention is limited to relatively low energies of 30 .mu.J, which 
require a very tightly focused beam to affect tissue ablation. The 
invention will thus not work well for larger areas or for high volume 
removal rates, which are required in many applications, e.g., dentistry, 
surgery, etc. This invention is also limited with regards to its ability 
to deliver pulses through optical fibers, hollow waveguides or 
conventional optics since the very shorted pulses of 1 ps are also very 
reactive and will interact with most material used as deliver media. 
Consequently, specialty optics has to be used and conventional lenses and 
mirrors as well as optical fiber and conventional hollow waveguides cannot 
be used. 
In the present invention, the inventor has recognized that a much wider 
range of pulse durations of up to approximately several hundred 
microseconds will allow the thermal diffusion to remain confined to within 
a distance of only a few micrometer of the ablated crater. Thus, the 
present invention is concerned with pulses up to several milliseconds 
long. With a combination of short pulse to pulse separation and with new 
requirement on both the number and the rate of the incident sequential 
pulses, the present invention allows large volume removal or volume 
processing with substantially little damage to surrounding regions of the 
target. 
The present invention thus allows the use of pulse laser systems that are 
substantially less expensive and in many instances safer and more 
efficient than those described by other inventions, while achieving 
unprecedented volume removal rate, high precision, high efficiency and 
minimal thermal or mechanical collateral damage. 
SUMMARY OF THE INVENTION 
The present invention specifically addresses and alleviates the above 
mentioned deficiencies associated with the prior art. More particularly, 
the present invention comprises a method for ablating a material. The 
method for ablating a material comprises the steps of directing a pulse of 
energy at the material and so as to permanently modify a quantity of the 
material. The pulse is specifically configured to increase a ratio of the 
quantity of the material which is ablated thereby with respect to the 
quantity of the material which is permanently modified thereby. 
Ablating the material with an energy pulse configured specifically 
configured to increase the ratio of the quantity of the material which is 
ablated thereby with respect to the quantity of the material which is 
permanently modified thereby minimizes undesirable permanent modification 
of the material. 
Preferably, at least one characteristic of the material to be ablated is 
first determined and then a pulse of the directed energy is defined which 
increases the ratio of the quantity of the material which is ablated 
thereby with respect to the quantity of the material which is permanently 
modified thereby. Thus, the characteristic(s) of the material at least 
particularly define the pulse which is used to ablate the material. For 
example, the characteristics of the material which may be determined may 
comprise thermal conductivity, effective electromagnetic energy depth, 
material energy gapped between valence and conductivity bands, material 
density or material strength, taken either alone or in combination with 
one another. 
Although the directed energy pulse is described herein as being comprised 
of laser radiation, those skilled in the art will appreciate that various 
different types of direct energy, accelerated electrons, accelerated ions, 
various forms of electromagnetic energy, etc., are likewise suitable. The 
directed energy may also comprise light from either an LED, a fluorescent 
lamp, or an incandescent lamp, taken alone or in combination with one 
another, the directed energy pulse may comprise either coherent or 
incoherent electromagnetic radiation or any combination thereof. 
The characteristic(s) of the material to be ablated may be determined in a 
variety of different ways, such as by directly sensing the 
characteristic(s) of the material, by looking up the characteristic(s) of 
the material in a reference, or by ablating the material with a pulse of 
the direct energy, determining the approximate quantity of the material 
ablated and also determines the approximate quantity of the material 
permanently modified. Thus, one way of determining the desired 
characteristic(s) of the material to be ablated is by first ablating a 
quantity of the material and then observing how much of the material is 
actually ablated versus how much of the material is permanently modified 
during the ablation process. This determination facilitates adjustment 
defining the pulse in a desired manner so as to minimize residual heat, 
thereby minimizing the quantity of the material permanently modified 
subsequent pulses. 
According to a further aspect of the present invention, a plurality of 
pulses of energy are directed at the material so as to ablate a quantity 
of the material and so as to permanently modify a quantity of the 
material. The pulses have a sufficient pulse rate so as to increase the 
ratio of the quantity of the material which ablated thereby with respect 
to the quantity of the material which is permanently modified thereby. In 
this manner, the material is ablated with a plurality of directed energy 
pulses having a sufficient pulse rate as to minimize undesirable permanent 
modification of the material. 
In a manner similar to that utilized for a single pulse, at least one 
characteristics of the material to be ablated is determined when utilizing 
a plurality of pulses. The characteristic(s) of the material to be ablated 
are then utilized to define the pulse rate of the directed energy so as to 
again increase the ratio of the quantity of the material which is ablated 
thereby with respect to the quantity of the material which is permanently 
modified thereby. 
Of course, both a pulse of the directed energy and a pulse rate of the 
direct energy may be defined by the characteristic(s) of the material to 
be ablated such that the combination of both the specifically configured 
pulse and the pulse rate cooperate to increase the ratio of the quantity 
of the material which will be ablated by the plurality of pulses with 
respect to the quantity of the material which will be permanently modified 
thereby. 
Thus, according to the present invention, a material is ablated by 
utilizing a laser. The laser is specifically configured for use with the 
material so as to cause a substantial quantity of the energy absorbed by 
the material to subsequently be removed therefrom with the material 
ejected during ablation. Removing a substantial amount of the energy 
absorbed by the material minimizes residual energy deposition while 
ablating, so as to mitigate collateral thermal damage to the material. 
Ablation of the material is preferably formed at a velocity greater than 
the thermal energy diffusion through the material so as to remove residual 
energy from the material. 
The material is preferably ablated using a laser having a sufficiently high 
pulse repetition rate to cause a substantial amount of the energy absorbed 
by the material to subsequently be removed therefrom with the ejected 
material. The characteristic(s) of a laser beam pulse are based upon 
properties of the material so as to provide a depth of the material 
removed by the pulse which is approximately equal to an electromagnetic 
deposition depth of the material. 
Optionally, the material is ablated utilizing a laser wherein 
characteristic(s) of the laser beam pulse are based upon properties of the 
material so as to provide a plasma. The plasma is generated by either 
multiphoton ionization or thermal ionization. The plasma effects an 
electromagnetic energy deposition depth which is approximate to a depth of 
the material removed by the pulse. 
Optionally, doping agents are added to the material being ablated. The 
doping agents cause the laser to provide an electromagnetic energy 
deposition depth which is approximately equal to the depth of the material 
removed by the laser. 
More particularly, according to the methodology of the present invention 
high precision, highly controllable, variable rate, material removal is 
provided by a pulsed electromagnetic radiation beam. The interaction 
between the pulse electromagnetic radiation beam and the material effects 
a material removal depth substantially equal to the energy deposition 
depth within the target material. 
The method comprises the steps of providing an electromagnetic radiation 
source capable of generating an output beam comprised of a sequence of 
electromagnetic pulses, each pulse having a pulse duration in the range of 
approximately 1 femtosecond to approximately 10 milliseconds. 
The sources operated and beam parameters of the electromagnetic radiation 
output beam are manipulated so that the electromagnetic pulse's power 
densities within the region targeted for energy deposition is in the range 
of approximately 10.sup.7 W/cm.sup.3 to approximately 10.sup.18 W/cm.sup.3 
and is larger than the power density threshold for material ablation. 
Thus, the material is ablated with electromagnetic energy from the source 
so that a substantial portion of the deposited electromagnetic energy is 
removed from the target material with an ejected portion of the material. 
Ablation of the material is repeated at a pulse repetition rate greater 
than approximately 0.1 pulses per second so that a substantial portion of 
the cumulative residual thermal energy left in the material by the 
electromagnetic energy is removed by the cumulative ablation. The pulse 
repetition rate is preferably smaller than approximately 500,000 pulses 
per second. This process continues until a sufficient depth of the 
material has been removed. 
The electromagnetic beam's energy deposition depth within the material 
defines a volume so that the power density within the volume is greater 
than the threshold power density for material ablation. 
The pulsed electromagnetic radiation source preferably produces an output 
beam having a wave length in the range of approximately 10 nanometers to 
approximately 50 micrometers. 
Each pulse of the pulsed force preferably has an energy in the range of 
approximately 0.001 microjoule to approximately 50 Joule. The output beam 
preferably has a diameter at the target material such that the target 
material experiences an energy fluence in the range of approximately 0.001 
Joule per square centimeter to approximately 100 Joule per square 
centimeter. 
The pulsed beam preferably exhibits a material removal rate in the range of 
approximately 0.01 micrometers to approximately 100,000 micrometers per 
pulse. The removal rate is preferably substantially constant. 
According to a further aspect of the present invention, precise, highly 
controlled, variable rate material removal is provided by a pulsed 
electromagnetic radiation beam. A source capable of generating an output 
beam comprised of a sequence of electromagnetic pulses is provided. 
Preferably, each electromagnetic pulse has a pulsed duration in the range 
of approximately 1 femtosecond to approximately 10 milliseconds. 
The source is operated and the beam parameters manipulated so that the 
electromagnetic pulse's power densities within the region targeted for 
energy deposition is in the range of approximately 10.sup.8 W/cm.sup.3 to 
approximately 10.sup.18 W/cm.sup.3 and is larger than the power density 
threshold for plasma formation. 
The formed plasma is allowed to decay such that a layer of the material is 
removed. The removed layer of material carries with it a substantial 
portion of the deposited electromagnetic energy from the target regions. 
The pulse source is operated so that once a critical electron density is 
reached within the formed plasma, the formed plasma substantially presents 
excess pulse energy form directly reaching the material and so that the 
formed plasma prevents excess pulse energy from substantially increasing 
the electromagnetic energy deposition depth and the depth of the material 
removed by ablation. 
The pulse source is operated at a pulse repetition rate greater than 
approximately 0.1 pulses per second and less than approximately 500,000 
pulses per second until a sufficient depth of material has been removed. 
According to a preferred embodiment of the present invention, the laser 
beam defines a spot on the target characterized in that fluence within the 
beam spot is greater than the threshold fluence for plasma formation. 
The plasma formation substantially prevents deep energy deposition in the 
material so that a substantial portion of the electromagnetic energy 
deposited in the material is removed with the material ejected. 
The pulsed electromagnetic energy source preferably produces an output beam 
having a wavelength in the range of from approximately 10 nanometers to 
approximately 15 micrometers. Each pulse of the pulsed energy source 
preferably has an energy in the range of approximately 0.001 microjoule to 
approximately 100 Joule. The output beam preferably has a diameter at the 
material target such that the material experiences an energy fluence in 
the range of approximately 0.001 to approximately 100 Joule per square 
centimeter. 
The pulse laser beam preferably exhibits a material removal rate in the 
range of approximately 0.01 to approximately 10 micrometers per pulse. The 
removal rate is preferably substantially constant without regard to 
material chromophore, material hardness or material state. 
Optionally, the target material is substantially transparent to the linear 
propagation of the electromagnetic pulses and the beam is focused below 
the surface of the target material so that the beam intensity exceeds the 
plasma formation threshold only at approximately the point of focus and 
the material is substantially removed at that desired point below the 
surface. In this manner, material can be ablated in a manner which forms 
caverns or hollow volumes within the material. Thus, cavities having 
various different desired shapes may be so formed. This may be 
accomplished using either a single pulse, or a plurality of pulses, as 
desired. 
Alternatively, the method for controlled variable rate material removal by 
a pulsed electromagnetic radiation beam comprises providing a source 
capable of generating an output beam comprised of a sequence of 
electromagnetic pulses, wherein each electromagnetic pulse has a pulse 
duration in the range of about 1 femtosecond to about 10 milliseconds and 
also comprises operating the pulse source and manipulating the beam 
parameters so that the electromagnetic pulses' peak intensity is in the 
range of approximately 10 W/cm.sup.2 to approximately 10.sup.16 W/cm.sub.2 
and adding to the target material absorption or scattering centers, 
defects, highly absorbing or highly scattering components, so that the 
electromagnetic radiation penetration depth is reduced and/or plasma is 
formed. 
Preferably, the electromagnetic energies absorbed by the material to 
complete the material disintegration and explosive ejection of the 
targeted material deposition volume, so that substantially most of the 
deposited energy is removed from the target material with the ejected 
portion of the material. The pulse source is preferably operated at a 
pulse repetition rate greater than approximately 0.1 pulses per second 
smaller than approximately 500,000 pulses per second until a sufficient 
depth of material has been removed. 
Further, according to the preferred embodiment of the present invention, 
plasma is formed and expanded, substantially preventing excess pulse 
energy from directly reaching the material and so that excess pulse energy 
does not substantially effect ablation depth. The plasma is preferably 
allowed to decay such that a layer of the material is removed and 
substantially most of the material radiation pulse energy deposited in the 
material is removed with the layer. The source is operated at a pulse 
repetition rate greater than approximately 0.1 pulses per second and less 
than approximately 500,000 pulses per second until a sufficient depth of 
material has been removed. 
In a further alternative method for controlled, variable rate material 
modification, a pulsed electromagnetic radiation beam is provided by 
providing a source capable of generating and output beam comprised of a 
sequence of electromagnetic pulses, each electromagnetic pulse having a 
pulse duration in the range of approximately 1 femtosecond to 
approximately 100 milliseconds. The pulse source is operated and the beam 
parameter is manipulated so that the deposited volumetric power density 
within the targeted material is greater than the threshold power density 
for material modification, such that control of the power density is 
achieved by varying either one or more of the following parameters: the 
beam spot size at the target location, the duration of the electromagnetic 
pulse emissions, the energy of the electromagnetic pulse emissions, the 
wavelength of the electromagnetic pulse emissions, or by spatially and 
temporally varying the absorption and/or scattering characteristics of the 
material at the target region. The interaction energy transients caused by 
the electromagnetic radiation pulse are allowed to substantially decay 
such that material modification is effected. Such material modification 
preferably includes one or more of the of the following alterations: 
Chemical and physical changes, changes to visco elastic properties, 
changes to optical or thermal properties, chemical and physical breakdown, 
disintegration, ablation, melting, or vaporization. 
The pulse source is preferably operated at a pulse repetition rate greater 
than approximately 0.1 pulses per second until a sufficient volume of the 
material has been modified. 
The target material is preferably substantially transparent to linear beam 
propagation and the threshold volumetric power density is achieved at a 
desired target location below the surface and within the material volume. 
Again, scattering and/or absorption centers, defects, or highly absorbing 
components are added to the target material with spatial and/or temporal 
selectivity to specific, predetermined locations within the target 
material. 
The pulse beam preferably exhibits a material modification rate in the 
range of approximately 0.01.sup.3 cubic micrometers per pulse to 
approximately 100,000.sup.3 cubic micrometers per pulse. The material 
modification rate is preferably substantially constant, depending 
substantially on the volumetric power density threshold characteristics of 
the material and on the target-beam characteristics thereof. 
Thus, a method and apparatus is disclosed for fast, precise and damage-free 
material processing and modification using a high pulse repetition rate 
electromagnetic energy source. The pulsed interaction uses a parameter 
regime which minimizes residual energy deposition while ablating. 
Advantageously, removal of cumulative pulse train residual energy is 
maximized through the rapid progression of the ablation front which moves 
faster than the thermal energy diffusion. Removal of residual energy thus 
minimizes collateral thermal and mechanical damage in material processing 
and also minimizes pain and suffering during surgical procedures. The 
operating parameters for the system are achieved through the selection of 
material properties and beam characteristics which ensure localization of 
incoming electromagnetic energy into a deposition zone comparable in its 
depth and lateral dimensions to the depth and lateral dimensions of the 
volume of ablated material. The disclosed method identifies either high 
linear absorption or plasma-mediated interactions, or a combination of the 
two, as potential avenues for fulfilling the deposition depth--ablation 
depth near--parity requirements which enable high pulse repetition rate 
operation and thus ensure rapid material removal. The disclosed apparatus 
then describes a variable repetition rate system which allows highly 
adjustable material removal rates ranging from very rapid to very slow. A 
set of possible energy delivery and collection systems is then disclosed 
which allow highly accurate delivery, monitoring, feedback, control, and 
automation for extreme precision and unprecedented accuracy that can be 
offered simultaneously with the rapid rate of operation. Finally, a method 
and apparatus are disclosed for fast, efficient, precise and damage-free 
material modification, utilizing the threshold nature of plasma-mediated 
interaction and/or selectively induced, high absorption regions. Making 
use of the same apparatus with the option to spatially and/or temporally 
control the addition of "doping agents", to induce selective power 
deposition, precise and highly localized material removal and/or 
modification can be induced at any desired location within the 
three-dimensional space of the target region while substantially sparing 
adjacent regions of the target material from any collateral damage. 
Further, a method for high precision, highly controllable, variable rate, 
material removal by a continuously emitting, continuous wave (CW) beam of 
electromagnetic radiation is provided. The interaction between the 
electromagnetic beam and the material is such that a material removal 
depth is approximately equal to an energy deposition depth within the 
target material. The method comprises the steps of: providing a source 
capable of generating an output beam comprised of continuously emitted 
electromagnetic radiation; and redistributing the beam in time and space 
to form at least one modified beam. This is accomplished by repeatedly 
selecting a portion of the beam in time and redirecting that portion of 
the beam so as to define a series of pulses. In this manner, a plurality 
of time sequential segments of the beam are redirected, preferably through 
an optical fiber. Thus, a short segment of the CW beam, enough to provide 
the desired pulse, is diverted from the remainder of the beam. Other 
portions of the beam may similarly be redirected such that the entire beam 
is utilized. 
In effect, the beam is time sliced, such that for a given duration, a 
portion of the beam is directed to one optical fiber, and then for another 
period of time the optical beam is directed to another optical fiber. This 
process is repeated for a desired number of optical fibers (optimally 
until the entire beam is utilized) and after the beam has been directed to 
each of the optical fibers, the process repeats. In this manner, the beam 
is sequentially directed from one optical fiber to another, so as to 
define the desired number of separated pulsed beams. Each of the optical 
fibers directs the beam to a desired location where material ablation is 
to occur. Generally, each portion of the beam will be directed such that 
it is incident upon adjacent (optionally overlapping) areas of the 
material to be ablated such that the different portions of the beam 
cooperate so as to effect material ablation in an efficient and effective 
manner which minimizes undesirable modification of adjacent material due 
to overheating. 
Thus, the beam is redirected so that either a single or multiple beams are 
formed and such that their energy distribution at any given location on 
the target material forms a sequence of electromagnetic pulses. Each 
electromagnetic pulse preferably has a duration between approximately 1 
femtosecond and approximately 10 milliseconds. 
Thus, the beam is modified such that the original beam is re-configured 
into a new single or multiple beams. In this manner, the energy of the 
original beam is utilized after having been redistributed in both time and 
space. 
The source of electromagnetic energy is operated and the beam parameters 
are manipulated so that the electromagnetic pulse's power densities within 
the region targeted for modification are between approximately 10.sup.4 
W/cm.sup.3 and approximately 10.sup.18 W/cm.sup.3 and are larger than the 
power density threshold for material ablation. The electromagnetic energy 
absorbed by the material is allowed to complete the material ablation 
process, so that substantially most of the deposited electromagnetic 
energy is removed from the target material with an ejected portion of the 
material, as discussed in detail above. 
Such electromagnetic energy absorption is repeated, as desired so that 
ablation and energy removal occurs at a pulse repetition rate greater than 
0.1 pulses per second, such that substantially most of the cumulative 
residual thermal energy left in the material by a pulse train is removed 
by the cumulative ablation. Thus, ablation is performed at a pulse 
repetition rate less than approximately 500,000 pulses per second until a 
sufficient depth of material has been removed with substantially no 
transfer of thermal or mechanical energy into the main material and 
substantially no collateral damage thereto. 
The step of redistributing the beam preferably comprises deflecting 
sequential portions of the beam and redirecting them to a distinguished, 
separate locations upon the target material, so that the net affect at 
each location is that of a sequence of pulses of a specified or desired 
duration and a specified or desired pulse repetition rate. 
In this manner, the switching device redirects sequential portions of the 
beam to separate locations so that the net affect at each location is that 
of a sequence of pulses of specific duration and the step of 
redistributing the beam comprises directing the beam to a device selected 
from a device such as a rapidly rotating mirror or other optical means for 
directing electromagnetic radiation, a Kerr cell, a Pockels cell, and 
acousto-optic modulator, an electro-optic modulator, or any other 
electro-optical, electrical, magnetic, or electromagnetic means for 
redirecting light. 
The switching device sequentially redirects the original beam energy into 
at least one optical guiding device such as an optical fiber or a hollow 
wave guide light conductors. The optical guiding device then redistributes 
the beam to separate locations on the target material. 
Preferably, the output of the single or multiple optical fibers or hollow 
wave guides is performed so as to focus the energy to a spot size such 
that the power density within the volume target is for material removal 
for modification is greater than the threshold power density for material 
ablation or the desired modification. 
The step of redistributing the beam preferably comprises redirecting the 
original beam energy into a single or multiple lenses or other optical 
focusing devices and then allowing the newly redistributing beams to 
propagate to separate locations on the target material. 
The pulse electromagnetic radiation source produces an output beam having a 
wavelength in the range of 10 nanometers to 50 micrometers. 
The continuously emitting beam source preferably has an average power in 
the range of approximately 0.0001 Watt to approximately 500 KWatts. The 
output beam preferably has a diameter at the target material such that the 
target material experiences a power per unit area in the range of 
approximately 1 Watt per square centimeter to approximately 10.sup.14 
Watts per square centimeter. 
The pulse beam is preferably configured to provide a material removal rate 
in the range of approximately 0.01 micrometer to approximately 10,000 
micrometers per pulse. The material removal rate per pulse is preferably 
substantially constant. 
Each of the redistributed beams comprises a sequence of electromagnetic 
pulses, each pulse preferably having a pulse duration in the range of 
approximately 1 femtosecond to approximately 10 milliseconds and has a 
pulse repetition rate greater than approximately 0.1 pulses per second and 
less than approximately 100,000 pulses per second. 
The redistributed beam preferably comprise a sequence of electromagnetic 
pulses which is directed to a target location adjacent one another. In 
this manner, the beams cooperate with one another so as to remove at least 
some thermal energy generated by preceding pulses and these adjacent 
beams. 
The step of redistributing the beam preferably further comprises changing 
the beam wavelength via a device such as an optical parametric oscillator, 
and optical parametric amplifier, or a non-linear frequency converting 
crystal such as KTP or KDP. In this manner, the frequency of the beam is 
doubled, tripled, quadrupled, etc., as desired. 
According to the preferred embodiment of the present invention, a device 
for high precision, highly controllable, variable rate, material removal 
by a continuously emitting, continuous wave (CW) beam of electromagnetic 
radiation wherein the interaction between the electromagnet beam and the 
material being characterized by a material removal depth which is 
substantially comparable to the energy deposition depth within the target 
material. The device preferably comprises an energy radiating device for 
providing a continuously emitted electromagnetic energy beam and a first 
controller for redistributing the energy beam into at least redistributed 
beam which is redistributed in space and time, i.e., time sliced. 
A controller redirects the redistributed beams so that the energy 
distribution at any given location on the target material forms a sequence 
of electromagnetic pulses, each electromagnetic pulse having a pulse 
duration in the range of approximately 1 femtosecond to approximately 10 
milliseconds. The device and its controllers are preferably operated such 
that the output electromagnetic power densities within the region targeted 
for modification is in the range of approximately 10.sup.4 W/cm.sup.3 to 
about 10.sup.18 W/cm.sup.3 and is larger than the power density threshold 
for material ablation. The electromagnetic energy absorption is permitted 
to continue until the desired material abrasion is complete, so that 
substantially most of the deposited electromagnetic energy is removed from 
the target material with the ejected portion of the material. 
Electromagnetic energy absorption is repeated at a pulse repetition rate 
greater than 0.1 pulses per second such that most of the cumulative 
residual thermal energy which remains in the material due to the pulse 
train is removed by the cumulative ablation. The pulsed repetition rate is 
thus preferably smaller than approximately 100,000 pulses per second and 
continues until a sufficient depth of material has been removed with 
substantially no transfer of thermal or mechanical energy into the 
remaining material and substantially no collateral damage thereto. 
The first controller preferably comprises a switching device which deflects 
sequential portions of the beam and redirects them to separate locations 
such that the net effect at each location is that of a sequence of pulses 
of specific duration and specific pulse rate. In this manner, rather than 
illuminating the entire portion of material to be ablated, different 
portions thereof are illuminated sequentially, thereby enhancing the 
ability of the cooperating beams to remove heat therefrom. 
The first controller preferably comprises a switching device such as a 
rapidly rotating mirror, a Kerr cell, a Pockels cell, and acousto-optic 
modulator, an electro-optic modulator, or other electro-optical, 
electrical, magnetic, or electromagnetic means for redirecting light. 
These, as well as other advantages of the present invention will be more 
apparent from the following description and drawings. It is understood 
that changes in the specific structure shown and described may be made 
within the scope of the claims without departing from the spirit of the 
invention. The method for ablating a material with a directed energy 
pulse, such as that of a laser, includes directing a pulse of energy at 
the material so as to ablate a quantity of the material and so as to 
permanently modify a quantity of the material, the pulse being configured 
to increase a ratio of the quantity of the material which is ablated 
thereby with respect to a quantity of the material which is permanently 
modified thereby. Alternatively, a plurality of pulses of energy are 
directed at the material so as to ablate a quantity of the material and so 
as to permanently modify a quantity of the material, the pulses having a 
sufficient pulse rate as to increase a ratio of the quantity of the 
material which is ablated thereby with respect to the quantity of the 
material which is permanently modified thereby. Ablating the material with 
an energy pulse or with a plurality of energy pulses configured so as to 
increase the ratio of the quantity of the material which is ablated 
thereby with respect to the quantity of the material which is permanently 
modified thereby minimizes undesirable permanent modification of the 
material.

DETAILED DESCRIPTION OF THE PREFERRED INVENTION 
The principles of operation for an exemplary material removal and 
modification system are described in detail below. The system comprises a 
source of pulsed electromagnetic radiation and complying with the 
requirements of the invention. In the following discussion, a laser source 
is used as an exemplary pulsed source of electromagnetic radiation. 
However, those skilled in the art will recognize that the invention is not 
limited to laser sources and that other pulsed electromagnetic radiation 
sources may serve equally well in the practice of the present invention. 
The principles of operation of such an exemplary laser system will now be 
developed in connection with the mechanisms for material and tissue 
processing such as, for example, the machining of silicon surfaces or the 
treatment and removal of dental tissue and materials. 
The description of the operation of this laser system with respect to 
applications of silicon machining or dental tissue processing is used for 
exemplary purposes only and is not intended to limit the applications of 
the present invention. As will be described in greater detail below, the 
apparatus and methods for this invention have application for a wide 
variety of material modification, removal and processing. Additionally, 
this laser system has exceptional utility for biomedical, surgical, 
machining, and micro-machining purposes. 
The inventor has identified an electromagnetic source-material operational 
parameter regime which provides interaction characteristics that are 
superior to conventional machining, other laser systems, and established 
material processing or material modification systems, and which provides 
material removal rates that are superior to or on a par with mechanical 
tools technology. Advantageously, the aspect of the present invention 
relating to the method's reliance on the system's ability to limit the 
amount of per-pulse-energy coupled to the material, and the system ability 
to remove most of the residual deposited energy generated by the 
interaction itself, results in a very significant reduction in the level 
of collateral damage while allowing large volume removal at very rapid 
rates. 
The aspect of the present invention relating to a method for rapid material 
removal capabilities is based on the inventor's novel discovery regarding 
the relationship between material removal rates and characteristics of a 
single pulse--interaction with the target material. Specifically, the 
parameter regime of the present invention, ensures that most of the 
incoming electromagnetic pulse energy that is absorbed by the material is 
subsequently removed with the ejected material. Within this parameter 
regime, variable pulse application rates--including very high pulse 
repetition rates (up to about five hundred kilohertz) and, 
correspondingly, very high material volume removal rates--can be achieved. 
The ability to vary operation rates continuously from the very high pulse 
repetition rates (on the order of a few hundred Kilohertz) to the very low 
(on the order of a single pulse every few seconds, or a fraction of a 
single Hertz), combined with the relatively small amount of material 
removed by a single pulse, corresponds to an unusually high degree of 
control over the material or tissue removal and/or modification, from the 
extremely rapid to the very slow. 
This capability of the invention corresponds to many unusual and highly 
beneficial uses which include: high precision, superb accuracy, 
minimization and control of pain sensation (in biomedical applications of 
the invention), and very high degree of control over removal rates. 
The inventor has identified four methods for advantageously defining the 
interaction parameters. 
The first method for advantageously defining the interaction parameters 
comprises utilizing material properties and beam characteristics or 
parameters, which results in an electromagnetic energy deposition profile 
that concentrates the tissue-modifying energy in a zone with a depth of 
same order of magnitude of the depth of material removed by each pulse. 
This criteria shall, in the context of the present invention sometimes be 
referred to as "the principle of near-parity". The principle of 
near-parity between ablation depth and the depth of permanently modified 
tissue implies a high ratio of ablation depth to depth of permanently 
modified matter. This criteria should also be applied in combination with 
sufficiently short pulse duration to prevent significant thermal diffusion 
from the energy deposition zone prior to material removal. Pulse duration 
shorter than 1 .mu.s, for example, means that all the pulse energy is 
deposited into a target water-like material before thermal energy in the 
deposited zone has time to diffuse more than about 1 pm away from the 
deposition volume. If, for example, the pulse energy is sufficient to 
raise the material temperature to above the boiling temperature, the 
material within the deposition zone will be vaporized and some of its heat 
will be ejected with the plume of debris. Alternatively, ionization 
threshold or threshold for explosive material removal, may be exceeded 
within in the volume, again, leading to material ejection and ejection of 
some of the heat with it. 
Energy deposition depth which is localized in space and in time naturally 
leads to the generation of very high power densities within the target 
material. "Power density" is defined herein as the amount of energy per 
unit time per unit volume. High power densities play a crucial role in the 
initiation of the desired interactions, as will be explained in details 
below. 
The shallow deposition, on the same order of magnitude of the depth of the 
depth of material removed by each pulse, in combination with sufficiently 
short pulse duration (to prevent significant thermal diffusion from the 
energy deposition zone prior to material removal), ensures that most of 
the deposited single-pulse energy in the material is removed with the 
ablation ejecta of that very same pulse. 
Employing a pulse repetition rate of sufficiently large value ensures that, 
if and when longer total treatment times are needed, most of the residual 
cumulative pulse train energy coupled to the material is ultimately 
removed by the cumulative ablative effect of the rapidly moving ablation 
front. Such a scheme has been identified by the inventor to ensure removal 
of most of the deposited energy and to allow a variable pulse repetition 
rate interaction which includes pulse repetition rate of up to about 
several hundred thousand pulses per second. 
As used herein "material properties" are defined as the material 
mechanical, thermal, optical and electromagnetic characteristics, for 
example, heat capacity, optical absorption, electrical conductivity etc. 
"Beam characteristics" are defined as the beam spot size at the target 
location, the beam pulse energy, the beam pulse duration, the beam pulse 
repetition rate, pulse-to-pulse separation time, etc. 
The second method for advantageously defining the interaction parameters 
comprises utilizing material properties and beam characteristics so that a 
plasma is generated through either multiphoton ionization and/or thermal 
ionization. Properties of such an interaction (as discussed below) often 
ensure: a) shallow depth of energy deposition (in accordance with the 
above), b) plasma shielding and (above critical electron density value) 
increased rejection of subsequent incoming radiation, and c) removal of 
much of the deposited energy with ejected layer. 
The shallow deposition, comparable in depth to the depth of material 
removed by each pulse, in combination with sufficiently short pulse 
duration (to prevent significant thermal diffusion from the energy 
deposition zone prior to material removal), ensures that most of the 
deposited single-pulse energy in the material is removed with the ablation 
ejecta of that very same pulse. 
Employing a pulse repetition rate of sufficiently large value ensures that 
most of the residual cumulative pulse train energy left in the material is 
removed by cumulative ablative effect of the rapidly moving ablation 
front. Such a scheme has been identified by the inventor to ensure removal 
of most of the deposited energy and allows variable pulse repetition rate 
interaction which includes pulse repetition rates of up to about several 
hundred thousand pulses per second. 
The third method for advantageously defining the interaction parameters 
comprises adding absorption centers, localized defects in the material, 
and/or highly absorbing or highly scattering components (collectively 
defined by the inventor as "doping agents") to the target material so that 
the electromagnetic radiation penetration depth is reduced and/or plasma 
is formed. Temporally and/or spatially marking the targeted material zone 
with a doping agent, prior to or during the incoming electromagnetic 
energy arrival time, in combination with sufficiently short pulse duration 
(to prevent significant thermal diffusion from the energy deposition zone 
prior to material removal) results in shallow incoming electromagnetic 
energy deposition depth. 
The shallow deposition, comparable in depth to the depth of material 
removed by each pulse, in combination with sufficiently short pulse 
duration (to prevent significant thermal diffusion from the energy 
deposition zone prior to material removal), ensures that most of the 
deposited single-pulse energy in the material is removed with the ablation 
ejecta of that very same pulse. 
Employing a pulse repetition rate of sufficiently large value so that, if 
longer total treatment time is needed, it ensures that most of the 
residual cumulative pulse train energy left in the material is removed by 
cumulative ablative effect of the rapidly moving ablation front. Such a 
scheme has been identified by the inventor to ensure removal of most of 
the deposited energy and to allow a variable pulse repetition rate 
interaction which includes pulse repetition rates of up to about several 
thousands pulses per second. 
The fourth method for advantageously defining the interaction parameters 
comprises utilizing the power density threshold nature of the interactions 
(for example through pulse temporal and/or spatial compression), or 
utilizing preferential time-dependent and/or space-dependent marking of 
the target material, it is possible to chose material properties/beam 
characteristics combination so that only a pre-selected volume at or below 
the target material surface, is modified or removed. Employing such 
selected parameter combination with sufficiently short pulse duration 
which prevents thermal diffusion from the energy deposition zone prior to 
material removal or modification results in significant minimization of 
collateral damage. 
Here, material modification pertains to altering the physical and/or 
chemical conditions of material without providing sufficient power 
densities to completely remove or ablate the targeted material. This 
condition for material modification will occur at power densities higher 
than those which allow linear propagation without sufficient energy 
deposition for irreversible changes to occur, yet lower than those defined 
by the ablation threshold. A selection of the appropriate time and 
space-dependent material properties/beam characteristics parameter will 
allow a time and space dependent interaction. The selected beam path can 
then allow the operator to define temporally and spatially pre-selected 
target regions, which will include unperturbed zones (where no 
irreversible changes occur), modified zones (where material physical or 
chemical characteristics have been modified but no material has been 
removed), and ablated zones (where complete or partial removal and/or 
vaporization of material has taken place). 
Here, a criteria for high ratio of the extent of a desired and controlled 
material modification to the extent of undesired material modification is 
strived for. 
Another advantage of the method of the present invention, is that longer 
wavelength, pulse laser systems can be used in many of the procedures 
currently employing lasers which operate in the ultraviolet region. 
Replacing ultraviolet lasers with the longer wavelength ultra-short pulse 
lasers of the invention would eliminate the risks associated with 
mutagenic radiation produced by short wavelength lasers, and the attendant 
dangers posed. 
A further advantage of the present invention is that pulsed, solid-state 
lasers can be used in most, if not all, procedures currently employing 
various fluid lasers (for example dye-based lasers), as well as gas and 
excimer lasers which involve manipulation and handling of expensive and 
dangerous gas components. Replacing ultraviolet excimer lasers as well as 
other types of dye and gas lasers with the pulse solid state lasers of the 
present invention would eliminate possible exposure of operators to 
carcinogens and poisonous liquids and gasses. 
Principles of Operation: High Ratio of Ablation Volume to Permanently 
Modified Volume 
Incident electromagnetic energy can propagate in some materials much as it 
does through free space, air, or any other transport media. Transport 
media is defined herein as the media which the beam has to transverse on 
its way from the source to the targeted material. Normally, the source 
parameters and the transport media properties are chosen so that minimal 
beam energy will be deposited or lost in the transport media. By 
definition, the desired alteration to the target material requires energy 
deposition at the designated volume. Once the electromagnetic pulse 
arrives at the target medium, more substantial energy deposition is 
accomplished through the interaction of the radiation with the media atoms 
and electrons. The interaction can be relatively weak in which case 
substantial amounts of energy are transported through the target material 
and are deposited in much deeper regions or, perhaps even, completely 
traverse the targeted material volume and emerge at the opposite boundary 
of the material. Radiation with a wavelength of 1.06 .mu.m loses 1/e, 
(approximately one third) of its original energy in a length (sometimes 
called "penetration depth") which, for this wavelength propagating in 
water is on the order of 16 mm. If the interaction is strong, the 
radiation loses energy at a very rapid rate as it propagates into the 
material. Radiation of 2.94 .mu.m radiation propagating through water, for 
example, drops to (1/e) (or about one third) of its incident energy value 
at a penetration depth of only about 1 .mu.m or 0.001 mm. 
Once the energy has been transferred from the beam to the material atoms, 
it will further propagate into adjacent, lower energy, regions of the 
material. This additional transport usually takes place through either 
mechanical or thermal energy propagation although some radiation transport 
is possible as well. 
The practice of the present invention maximizes deposition of the incoming 
radiation within the area targeted for ablation or alteration, and 
minimizes deposition or further transport of the energy to adjacent region 
thus minimizing the depth of the zone of matter which has been permanently 
modified. Moreover, the inventor realized that if most of the deposited 
energy is removed with the ejected debris, very little energy is left 
within targeted material, thus allowing a large number of pulses to be 
deposited within the same area of the targeted material within a short 
time duration. The inventor recognized that the deposition of large number 
of pulses within a short time duration, which corresponds to high pulse 
repetition rate, is only possible because of the condition which the 
present invention imposes on the interaction, namely, that most of the 
energy deposited by a single pulse will be removed by the ablation 
products ejected from the material due to the action of the very same 
pulse. 
The above discussion can be summarized by defining (1) x.sub.irr, the depth 
of the zone of irreversible damage, as the depth to which most of the 
pulse energy capable of irreversibly modifying the target material has 
been transferred (either by direct interaction with the electromagnetic 
pulse or through subsequent thermal diffusion, or both), prior to the 
ablative removal of the material. "Irreversibly modifying" the material is 
defined as ejecting, ablating, and/or otherwise irreversibly changing 
material characteristics. We also define X.sub.abl as the depth of 
material ablatively removed through that very same incident pulse 
deposited energy. The condition for high ratio of ablation to permanently 
modified material depths amounts to requiring that the ratio (X.sub.ab 
/X.sub.irr) be as high as possible. 
As the above ratio approaches one, this requirement can be expressed as 
X.sub.irr .about.X.sub.abl, which corresponds to near-parity between 
energy penetration depth and the depth of material ablated per pulse. The 
requirement that the ratio X.sub.ab /X.sub.irr 15 as long as possible is 
of paramount importance to the practice of at least one embodiment of the 
present invention. 
FIG. 1 illustrates the concept of parity between thermal penetration depth 
and the depth of material ablated per pulse. In FIG. 1, electromagnetic 
energy 20 impinges on a slab of material 22 from the left. The curve 24 
depicts the power density as a function of distance (or beam propagation 
depth) into the target material and corresponds to an exemplary energy 
deposition profile within the material. If the line 27 represents the 
threshold for material modification and the line 23 represents the 
threshold for material ablation, then the vertical line 26 represents a 
material removal depth which is insufficient to meet the criteria of high 
ratio of ablation to energy deposition depths. Since the area under the 
curve 24 is proportional to the total amount of incoming energy deposited 
in the material, removal of the layer to the left of 26 clearly represent 
only a small fraction of the deposited energy. On the other hand, if the 
lower line 25 represents the threshold for material ablation, then the 
vertical line 28, represents the depth of material removal which 
corresponds to an exemplary depth which adequately meet the requirement of 
the above criteria, since ablation to this depth clearly removes most of 
the deposited energy. 
The requirement for a high ratio of ablation volume to permanently modified 
volume can be achieved in several ways. One avenue to satisfy this 
requirement is to employ wavelength which results in shallow 
electromagnetic energy deposition and high power density within this 
volume--a power density which leads to near-parity of the ablated volume 
and the energy deposition volume. A second avenue is presented when plasma 
is generated in the course of the interaction between the pulsed energy 
and the targeted material. This avenue will now be described below. 
Previously known and frequently used laser systems, characterized by the 
lack of a high ratio of ablation volume to permanently modified volume 
(usually operating in the low pulse intensity regime ranging up to 1,000 
watts/cm.sup.2 and often based on continuous emission sources), were 
demonstrated to be generally unable to remove substantial amounts of 
material without causing extensive collateral effect. 
In conventional long pulse laser systems (for example, conventional low 
intensity Neodymium:YAG or a continuous wave CO2 or dye laser systems) 
much of the optical energy delivered to a material target site does not go 
into disrupting the structural integrity of the target material, but is 
transferred into the surrounding tissue as thermal, acoustic, chemical or 
mechanical energy. This energy propagates through the surrounding tissue 
as both transient mechanical energy and heat energy. These, in turn, 
manifest themselves as undesirable cracks in the material, material 
charring, discoloration, surface melting, chemical alterations, and, in 
the case of living animals and human beings, in the sensation of pain. 
Conventionally, for long pulses or continuous wave sources, large 
penetration depths or low power density interactions, bulk material 
removal involves the heating of conduction band electrons by an incident 
beam of photons and the transfer of this thermal energy to the bulk 
resulting in melting, boiling, and/or fracture of the material in the 
region in which removal is desired. 
Because the controlling rate for material removal depends on thermal 
response of the material lattice and the lattice's thermodynamic 
properties (heat capacity, heat of vaporization, heat of fusion, and the 
like), the minimum amount of energy required to effect an observable 
change in the materials properties, (the threshold damage fluence defined 
as the incident beam energy per unit area) is approximately proportional 
to the square root of the pulse duration. 
In such systems, the total amount of material removed is limited by the 
amount of material removed with each pulse, the number of pulses per 
second, and the total beam application time (i.e., the total time that the 
material is allowed to be exposed to the beam). Also, the amount of 
material removed by a single pulse, is proportional to the volume effected 
by the electromagnetic energy deposition, thermal energy penetration, 
diffusion, and mechanical energy propagation due to a single pulse 
deposition event. As a consequence, high pulse energy has, in the past, 
been considered necessary in order to obtain adequate material removal 
characteristics. 
Unfortunately, high per-pulse energies which are often required by 
conventional longer pulse or continuous wave laser systems are often the 
source of many undesirable side effects such as, extensive melting and 
boiling beyond the intended target volume, explosive vaporization and 
tearing at the boundaries, as well as fracture of the material surface. 
Much improved and unexpected results are obtained, however, when material 
removal is performed with sources yielding high values of X.sub.ab 
/X.sub.irr through, for example, plasma-mediated interactions. When laser 
systems are operated in a parametric regime where power densities are 
larger than plasma formation threshold, the physical mechanism of material 
removal radically changes as explained below. 
Plasma is a highly ionized gas in which the number of free electrons is 
approximately equal to the number of positive ions. It is generated in the 
material by the incoming radiation through either multiphoton ionization 
and/or intense heating of the material leading to collisional ionization. 
Plasma-induced damage is typically confined to small volume bounded by the 
region of the beam's intensity profile which is above the ablation fluence 
threshold and with sufficient beam intensity to produce ionization. 
The beam temporal and spatial power density distribution can be achieved in 
one of several ways: 1) the photons can be concentrated in a short 
time-duration bursts, where a shorter pulse duration yields a greater 
photon concentration, 2) the beam can be strongly focused to a smaller 
spot where the smaller the spot, the greater the photons spatial 
concentration, 3) the material absorption and/or scattering 
characteristics are such that most of the photons penetrating the material 
are confined to a small depth, and finally, 4) by adding highly absorbing 
and/or scattering doping to the material, the same effect of confining 
high photon energy deposition to a small volume can be achieved. 
If a high photon concentration is achieved, through either one or a 
combination of the above avenues two effects may follow: 1) the radiation 
ceases to propagate linearly, and non-linear multi-photon absorption and 
multi-photon ionization lead to the production of free electrons, 2) a 
significant increase in thermal energy density and thermal ionization of 
the material also leading to the production of free electrons and ions. 
These two processes can and often do occur simultaneously. 
The free electrons, then act as seed electrons which cause an avalanche 
process or an electron ionization cascade through collisional processes in 
which material conduction band electrons, oscillating in response to the 
laser optical field, transfer their energy to additional electrons and to 
the material lattice through phonon scattering. Once an electron acquires 
kinetic energy equal to or larger than the band gap energy for the 
materials, subsequent collisions with adjacent electrons and impact 
ionization promotes an additional valence electron into the conduction 
band. The resulting avalanche leads to destruction of the material lattice 
and to an irreversible change in the bulk material structure. 
If the target material linear absorption at the selected source wavelength 
is low, the beam will propagate with little or no effect on the target 
material. Thus, regions where the beam power density is below that which 
are required for plasma generation will remain unaltered. Only those 
regions within the beam power density profile which are capable of 
creating plasma will interact with the targeted material and will result 
in material alteration and removal. As a consequence, damage occurs only 
in the material volume irradiated by sufficient power densities to produce 
ionization. 
In addition, because the plasma-mediated interaction process is 
threshold-dependent and based on the principle that only material which 
experience above-threshold optical energy deposition is removed, melting 
or boiling is minimized and the energy deposition does not correspond to 
significant heating or thermoelastic stress. 
Also, since most of the energy is deposited in a thin outer layer of the 
material, and since after the ablative interaction with the leading 
portion of the pulse, subsequent energy is coupled mainly to the plasma 
which shields the target material from non-ablative energy, most of the 
energy within the target material is removed with the ablated ejecta. This 
condition is part of the requirements for the practice of the present 
invention as the inventor described in the discussion above. 
Plasma-mediated interactions are, therefore, a class of interaction that 
naturally fulfill this requirement. 
The amount of residual heat left in the material depends on the 
laser-material coupling characteristics. Once plasma is formed, its 
presence defines the coupling and shielding characteristics which are 
relatively uniform (with little dependence on material properties) for a 
given plasma density. 
Thus, in the practice of the present invention, once the ablation 
characteristics for a given plasma electron density have been established, 
pulse duration can be adjusted so that additional source energy and plasma 
expansion will not result in excessive accumulation of residual heat and 
will not lead to rise in material temperature above a given limit (for 
example: the limit for material carbonization in biological tissue during 
surgery, or melting in silicon during a material processing procedure). 
Source maximum pulse repetition rates and maximum material removal rates 
can then be established based on these single pulse ablation 
characteristics and the single pulse minimal residual heat deposits. 
As will be discussed below, an additional consequence of the method of the 
present invention is the ability to manipulate the power densities in the 
material through the manipulation of beam parameters and/or addition of 
material doping agents. This allows the user to achieve: a) a selective 
interaction, and, b) a relatively high level of insensitivity of the 
ablation threshold and the material removal rate to the laser wavelength, 
material chromophore, material structure, material state of hydration, and 
material state of oxygenation. Some of the basic concepts described above 
will now be developed. 
The physical characteristics of an exemplary system for use in removing and 
modifying material, as illustrated by the present invention, will be best 
understood by initially referring to both FIG. 2 and FIG. 3. 
FIG. 2a depicts the evolution of the plasma free electron density (which 
corresponds to the state of the plasma) as a function of time following 
the start of the interaction with the leading edge of the electromagnetic 
pulse. Production of free electrons by multiphoton ionization alone 32 
(dotted curve) and by multiphoton and collisional ionization 34 (solid 
curve) is shown. For reference, the time-dependent intensity profile of 
the incident light pulse 30 (the "bell-shape" curve in the figure) is also 
shown. 
As FIG. 2a clearly indicates, the leading edge of the pulse rapidly yields 
high power densities in the outer layer which generates plasma whose 
electron density increases over the leading portion of the pulse and 
gradually reaches a maximum level during the second part of the pulse. 
Note that while the time and intensity scales are linear, the electron 
density scale is logarithmic and the FIG. 2a indicates a very rapid rise 
in electron density. It is the use of plasma's electron density properties 
that, according to one aspect of the present invention, allows some of the 
unique interaction characteristics of plasma-mediated interactions as 
contemplated by the present invention. 
As the electron density increases, reflection and absorption in the plasma 
increases correspondingly. Consequently, a large portion of the trailing 
segment of the pulse does not reach the target material. 
In FIG. 2b the intensity profile of an exemplary, unperturbed, incident 
pulse 40 is shown as a dotted line. In the case of linear propagation 
through the material, the shape of the intensity profile is maintained. 
The only difference between a pulse transmitted through a vacuum and that 
transmitted linearly through matter is that in the linearly absorbed 
pulses the profile intensity is reduced (or attenuated). The shape of the 
pulse, however, is maintained. In the example of FIG. 2b, if a linear 
propagation through 1 mm of material results in 10% absorption, the beam 
intensity profile after propagating through the material will be 
approximately 7.2 A.U. at -0.1 ps, down from the 8.0 A.U. shown for the 
incident beam at -0.1 ps. For the same conditions, the beam peak intensity 
at time 0 ps will be 18 A.U. as opposed to the 20 A.U. shown for the 
incident beam at 0 ps, and so on. Every portion of the pulse intensity 
will be attenuated by the same proportion, i.e., 10% for this example. 
An entirely different situation is encountered when the pulse interacts 
with the material non-linearly and plasma is formed. Here, because more 
free electrons are generated by higher intensities, the attenuation is 
proportional to the incident beam intensity and are not constant (for 
example 10% as in the example above) for every portion of the beam time 
profile, nor is the attenuation constant for different beams with 
different intensity profiles. 
As one can see from FIG. 2b, an increase in the incident pulse intensity 
(which corresponds to an increase in the electron density generated within 
the plasma) results in a larger and more significant photon reflection and 
absorption by the plasma. These effects truncate the pulse and prevent 
most of the latter portion of the pulse energy from reaching the target. 
An increase in the incident pulse intensity results in a correspondingly 
larger portion of the pulse being shielded by the plasma and prevented 
from reaching the target. Thus, a higher intensity of the original beam 
results in a larger portion of the incident pulse being truncated. 
If, for example, the incident beam intensity is progressively increased 
from intensity profile level I.sub.1 (where the beam intensity is very 
week and propagates linearly) to an intensity level I.sub.5, where the 
beam assumes its highest intensity, then a progressively larger portion of 
the incident beams will be eliminated through increased reflection and 
absorption by the plasma. 
FIG. 2b illustrates this plasma shielding by showing the effect of the 
plasma on removing progressively larger portion of energy from the 
incident pulse. Thus, the curve 40 corresponds to the unperturbed incident 
beam while curves 42, 44, 46, and 48 show the elimination of progressively 
larger and larger portion of the original beam as the beam intensity is 
progressively increased from level I.sub.1 to I.sub.5. The portions to the 
right of each of the curves 42, 44, 46, and 48 represent the amount of 
energy absorbed or reflected by the plasma, while the portions to the left 
of these curves, correspond to the fraction of the incoming beam that is 
able to arrive at the material. Note that until the point where the 
plasma's electron density is high enough to initiate truncation, the beam 
intensity profiles of curves 42, 44, 46, and 48 share the same intensity 
profile of the original unperturbed beam (the left portion of each of 
these curves). It is only when plasma reflection and absorption are 
significant that the shielding effects truncate the beam into the shapes 
represented by the right-hand-side of each curve. 
FIG. 2b also shows that as the intensity of the incident pulse increases 
truncation begins earlier in time and a smaller fraction of the beam 
arrives at the target material before shielding takes effect. 
Finally, FIG. 2b also shows that when some critical level of electron 
density is reached, the fraction of the beam that can arrive at the target 
material before shielding takes effect becomes substantially constant. 
This is indicated by the fact that the shape of the intensity profiles 
remains essentially unchanged in response to an increase in the incoming 
beam energy. Thus, the curve 46 and the curve 48 in FIG. 2b remains 
essentially constant. This means that the excess energy packed into the 
incoming beam I.sub.5 has been reflected or absorbed by the plasma to 
leave the portions of the beam allowed to penetrate into the target 
material--essentially unchanged. 
Again, this saturation in the amount of energy that is able to arrive at 
the target material occurs because both I.sub.4 and I.sub.5 (the incoming 
beam profiles corresponding to the curve 46 and curve 48) are intense 
enough so that the critical electron density is reached substantially 
simultaneously for curve 46, and curve 48, and the subsequent additional 
beam energy in the more intense pulse I.sub.5, either increases the free 
electrons kinetic energy (i.e., increases the heating of the plasma) or is 
simply being reflected. 
FIG. 2c illustrates another useful feature of the plasma characteristics 
used in the present invention. As was indicated above, plasma shielding 
prevents excess energy from reaching the target material. Thus, once a 
high electron density has been generated, an increase in the incident 
laser pulse intensity results in an increase in the amount of reflection 
and absorption by the plasma electrons and a corresponding increase in 
their average energy. Thus, in FIG. 2c, an increase in the incident pulse 
intensity from level 56 to level 50 results in a corresponding increase in 
deposited energy density but not in a corresponding increase in the 
deposition layer thickness. In fact, as FIG. 2c clearly shows, the 
thickness of energy deposition corresponding to the lowest energy beam 56 
is not much deeper than the deposition layer thickness due to the highest 
energy beam 50. 
Thus, as FIG. 2c shows, the plasma shielding naturally ensures that the 
energy deposition layer does not become correspondingly thicker but is, 
instead, maintained at a relatively constant thickness. This relatively 
constant energy deposition depth was also which is relatively which is 
relatively insensitive to increase in incidence beam energy was also 
indicated by the ablation depth data (see discussion below), which clearly 
shows that increase in incoming energy does not yield a significant 
increase in the amount of material removed. 
The present invention makes use of the effects described above. Simply put, 
it is these plasma characteristics which act as a natural limiting factor 
for the amount of light that can be directly coupled to the material, and 
it is the plasma properties that limit the thickness of the energy 
deposition layer and the depth of the material being affected. Thus, if 
the material and/or beam characteristics allow plasma and free electron 
generation, the interaction characteristics become relatively uniform. As 
was shown above, regardless of other material or beam properties, (such as 
the exact details of the material thermal, optical, and mechanical 
properties, or the beam wavelength characteristics), the interaction is 
dominated by the plasma electrons absorption and reflection exhibited in 
FIG. 2a to FIG. 2c. Therefore, as the inventor recognized, it is the 
plasma interaction properties that dominate the material removal and 
modification process. 
While light penetration of and absorption by the plasma also depends on the 
wavelength of the incident radiation, and to some extent on other material 
and beam characteristics, this dependence, especially when multiphoton 
ionization is involved, is indirect and much weaker than in the linear 
case. Thus, plasma interactions with the incident light are more uniform 
and much less sensitive to beam and material parameters than in the case 
of linear interactions. As will be explained further, it is this unifying 
characteristic of the plasma-mediated interaction, that is used, according 
to one aspect of the resent invention, to improve material processing 
procedures and make the present invention relatively insensitive to 
material properties and material type. 
Thus, FIG. 2a through FIG. 2c illustrated the advantages of the aspect of 
the invention using plasma-mediated interaction: once plasma is formed, 
the interaction ceases to depend on the specifics of the targeted material 
and becomes much less sensitive to the beam parameters. This significant 
reduction in sensitivity to beam parameters also means that once plasma 
formation is accomplished, excess beam energy is accommodated by the 
electrons in the plasma. In this case, excess energy is mostly rejected 
instead of reaching the material directly and increasing the heating and 
mechanical coupling to the material. 
The examples and illustrations presented below, now show how some of the 
parameters required for achieving high volumetric power density, onset of 
plasma, and critical electron density, (namely, pulse duration, beam spot 
size, scattering, absorption and wavelength), can be used in the practice 
of the present invention, to take advantage of the above outlined unique 
characteristics of plasma-mediated interaction. 
FIGS. 3a through 3f represent an additional aspect of the operation as 
described by the present invention, and manifested through the dependence 
of the material removal rates, on the beam power density at the targeted 
volume of material. The figures illustrate the observed removal rates 
dependence on the beam's fluence (beam energy per unit area), wavelength, 
and pulse duration. Through these figures we can understand the invention 
principle of controlled interaction through control of the volumetric 
power density and the plasma interaction regime. 
The Laser beam power density at the target area defines the dominant 
ionization process, subsequent electron density, and ultimately, the 
plasma interaction regime, which, in turn, result, in unique ablation 
characteristics. For a final removal rate on the order of a few micrometer 
per pulse, the inventor identified the following approximate divisions 
into three characteristic interaction classes: 
Class 1. Very high power density regimes, generated through either, very 
short pulses (less than about 10 ps) and/or very high pulse energy, and/or 
very high absorption. Regardless of the dominating mechanism, the 
resulting power densities at the target material are in the range of more 
than about 10.sup.15 w/cm.sup.3. In this range multiphoton absorption 
plays a dominant role and ablation rates are very uniform and are 
relatively independent of the precise details of the material 
characteristics and the wavelength of the beam. 
Class 2. Moderate power density regime generated through either, short 
pulses (from about 10 picosecond to about 100 nanosecond) and/or moderate 
pulse energy and/or moderate energy deposition depths resulting in power 
densities at the targeted volume in the range of from about 10.sup.11 
w/cm.sup.3 to 10.sup.15 w/cm.sup.3, and characterized mostly by thermal 
ionization. In this regime the interaction process becomes more sensitive 
to material type and to beam wavelength. In this case depth of ablated 
material tends to be slightly larger than class 1 because of the deeper 
linear penetration prior to full development of the plasma. Here, ablation 
depth per pulse tends to range from a single to several micrometers in 
depth. Because of the lower power densities involved, ionization is slower 
and plasma shielding is not as effective as that of class 1. As a result, 
a deeper energy deposition is often the consequence This consequence may 
violate the inventor's requirement for approximate parity between 
deposition and ablation depth and may lead to larger residual energy left 
in the material and a more significant cumulative heating will follow. The 
possible development of some thermal and/or mechanical collateral damage 
is the ultimate outcome of the this class of interaction. 
Class 3. Lower power density regime generated through either longer pulses 
(from about 100 nanosecond to about 10 ms) and/or lower pulse energy 
and/or larger energy deposition depths resulting in power densities at the 
targeted volume in the range of from about 10.sup.7 w/cm.sup.3 to 
10.sup.11 w/cm.sup.3. Here, the interaction is even more sensitive to 
material characteristics and to the beam wavelength. The ablation rates 
fluctuate widely from about a fraction of a micrometer to over about five 
micrometer per pulse. At the same time both collateral thermal and 
collateral mechanical damage fluctuate significantly in response to the 
conditions for volumetric energy densities deposition and to plasma 
initiation and to how close conditions are to satisfying the parity 
condition discussed above. The ultimate characteristics of this class of 
interaction is a relatively less predictable material removal and 
modification performance of systems operating within this interaction 
class. 
These divisions are rather imprecise and are made only for the purpose of 
general classification of the categories of the interaction classes, all 
of which are used in the practice of the present invention. Some overlap 
and increased interaction complexity may obscure this simplified 
classification. 
FIG. 3a depicts the ablation rates (in micrometers of material removed by a 
single pulse) for both an exemplary enamel and an exemplary dentin 
material, ablated by 60 fs laser of 1.05 micrometer radiation wavelength. 
Note that the range of fluence used for the 60 fs pulses corresponds to 
power densities in the range of about 0.1 10.sup.17 to 5 10.sup.17 
W/cm.sup.3. For purposes of identification, dentin is represented by 68 
while enamel is represented by 65. 
FIG. 3a also illustrates an important characteristic of plasma-mediated 
interaction which was pointed out in the discussion above: both enamel and 
dentin exhibit a clear ablation rates saturation pattern as pulse energy 
is increased. From the ablation threshold at about 0.5 Joules per square 
centimeter, ablation rate increases rapidly to about 0.7 .mu.m/pulse for 
enamel and 0.9 .mu.m/pulse for dentin at a fluence level of about 1.7 
Joules per square centimeter, where ablation for both tissue types 
stabilizes at about the same rate. Beyond this point, only a very small 
increase in ablation rate occurs with increases in fluence. Ablation rates 
of 1.5 microns per pulse are achieved for dentin material at 16 Joules per 
square centimeter. This represents only about a 50% increase in ablation 
rate for over an eight fold increase in fluence level, as compared to 1.7 
Joules per square centimeter level. 
The diminished return in ablation efficiency is a natural consequence of 
the plasma interaction characteristics. As the pulse energy is increased, 
a denser plasma is generated by the leading edge of the laser pulse. The 
denser plasma absorbs and reflects subsequent radiation, thus shielding 
the surface and preventing additional energy to be used for deposition. 
For purposes of comparison, the ablation rates of dentin and enamel when 
processed with one nanosecond pulses at a fluence of 34 Joules per square 
centimeter (about 3 10.sup.10 W/cm.sup.2) were also studied. The 
nanosecond pulses were produced by the chipped pulse amplifier laser 
system that also produced ultra short pulses of 350 fs (i.e., the pulses 
were simply left uncompressed at their 1 nanosecond stretched value) and 
shared the same 1.05 .mu.m radiation wavelength. This wavelength is 
characterized by a relatively deep linear penetration, (on the order of a 
centimeter). Combined with the much longer pulse duration (a factor of 
approximately 3,000 longer than the 350 fs pulses) the power densities 
generated by the one nanosecond pulses much lower and are approximately on 
the order of 10.sup.10 W/cm.sup.3, or class 3 interaction. 
Nanosecond pulses exhibit an ablation rate of about 4 microns per pulse for 
dentin, and about 1.4 microns per pulse for enamel, at the 34 Joules per 
square centimeter fluence level. The inventor has determined that a 3 
Joule per square centimeter fluence was well below the ablation threshold 
of either dentin or enamel for nanosecond pulses, which threshold was 
determined by experimentation to be in the range of about 20 Joules per 
square centimeter. 
The experiments with nanosecond pulses thus illustrate several important 
points about the principles of interaction: 1) if the intensity is too low 
no plasma is formed and no explosive interaction occurs; 2) above a 
certain threshold--probably around 20 J/cm.sup.2 in the case of dentin, 
plasma is formed and interaction does takes place, and 3) that because 
light has had a chance to penetrate and heat directly a much deeper region 
of the target, significantly larger depth ablation is achieved. Since the 
initiation of plasma in this case is dependent on thermal ionization, much 
larger power densities are required and much larger quantities of heat 
must be generated throughout the larger deposition volume. 
Also, absorption and scattering characteristics of the two types of 
materials play an important role in determining the energy densities, thus 
as is clear from FIG. 3a, the ablation rates for the same fluence level in 
the nanosecond regime are very different for dentin and enamel, with 
dentin ablation being almost a factor of four greater. 
The role of linear absorption and scattering for pulse durations even 
longer than the exemplary one nanosecond discussed above, can be 
demonstrated by the results of FIG. 3b. Here, the pulse duration is 
approximately 15 ns and approximately 300,000 time longer than the 60 fs 
pulses of FIG. 3a. Significantly, however, the radiation wavelength here 
is in the far ultraviolet range at about 193 nm, where scattering and 
absorption are very large. Thus, in spite of the longer pulse duration (15 
nanosecond as compared to the 1 nanosecond example presented above), large 
power density (10.sup.12 to 10.sup.13 W/cm.sup.3) are achieved due to the 
concentration of pulse power within a very shallow deposition depth (on 
the order of a micrometer) and many of the characteristics of the 60 fs 
class 1 interaction are observed here as well. Thus, similar to the 60 fs 
case, we observe the same ablation saturation effect (i.e., no significant 
increase in ablation depth with increasing pulse energy) due to rapid 
plasma formation at energies beyond 5 mJ per pulse (or fluence of 0.12 
J/cm.sup.2. Also, note that similar to the case of the 360 fs, the 
interaction and removal rates are not very sensitive to water content 
(since both water-saturated, as well as dehydrated, samples strongly 
absorb and scatter this far ultraviolet wavelength, thus easily generating 
the high power densities necessary for plasma formation. 
For the purpose of demonstrating the practice of the present invention, it 
is also useful to consider the rather long pulse regime of 1 .mu.s. In the 
exemplary system of FIG. 3c mid-infrared laser system of Erbium:YAG 
emitting light in the normal mode of oscillation with macro pulse duration 
of 250 .mu.s and wavelength of 2.9 .mu.m. The power densities 
corresponding to the approximately 1 .mu.m absorption depth of this 2.9 
.mu.m wavelength and 250 .mu.s macro pulse are on the order of 10.sup.8 
W/cm.sup.3, and can belong to the lower portion of class 3. This macro 
pulse of this system, however, consists of a train of about 20 micro 
pulses each of 1 .mu.s pulse duration. The power density for these shorter 
micro pulses is thus on the order of 10.sup.10 W/cm.sup.3, almost in the 
range of interaction class 2. Thus, as can be seen from the Figure, the 
ablation rate per micro pulse is on the order of 1 to 2 .mu.m, and there 
is little sensitivity to water content. This illustrates the point that if 
the interaction is carried out under strongly absorbing conditions (as in 
the case of the Er:YAG laser radiation) which yield high volumetric power 
density, the result is ablation behavior similar to the nanosecond and 
even sub-picosecond systems. 
An example of deeper penetrating wavelength is provided by FIG. 3d and FIG. 
3e. Here, two plasma regimes are considered. FIG. 3d shows the XeCl system 
at 308 nm and 15 ns pulse duration. The beam intensity at the target is 
approximately 10.sup.9 W/cm.sup.2 because of the relatively short pulse 
duration. The relatively deep penetration, on the order of 100 cm reduces 
the volumetric power density to about 10.sup.7 W/cm.sup.3. On the other 
hand, the effect of relatively strong scattering in this ultraviolet range 
reduces the effective deposition depth and help raise the power density 
value back to 10.sup.8 W/cm.sup.3 to 10.sup.9 W/cm.sup.3. The results are 
similar to all those obtained with power densities of class 3 and 
remarkably similar to those shown in FIG. 3a for the one nanosecond Nd:YAG 
system (where power densities were on the order of 10.sup.10 W/cm.sup.3 as 
well). As FIG. 3d and other data collected by the inventor show, there is 
a strong sensitivity to tissue type (e.g., 4 .mu.m/pulse for dentin, and 1 
.mu.m/pulse for enamel at these 10.sup.10 W/cm.sup.3 power density 
levels.) As FIG. 2e also shows, a distinctive ablation rate difference 
exists between high water content exemplary dentin material and between a 
dehydrated samples. Since in the case of hydrated dentin absorption is 
increased, volumetric power densities created at the surface also increase 
and plasma generation is enhanced and ablation rates are increased. As in 
the Nd:YAG ablation case, the scanning electron micrographs show a similar 
surface pattern which includes partial melting and surface cracks. 
As a final example we consider yet another system of the relatively long 
pulse regime of 1 .mu.s. In the exemplary system of FIG. 3e, a 
mid-infrared laser system of Ho:YAG emitting light in the normal mode of 
oscillation with macro pulse duration of 250 .mu.s and wavelength of 2.1 
.mu.m. The power densities corresponding to the approximately 300 .mu.m 
intermediate absorption depth of this 2.1 .mu.m wavelength and 250 .mu.s 
macro pulse are on the order of just below 10.sup.7 W/cm.sup.3, and can be 
classified with the lower portion of class 3. This system macro pulse, 
however, consists of a train of about 20 micro pulses each of 1 .mu.s 
pulse duration. The power density for these shorter micro pulses is thus 
on the order of almost 10.sup.8 W/cm.sup.3, within the range of 
interaction class 3. The observed interaction are indeed inconsistent and 
strongly change as power densities are increased from below class 3 where 
little ablation and mostly heating, charring and cracking occur to above 
the class 3 threshold for plasma generation. When plasma is formed, 
ablation rate improves and increases linearly up to over 3 .mu.m per pulse 
for the highest power densities tested for the water-contained samples. 
The inventor also noted the strong dependence on tissue type and water 
content (exemplary fresh dentin was ablated at rates 3 to 4 times higher 
than the exemplary dehydrated dentin, see FIG. 3e). Also noted was the 
typical class 3 ablated surface features which included some cracking 
melting and thermal loading. 
Principles of Operation: Thermal Effects 
Further advantages of the present invention are the control and influence 
that the operator is able to exert over thermal energy deposition in the 
tissue by the manipulation of plasma parameters. As was demonstrated 
above, the presence of plasma completely changes energy transmission and 
deposition in the material. As a consequence, the characteristic initial 
linear energy deposition and the subsequent reflection and dispersion of 
the incoming energy by the expanding plasma plume will ultimately be the 
most significant factors determining the amount of residual thermal energy 
left in the target material. 
FIG. 4a and FIG. 4b illustrate the effect of the interplay between linear 
absorption and the onset of plasma on the residual temperature measured in 
exemplary dentin and rabbit cornea, respectively. FIG. 4a shows infrared 
camera temperature measurements corresponding to the ablation events 
depicted by FIG. 4a. Thus, FIG. 4a shows a graphical representation of 
thermographic measurements of the residual temperature increase, as a 
function of time, in exemplary dentin material processed with a laser 
having 1 nanosecond pulse duration and a fluence of 32 Joules/cm.sup.2 
168, compared to an ultrashort pulse laser having pulse duration of about 
350 femtoseconds at a fluence of 3 Joules/cm.sup.2. Both pulse durations 
were delivered at 10 Hertz pulse repetition rates. As can be seen from 
FIG. 4a, the nanosecond laser system exhibits an 8.degree. C. temperature 
differential over the femtosecond laser after only about 5 seconds 
operation. The residual temperature of the nanosecond laser continues to 
increase at a rate of about 1 degree per second. In contrast, the residual 
temperature of the femtosecond laser remains substantially within 2 to 
3.degree. C. of room temperature after application times in excess of one 
minute. The difference lies in the larger amount of energy needed by the 
longer pulse to initiate plasma, but also by the deeper optical energy 
deposition of the 1 ns system. With the longer pulses, linear propagation 
at this 1.05 .mu.m pulse duration proceed until plasma generation occurs. 
Penetration depths are as deep as several centimeters and energy is spread 
much more evenly throughout the tooth, in significant violation of the 
inventor principle of high ratio of ablation depth to energy deposition 
depth as described above. This deeper lying energy is not removed by the 
ablative event and is then allowed to accumulate between consecutive 
pulses at the exemplary 10 pulses per second tested and result in the 
thermal build up observed for the 1 ns pulses in FIG. 4a. 
For the 1 ns pulses, an increase in pulse fluence to 32 J/cm.sup.2 yielded 
plasma and ablation. However, since a larger amount of volumetric power 
density was required to initiate the plasma, larger amount of energy is 
also left as residual energy in the 32 J/cm.sup.2 pulse interaction with 
an exemplary dentin material. As a consequence, cumulative heat which is 
manifested in the surface temperature, is considerably larger. The case of 
the 1 nanosecond pulses at the relatively low absorption regime of the 
1.05 .mu.m light corresponds to class 2 in the classification described 
above. 
A dramatically different situation is exhibited for the much shorter pulse 
of 350 femtosecond (also shown in FIG. 4a) Here, the class 1 interaction 
with high very high intensities of 10.sup.13 w/cm.sup.2 lead to 
multiphoton ionization which was immediately followed by plasma 
generation. In the 350 fs case, ablation threshold for dentin is on the 
order of 0.5 J/cm2 and at the 3 J/cm2 interaction demonstrated by FIG. 4a, 
only 2 to 3.degree. C. temperature increases are recorded even 60 to 80 
seconds after the initiation of the interaction. 
When the fluence of the 350 fs pulses is increased to 16 j/cm.sup.2 the 
corresponding target temperature does increase to a 40.degree. C. level as 
shown in curve 166 of FIG. 4a. This increase actually takes place due to 
plasma shielding where absorption of the excess pulse energy by the plasma 
raises its temperature and heats up the target material as well. On the 
other hand, lowering the 1 ns pulse energy by a half (to about 16 mJ) 
bring the fluence level to below threshold. Ablation ceases and, the 
material temperature (curve 164 in FIG. 4a) corresponds to linear 
absorption of the pulse energy by the very large penetration depth and 
volume. Consequently, the material temperature is significantly lower 
(about 30.degree. C.). 
The importance of the two mechanisms discussed above, namely, the role of 
the parity principle in ensuring removal of much of the deposited heat, 
along with the role played by the plasma as a means of controlling 
residual excess temperature, are further illustrated by FIG. 4b. Here the 
relatively low pulse fluence (0.25 J/cm.sup.2) and pulse duration (15 ns) 
put the beam intensity at 10.sup.7 W/cm.sup.2 or in class 2, as in the 1 
ns interaction of FIG. 4a. However, since the beam wavelength in this case 
(193 nm) is highly absorbed in scattered by the exemplary rabbit cornea 
material, volumetric power density levels are significantly increased and 
result in rapid generation of seed electrons and plasma. As a consequence, 
the interaction is plasma mediated and shows the same interaction 
characteristics of the 350 fs pulses rather than the 1 nanosecond regime 
to which the pulse belongs. Similarly the temperature increase is only a 
few degrees and the heating shows the same temperature saturation behavior 
(or steady state behavior) for a time scale greater than about 10 seconds. 
The effect of plasma shielding is further illustrated by FIG. 4c for an 
exemplary 120 ns XeCl with 308 nm radiation. Here, as is clearly evident 
by the Figure, an increase in fluence level by 1,000% (from 0.5 J/cm.sup.2 
to 5.0 J/cm.sup.2) results in a temperature increase of less than 70%. 
Such rejection of excess energy allows an increase of repetition rate by a 
factor of 7 with a temperature increase by less than a factor of 2. This 
aspect of the invention allows for the principle of high repletion rate 
operation which will be discussed below. 
In conclusion, we see that the principle requiring high ablation depth to 
deposition depth ratio and the role of the physical ejection of much of 
the material with significantly elevated energy densities, are of critical 
importance to the practice of the present invention. Similarly, by 
reflecting and dispersing excess energy, plasma shielding too serve in all 
classes of power densities to minimize the amount of residual single pulse 
energy available for heating the material. Expressions of plasma effects 
and physical heat removal through ablation of much of the deposited energy 
are indeed seen in all three classes of source power density. 
As the preceding discussion showed, the ablation rates of all three plasma 
classes are only on the order of a single micrometer per pulse. Thus, the 
application rate of about 1 to 10 pulses per second, found in most 
conventional and commercial lasers, is quite inadequate, because many 
material removal procedures require the removal of a large volumes of 
material in a relatively short period of time. As a result, despite the 
many advantages of the plasma-mediated interactions, the practical 
application of lasers within these three classes would normally remain 
unfeasible. In addition the inventor has realized that the application of 
high pulse repetition rates also serves to remove cumulative residual 
heat. 
Principles of Operation: Heat Removal Through the Use of High Pulse 
Repetition Rate 
In accordance with practice of principles of the invention, these 
disadvantages are mitigated by the use of rapidly pulsed laser systems 
which can generate pulse repetition rates in the range of up to 100,000 
pulses per second (100 kilohertz). Such high repetition rates are made 
practical because of two important factors: 1) the low residual thermal 
energy and low residual mechanical energy depositions which characterize 
the single pulse interaction in the practice of the present invention 
(this low residual energy deposition is a consequence of the inventor's 
principle of parity between single pulse energy deposition depth and depth 
of a single pulse ablation as discussed above); and 2) an intrinsic 
characteristic of sufficiently high pulse repetition rate which 
significantly help minimize cumulative heat deposition. The latter 
property will now be discussed below. With such high repetition rate 
systems, high material removal rates (up to several centimeter per second) 
can be achieved through the practice of the present invention, while 
maintaining the minimal collateral damage characteristics of a the single 
pulse interaction. 
As explained above, high pulse repetition rate plays a crucial role in 
allowing the material processing method and apparatus as contemplated by 
the present invention to meet and even exceed material removal rate of 
conventional systems including mechanical instrument, chemical devices or 
conventional laser system. In addition, as was also pointed above, 
combined with low per-pulse material removal rates (for example, ablation 
depth on the order of a single micrometer pulse were discussed in the 
exemplary ablation of very short pulse lasers), very high precision can be 
achieved. This accuracy and precision in can be combined with the high 
removal rate only because the laser system can be electronically 
controlled by a feedback device which can stop an exemplary 1 KHz 
operation within a single pulse (i.e., within the 1 ms pulse-to-pulse 
separation). Such an exemplary system, thus, can remove 1 mm of material 
in one second to a tolerance on the order of 1 .mu.m, an unprecedented 
combination of precision and speed. 
However, as the inventor recognized that high pulse repetition operation 
plays another unique and very important role in achieving a successful 
practice of the invention. Namely, high pulse repetition rates serve as an 
additional and very critical mechanism in removing residual heat 
accumulate by the total operation and application time ("ON" time) of the 
an ablation procedure. To understand this concept, which the inventor 
terms "self removal of cumulative heat by high pulse repetition rate 
operation", consider FIG. 5a. FIG. 5a the horizontal axis corresponds to 
the time axis, and the vertical axis correspond to distance. Curve 1 shows 
the location (depth) of the heat diffusion front as a function of time for 
an exemplary isotropic heat conduction parameters. Exact depth the heat 
has diffused to from the region of deposition is proportional to the 
square root of a proportionality parameter K and the time, t, 
EQU X.sub.diff =(K.sup.1/2 t.sup.1/2) (1) 
The parameter K is proportional to the material thermal conductivity and is 
known as the "thermal diffusivity". It is equal to the "thermal 
conductivity" divided by the product of the material density and heat 
capacity. For an exemplary water or soft tissue can be roughly 
approximated as 10.sup.-6 m.sup.2 /s. As can be seen from the FIG. 5a, the 
diffusion front 220, is a parabola curved about the time axis. It indicate 
very rapid initial heat diffusion which slows down very significantly as 
time progress. 
The linear curves 222, 224, 226, and 228, in FIG. 5a, represent the 
position (or depth) of the ablation front below the initial surface. As 
can be seen from FIG. 5a, the ablation depth is directly proportional to 
time and can be described by the linear equation 
EQU X.sub.abl =(a.sub.r .nu.)t (2) 
Where the slope of the line, 5, is equal to (a.sub.r .nu.), the product of 
a.sub.r, the ablation rate per pulse and (nu) .nu., the pulse repetition 
rate. If, as we discussed above, a constant ablation rate per pulse of 1 
.mu.m/pulse is assumed, then the slope of the curves representing the 
ablation front of various pulse repetition rates are proportional to the 
pulse repetition rate. Thus, as can be seen from FIG. 5a, high pulse 
repetition rate will yield a steep slope and a low pulse repetition rate 
will yield a shallow line. 
Significantly, FIG. 5a reveals a very important feature of the present 
invention. If the material processing system is allowed to operate long 
enough, the depth of the ablation front (or material removal) will 
ultimately surpass the depth of heat diffusion from the original pulses 
and the ablation itself will completely remove any residual heat that was 
deposited in the material by earlier pulse. 
Since heat initially diffuses relatively rapidly, the heat from the most 
recent pulses will move faster than the ablation front and part of it will 
not be removed by later pulses if the system is stopped at some finite 
time. However, heat from earlier pulses will not diffuse as fast and will 
eventually be contained within a volume that will ultimately be completely 
removed by the system. 
The point can be made clearer by considering an exemplary system operating 
at 1000 pulses per second for 3 second and to, for example curve 224 in 
FIG. 5a. In water from the first pulse to interact with the sample will 
diffuse a distance of 1 mm into the material at about 1 second. The 
ablation front, assuming ablation rates of 1 .mu.m per pulse and 1000 
pulses per second will cut 1 mm of material in 1 second as well. Thus, the 
point at which the ablation front overtakes the first-pulse heat diffusion 
front, designated in FIG. 5a as X.sub.xo, and named by the inventor the 
"cross-over" depth", is approximately at 1 mm depth. The cross-over occurs 
approximately 1 second after the start of the interaction for an exemplary 
high water content tissue or material. This point in time is, 
consequently, named the "cross-over time" and is labeled t.sub.xc. 
If the exemplary system above is operated for 3 second, the heat from the 
first few pulses after 3 seconds of operation would be at some point 
X.sub.diff (3 seconds) along curve 220, but since 3 seconds is longer time 
than the 1 second t.sub.xo, X.sub.diff (3 seconds) will be a shorter 
distance that the ablation front at t=3 sec as indicated by the fact that 
the position of curve 224 is higher than that of curve 226 for t&gt;txo. 
Those skilled in the art will readily recognize that the heat diffusion 
front due to heat deposited by ALL pulses originated within the first 2 
seconds of the procedure will be at some location X.sub.diff on curve 220 
beyond t.sub.xo, which will also be below the ablation front depth. This 
condition, thus indicate that all the volume of the material heated by 
pulses pulse number 1 to pulse number 2000 was removed by the ablation. 
The situation is different for the last 1000 pulses in our exemplary 1000 
Hz system. These pulses are characterized by the fact that the time 
remaining in the interaction is shorter than the time necessary for the 
ablation front to overtake their thermal diffusion position, T.sub.xo. An 
exemplary pulse interacting with the material a time t.sub.lp before the 
source ceases operation, will have its heat diffuse to a position 
X.sub.lp, which is deeper than depth of material removed by the (n 
t.sub.lp) pulses left within the time interval t.sub.lp before the source 
ceases operation. 
As FIG. 5a shows, however, even these last few pulses have some of their 
residual heat removed by the subsequent pulses. Clearly, pulses just 
behind pulse 2000 will have most of their heat removed by the subsequent, 
nearly 1000 pulses, while pulse number 3000 and the last few pulses in the 
sequence--will have none or very little of their residual heat removed by 
subsequent pulses. Interestingly, the inventor also recognized that the 
fraction of the deposited heat left by each one of the last 1000 pulses in 
the exemplary 1000 Hz system, is proportional to the ratio of the distance 
between the depth of thermal diffusion and the position of the ablation 
front (i.e., the distance between position X.sub.diff, given by curve 220 
minus the position Xab given by curve 224, (X.sub.diff -Xab)), and the 
total diffusion depth, X.sub.diff. Furthermore, the total amount of 
cumulative heat not ablated by the exemplary laser system is proportional 
to the area bounded between curve 220 and curve 224 to the left of 
t.sub.xo. 
FIG. 5a also shows that if for high pulse repetition a steeper slope will 
mean that t.sub.xo occurs earlier and smaller proportion (in comparison 
with the total amount of cumulative heat deposited in the material will be 
left. For very slow ablation rate, on the other hand, txo may not occur in 
pratical times (for example t&lt;5 second, a reasonable upper limit time 
scale for an exemplary dental application system), and only small potion 
of the deposited heat will be removed by the ablation front as indicated 
by curve 228 in FIG. 5a. This situation invariably occurs with the low 
pulse repetition rate of conventional surgical and material processing 
system. The ability to operate in the high pulse repetition regime and to 
ablatively remove much of the residual heat thus represent a major 
advantage of the present invention over conventional tools and 
conventional laser system. The ability to remove most of the heat was also 
confirmed by Scanning electron micrographs studies and by infrared 
Thermographic measurement of ablation temperatures as discussed below. 
FIG. 5b reproduces the concept of FIG. 5a for actual computed values off 
our exemplary systems operating at 4 different repetition rates ablating 
and depositing heat in a water-like system. In order to illustrate the 
effects described above over a large range of time logarithmic scales were 
used and, consequently, the diffusion curve 220 appear linear and the 
ablation front appear curved. Non the lest the cross over point can be 
clearly identified. FIG. 5b clearly shows that the ablation front position 
of pulse repetition rate of 100 Hz does not reach the diffusion front 
position until 100 second after start of interaction. The 100 second time 
scale is clearly too long and not a practical time scale for almost all 
operations or procedures. Yet in terms of operating pulse repetition rate 
regimes of conventional laser sources, 100 Hz is usually considered very 
high and outside of safe operating regime due to considerable thermal 
loading and risk of collateral damage. 
To take advantage of the total cumulative heat removal of high repetition 
rate system one would want to operate at pulse repetition rates that bring 
one quickly to the regime beyond the Cross over operating point. The 
Cross-over times and depths can be given in terms of the thermal 
diffusivity and the ablation rate and expressed as a function of the 
source pulse repetition rates n. FIG. 5c shows the calculated values for 
both the cross-over time and cross-over distance as a function of source 
pulse repetition rate (or frequency of pulses in Hz). The values were 
calculated, again, assuming a water-like media and an assumed ablation 
rate of about 1 .mu.m per pulse. In order to fit in one figure the 
behavior for a wide range of pulse repetition rates (ranging from 0.1 Hz 
to one megahertz) the graphs were plotted on a logarithmic-logarithmic 
scale. The x-axis corresponds to pulse repetition rates (or source 
frequency, in Hertz), and the y-axis is shared by the cross over depths 
(in meters) and the cross-over times (in seconds). Both share the same 
numerical values and range from 10.sup.-6 to 10.sup.6. The cross over 
times, t.sub.xo, are given as a function of source frequency (or pulse 
repetition rates) and can be found on the linear curve 260, while the 
crossover depths, X.sub.xo, for a given pulse repetition rate can be found 
on the linear curve 262. Practical procedure length of time require that a 
procedure will be limited to less than about ten second of a continuous 
application duration. This upper limit for procedure time which is 
indicated by the line 264. 
The ten second maximum application time implies that material removal 
procedures (for the exemplary system considered) carried out at pulse 
repetition rates lower than about 300 Hz will never cross-over and the 
ablation front will never surpass the initial diffusion front. The 
approximate limit at 300 Hz that corresponds to the ten second procedure 
limit is indicated by the vertical line 266. 
The 300 Hz pulse repetition rate bench-mark is important in cases were 
large volume removal is intended. As FIG. 5c shows, this pulse repetition 
rate implies a cross-over depth of about 3 mm. For any volume with depth 
larger than 3 mm, several exposure will have to be applied, no complete 
heat removal of earlier pulse train is possible, and larger fraction of 
the incident energy will remain as residual heat. As a consequence, larger 
amount of heat will remain in the target material with the possibility of 
generating collateral damage. However, if only small volume are targeted 
for removal (i.e., small in the sense that the desired removal depth is 
shorter than the cross-over depth), then lower frequency are acceptable 
since the total number of interacting pulses is, (by the definition of the 
procedure's goal), limited. 
The duration of plasma plume (on the order of a few microsecond) and the 
need to avoid pulse-to-pulse plasma shielding, among other things, thus 
dictate an operating pulse repetition rate regime between about 300 Hz and 
about 100,000 Hz. This range of pulse repetition rates is indicated on 
FIG. 5c by the thick dotted line 268. 
The range of about 300 Hz to about 100,000 Hz of pulse repetition rates 
defines the practical pulse repetition rates that should be applied for 
large volume removal large in the sense that the desired removal depth is 
larger than the cross-over depth. For this range the cross-over times 
range 270, is from about ten seconds to about 100 .mu.s, respectively. The 
cross over depths curve 262 defines the range of cross-over depths 
corresponding to this pulse repetition rate range. The cross-over depths 
range 272, stretches from approximately 3 mm at 300 Hz to about 10 .mu.m 
at 100,000 Hz. 
Finally, in considering the practical application of the present invention, 
one must recognize that while high pulse repetition rates ablate much of 
the cumulative heat left in the tissue, very high repetition rate also 
translate to very rapid material removal rates. Application of 100 KHz 
system for one second will result in 10 cm of material being removed. To 
avoid removal rates that are exceedingly fast, exposure time would have to 
be limited (by adjusting a controller) to, for example 100 .mu.s or 5 ms 
intervals so that removal will be automatically stop at 50 to 500 .mu.m 
and allow the operator to reapply the procedure to achieve incrementally 
larger volume removal. 
FIG. 5d shows an experimental confirmation of the minimal temperature 
increases produced by an exemplary 1000 Hz system. The figure depicts a 
graphical representation of residual temperature as a function of time of 
a laser operating in accordance with the invention at a repetition rate of 
1000 Hertz. The pulse duration is 60 femtoseconds at a fluence of about 
2.0 Joules/cm was used. As can be seen from FIG. 5d, the residual 
temperature increases only slowly to about five degrees 8.degree. C. over 
room ambient after 20 seconds application time and to a maximum increase 
of 14.degree. C. after 90 seconds of application time. 
A general estimate of the relative amount of heat removed due to the 
principle of operation concerning high pulse repetition rate ablation of 
earlier pulses residual heat, can be obtained from the following example. 
If the exemplary 1000 Hz, system considered above, operated with an 
exemplary 3 mJ/pulse to remove approximately 1 .mu.m of material with each 
pulse, is used to drill through 5 mm of an exemplary dentin material, we 
need only consider the heat due to pulses applied t.sub.xo seconds before 
the end of operation (see FIG. 5a). t.sub.xo is approximately 1 second for 
the exemplary system considered, and at 1000 Hz, only the last 1000 pulses 
need be considered. The total amount of energy emerging from the exemplary 
1000 pulses of the system considering is thus 3 Joules. A reasonable 
percentage of this incident energy that is eventually coupled to the 
material as residual heat can be estimated at 10 percent. Thus the total 
amount of energy couple after the drilling of 5 mm exemplary dentin is 
approximately 300 mJ. As was discussed above in connection to FIG. 5a, 
even out of this remaining 300 mJ energy only a fraction, proportional to 
the ratio between the area bounded between curve 1 and curve 3 to the left 
of t.sub.xo and the total area under curve 1 and to the left of t.sub.xo, 
is left actually left in the tissue. From FIG. 5a this ration can be 
roughly estimated at about one third. Thus, only about 100 mJ of energy 
will remain as a residual heat in the exemplary dentin. This compared to 
(3 mJ/pulse) * (5000 pulses)=15 Joules actually applied by the beam for 
the actual drilling of the entire 5 mm depth. 
For comparison with an exemplary conventional laser system, a 2.94 .mu.m 
wavelength, Er:YAG operating at an exemplary 10 Hz with, 100 mJ per pulse 
incident energy, packed into 250 .mu.s long pulse each capable of removing 
30 .mu.m with each pulse. To drill through 5000 mm of dentin, 
approximately 170 pulses are needed which, at 100 mJ/p correspond to 17 
Joule of total energy. Again, using the same 10 percent coupling ratio, an 
estimated 1.7 Joule is estimated to remain in the tissue as residual heat 
energy. This amount of energy is 17 times as large as that of the 
exemplary 1000 Hz system. Indeed, infrared thermography and scanning 
electron micrographs clearly shows charring, cracking and carbonization 
for ablation of dentin with an exemplary 10 Hz Er:YAG system. 
Thus since the total amount of energy applied to the material by this 
entire exemplary procedure (15 Joules by the exemplary 1000 Hz system and 
17 Joules by the Er:YAG system) and since the residual thermal energy left 
in the tissue was assumed to be the same in both system (10 percent of 
incident), is almost the same, the example above serve to dramatically 
illustrate that it is the high repetition rate system ability to ablate 
and remove its own heat, that make an important contribution in limiting 
the amount of cumulative residual energy and limiting collateral damage 
due to that residual thermal energy. Again, these conclusions are 
confirmed by infrared temperature measurements of FIG. 5d above compared 
to the several hundreds of degrees Celsius measured for 9 Hz ablation of 
an exemplary Er:YAG system, and by surface examination of the ablated 
crater (including scanning electron micrographs) clearly showing damage 
free surfaces for the 1000 Hz system in contrast to the tremendous 
charring, burning and cracking of the Er:YAG system. 
For even higher pulse repetition rates, for example 10 KHz t.sub.xo is 
about 0.01 second so that only approximately the last 100 pulses need be 
considered. At the maximum pulse repetition rate contemplated by the 
invention, namely 100 KHz, t xo is about 10.sup.-4 seconds and thus only 
approximately the last ten pulses effect tissue cumulative heat. 
The discussion above considered water-like material with K approximated at 
about 10.sup.-6 m.sup.2 /s. However, in the practice of the invention in 
material processing, however, a large number of exemplary target materials 
may be contemplated. In general these may be divided into two broad 
categories of dielectric and conductors. The thermal conductivity of 
dielectric is similar to that of water. Conductors thermal conductivity 
can be higher by about three orders of magnitudes. If, for example, an 
exemplary aluminum is considered, the time required by the thermal 
diffusion front to reach a depth of 1 mm may be estimated at about 0.001 
second. In such instances, even if the ablation rate per pulse is 
maintained at about 1 .mu.m/pulse (and in general the ablation rate in 
metals are often 2-3 time lower than dielectric, i.e., 0.3-0.5 
.mu.m/pulse) and even at the highest pulse repetition rates if 100 KHz, 
the ablation front will be able to catch up with the thermal diffusion 
front only at about Xco of 10 mm and txo of about 10 seconds. With 10 
seconds of 100,000 Hz, one million pulses will constitute the residual 
cumulative heat pool (before ablation begins to remove additional pulses 
energy. (e.g., pulses 1000,001 to 1,500,000). Thus too much heat will be 
deposited in the material to make the high repetition rate removal of 
heat, impractical. A better approach for the conductor case would be to 
take advantage of it's fast thermal diffusion which allow the ablated 
material to quickly rid itself of the excess heat, by either using a 
target consisting of a large thermal mass to dissipate the heat, or having 
the a heat sink in thermal contact with the target conductor material. 
As the discussion above showed, for dielectric, the ablation processes as 
contemplated by the practice of the present invention, result in highly 
localize, self-terminating, shallow energy depositions. The inventor has 
determined that by manipulating absorption and scattering characteristics, 
the pulse electromagnetic energy source can used in the practice of the 
present invention, will allow per-pulse removal of only a thin layer of 
material "Thin" is measured in comparison to the total depth of desired 
material removal, which, for a typical removal depths required for an 
exemplary hard dental tissue procedure will be typically on the order of 1 
micrometer, and for a typical depths required for microchip processing may 
be one tens of that (or about 100 nanometer). Thus, varying the number of 
pulses provides a means of controlling the volume of material removed to 
within a single pulse precision. 
For example, if the laser systems were contemplated as substituting for a 
paradigm mechanical dental drill, the system would be required to drill 
dental tissue at a rate approximating the 300 micron per second removal 
rate of the mechanical drill. From the discussion of plasma-mediated pulse 
ablation rates, in connection with FIGS. 3a through 3e, above, it is clear 
that a 300 micron per second removal rate can be easily achieved by 
operating the laser system of the invention at a repetition rate of 
between about 100 to 300 pulses per second (100-300 Hertz). In fact, in 
view of the discussion above it is clear that with the capabilities of the 
a laser system contemplated by the invention, much larger removal rates 
are possible and, indeed, may be advisable. 
Characteristically, conventional and prior art laser systems are unable to 
operate at such high repetition rates because of the high degree of 
residual heat and significant thermal loading in the ablation area. In 
these systems, as was discussed above, linear optical propagation allows 
deep penetration into the target material and significant heat remains in 
deeper layer of target and is not removed by the ablation event. Rapid 
operation of these systems results in very significant accumulation of 
heat. 
Lasers conventionally used for the removal of hard and/or soft tissue 
operate in the infrared region of the electromagnetic spectrum, have pulse 
duration in the range of about 10 nanoseconds to in excess of 350 
microseconds, and exhibit characteristic removal rates of exemplary 
dentin-type material of about 20 to 50 microns per pulse. IR lasers are 
additionally known to cause objectionable charring of target material, 
such as exemplary dentin, when operated at pulse repetition rates as low 
as 2 to 3 Hertz. Thus, it will be apparent that conventional pulsed IR 
systems are only capable of effecting material removal at a maximum rate 
of about 150 microns per second. The addition of air and/or water cooling 
mitigates the excessive heat problem but complicates the system operation. 
Even with cooling removal rates, such systems are limited to about 300-400 
.mu.m per second, well below the 700 .mu.m per second observed with the 
mechanical drill. 
Thus, it will be apparent that a laser operating in accordance with 
practice of the invention is able to comprise a material removal system 
that results in minimal thermal loading in the ablation target area and 
thus can tolerate pulse repetition rates as high as 100,000 Hertz, without 
the need for any type of additional target cooling mechanism, for periods 
of time substantial enough to effect volume material removal. It is also 
apparent that such a system cannot be realized by conventional laser 
systems operating with low ablation-to-deposition depths ratio, and/or low 
pulse repetition rates, if any significant volume removal or modification 
is required. 
In summary, high ablation-to-deposition depth ratio, operating at high 
repetition rates have several advantages over conventional systems. As 
energy coupled to the material decreases and is confined to shallow 
deposition zone, the material removal system of the invention becomes more 
efficient. Minimal collateral damage occurs because of the high 
ablation-to-energy deposition ratio ensures residual energy removal 
instead of residual energy build up which leads to collateral damage. The 
ablated material carries away a large fraction of the energy deposited by 
the laser. Indeed, the minimal collateral damage and low residual thermal 
energy left in the material due to the single pulse interaction, combined 
with the inherent additional energy removal associated with the high pulse 
repetition rate of the laser systems in accordance with the invention, 
allow pulse repetition rates far in excess of those achievable with 
conventional systems, thereby allowing substantially greater bulk material 
removal rates. 
Finally, since the invention relies on high pulse repetition rate for large 
volume material removal, the mass of the material removed by a single 
pulse as practiced by the present invention is very small, (in many cases 
which can be conceived in practice "very small" means on the order of 
single micron), very little recoil momentum or mechanical transients will 
be generated by each single pulse. Since mechanical transients travel at 
the speed of sound (or faster, in the case of shock waves) pulse-to-pulse 
accumulation at the repetition rates considered by the invention will not 
be significant and will not effect the remaining material adversely. 
Principles of Operation: Use of Doping Agents and Selective Marking of 
Targeted Regions Within the Material 
As was discussed above, a key to the practice of the present invention is 
meeting the parity requirement for equivalence between the depths of 
deposition and ablation. As was also shown above, one class of 
interactions that fulfill this requirement include the ablation processes 
which follow the generation of plasma, because plasma characteristics 
ensure generation of high power densities within very shallow deposition 
depths. 
In many instances the material/beam parameters are such that this 
requirement is fulfilled naturally. However, As part of the contemplation 
of the present invention, it is possible to convert systems with 
relatively deep optical penetration and/or lower power pulse energy, 
and/or longer pulse duration into efficient plasma-mediated material 
processor. The principle of operation for converting a linearly absorption 
system into a system that meet the criteria for the principle of parity 
can be understood with the aid of FIG. 6a. 
FIG. 6a illustrates the role that a doping agent with high absorption 
coefficient can play in allowing plasma generation at lower power 
densities. The figure shows the ablation threshold fluence (in J per 
cm.sup.2) for three types of absorbers. The upper line 284, corresponds to 
week absorber with characteristics absorption coefficient of 0.01/cm. The 
intermediate line 282 correspond to absorption coefficient of 22/cm and 
the lower curve 280, corresponds to a very strong absorber with absorption 
coefficient of 1000/cm or penetration depth of about 10 .mu.m. 
As both the curve corresponding to a weak absorption 284, and the curve 
corresponding to intermediate absorption 282, show, since plasma mediated 
ablation depends on achieving high power densities and the subsequent 
generation of sufficiently high electron density in the plasma, greater 
fluence is required to achieve ablation threshold if the pulse duration is 
longer. On the other hand, the FIG. 6a also shows that if a strong 
absorber like the one represented by the curve 280 is used (for example a 
doping agent or a naturally colored and highly absorbing target), the 
ablation threshold is essentially uniform and independent of the pulse 
duration. In the strong absorber case, concentration of photons in shallow 
deposition layer and high power density are achieved for all pulse 
duration and ablation naturally follows. 
If the material absorption characteristics are such that high energy 
concentrations and energy densities are generated, either multiphoton 
ionization or thermal ionization will quickly initiate seed electrons 
followed by an electron avalanche and plasma-mediated processes. As was 
already explained above, once plasma is formed, ablation characteristics 
are relatively uniform. This effect is illustrated by the lower curve of 
FIG. 6a. This curve corresponds to ablation threshold of a highly 
absorbing material. 
As stated above, the upper two curves (284 and 282) correspond to a 
material which is relatively transparent to the 1.054 .mu.m radiation of 
the exemplary laser pulse tested. Here long pulse duration combined with 
deep beam penetration results in relatively low volumetric energy 
densities and does not yield plasma-mediated interaction. Instead, heating 
and vaporization are the main ablation mechanism. These damage processes 
require much larger total energies over the much larger volume of 
interaction and thus translate into higher damage threshold as shown in 
FIG. 6a. 
On the other hand, at shorter pulse duration (&lt;10 ps), even with relatively 
transparent target materials, the beam volumetric power densities become 
high due to the very short time duration of the pulse which concentrates 
the same amount of energy in a much shorter length of time. The result is 
volumetric power densities sufficient to generate plasma and interaction 
characteristics (in this case ablation threshold) which corresponds to 
that of the naturally occurring highly absorbing materials. 
The desired conversion, as contemplated by the present invention, of a 
system with a naturally occurring high penetration depth into a system of 
with very shallow depth of energy deposition which easily fulfill the 
parity requirement can be made both time and space dependent and can be 
achieved in several different ways: 
i) Through the deposition of an absorbing agent on top of the material 
surface, or within a predetermined thickness layer of within the material 
surface prior to initiation of treatment. This concept is illustrated in 
FIG. 6b. The high absorption agent is deposited on top of the surface in 
an external layer 304, or, alternatively, is allowed to penetrate the 
material surface and be absorbed within a layer of predetermined thickness 
302. The beam emanating from the lens 314 would normally not interact with 
the native target material 300 (as indicated by the dotted line 
representing the beam penetration into the target material) However, with 
the application of a highly absorbing agent (such as an exemplary black 
china ink or microscopic carbon particles), the beam emanating from the 
lens 314, will now be strongly absorbed by an externally applied doping 
agent at 304, the absorbed doping agent layer 302, or the doping agent 
applied to locations within the material volume at 306. Targets 310 and 
312 represent additional exemplary target shapes which can be marked 
through auxiliary doping and then removed by or modified by the beam. 
Once the beam whose power densities within the native target material, is 
below interaction threshold, encounter either one of doped volumes, high 
absorption of the pulse radiation into the tissue will ensure initiation 
of ablation within the high power density volume, and/or plasma initiation 
because of the high energy level deposited in the small layer of the 
absorbing agent. Ablative interaction with the absorbing agents are 
indicated by the symbol 318. 
Often small residual modifications to the surface follow the interaction 
with the laser source, act as subsequent absorbing agents and perpetuate 
the process at any desired pulse repetition rates. Consequently, all the 
advantages and unique characteristics of the plasma-mediated ablation as 
contemplated above, also apply in this case. 
Finally, in some cases where focusing inside the target volume is possible, 
plasma-mediated interactions can be initiated without the application of a 
doping agent, simply by focusing the beam to spot sizes which allow 
concentration of power to above the threshold power density for initiation 
of interaction with the material. This condition is illustrated in FIG. 6b 
by the beam emerging from lens 316 and focused down to above the threshold 
power density at a predetermined targeted location 308 well within the 
targeted material. Again, once power density inside the targeted volume is 
above the threshold power density an interaction is initiated as indicated 
by the symbol 318. 
ii) In some cases and material types, the modified absorbing layer created 
by the absorbing agent will be completely removed by one or more pulses 
and it will be necessary to apply the absorbing agent after one or several 
pulses. To this end, it is contemplated by the practice of the present 
invention to construct an absorbing agent deposition device which will 
very accurately and synchronously to the pulse laser operation, eject an 
absorbing agent source onto the targeted area. For an exemplary 1 KHz, 
1.05 .mu.m radiation source, such an ejection source will have to eject a 
drop of absorbing agent sometime after the completion material ejection 
due to previous pulse action, but within the 1 ms time interval between 
the pulses. FIG. 6c shows an apparatus for a repeated, synchronous (with 
the laser pulses) application of a highly absorbing agent to the targeted 
material surface. In the figure the ejector 342 draw the absorbing agent 
from a reservoir 340 and direct a drop of a predetermined volume into the 
desired interaction location 344. The ejector can be, in principle, 
similar to an exemplary ink jet injection technology available from the 
commercial ink jet printer industry. The beam 346, emanating from the lens 
348, will normally not interact to modify or ablate the material 352. The 
presence of the absorber spot 344, however, will now ensure strong 
interaction 350 at the targeted location. 
iii) Finally, material can be temporally and spatially prepared and/or 
injected with absorbing agents at predetermined location within the 
three-dimensional volume of the target material. Such preparation will 
then be selectively activated by the penetrating laser in order to create 
highly precise material removal or modification in three dimension. 
Injected or prepared high-absorbance at locations 306, 310, and 312 in 
FIG. 6b illustrates selective deposition of absorbing agents of various 
shapes which can assure time- and space--dependent, selective interactions 
within the three-dimensional material volume. 
Principles of Operation: Non-ablative Material Modification 
The method of the present invention also offer the possibility for a 
controlled, variable rate material modification by a pulsed 
electromagnetic radiation beam. The interaction between the pulsed 
electromagnetic radiation beam and the material is characterized by a 
modification threshold volumetric power density, which is a function of 
the target material properties. 
The principle of non-ablative beam modification is based on the fact that 
between the threshold for material ablation and the very low power density 
which leave the material unaffected, there is a transition power density 
range whereby the beam energy deposition characteristics yield 
sufficiently high power densities to induce irreversible changes within 
the target volume, but do not result in ablation, or explosive events. 
Specifically, at very low power densities there will be no modification or 
any irreversible changes in the target material. However, as the power 
density is increased, irreversible changes may occur before the threshold 
for complete ablation takes place. In soft tissue this may corresponds to 
coagulation or evaporation of water molecules with no ionization or a 
large number of molecular bonds are broken. In crystals such changes may 
correspond to changes in crystalline structure and substations. In hard 
tissue or porous, water saturated lattices this may appear as dehydration 
of the material and/or partial melting of the lattice. In an exemplary 
dentin hard tissue material as well as for ceramic-like materials, quartz 
and fused silica, the inventor has determined that the threshold for 
ablation with a 0.35 ps source is on the order of 10.sup.12 w/cm.sup.2. 
For soft tissue this ablation threshold is somewhat lower--on the order of 
10.sup.10 to 10.sup.11 w/cm.sup.2. It is thus possible to select 
beam-target parameters yielding power densities below these limits yet 
sufficiently high for irreversible material modification. 
In general, such irreversible modification may include one or more of the 
following alterations: chemical and physical changes, changes to 
viscoelastic properties, changes to optical or thermal properties, changes 
in chemical properties, changes in physical properties or physical 
breakdown, partial or complete melting of the targeted region, melting, 
and partial or complete vaporization of the targeted volume. 
Using a source capable of generating an output beam of a sequence of 
electromagnetic pulses each having a pulse duration in the range of about 
3 femtosecond to about 10 millisecond; such a beam can be directed toward 
the target at or below the surface. The beam may, for example be 
redirected by a lens or reflective optics so that it converges spatially 
as it nears the target area. Once the beam converges into a threshold 
volume, the resultant power density may be sufficiently high to induce 
irreversible modification. The beam conversion, on the other hand, may be 
designed so that power densities may never reach the threshold for 
ablation. 
Also clear is the fact that as the pulse duration decreases from the upper 
10 ps range to the femtosecond range, the beam power densities are 
generally high because of the shortest of the pulse duration. Thus, small 
changes in spot size (as the beam converges toward the target) will result 
in large changes in the power densities and may increase their values 
beyond the threshold for modification or ablation. The ultimate result is 
then much increased sensitivity to spatial location and increased spatial 
resolution with decreased pulse duration. 
Selective locations within the target material volume surface may possess 
properties that enhanced their scattering and/or absorption. A collimated 
or slightly converging beam impinging on the target material may continues 
its propagation through the material below modification threshold until 
they encounter such high absorption regions where energy deposition is 
increase and deposited power densities are increased above the 
modification threshold. Such selective location may occur naturally or may 
be inserted or induced artificially, by the operator. 
Finally, in some cases it is also possible to modify the pulse frequency 
components temporal distribution so that as the incident pulse transverse 
the material, slower moving components that were arrange to initially lead 
the pulse, are being overtaken by faster, initially trailing frequency 
components. Such a velocity dispersion effect will shorten the pulse 
duration as it transverses the material volume. This effect can be design 
to yield the shortest pulse duration precisely at the target region, thus 
resulting in increasing the power density at that location above the 
modification threshold, or if so desired, above ablation threshold. 
Once a single pulse modification interaction has occurred, allowing 
mechanical or thermal transients caused by the electromagnetic radiation 
pulse to substantially decay would make subsequent pulse interaction 
possible. Operating the pulse source at a pulse repetition rate greater 
than 0.1 pulses per second until a sufficient volume of the material has 
been modified would allow large volume modification. 
Alternatively, scanning and moving either the beam or the target in three 
dimensional space would allow the operator to generate virtually any 
modification pattern desired. Combination with control and feedback 
devices (to be discussed below) along with such translation mounts and 
temporal control over the beam source on/of times and pulse repetition 
rate can provide a completely automated method for generation of such 
material modification patterns. 
Taking advantage of various intensity profiles of the beam and utilizing 
the threshold nature of the modification interaction, modification cross 
section smaller than the diffraction limits can be obtained because only 
portion of the beam spot size may reach the above-threshold power density 
values. In a Gaussian beam profile, for example, power densities at the 
center of the beam significantly exceed those in the wing. Making further 
use of non-linear absorption which are very sensitive to the beam power 
density distribution, modification cross section as small as 100 or even 
10 nanometer can be envisioned. 
Thus, material modification rate can possibly be varied from the range of 
from about 0.01.sup.3 micrometers cube per pulse to about 100,0003 
micrometers cube per pulse, said modification rate being substantially 
constant depending substantially on the volumetric power density threshold 
characteristics and on the source electromagnetic beam characteristics. 
The principle of operation of the material modification system according to 
the practice of the present invention can be further understood with the 
help of FIG. 7. 
In FIG. 7, the beam 360, emanating from the lens 362 is impinging on the a 
target at power density which are below the threshold levels for either 
material modification or material ablation. As the beam converges, its 
power density increases until it reaches the threshold for material 
modification. Modification can include any type of permanent changes to 
the target volume visco-elastic, mechanical or thermal properties. The 
dashed lines continuing from the beam 360 below the modification target 
zone 364 indicate that had the material threshold for modification not 
been exceeded the beam would have continued past the modification zone 364 
undisturbed. The three concentric circles inside the volume indicate that 
material modification can correspond to changes in material densities and 
the creation of compression zones within the modification volume 
364--zones where the modified material density might vary spatially. While 
material modification may not entail material removal, an escape chamber 
368 may be drilled by the ablating system itself, or may be provided by 
other means in cases where ablation or vaporization of part of the 
modified volume of material is desired. 
In addition to achieving above modification threshold by spatially focusing 
the beam, modification threshold can be reached by changing the pulse 
duration as a function of time through dispersion effects (pulse 
compression) or through the injection or application of high absorption 
agents to allow the beam power density to reach 
above-modification-threshold levels. Pulse compression can be achieved 
through reverse dispersion when the arrangement of the pulse frequency 
components is such that faster propagating light frequency components 
spatially trail the slower components. When arriving at the material the 
faster components will catch up with the slower components thus 
compressing the pulse duration. Knowing the frequency dependent of the 
light propagation speed within the material can allow the designer to 
predict the exact location at which a desired amount of pulse compression 
will occur. Thus compression then will bring the pulse power density above 
the threshold for modification and initiate the interaction. Such and 
effect can of course be used for bringing the beam power density above 
ablation threshold at predicted pre-selected time and location. 
Also shown in FIG. 7, is a high absorption agent applicator, indicated by 
the dye reservoir 372 and an injector 374. In this case application to the 
surface 370 or to a deeper lying region 380 can be accomplished. When an 
above-modification-threshold beam 378 emanating from the lens 376 arrives 
at 379, absorption will increase the deposited power density within the 
intended volume and modification will occur. The dotted lines at the end 
of the beam 378 indicate that the beam would have continued its path 
uninterrupted had it not encounter the deposited absorber which forces 
selective modification of the targeted region of the material. 
Principles of Operation: System Construction 
In the practice of the present invention a pulsed output beam having a 
selectively variable output pulse duration from about 3 femtoseconds to 
approximately 10 millisecond at a variable pulse repetition rate from 
about 0.1 to about 500 Kilohertz, with a minimum pulse-to-pulse separation 
of a minimum of about one .mu.s to allow ejected debris and plasma from 
previous pulses to clear the target area. 
As was pointed out above, a key element in the practice of the present 
invention is the selection of parameters such that pulse characteristics 
will ensure removal of most of the deposited energy by the ablation (high 
ablation depth to energy deposition depth ratio), coupled with high pulse 
repetition rate so that on a time scale of a practical total exposure time 
(i.e., on the order of single treatment event, longer than, for example, 
1.0 seconds) the overall material removal will ensure ejection of most of 
the deposited energy. 
Depending on the target material and the type of processing required, the 
energy per pulse can range from about 1 nanojoules to over about 50 
Joules, while the beam spot size can vary from about 0.1 micrometers to 
over 5 centimeter in diameter. Adjusting and focusing the output beam spot 
size, energy, and pulse duration should create a fluence at the target in 
the range of 10.sup.2 W/cm.sup.2 to 10.sup.16 W/cm.sup.2. 
Several classes of pulsed laser systems are capable of generating at least 
some of the parameter requirements described above and thus serve as a 
radiation source for some of the applications envisioned in the practice 
of the present invention. Those having skill in the art will recognize 
that the pulsed laser classes known as flash lamp pumped normal mode 
lasers, Q-switched lasers, pulsed excimer lasers, mode locked lasers and 
chirped pulse amplified lasers may serve as a suitable source for the 
practice of the invention. This list, however, is only partial, and in 
principle, additional pulsed sources of electromagnetic radiation capable 
of producing output parameters which fulfill the requirement specified by 
the present invention, may serve equally well in the practice of the 
present invention. 
In one possible embodiment for the longer pulse regimes, a 
flash-lamp-pumped solid state laser may be equipped with a variable pulse 
width controller permits the laser operator to vary the pulse width of the 
flash lamp from a microsecond range to the 1 ms in increments on the order 
of several microsecond. This capability will allow optimization of the 
performance through temporal variation of the laser pulse. The electronic 
pulse controller can be designed to provide for continuous, batch, single 
shot, or external triggering capable of controlling the repetition rate in 
1 Hz increments up to several KHz repetition rates. 
Shorter pulses can be generated by Q-Switching. Rotary, acoustic-optic, and 
electro-optic Q-switching are only a few possible mechanisms for 
generating pulse in the nano-second to the microsecond range. 
Shorter pulse yet may be provided by mode-locking and using chirped pulse 
amplifiers or through saturable absorbers technologies well-known to those 
skilled in the art. 
A diagram of an exemplary, high repetition rate laser system, suitable for 
practice of principles of the present invention is depicted in FIG. 8a. 
The exemplary laser systems depicted represents a laboratory-model 
prototype devices in accordance with principles of the invention. As such, 
the laser system depicted in FIG. 8a and described below comprises a 
degree of complexity and control variability suitable for laboratory 
experimentation, but which may exceed what is necessary for practice of 
the invention. 
The exemplary laser systems depicted in FIG. 8a includes a parameters 
regime which has been determined by the inventor to be efficient in 
ablating most types of material. Some of the exemplary laser systems 
depicted in FIG. 8 has been shown to efficiently ablate most material. As 
will be described in greater detail below, any type of laser system, 
capable of operating within the parameter regime described above, can be 
employed in practice of the invention. 
Several additional classes of pulsed laser systems are capable of 
generating at least some of the parameter requirements described above and 
thus serve as a radiation source for some of the applications envisioned 
in the practice of the present invention. Those having skill in the art 
will recognize that Q-switched flash lamp pumped or diode pumped lasers 
may serve as a suitable source for the practice of the invention. Other 
possibilities may even include a continuously emitting source of 
electromagnetic energy (for example, continuously emitting laser sources 
known as continuous wave (CW) lasers). Such sources output may be modified 
by various means to result in electromagnetic beam characteristics which 
effectively fulfill the requirement of the present invention. 
Some possible laser system configurations are depicted in FIG. 8. The first 
system, depicted by the components inside the box 400, in FIG. 8a 
corresponds to the a pulse regime ranging from about a single nanosecond 
to about several millisecond range. It can include an exemplary flash-lamp 
pump 402 pumping an exemplary Q-switched solid-state laser 404, with pulse 
duration ranging from the nanosecond to the microsecond, or an excimer 
laser 406 in the nanosecond to the several hundreds nanosecond range, and 
up to several KHz of pulse repetition rate. An exemplary flash lamp pump 
402, pumping a normal-mode solid-state laser (not shown) which would fit 
in the location 404, generating pulse duration from about the microsecond 
to about the several millisecond range. 
The second system 380, corresponds to a the shorter pulse duration regime. 
It is capable of producing pulses in the range from about 3 femtoseconds 
to over 5 nanosecond. This system produces a pulsed output beam having a 
selectively variable output pulse duration which can be changed 
continuously over the about 3 femtoseconds to over 1 nanosecond range. It 
is also capable of producing a variable pulse repetition rate from about 
0.1 to over several KHz by selecting the proper pump laser 389 for the 
regenerative amplifier. The energy per pulse, obtainable from the 
exemplary shorter pulse regime laser system is variable from about 1 nj to 
over 50 millijoules, deliverable in a beam having a spot size variable 
from about 5 micrometers to over 1 centimeter in diameter. 
Although, as this discussion demonstrates, any type of laser system, 
capable of operating within the parameters described above, can be 
employed in practice of the invention, the shorter pulse regime laser 
system, 380 of FIG. 8a, preferably comprises a mode-locked oscillator 384 
which operates to provide pulses having the same or shorter durations than 
the desired final pulse duration. The mode-locked oscillator 384 is pumped 
by a solid-state laser, a diode array, or an Argon-ion pump lasers 382. 
Commercially available oscillators, providing 100 femtosecond pulses, as 
well as laboratory built oscillators, providing 15 femtosecond pulses, 
have shown themselves suitable for practice of the invention. Both 
oscillator embodiments often employ Titanium-doped sapphire as the lasing 
material and utilize the well known Kerr effect for mode-locking, although 
the well known acousto-optic effect is often also suited for mode-locking. 
The pulses produced by such oscillators are typically low in energy, 
particularly on the order of about 1.0 nanojoules. 
These low energy pulses are then stretched in time by over about four 
orders of magnitude (a factor of ten thousand) by a grating pulse 
stretcher 386. The pulse stretcher 386 suitably comprises a diffraction 
grating to disperse the various frequency components of the 
broad-bandwidth pulse produced by the oscillator. By transmitting the 
various frequency components along different paths through an imaging 
telescope, pulses are lengthened in time by an amount .DELTA.L/C, where 
.DELTA.L is the difference in the optical path length between the various 
frequency components and c is the speed of light. 
The stretched pulse is then amplified by several orders of magnitude, 
preferably to the millijoule range, in an amplifier stage. The amplifier 
stage may comprise any one of various types of laser amplifiers familiar 
to those skilled in the art. Most commonly, however, a regenerative 
amplifier, wherein a pulse is able to make multiple passes through a 
single amplifier media is used. The regenerative amplifier employs 
Titanium-doped sapphire (Ti:sapphire) as the gain medium. Because of the 
short storage time of Ti:Sapphire, a second, pump laser 389 of FIG. 8a, is 
used to pump the Ti:Sapphire gain medium. Such a pump laser can be a 
frequency-doubled, Q-switched, Neodymium-yttrium-aluminum-garnet (Nd:YAG) 
laser. The energy required to pump the Ti:Sapphire regenerative amplifier 
388 is typically greater than five times the energy output of the 
regenerative amplifier. 
The repetition rate of the system is determined by the repetition rate of 
the pump laser 389. By changing the repetition rate of the pump laser, 
operation at repetition rates up to and in excess of 1000 Hertz can be 
achieved. Switching of the pulses into and out of the regenerative 
amplifier 388 is accomplished with conventional pulse switching technology 
based on the well-known Pockels effect for polarization rotation. Pulses 
are switched out of the regenerative amplifier when saturation is 
achieved. 
The regenerative amplifier 388 produces pulses of up to about 10 
millijoules in energy. These pulses can be sent directly to a pulse 
compressor 390 or, alternatively, further amplified, by an additional 
Ti:Sapphire regenerative amplifier to increase the pulse energy. 
Following amplification, the stretched and amplified pulse is compressed by 
a variable length pulse compressor 390, employing a diffraction grating. 
In a manner similar to the pulse stretcher 386, pulse compression occurs 
by controlling the optical path of the various frequency components of the 
laser pulse through the compressor. Different frequency components are 
directed along different paths by the angular dispersion of the grating. 
By controlling the dispersive path length taken by the various frequency 
components, a variable duration output pulse is obtained. 
The exemplary laser system 380 has demonstrated a final pulse duration 
which is adjustable in the range of between about 60 femtosecond and about 
1000 picosecond. The laser pulse is directed to a material target 394, 
through a focusing lens 392, by a delivery system which may comprise an 
open beam transport system, an articulated arm, an optical fiber, or a 
hollow core optical wave guide. If desired, the delivery system may be 
adapted to provide additional stretching or compression of the pulse 
duration. The spatial profile of the final pulse is then modified by the 
lens system 394, assuming its final shape, the beam then continues towards 
the target 394. Suitable focusing elements may be comprised of refractive 
(lenses) or reflective (mirrors) elements. A typical exemplary focusing 
element may consist of a simple large f-number single lens for focusing 
the beam onto the target area in a spot size greater than 1.0 micrometers. 
Spot size is easily adjusted either by moving the target away from best 
focus, or by simply changing the delivery lens/mirrors configuration. 
This exemplary laser system 380 of the present invention is thus able to 
produce a continuously tunable output by changes in optics and 
adjustments. Operation at the second harmonic (350 to 532 nanometers) is 
accomplished by passing the beam through a thin potassium di-deuterium 
-phosphate (KD*P) crystal after compression. The KD*P crystal is cut for 
type-I phase matching and is typically between 0.5 and 4 millimeters in 
length. 
Although the high repetition rate laser systems has been described with 
reference to the exemplary q-switched laser, flash-pumped normal-mode 
solid-state laser, mode-locked and chirped-pulse amplified solid-state 
laser, embodied in FIG. 8a, it will be understood by those having skill in 
the art that many different laser systems, operating in various portions 
of the electromagnetic spectrum and capable of providing pulses having 
durations of from about 3 femtoseconds to about 10 ms, at repetition rates 
of up to 100,000 Hertz, are within the contemplation of the present 
invention. What is desired from such systems is that the amount of 
material and residual energy left by a single pulse is small, that the 
ratio of the single-pulse ablation depth to energy deposition depth is 
high, and that, if high material volume removal rate is desired, the 
system pulse repetition rates is sufficiently large that substantially 
much of the residual energy accumulated in the target is removed by 
subsequent pulses within the pulse train so that most of the deposited 
energy is completely removed by the ablation process itself, with the 
entire procedure yielding substantially no collateral damage to 
surrounding material. 
FIG. 8b illustrate additional systems. 410 is a solid state pulsed system 
which is pumped by a CW or a Quasi-CW laser source. For example, a pulsed 
or a CW flash-lamp may serve well as a pump source. A CW or a quasi-Cw 
diode source can also serve very well for this purpose. Such diode laser 
sources may be arranged as diode arrays and diode bars as well as stacks 
of bars to produce substantial pump power of up to kW of continuous power. 
Such sources 412 may be used to pump a Solid-State crystal 414 with 
Q-switching 416 (such as an acousto-optic, electro-optic, or other means 
for producing a Q-switched output pulse characteristics in accordance with 
the requirement of the present invention). The output of these crystals 
than can be modified to longer wavelengths using an Optical Parametric 
Oscillator (OPO) 318. Alternatively, the output may be further modified by 
passing the beam from 314 through a thin potassium di-deuterium-phosphate 
(KD*P) crystal. The KD*P crystal is cut for type-I phase matching and is 
typically between 0.5 and 4 millimeters in length. Additionally other 
non-linear crystal such as KTP may serve equally well for many 
applications requiring output frequency conversion. 
FIG. 8b also illustrates other possible preferred embodiments. The system 
420 may consists of a CW electromagnetic source 422. Any continuously 
emitting (CW) electromagnetic energy source may serve for this purpose. 
For example a CW laser source such as a Carbon Dioxide, an Ar.sup.+ ion, 
a Tunable Ar.sup.+ ion--pumped Dye laser, a Krypton Gas laser, a Ruby 
laser, or even a non-coherent radiation source (such as, for example a 
Xenon flash lamp). A CW diode source can also serve very well for this 
purpose. Such diode laser sources may be arranged as diode arrays, diode 
bars, as well as stacks of bars to produce substantial pump power of up to 
kW of continuous power. Such source 422 output may then be temporally and 
spatially modified in an output modifying device 424 to produce a pulsed 
output characteristics in accordance with the requirement of the present 
invention. 
Modifying the Continuous Wave (CW) output beam characteristics so that they 
conform to the operating characteristics described by the present 
invention can be understood with the help of FIG. 8c and will be described 
below. The beam modifier 424 is shown in FIG. 8b: In the device 420 it is 
shown before the phase/wavelength modifier, while in 421 it is shown 
placed behind the phase/wavelength modifier. Those skilled in the art will 
recognize that the differences and advantages may be in the ease of 
delivery and manipulation of the output but may both be used equally well. 
The principles of operation of an output modifying device 424 is now 
described using FIG. 8c. 
The source Continuous Wave output 440 is directed towards a beam modifying 
device 424 containing a reflector 427 which direct the beam towards a 
series of switches 1, 2, 3 . . . N . . . The switches allow the beam to 
continue uninterrupted except for a short time duration .tau. when they 
turned on to allow reflection of the beam of light towards their 
respective fibers 429 whose output at the target may look like 432 of FIG. 
8c. Alternatively, the switching devices can also reflect the beam 440 
directly towards a specific location on the target (or through a lens 
which focus the deflected beam onto the target) for time duration .tau.. 
Following the period .tau. for which the switch is on, the switch is 
turned off again and the beam 440 continue to propagate directly thorough 
switch 1 and the rest of the switches. At some later pre-determined time 
switch 2 is turned on and it reflects a portion of the beam 440 for a 
period .tau. towards its own coupled fiber or directly to the target (or a 
lens which focus the beam onto a unique location on the target) at which 
time it is turned off. This procedure is repeated for all switches 1,2,3, 
. . . N and then the entire sequence is repeated all over again. 
Again, the energy from the continuously emitting beam 440 is directed with 
a delivery system to a selected separate spatial location on the target. 
The delivery system can consist, for example, of an optical fiber, an 
optical fiber and lenses combination, a hollow wave guide and lenses, and 
a combination of lenses and mirrors. 
The output laser beam 440, is then directed by a beam-switching device 427 
as shown in FIG. 8c. Such a beam switching device may, for example, 
comprise the well known Pockels Cell, the well-known Kerr Cell, a rapidly 
rotating mirror. It may also consist of other mechanical, optical, 
electrical, magnetic, electromagnetic or any other means of rapidly 
switching out a portion of the electromagnetic beam so that a 
pre-determined time duration can be precisely selected. 
Alternatively, the source CW beam 440 can be directed towards a slightly 
different beam modifying device 428 containing of sequence of optical 
switches 1,2,3 . . . N which sequentially redirect the CW beam towards the 
lenses 433 which then focus their respective beamlets into a pattern 
similar to 432 where each spot size is small enough to allow power 
densities (energy per unit volume) above the threshold for material 
ablation. 
The output from such a sequential switching device is shown in FIG. 8d. At 
the top of the figure, the output of a continuous wave source, 440 is 
shown as a function of time. The output 444 from one of the switches (for 
example, switch #1) is shown in the second set of axes. This short output 
444 lasts for a time duration .tau. while the corresponding switch is 
turned on. The time duration 444 can, for example, be as short as one 
nanosecond or even shorter. The remaining energy of the output is not used 
at that particular target location until an interval of time 445 has 
passed. The time interval 445 corresponds to the inverse of the desired 
output pulse repetition rate. The pulse repetition rate is selected in 
accordance with the requirement of the present invention. For example, to 
achieve a 1 KHz pulse repetition rate the fiber 429 coupled to switch #1 
(see FIG. 8c), a time interval 445 of about 1 ms must be allowed to pass 
before the next beam output is used for the specified time duration 444. 
Additionally, other portions of the output beam, for example portion 446 
and 448 in FIG. 8d, can be used in addition to the first portion 444. Many 
sequential portions 444, 446, 448 . . . can be used as long as these 
segment selection does not overlap (for example there is no time overlap 
between portion 444 and 446) and as long as the energy output from each 
beamlet and fiber-optic conduit 429 , comprises a pulse train with a 
generated pulse repetition rate and pulse duration characteristics as 
described by the present invention. 
The modified portions (444, 446, etc.) can be generated from the CW 
electromagnetic beam 440 using the modifier 424 containing a beam 
switching device 424 for selecting and redirecting portions of the 
continuous emission output beam 440. Such modified portions 444, 446, etc. 
can then be directed to desired target locations. 
Directing Such modified portions 444, 446, etc. to adjacent target 
locations to generate beamlet ablation pattern 432 shown in FIG. 8c, 
creates some additional benefits as described below. 
In a preferred embodiment, the segments 444, 446, etc. of the CW beam 440 
can be directed to the opening of an input coupler of a number of fiber 
optic cables leading these pulse trains to adjacent locations in the 
target area. 
In a second preferred embodiment, the segments 444, 446, etc. of the CW 
beam 440 can be directed to the opening of focusing devices so that these 
newly created beamlets of pulse trains conforming to the requirement of 
the present invention, can be directed to adjacent locations in the target 
area. 
In a second preferred embodiment, the segments 444, 446, etc. of the CW 
beam 440 can be directed to the opening of an input of articulated arms or 
Hollow Wave Guides so that these beams of pulse trains which conform to 
the output characteristics in accordance with the requirement of the 
present invention, can be directed to the same location or to adjacent 
locations. 
Additional preferred embodiment of the present invention utilizing an 
optical fiber bundle 429 can be understood with the help of FIG. 8c and 
FIG. 8e. 
The beam from the electromagnetic energy source 422 (see FIG. 8c) is 
redirected into the output modifier 424 through 1,2,3 . . . N couplers to 
the optical fibers 429. The switching (or redirecting) optics 327 can be 
made for example from Kerr or Pockels cell switches, non-linear crystals, 
or even mechanical mirror which deflect the light into 1,2,3, . . . N 
couplers which couple the energy from the original beam 440 into the 
couplers and the optical fibers 429. 
The source energy may be deflected for a period of from 1 ps and up to 
10,000,000 .mu.s in accordance with the requirement of the present 
invention. These (see FIG. 8d) selected time-segments 444, 446, 448, etc. 
(for example a time segment of duration .tau.), are sequentially directed 
into sequential, separate and different optical fibers. When each of the 
pre-selected 1,2,3, . . . N, fibers has received a single time-segment of 
energy, an "off time" of .DELTA.t is allowed to pass before the next cycle 
of sequential time segment is redirected into the same set of N fibers at 
exactly the same sequence. The off time interval .DELTA.t is selected so 
that (.tau.N)+.DELTA.t=(1/PRR) where PRR is the desired pulse repetition 
rate as specified by the present invention. 
The result is an output from each and every fiber in the bundle. The output 
of each fiber in the bundle is a sequence of pulses each of durations 
.tau. and of pulse repetition rate PRR, equal to the inverse of the time 
interval 445 of FIG. 8d. 
An additional preferred embodiment is shown by the Rotating Mirror 
arrangement of FIG. 8e. This exemplary depiction of the preferred 
embodiment shows the CW beam 440 from the source being directed to a 
mirror 452 which redirects the beam to a rotating mirror 454. The rotating 
mirror, in turn, redirect the light towards a series of couplers 456 
arranged around the circumference of a circle. The couplers couple the 
rotating light to either optical fibers 459 openings, to hollow 
waveguides, or to a set of articulated arms or mirrors to redirect the 
beams energy so that a sequential multiple beam pattern is formed at the 
target. The spinning mirror 454 is located at the center of the circle. 
The mirror, may, for example, be suspended from a driving high precision 
motor by a spinning rod 463. The combined array of fibers/beamlets output 
may assume the shape 432 in FIG. 8e. 
To show how the spinning mirror arrangement of FIG. 8e allows for the 
generation of pulsating beamlets sequence of figure of FIG. 8c, consider 
the a mirror spinning with a rotational velocity .omega. of 1000 cycles 
per second. With the aid of a focusing lens 458 the CW beam 440 is focused 
onto the couplers 456 so that its beam size is 100 .mu.m and is focused 
onto each fiber opening for a dwell time of 1 .mu.s. 
The linear velocity of the beam at the fiber opening (on the circumference 
of the circle) must then be 
V=(100 .mu.m/1 .mu.s)=100 m/s 
With V=.omega.R (where R is the radius of the circle of couplers, V=100 m/s 
and the rotational velocity, .omega.=1000 cycles per second). Thus, R is 
approximately 1.7 cm and the circle circumference is approximately 10 cm. 
In another preferred embodiment (FIG. 8e) the driver 467 which drive the 
spinning mirror 454 can be a high precision stepping motor electronically 
synchronized with a shutter 465. The CW beam is allowed to pass through 
the shutter 465 for a time duration .tau. (for example .tau. can be 344 in 
FIG. 8d) when the Mirror 454 is pointing to towards one of the coupler 456 
for a time duration .tau.. Following this desired exposure, the shuttered 
465 is turned off and the mirror 454 which was stationary for the time 
duration .tau. is moved by the stepping motor 463 to the next coupler 456 
and fiber 459. After a period .DELTA.T (for example 345 in FIG. 8d) the 
shutter 465 is opened again for a period .tau. and the beam is allowed to 
couple again with the next coupler 456. As will be evident to those 
skilled in the art, the shutter 465 can also be constitute a deflecting 
mirror or any other optical switch. 
A 10 cm circle has room for approximately 1000 fibers each 100 .mu.m in 
diameter. 1000 fibers each 100 .mu.m in diameter cover an area of 
approximately 0.075 cm.sup.2. This cumulative fibers and beamlets area is 
large enough to cover a rectangle whose side is 2.7 mm long--a practical 
spot size for many applications in material processing and tissue 
ablation. 
In all preferred embodiments the fiber assembly, hollow waveguides, or 
focus free beams may then be directed into the target so that an ablation 
spot pattern like the exemplary assembly of holes 432 in FIG. 8c is 
formed. 
The time-space tailoring of the CW source beam into an array of adjacent 
pulsing beams (each necessarily time-delayed with respect to the other) as 
described above carries some additional advantages regarding the 
minimization of thermal and mechanical collateral damage. The advantages 
are due to the arrangement of the fiber and focused free-beams in a 
configuration of adjacent shapes that looks like 432 in FIG. 8c and are 
fired in a sequential manner as illustrated in FIG. 8e. 
Advantages of a Fiber Bundle and Focused Free-beams in Configuration of 
Adjacent Beams 
Using a Continuously Emitting CW source and dividing the CW energy 440 (see 
FIG. 8d) into several beamlets of duration t characterized by a certain 
pulse repetition rate (for example 444 and 445 respectively, in FIG. 8d) 
which are then either directly or through fiber/hollow waveguide delivered 
to the target, carries some additional advantages. It should be noted, 
however, the benefit of these advantages can also be realized through the 
use of an inherently pulsed-source (i.e., a source that emits pulse train 
rather than CW emission) as long as the source pulse repletion rate is 
larger than the requirement of the present invention and some of the 
pulses in the source's pulse train can be deflected out of the pulse train 
and manipulated to be brought to adjacent locations on the target in a 
manner described bellow. 
By arranging the fibers output (for example the fibers 459 of FIG. 8e), or 
the focused beamlets (for example, the beamlets 435 in FIG. 8c) in a 
spiraling manner 470 of FIG. 8f the deposition of thermal energy in the 
tissue can thereby be minimized. Starting to couple the continuously 
emitting CW source beam 340 to the fibers/beamlets which deliver energy to 
the center and then proceeding to the fibers/beamlets that deliver energy 
to the outward locations, subsequent fibers/beamlets ablation actually 
REMOVE heat generated by earlier shots in the central, already fired 
fibers/beamlets. In addition, the laterally diffused energy can be used to 
enhance material ablation and minimize energy and power requirement for 
the interaction of these subsequent, laterally displaced pulses. 
Such spiraling fibers/beamlets arrangement can be enhanced by varying the 
time separation 449 between sequential pulses (for example between pulse 
444 and 446 in FIG. 8d) so that 449 become shorter for pulses directed 
towards fibers/beamlets at external perimeter of the spiral 481, and 449 
is longer for the internal region of the spiral 482. This, in effect, will 
translate to an increased firing rate from fibers/beamlets on the outsider 
of the spiral where there is larger linear circumference to be covered 
and, therefore, the diffusing heat is more effectively encircled, encased, 
and ablated away. 
Similarly, the same sequential distribution of source energy described 
herein, can be used for non-ablatively modifying a tissue in accordance 
with the principles of operation of the present invention (that is 
modifying the target material irreversibly but not ejecting or removing 
material from the target). Here, the adjacent fibers/beamlets can make use 
of thermal energy diffusing from earlier, adjacent pulse interactions to 
enhance to material modification and minimize energy and power requirement 
for the interaction. 
Another preferred embodiment utilizes an alternating rows arrangement shown 
in FIG. 8f. Alternative fibers in subsequent adjacent rows (for example, 
472, 473, 474, and 475 in FIG. 8f) firing in alternating order with 
respect to each other. Such sequential ablation will also help eliminate 
at least some of the residual left-over thermal energy generated in the 
target through the interaction of earlier pulses. 
Note that a 10 ms delay between adjacent fibers outputs translates to a 
thermal diffusion length of about 100 .mu.m. Thus, a single 100 .mu.m 
fibers positioned adjacent to one that was fired 10 ms earlier, would be 
perfectly positioned to capture the entire heat which has diffused 
laterally form the first fiber. 
In another preferred embodiment the beam from a very high pulse repetition 
rate source 314 in FIG. 8c, is focused down to 100 a spot size on the 
target sufficient to allow the generation of power densities in accordance 
with the requirement of the present invention, and this focused beam is 
then scanned across the target. The scanning is done in such a way as to 
allow lateral heat removal in accordance with the principles described 
above for multiple beamlets. The scan timing is then synchronized to 
ablate heat as it diffuse within the targeted area as was described in the 
previous paragraphs. 
As pointed out above, the effective pulse repetition rate (PRR) in each 
fiber/beamlet is the inverse of the time separation 445 before the beam 
modifier 424 of FIG. 8c switch another segment of the CW beam 440 into 
that same fiber/beamlet. Such PRR can reach up to a few hundreds KHz in 
accordance with the requirement of the present invention. The power 
requirement for such PRR can be satisfied with CW source of as little as 
about 1 W average power. Such small (and even smaller) power requirement 
can be used because utilizing a small spot size fibers/beamlets of 100 
.mu.m or less, achieve peaks power in excess of 10.sup.+4 W/cm.sup.2 which 
are sufficient to initiate ablative interactions. Significantly, many 
practical commercially available continuously emitting sources can achieve 
average power level in access of hundreds of kilowatts and even megawatts. 
For many practical situations, the spot size of each fiber/beamlet should 
be on the order on the order of about 100 .mu.m (or less) so that the peak 
power per unit area is on the order of about 10.sup.7 W/cm.sup.2. Such 
power densities have been shown by the inventor to easily result in 
effective and efficient ablation material removal. 
An area of 10.times.10 fibers (i.e., 100 fibers) will create an Effective 
Spot Size of about 1 mm.sup.2 less fiber or more fibers can of course 
change the size of the Effective Spot Size. 
An additional advantage of this "time sharing" high average beam source is 
that the many spots cool faster. This is because at the smaller sizer of 
the many spots size, corresponding to the many fibers/beamlets, three 
dimensional heat transport dominates. Such three dimensional heat 
transport and cooling is much more effective at cooling the many targeted 
spots than a single large spot size whose area is equivalent to the sum of 
the many spots of the fibers/beamlets. 
An additional advantage of this preferred embodiment is that utilizing a 
continuously emitting CW source (for example, diode laser, diode arrays, 
COWP2 or high power solid state laser) can be considerably less expensive 
and much easy to handle in a wide range of environments. 
Finally, the output of many of the systems described above can be further 
modified to shift their output wavelength. Such shifting can be towards 
the shorter wavelength through the us of non-linear crystals. Such 
crystals are made of, for example, a thin potassium di-deuterium-phosphate 
(KD*P) crystal or other non-linear crystals such as KTP. They allow 
frequency doubling, tripling, quadrupling etc. and allow generation of 
much shorter wavelength. To achieve longer output wavelength, optical 
parametric oscillators and optical parametric amplifiers can also be used 
to tune the output beam wavelength to a longer wavelength of up to about 
several micrometer. Shifting of the output to the wavelength range of 0.8 
.mu.m to 11 .mu.m may be particularly beneficial. 
Such wavelength tunability achieved through the action of output beam 
modifiers 326 of FIG. 8b, allow selection of more highly absorbed 
wavelengths which, in turn, increase the power density deposited within 
the targeted material according to the principle of operation of the 
present invention. The pulse output characteristics of such output 
wavelength tuning device will (except for shifting the wavelength) 
frequently be similar to those of the original input devices and can, 
therefore be selected to completely conform to the requirement of the 
present invention. 
The described preferred embodiments can also apply to Longer wavelength 
such as those from about one to eleven micrometer. This wavelength range 
possess several high absorption peaks (for example at 2.1 and 2.7 .mu.m, 
at 2.94 .mu.m for Er:YAG and at 9.6 .mu.m and 10.6 .mu.m for CO.sub.2). 
These wavelengths can be delivered through Hollow waveguides, through 
silver halides and through Zichronium or Sapphire fiberletes much like the 
embodiments that was described above. Lasing in the infrared where the 
absorption is very high and penetration very shallow shall help to 
increase power density per unit volume in accordance with the requirements 
of the present invention. 
One such embodiment may involve delivering the infrared beams for most of 
the way through articulated arm and then at the end have a series of 
fiberletes in a fiber bundle configuration in accordance with principles 
of the invention as described above. These small fiberletes can be 
disposable and because they are used for only a short distance--made of 
relatively higher loss material such as glass or fused silica. As long as 
the small focusing for overall high power density per unit volume is 
achieved at the target, favorable results according with the practice of 
the invention can be obtained. 
Turning now to FIG. 8g, there is depicted a simplified block level 
schematic diagram of a material removal apparatus (for example, a dental 
drilling system or a ceramic cutting instrument) incorporating a variable 
repetition rate laser system 1460 in accordance with the present 
invention. The material removal apparatus further includes an OPO, KDP, 
KTP, etc., an optical delivery system, for directing the laser beam to a 
specific area of a material target. The optical delivery system depends on 
the design parameters of the material removal system and may alternatively 
comprise a fiber optic cable 1470, an articulated arm 1466, or an open 
beam delivery system 1467, including reflectors 1462 and lenses 1464 to 
focus the beam. A handpiece 1468 is indicated as attached to the distal 
end of the articulated arm 1466, to allow a dentist, a clinician, or a 
machinist to maneuver the beam into close proximity with a material target 
1474. The handpiece 1468 may also be fitted onto the distal end of the 
optical cable 1470, to allow the cable to be more easily manipulated. 
A laser controller 1478 is connected to the laser system 1460, and controls 
the activation of the laser, as well as the pulse repetition rate, in 
response to control signals provided by the operator. An on-off switch 
1480 (a foot pedal or alternatively, a hand switch) is-connected to the 
laser controller and provides laser activation signals in response to the 
dentist or clinician's depressing the switch. Likewise, a pulse repetition 
rate controller 1482 is also connected to the laser controller and may be 
provided as a rheostat control which increases or decreases the pulse 
repetition rate of the laser system in response to the clinicians turning 
the knob. 
A feedback analyzer 1476 and a feedback transducer 1472 operate in 
conjunction with the laser to allow precise control of ablation end 
points. Because many embodiment of the variable repetition rate laser 
system of the present invention involve plasma generation during the 
material removal process, material-type-differentiation diagnostics and/or 
tissue-type differentiation diagnostics can be performed on the material 
target region based on the material own spectroscopic luminescence 
emission signatures. 
In this case, feedback transducer 1472 is provided in the form of a 
spectroscope which further includes a collection fiber 1473 for collecting 
emitted light from the plasma generated by the removed tissue. The light 
is dispersed and analyzed by the feedback analyzer 1476, preferably an 
intensified, gated, optical multichannel analyzer/spectrograph. Emission 
peaks characteristic of different tissue types, e.g., dentin, enamel, and 
pulp, and different tissue states, e.g., diseased versus normal, are 
compared to reference data contained within the analyzer 1476. When tissue 
characteristics change, a feedback signal is provided by the feedback 
analyzer 1476 to the laser controller which then either reduces laser 
pulse repetition rates or ceases laser delivery in response. 
Alternatively, the feedback transducer 1472 may be provided in the form of 
an optical coherence tomography head, suitable for performing crater depth 
diagnostics on the material target. As the laser system is ablating 
material, the depth of the ablation crater is monitored continuously by 
the optical coherence tomography head. Crater depth data is provided to 
the feedback analyzer 1476 which, in turn, may be programmed to issue a 
feedback signal to the laser controller 1478 and, thus, stops laser 
delivery when a predetermined crater depth is reached. 
The feedback transducer 1472 may also be provided in the form of an 
infrared detector (for example, an InSb detector, or a HgCd infrared 
photodiode), or an infrared detector array or an infrared camera head, 
suitable for performing evaluation of spatial and temporal temperature 
distribution diagnostics on the material target. As the laser system is 
ablating material, the temperatures at the vicinity of a predetermined 
boundary is monitored continuously by the optical infrared thermograph 
head. Temperature data is provided to the feedback analyzer 1476 which, in 
turn, may be programmed to issue a feedback signal to the laser controller 
1478 and, thus, stops laser delivery when a predetermined temperature is 
exceeded at a pre-assigned location. 
The most common application of the apparatus will involve foot-pedal 
operation by a dentist, a clinician, or a machinist, who first determines 
and sets the pulse repetition rate and who then starts and stops laser 
operation on the basis of a visual examination of the target tissue and 
evaluation of the progress of the procedure. Thus, it can be seen that the 
apparatus is suitable for performing many different dental procedures 
including the elimination of carious lesions, removal of stains on the 
outer tooth surface as well as stained embedded within the inner regions 
of a tooth, and tooth desensitization. Using the apparatus in combination 
with various feedback devices allows the dentist or clinician to perform 
various delicate and difficult procedures including the ablation of 
enamel, dentin, diseased soft gum tissue as well as diseased nerve tissue 
in endodontics procedures without fear of damaging healthy pulp or nerve 
tissue. 
Although the high repetition rate systems of the present invention has been 
described in connection with an exemplary material processing and dental 
drilling application, it will be clear to those having skill in the art 
that the laser system has operational characteristics that are suitable 
for a very wide range of material removal applications. For example, in 
the treatment of ear, nose and throat disorders, volumetric material 
removal is required in various surgical procedures, such as middle ear 
bone surgery, cholesteatoma, skull and jaw bone surgery, selective removal 
of malignant tissue, and tympanic membrane surgery. Many of these 
procedures require the operating physician to have a very deft touch 
because the structural features of interest are in very close proximity 
with one another. In addition, because of the proximity and delicacy of 
the structure associated with such procedures, great care must be taken to 
process only the target tissue and avoid damaging anything else. 
Thus, it can be seen that the characteristics of the laser system of the 
present invention would be eminently suitable for application in such 
surgical procedures. In addition, the laser system of the present 
invention is suitable for use in the field of burn debridement. Skin 
resurfacing and burn tissue removal are particular applications to which 
the plasma-mediated pulse high repetition rate laser may be applied. The 
precision of material removal of the present invention is derived from the 
fact that only a thin layer of material is removed per laser pulse. By 
controlling the number of pulses, a surgeon controls the amount of 
material that is removed. The application of this removal method to burn 
debridement, in combination with a tissue-differentiation diagnostic 
feedback apparatus would allow very precise texturizing of the skin 
surface. By either dithering where the laser beam is directed, by 
rasterizing, or by controlling the laser beam profile, a clinician is able 
to sculpt into a pre-defined texture. 
Additional procedures in which the laser system of the present invention is 
suitable include arthroscopic surgery, including partial neniscectomy, 
synovectomy, chondroplasty, cartilage and tendon removal, and micro 
perforation, resurfacing, and texturing of cartilage, tendon and bone 
material. 
From the foregoing, it can be seen that the present invention provides an 
apparatus and method for fast, efficient, precise and damage-free 
biological tissue removal, including a pulsed laser system having pulse 
durations on the order of from about 3 fs to about 10 ms. The invention 
requirement on the ratio of per-pulse material removal depth, duration of 
the laser pulse, and pulse repetition rates in cases where larger volume 
removal is required, is such that there is minimal transfer of energy from 
the beam to the target material lattice in the form of thermal energy. As 
pulse duration becomes shorter, and/or if absorption and power densities 
become sufficiently large, multiphoton and/or collisional ionization 
produces a plasma which ablates from the target surface in the time period 
between pulses. When operating with short pulses, high absorption, and 
high power densities, energy deposition is localized in a small depth and 
ablation occurs before significant thermal conduction can take place in 
the material. While the depth of material removed per pulse is generally 
small in the practice of the invention, the minimal thermal and mechanical 
effects associated with plasma mediated ablation allow operation of the 
laser system at a high pulse repetition rate which, in turn, achieves high 
material removal rates. 
Summary of Principles of operation: High Ratio of Ablation Volume to 
Permanently Modified Volume 
To further clarify the issues involved in minimization of the zone of 
thermal damage generated by each pulse, let us consider the following 
regions as depicted in FIG. 9. 
The energy of a beam of light coming form above will crate three principle 
regions: 
1. The outer layer of X.sub.ab is ablated which is ejected away; 
2. The middle layer of X.sub.ir is the zone of irreversible damage--usually 
thermal (i.e., zone of Coagulation, charring and/or Melting; and 
3. The lower region X.sub.rev is the zone where light and energy has 
penetrated and been felt but only in a reversible way. 
The combined depth of region Xab+Xir is termed X.sub.observ which is the 
only volume with observed effect. 
FIG. 10a defines the energy components involved in the interaction. The 
energy components are the incident electromagnetic energy (E.sub.inc), the 
transmitted electromagnetic energy (E.sub.trans), the reflected 
electromagnetic energy (E.sub.ref), as well as Ec, the converted 
electromagnetic energy now appearing as chemical, acoustical, and thermal 
energy components generated by the interaction and used for altering the 
material properties, removing and ablating a portion of the material and 
energizing the ablated products. 
We designate the energy components used for removal of material is shown in 
FIG. 10a as E.sub.abl, while the energy left in the unablated tissue and 
used to irreversibly alter the material is shown in FIG. 10a as E.sub.ir. 
It is also possible to define what may be called "the observed energy" 
Eobs, i.e, the energy whose effect can be detected by observing the 
ablated material after the interaction energy is E.sub.abs and is equal to 
the sum of the energies used for ablation and to irreversibly altering the 
tissue. Thus E.sub.obs =E.sub.abl +E.sub.ir. The sum of all the energy 
components forms the energy balance for the interaction: E.sub.inc 
=E.sub.ref +E.sub.trans +E.sub.abl +E.sub.ir +E.sub.c. 
When the energy E.sub.inc from a single pulse impinges on the material, 
much of the material may experience transient effects of the incoming 
energy. Unfortunately, the entire depth of energy deposition can not 
always be measured. While it is possible to place a thermal, optical or 
mechanical detectors within the affected portion of the target to observe 
the transient energy effect, by our definition of Xrev--the zone of 
reversible energy effects, no permanent alterations remain. 
The portion of the energy traversing the material without leaving 
irreversible damage (for example light energy propagating through the 
material and/or thermal energy diffusing down the material but which does 
not raise the material temperature above, for example, 50.degree. C., 
cannot easily be detected (certainly not after the interaction has been 
completed). 
Consequently, it is convenient to quantify the above requirement by 
considering only the readily observable, measurable quantities: 
EQU X.sub.obs,=X.sub.abl +X.sub.ir (3) 
Here, X.sub.abl =the ablated material depth and, X.sub.ir is the zone of 
permanent, irreversible damage of material which has not been ejected from 
the bulk. 
X.sub.obs is, thus, the depth of material in the tissue to which, as a 
result of a single pulse action, observable, irreversible changes have 
occurred. Thus, characterization of the interaction in terms of 
observable, measurable quantities (X.sub.abl and X.sub.ir) is achieved. 
According to the practice of the invention, the objective is to maximize 
X.sub.abl and minimize X.sub.ir. 
The depth of the two zones and the ultimate size of X.sub.obs are a 
consequence of two factors: the energy deposition depth, and the energy 
distribution profile of the incoming energy. 
The energy can arrive at the effected volume of depth X.sub.obs, either 
through direct optical deposition, or through subsequent thermal diffusion 
of energy. 
Unless heat deposition or coagulation are actually desired, the ideal 
surgical result is, a situation where X.sub.ir approach zero 
(Xir.fwdarw.0) and X.sub.abl approaches X.sub.obs. 
In reality, this is impossible as some (even if very small) narrow layer of 
modified material will always be left behind. It is virtually impossible 
to design an interaction where the energy deposition is so finely 
distributed that the deposited energy density .epsilon. (x) is sharply cut 
off as in a step-function. 
Thus, it is useful to quantitatively define the requirement in terms of the 
invention's practical needs: For most biomedical and some 
industrial/micro-processing tasks a zone of X.sub.ir on the order of 1 
.mu.m is acceptable. 
The term "on the order" is generally meant to imply from a single to a few 
micrometers, i.e., 1 to 9 .mu.m). 
The zone X.sub.ir is most often modified through thermal effects (although 
mechanical and chemical alterations must also sometimes be considered). 
For simplicity let us concentrate on this thermal energy form of 
material-modification where the zone of thermal modification is on the 
order of 1 micrometer. 
Permanent thermal modification (but not ablation) in soft tissue will occur 
if temperature rises are less than 100.degree. C. Temperature rise above 
this level will result in vaporization, explosive vaporization, and 
ablation. 
In hard tissue (e.g., enamel, bone and dentin) melting of hydroxyapatite 
occurs at temperatures greater than 900.degree. C. 
To calculate the energy requirement for material modification consider the 
following: 
In Soft Tissue: 
(Consider a exemplary skin tissue with a permanent thermal modification of 
.mu.m. 
In this case the increase from body temperature, .DELTA.T, is: 
.DELTA.T=.DELTA.T=100-37=63.degree. C. 
and the temperature rise, .DELTA.T, must be smaller than 63.degree. C. to 
avoid irreversible material modification. 
Thus, .DELTA.T&lt;63.degree. C. 
Now, from Thermodynamics: 
EQU .DELTA.E=m C DT 
Where m is the effected mass C is the specific heat capacity and .DELTA.T 
is the temperature increase, 
or, units m=.rho..DELTA..nu.=.rho.A.sub.beam dz 
EQU .DELTA.E=.rho.A.sub.beam C dZ DT (4) 
Where .rho. is the material mass density, .DELTA..nu. is the modified 
volume, dz is the depth of the modified volume, X.sub.ir, and A.sub.beam 
is the area of the beam Dividing equation 4a by the area we get on the 
left hand side the increase in Fluence (fluence is the energy per unit 
area) .DELTA.F=.DELTA.E/Area. 
And with the depth of the considered altered zone--.DELTA.Z=X.sub.ir, and C 
of water=4.35 KJ/(Kg K.sup.0) 
then equation 4 becomes, 
EQU .DELTA.F=.rho.Xir C DT (5) 
With X.sub.ir assumed on the order of 1 .mu.m and .DELTA.T&lt;63.degree. C. 
required to achieve coagulative damage to the tissue, fluence needed is 
less than, 
.DELTA.F&lt;(1 g/cm.sup.3) (0.001 cm) (4.35 kj/kg K.sup.0) 
or 
.DELTA.F&lt;277.2 E.sup.-4 J/cm.sup.2 =0.027 J/cm.sup.2 
i.e., 
.DELTA.F&lt;0.027 J/cm.sup.2 
Or, for an exemplary 0.5 mm Diameter beam, the energy required to modify a 
1 .mu.m thick soft tissue is, 
.DELTA.E&lt;0.05 mJ. 
With typical incident Energy E.sub.incidence, ranging from 0.3.sub.mJ (at 
threshold for hard tissue ablation) to energy on the order of 15 mJ, the 
ratio of the required-energy for 1 .mu.m zone of modification to incident 
pulse energy. 
______________________________________ 
DE/DE.sub.incidence = 
17% @ Threshold Energy 0.3 mJ 
1.7% @ typical ablation Energy of 3 mJ, and, 
0.17% @ higher fluence of 15 mJ 
______________________________________ 
Again, note that the percentage mentioned, are the percentage of the 
incident Energy. 
Experimentally, (for hard tissue, see FIG. 10b) it is observed that for 350 
fs (1.06 .mu.m) pulses at 1 J/cm2 (i.e., 1 mJ pulses with a spot size of 
0.5 mm), it takes 1 mJ to ablate 1 .mu.m which leaves a region of about 1 
.mu.m irreversibly modified (X.sub.ir .about.1 .mu.m). 
Thus, in a 1 mJ short pulse interaction about 7% of the energy is used for 
permanent tissue modification and the rest is used for ablation, ejection 
and other energy-consuming components of the interaction. 
If a more typical pulse of about 3 mJ is used on a 1 mm dentin slice, 
experimental data show that about 20-30% of the energy is transmitted, 
less than 2% irreversibly damage a region of about 1 .mu.m of tissue, and 
the balance (about 70%) of the incident energy is responsible for 
ablation, energizing the ablation products, plasma formation, or released 
as acoustical and mechanical and other forms of energy. 
Er:YAG (2.94 um) interaction yield a smaller percentage since it takes a 10 
to 20 mJ per micropulse to ablate 1 to 2 .mu.m leaving a zone of thermally 
damaged material of about 1 .mu.m. Thus, in a 10 mJ micropulse about 0.7% 
of the energy is used for permanent tissue modification. Also in this 
case, virtually no energy is transmitted through a 1 mm thick slice, and 
the vast majority of the incident energy goes into ablation, energizing 
the ablation products, plasma formation and acoustical and mechanical 
energy. Since in the Er:YAG interaction 10 to 30 mJ are used to ablate 
about a 1 to 3 .mu.m while the interaction of ultrashort pulse require 1-2 
mJ to ablate the same amount of tissue, the interaction of ultrashort 
pulse is more efficient (see FIG. 10b). While Er:YAG interaction devote 
smaller fraction to material modification and negligible amount is 
transmitted, a much larger fraction is used to energizing the ablation 
components, or is released as mechanical and acoustical energy. 
With Ho:YAG (2.1 .mu.m) about 4 mJ per micropulse are required to ablate 1 
.mu.m, (FIG. 10b) leaving Xir of tens of microns of thermal damage. The 
micropulse energy is 4 mJ and thus about 1.75% of the energy is used for 
material removal and most of the incoming pulse energy is spread over tens 
of microns resulting in such deep irreversible tissue modification. In 
this case a few percent of the pulse energy is transmitted through a 1mm 
thick slice and most (.about.80%) of the energy is spread through tens of 
microns of thermally damaged tissue. 
For the XeCl (0.308 .mu.m) about 10 mJ is required to ablate 1 .mu.m 
leaving (FIG. 10b) X.sub.ir of tens of microns of thermal damage. The 
entire 15 ns pulse energy is 80 mJ and in this case perhaps 20-30% of the 
pulse energy is transmitted through a 1 mm thick slice and 10-30% results 
in tissue heating. The rest of the energy (40% to 70%) is used for 
ablation, energizing the ablation products, generating and heating plasma, 
or used in acoustical and mechanical energy. 
Thus, an estimate of about 10% of the energy is used for permanent tissue 
modification of several tens of microns. This large amount of energy, 
however, is distributed over a much larger damaged tissue volume. 
The above first two examples correspond to small thermal damage X.sub.ir 
zones and high X.sub.ab /X.sub.obs ratio (from about 0.2 to about 0.5). 
The last two examples (Ho:YAG and XeCl) correspond to deeper thermal damage 
X.sub.ir and small X.sub.ab /X.sub.obs ratio (from about 0.01 to about 
0.1). 
Further Comments Regarding Principles of Operation: High Repetition Rate 
An additional insight of the role, according to the present invention, of 
high pulse repetition rate operation can be obtained by considering FIG. 
11. 210 in FIG. 11 shows a sequence of pulses 1,2,3, . . . N-1, N, N+1 . . 
. M. This train of pulses is incident on the targeted material (where 
pulse number 1 is the first pulse to reach the material and the pulse M is 
the last pulse in the train). 
212 shows three exemplary curves illustrating a one-dimensional thermal 
energy distribution as a function of distance from the target material 
surface. The curves 214, 215, 216, show that with time, the deposited 
thermal energy associated with first pulse diffuses into deeper regions 
(larger X values) of the targeted material. Here 214 represents an 
exemplary thermal energy distribution following the first pulse energy 
deposition at t=0+.tau. (where .tau. is the pulse duration). If .tau. is 
short enough (for example, less than 1 .mu.s in an exemplary water-like 
material) so that thermal diffusion is negligible (e.g., less than 1 
.mu.m) 214 will essentially correspond to the optical energy distribution 
where optical energy has been converted to thermal energy. The curve 215 
is the thermal energy distribution at some later time, and 216 is the 
thermal energy distribution at a later time yet. The sequence of the three 
distributions at three subsequent times (for example--100 .mu.s, 1 ms and 
100 ms) show the general characteristics of thermal energy diffusion. They 
show that as the thermal energy penetrates (diffuses) deeper into the 
material its amplitude is lowered at the surface is reduced (the surface 
is being cooled) while its amplitude at deeper regions is increased 
(deeper regions are being heated up). 
213 shows the ablative effect of subsequent pulses on the thermal energy 
diffusion due to the first pulse (N-1). For example, if we consider the 
last thermal energy distribution 216, the ablative effect of the first 
pulse N=1 is to remove part of the deposited thermal energy by 
self-ablating a slab of material 217 of thickness a.sub.r. As the energy 
of the first pulse diffuses further inward, the effect of the following 
pulse (N=2) is to ablate an additional slab of material 218 also of 
approximately the same thickness a.sub.r (it is assumed that the ablation 
rate remain relatively unchanged from pulse to pulse). The third pulse 
will again remove about a.sub.r of material in 219 while the remaining 
heat generated by the first pulse N=1 continues to diffuse towards deeper 
material regions. Clearly, the portion of the thermal energy distribution 
represented by the curve 216 that is included within the boundaries of 
217, 218, and 219, is physically removed with the ejected material and is 
no longer available for further diffusion and heating of the material. 
The penetration depth--as a function of time--of the diffusing thermal 
energy, after it has been optically deposited near the surface is given by 
equation 1 above. 
We shall also refer to X.sub.diff as the location of the thermal diffusion 
front. The location of the thermal diffusion front as a function of time 
was illustrated by the curve 220 of FIG. 5a. In FIG. 5a, Equation 1 
corresponds to the diffusion front as a function of time 220, which is a 
curve about the time axis. It demonstrates a very rapid initial heat 
diffusion which slows down very significantly as time progress. 
The linear curves 222, 224, 226, and 228, in FIG. 5a, represent the 
time-dependent position (or depths) of the ablation front below the 
initial surface. As can be seen from FIG. 5a, the ablation depths are 
directly proportional to time and can be described by the linear equation 
2 above. 
Where the slope of the lines 222, 224, 226, and 228 is equal to (a.sub.r 
.nu.), the product of a.sub.r, the ablation rate per pulse and the pulse 
repetition rate .nu. (nu), the pulse repetition rate. If, for example, for 
a given laser system a substantially constant ablation rate per pulse (for 
example 1 .mu.m/pulse) is assumed, then the slope of the curves 
representing the ablation front of various pulse repetition rates are 
proportional to the pulse repetition rate, .nu.. Thus, as can be seen from 
FIG. 5a, high pulse repetition rate will or a high ablation rate per pulse 
a.sub.r will yield a steep slope as in 222. On the other hand, a low pulse 
repetition rate or a low ablation rate per pulse a.sub.r will yield a 
shallow slope as in 228. 
Significantly, FIG. 5a reveals a very important feature of the present 
invention. If the material processing system is allowed to operate long 
enough, the depth of the ablation front (or material removal) will 
ultimately surpass the depth to which heat from the original pulses has 
reached, and the ablative interaction itself will completely remove any 
residual heat that was deposited in the material by earlier pulse. 
This effect also can be seen in FIG. 11. If pulses N=1, 2, 3, . . . N 
remove slabs of a relatively constant thickness a.sub.r, and do so at a 
faster rate than the rate of heat diffusion, the sequence of ablation 
slabs will eventually catch up with and completely eliminate all thermal 
energy due to pulse 1. If we use 212 in FIG. 11 as an example, the spatial 
position of the thermal diffusion front increases from 214 to 215 to 216 
but the increase in position is slower at later times. Thus, the constant 
rate of ablation will eventually remove the entire heat deposited by the 
first pulse (pulse 1). 
If we differentiate equation (1) with respect to time, we obtain an 
expression for the TIME RATE OF CHANGE of thermal penetration depth (i.e., 
the time rate of change of the position of the heat diffusion front). This 
expression is given by, dX/dt=0.5 (K/t).sup.1/2. 
As can be seen from this expression and also from the curve 220 in FIG. 5a, 
for small values of time t (i.e., earlier times after the electromagnetic 
pulse energy deposition) the heat diffuses very fast (indeed this rate 
approaches very large values for very small values of time). 
As a consequence, if a sequence of pulses 210 of FIG. 11 is incident upon a 
material surface, the heat from the most recent pulses will move faster 
than the ablation front and part of the heat of the most recent pulses 
will not be removed by later pulses as the system is stopped at some 
finite time. However, heat from earlier pulses will not diffuse as fast 
and will eventually be contained within a volume that will ultimately be 
completely removed by the interaction. 
The point can be made clearer by considering an exemplary system operating 
at 1000 pulses per second for 3 seconds and represented by curve 224 in 
FIG. 5a. In a water-like material, energy from the first pulse to interact 
with the sample will diffuse a distance of 1 mm into the material at about 
1 second. The ablation front, assuming ablation rates of 1 .mu.m per pulse 
and 1000 pulses per second, will cut 1 mm of material in 1 second as well. 
Thus, the point at which the ablation front overtakes the first-pulse heat 
diffusion front, designated in FIG. 5a as X.sub.xo, and named by the 
inventor the "cross-over depth", is approximately at 1 mm depth. The 
cross-over occurs approximately 1 second after the start of the 
interaction for an exemplary high water content tissue or material. This 
point in time is, consequently, maned the "cross-over time" and is labeled 
t.sub.xo and corresponds to the vertical line 230 of FIG. 5a. 
Each system, characterized by its pulse repetition rate, by the material 
heat diffusion rate, and by the specifics of the interactions between the 
pulse and material (which, in turn, define the ablation rate per pulse), 
will have its own unique cross-over time t.sub.xo. An exemplary system 
with a low pulse repetition rate or low ablation rate per pulse may 
operate for a long time the ablation front reaches the cross over distance 
X.sub.xo. If such a cross over time is very long the ablation front may 
never reach X.sub.xo before the end of the procedure. 
This is shown in FIG. 5a by comparing the distance X.sub.diff of curve 220 
to that of X.sub.abl of curve 228 for some exemplary time t. As can be 
seen in FIG. 5a, the positions given by curve 220 are always of higher 
value than those given of curve 228 and the system defined by the curves 
220 and 229 never reaches a cross-over time. 
Since for the line 228 the diffusion front is (for all times shown in FIG. 
5a) ahead of the ablation front, not all the heat deposited by the first 
pulse is removed by the ablation of subsequent pulses during the procedure 
and some of the heat of even the very first pulse remain in the target 
material. 
The situation is different for the ablation front described by 224. Here, 
pulses launched after t will ablate material that has not been exposed to 
the first pulse energy at all, since all the heat of the first pulse has 
been removed by pulses launched from t=0 to t=t.sub.xo. 
For an exemplary heat diffusion curve 220 and ablation front curve 224, 
corresponding to an exemplary ablation rate of 1 .mu.m per pulse and pulse 
repetition rate of 1000 Hz in an exemplary water-like dielectric (e.g., 
material with water-like characteristics), subsequent pulses (to pulse 
N=1000) will ablate the entire heat generated by second pulse (N=2), and 
then additional pulses will remove all of the thermal energy deposited by 
pulse 3 (N=3), then N=4, etc. 
On the other hand, it is equally clear that the heat generated by the very 
last pulse (N=M) will not be ablatively removed at all since no subsequent 
pulses follow that pulse. 
In the above numerical example (curve 224) of ablation of water-like 
material (i.e., 1 KHz, and 1 .mu.m/pulse), the situation for the last 1000 
pulses is unique. These pulses are characterized by the fact that the time 
remaining in the irradiation procedure is shorter than the time necessary 
for the ablation front to overtake their thermal diffusion front position 
by the time the end of the procedure is reached. An exemplary pulse L 
(within the last 1000 pulses) interacting with the material a time 
t.sub.lp before the source ceases operation, will have its heat diffused 
to a position X.sub.lp, which is deeper than the depth of material removed 
by the (.nu.t.sub.lp) pulses left within the time interval t.sub.lp before 
the source ceases operation. 
As FIG. 5a shows, however, even these last few pulses have some of their 
residual heat removed by the subsequent pulses. For instance, in the 
exemplary 1000 Hz system, if a total of 3000 pulses is applied, pulses 
just after pulse 2000 will have most of their heat removed by the 
subsequent, nearly 1000 pulses. On the other hand, pulse number 3000 and 
the last few pulses in the sequence--will have none or very little of 
their residual heat removed by subsequent pulses. 
Interestingly, the inventor also recognized that the fraction of the 
deposited heat left by each one of the last 1000 pulses in the exemplary 
1000 Hz system, is proportional to the ratio of the distance between the 
depth of thermal diffusion and the position of the ablation front (i.e., 
the distance between position x.sub.diff -Xab), and the total diffusion 
depth, X.sub.diff. A more precise analysis of this is provided below. 
Furthermore, the total amount of cumulative heat not ablated by the 
exemplary laser system is proportional to the area bounded between curve 
220 and the curve 224 to the left of t.sub.xo. This observation is true 
because each of the last 1000 pulses send a thermal diffusion front into 
the material which has the same characteristic diffusion curve 220 of FIG. 
5a. As time progresses subsequent pulses will allow the ablation front to 
reach their respective depth as shown by the linear curves 222 to 228. 
By contrast, as we have seen from the discussion above (with M being the 
last pulse in the pulse train) all the heat from pulses M-1001, M-1002, 
M-1003, etc., is completely removed by the subsequent 1000 pulses. 
As a consequence, in considering the problem of residual heat left in the 
target material by a train of pulses of sufficiently high repetition rate, 
only the last pulses--those whose heat is not completely removed by the 
subsequent incoming pulses--need be considered. For simplicity we shall 
refer to these last pulses as the "residual-heat pulses". 
To generalize the problem it is useful to consider FIG. 12. 
While FIG. 12 is visually similar to FIG. 5a it actually differ 
substantially. In FIG. 12 the horizontal time-axis is replaced by an axis 
describing the pulse number starting from the last pulse in the 
pulse-train under consideration, M, and ending in the last pulse whose 
heat is completely removed (in our exemplary 1000 Hz system it is Pulse 
M-1000). Thus, in FIG. 12, the curve 250 represents the locations of the 
heat diffusion fronts of the diffusing thermal energy deposited by pulse 
M, M-1, M-2, M-3, . . . N, . . . to M-1000, at the time that the source is 
turned off and the pulse-train is terminated. 
The exemplary curve 254 of FIG. 12, on the other hand, represents, for each 
pulse, N, the depth of material ablated by the subsequent pulses M-N which 
follow the pulse N (and thus, the depth of material removed by the number 
of pulses remaining in the train and following each pulse N, (where 
M&gt;N&gt;M-1000). 
The curves 252 and 258, correspond to pulse trains with, respectively, 
higher and lower pulse repetition rates. 
To simplify the analysis we make an assumption that the energy density in 
the tissue is uniformly distributed throughout the volume of material 
where incident electromagnetic energy is being deposited. This assumption 
is clearly not correct and, instead, represents a worst-case situation. 
Normally optical deposition does not behave like a "step function" where 
energy is uniformly distributed throughout some penetration depth. 
(i.e., a step--function distribution is given by, 
.epsilon.=.epsilon..sub.0 for X&lt;X.sub.0 
and 
.epsilon.=0 for X&gt;X.sub.0) 
Instead, an actual electromechanical energy deposition follows some 
exponential decays (for example, Beer Law) where the beam intensity falls 
off according to an expression such as I=I.sub.0 e-(x/.delta.). 
Similarly, as FIG. 11 illustrates, that the thermal diffusion front at any 
given time also drops-off according to an exponential decay and does not 
progress as a step function. 
Our simplification, however, assumes that the source's deposited energy is 
distributed uniformly (as in the step function described above) throughout 
the material volume where the incident energy was deposited. This volume 
is given by the product of the beam spot size, A, and the thermal 
diffusion front position X.sub.diff. 
V=A X.sub.Diff 
Thus, the one-dimensional energy density, as a function of depth into the 
tissue X, and time, t, since the pulse energy was deposited in the tissue 
is simply given by: 
EQU .epsilon.(X,t)=E.sub.0 /(A X.sub.Diff) (6) 
Where .epsilon..sub.0 is the total incident pulse energy. Since our goal is 
to calculate the residual single pulse energy and residual total energy 
left in the tissue (i.e., the fraction of the incident energy which will 
actually thermally damage the tissue), and since more energy is actually 
concentrated in the shallower layers of the material than in the above 
assumption of a step function deposition, the above approximation 
represents a worst-case scenario. 
Given the above, the amount of energy left in the material (E.sub.lo) at 
the end of the pulse train, due to the energy deposition of the (single) 
N.sub.th pulse and after the removal of the heated material by pulse M-N 
through M (where M is the last pulse in the train), is given by the 
product of the energy density and the remaining heated volume: 
EQU E.sub.lo =.epsilon.(X,t) A (X.sub.diff -X abl) (7) 
Again, E.sub.lo is the total left-over energy due to the Nth pulse (a 
single pulse) with incident energy E.sub.0. 
Substituting from the expression for the energy density .epsilon.(X,t) from 
equation (6) we have: 
E.sub.lo =(E.sub.0 /(A X.sub.Diff)) A (X.sub.diff -X.sub.abl) 
Which translates to: 
EQU E.sub.lo =E.sub.0 (1-X.sub.abl /X.sub.diff) (8) 
The total amount of energy left over is the tissue is just the sum over the 
energy contributions E.sub.lo from each one of the M-1000 last pulses in 
the ablating pulse train. i.e., 
##EQU1## 
For example, in the case of a 1000 Hz system ablating a water-like 
substance, we sum from pulse N=M-1000 to pulse N=M. 
A more general expression can be formulated if we consider that the last 
pulses in the pulse train (see FIG. 12) i.e., those pulses in the train 
whose energy will not be completely removed, are the pulses contained 
within a time interval equal to the cross-over time prior to the end time 
of the pulse train. (Again, this is so because, by definition, this is the 
time duration required by subsequent pulses in the train to ablate the 
entire energy deposition of a single pulse). 
To get the total amount of left-over energy, we substitute the expression 
for a single-pulse left-over energy, E.sub.lo, from equation (8) into 
equation (9) and replace the summation over the last few individual pulses 
that leave residual energy in the material by an integration over the 
corresponding time interval. 
Since the total number of pulses in a pulse train of pulse repetition rate 
.nu. in an interval of time t is given by, (# of pulses)=.nu.t, and since 
an increment of d (# of pulses) is given by d(.nu.t)=.nu.dt=(.nu. dt), 
(because in this discussion the pulse repetition rate, .nu. is held 
constant with respect to time). Thus, the summation over the last pulse in 
the train that contribute to the left-over thermal energy (i.e., the 
summation over (# of pulses)), becomes an integration over time, i.e., 
##EQU2## 
and from equation (8) and (9) we obtain the integral expression, 
EQU E.sub.TLO =E.sub.0 .intg.(1-X.sub.abl /X.sub.diff).nu.dt (10) 
Where the integration is carried out over the time interval from t=0 to 
t=t.sub.xo 
Substituting the values for X.sub.diff and X.sub.abl from equation (1) and 
equation (2) and integrating, we obtain the general expression: 
EQU E.sub.tlo =E.sub.0 .nu.t.sub.xo [1-(2/3)a.sub.r .nu.(t.sub.xo /k).sup.1/2 
](11) 
Where a.sub.r is the ablation rate per pulse (e.g., micrometer per pulse). 
If, for example, the 1000 Hz system interacting with a water-like substance 
is considered, t.sub.xo =1 second and equation (11) is reduced to, 
EQU E.sub.tlo =E.sub.0 .nu.[1-(2/3)a.sub.r .nu.(1/k).sup.1/2 ] (12) 
In general t.sub.xo for a given system can be found by setting X.sub.ab 
=X.sub.diff which yields 
EQU t.sub.xo =k/(a.sub.r .nu.).sup.2 (13) 
substituting (13) in (11) we obtain, 
EQU E.sub.tlo =(1/3)E.sub.0 (k/.nu.)1/a.sub.r.sup.2 (14) 
Note that by dividing and multiplying by .delta..sup.2 /.delta..sup.2. 
Equation 14 can also be written as: 
EQU E.sub.tlo =(1/3)E.sub.0 (k/.nu.)1/f.sup.2 (15) 
Where: 
f=a.sub.r /.delta. 
the ratio of ablation rate to optical deposition depth. 
Equation 14 provides some important insight regarding the amount of 
left-over energy in the tissue and its relation to the important 
parameters E.sub.0, k, .nu. and the ablation rate a.sub.r (or the ratio of 
ablation depth per pulse to optical deposition depth, f). 
From equation (14) it can be seen that the total left-over energy E.sub.tlo 
: 
Increases with the incident pulse energy E.sub.0 
Increases with increased thermal diffusivity k (since more energy is able 
to escape ablative removal by being conducted to deeper layers of the 
material). 
Drops with increase pulse repetition rates are able to catch up and ablate 
more material. (Note however that from equation (8), for small values of 
t.sub.xo, small values of a.sub.r or large values of k, E.sub.tlo will 
initially increase with .nu. and only later, after reaching a maximum 
value of left-over energy will begin to decrease again with increasing 
pulse repetition rates, .nu.. A more detailed discussion of the dependence 
of E.sub.tlo on the laser pulse repetition rate is provided below.) 
Drops with increased ablation rate per pulse, a.sub.r, (or f) as the square 
of these quantities. (Again, this makes sense since a larger ablation per 
pulse leave less residual energy in the material and thus the smaller Etlo 
is.) 
Another interesting observation is that from equation (11) the ratio of the 
total left-over energy to the total incident energy impinging on the 
sample between the time t.sub.xo prior to the end of the pulse train and 
the end of the pulse train is a constant and is equal to 1/3. This is so 
because the Total incident pulse energy for this interval of time is 
E.sub.inc =E.sub.0 .nu. t.sub.xo. 
Thus, the ratio between the total left-over energy and incident energy 
becomes, after substituting E.sub.tlo from the equation (11) and t.sub.xo 
from (13): 
EQU E.sub.tlo /E.sub.inc =1/3 (16) 
It is also interesting to note that if the source's pulse sequence is 
applied to a time interval t shorter than the cross-over time for a given 
set of laser parameters, (i.e., t&lt;t.sub.xo) then obviously the valve of 
t.sub.xo from equation 9 cannot be used, and the ratio R of left-over 
residual energy to that of Total Incident Energy is given by: 
##EQU3## 
This is an important expression because it describes the ratio of left-over 
energy to incident energy for ALL interactions where the interaction time 
is less than the Cross-over time and thus all interactions where complete 
ablative removal of the heat from ANY of the incoming pulses is not 
achieved. 
Again, analysis of the ratio of equation (17) shows that the ratio, R, 
Decreases with .nu. 
This is interesting because the ratio R, unlike E.sub.tlo, decreases with 
increasing pulse repetition rate and does not show a maximum. This 
behavior is so because while the total incident energy increases with 
frequency, the total left-over energy decreases with as more ablation 
pulses are packed into each time interval. 
Decreases with a.sub.r and f. 
The larger the amount of material removed with each pulse, the more heated 
material that is removed and the less left-over energy remaining in the 
material. 
Decreases with the square root of the time (t.sup.1/2) the pulse train is 
interacting. 
The longer the ablation interaction continues the more heated material (and 
its content of thermal energy) is removed. 
Increases with one over the square root of the thermal diffusivity k. 
Again, with a larger thermal diffusivity, a larger portion of the left-over 
residual energy remaining after each pulse is able to diffuse to deeper 
regions of the material and the less likely this energy is to be removed 
through ablative interaction with subsequent pulses. Three other important 
observations are: 
We also see from equation (17) that for all cases where t.sub.xo has been 
reached, t.sub.xo can be substituted and R is equal to 1/3 (R=1/3) or, put 
differently, about 33.3% of the incident energy arriving between the last 
pulse M and pulse (M-.nu.t.sub.xo) is left in the material as residual 
energy. 
R is independent of a.sub.r (and f) if t.sub.xo has been reached. In this 
case, the ratio R of the left-over energy to the incident energy is 
constant and equal 1/3 regardless of the amount of material removed with 
each pulse and the ratio of this amount to that of the optical deposition 
depth. 
This point is important because it clearly demonstrates that once a high 
pulse repetition rate ablation is allowed to go on for a sufficiently long 
period of time so that txo is reached, the control of the residual heat in 
the material is dominated by the total removal of most of the interaction 
energy by the rapid sequence of pulse themselves. 
Finally, it is also important to note that if .nu. is such that the 
cross-over is not reached, a.sub.r (and f) do play a role in the 
determining the amount of left-over thermal energy. 
Ultimately, however, it is not the ratio R that is of most importance in 
determining the amount of thermal damage that can be caused, but rather, 
the absolute value of the total left over energy, left in the tissue 
following an interaction of a pulse train. This expression was given by 
equation (11) for a general time t&lt;t.sub.xo. 
EQU E.sub.tlo =E.sub.0 .nu.t[1-(2/3)a.sub.r .nu.(t/k).sup.1/2 ](18) 
This expression clearly indicates the presence of a maximum E.sub.tlo as 
the pulse repetition rate .nu. is varied. This is so because there are two 
competing effects to the pulse repetition rate .nu.. First, E.sub.tlo is 
increased with the increase in the deposited energy which increased with 
.nu.. On the other hand, two: as the pulse repetition rate .nu. is 
increased so does the removal rate due to the ablation term (second term) 
in equation (18). 
To find the maximum we differentiate E.sub.tlo with respect to .nu., 
EQU d(E.sub.tlo)/d.nu.=E.sub.0 t[1-(4/3)a.sub.r .nu.(t/k).sup.1/2 ] 
When the pulse repetition rate is very low i.e., .nu..fwdarw.0 Then from 
(18) E.sub.tlo .fwdarw.0 as well [More precisely E.sub.tlo is simply equal 
to the incident energy deposition rate which is: 
EQU .epsilon..sub.0 (A (.delta.-a.sub.r)).nu. 
With .epsilon..sub.0 being the incident energy density Per Pulse. Obviously 
E.sub.tlo =.epsilon..sub.0 A(.delta.-a.sub.r) per second for 1 Hz and 
E.sub.tlo goes to zero as .nu. goes to zero]. 
B 
By setting the derivative (19) equal to zero, we find the frequency for 
which maximum left-over energy occurs. 
EQU .nu..sub.max =(3/4)(1/a.sub.r)(k/t).sup.1/2 (20) 
Substituting back in (8) yields 
##EQU4## 
Also we note that when: C 
EQU .nu.=3/(2a.sub.r)(k/t).sup.1/2 (22) 
EQU E.sub.tlo =0 (23) 
Ci 
If we are evaluating the above at t=t.sub.xo for some frequency .nu..sub.0 
then, by the definition of t.sub.xo (.nu..sub.0 =(1/a.sub.r) 
(k/t.sub.xo).sup.1/2) equation 22 becomes: 
EQU .nu.=3/2.nu..sub.0 (24) 
and, 
EQU E.sub.tlo =0 (25) 
In other words: 
Since for a time selected for evaluation, t.sub.0 there is a corresponding 
frequency .nu..sub.0 for t.sub.0 which is the cross-over time, operating 
at a frequency given by (3.nu..sub.0 /2) will result in no residual 
thermal energy deposition leftover in the material. 
We can also rewrite case B in terms of .nu..sub.0 =(1/a.sub.r) (k/t.sub.o) 
.sup.1/2 since equation (20) can be expressed as: 
Bi 
EQU .nu..sub.max =(3/4).nu..sub.0 (26) 
So that equation (8) yields 
##EQU5## 
Finally when .nu. is exactly equal to .nu..sub.0 then the time is 
precisely the crossover time and (recall from earlier discussion), 
D 
EQU .nu.=.nu..sub.0 (28) 
So that equation (18) yields 
EQU E.sub.tlo =(1/3)E.sub.0 .nu..sub.0 t (29) 
Or 
EQU E.sub.tlo =1/3Einc (30) 
@ cross-over time t.sub.xo 
The dependence of E.sub.tlo on the pulse repetition rate .nu. is 
illustrated in FIG. 13. 
From FIG. 13 and from 
EQU E.sub.inc =E.sub.0 .nu..sub.0 t 
EQU .nu..sub.0 =(1/a.sub.r)(k/t).sup.1/2 
We see that both Einc and .nu..sub.0 are proportional to 1/a.sub.r. 
Thus the larger a.sub.r is the lower E.sub.tlo is and the lower the 
frequency .nu..sub.max =(3/4) .nu..sub.0 at which the maximum total 
left-over energy, E.sub.tlo occurs. (i.e., the entire curve in the figure 
above shift to the left and to the bottom) 
Typical numbers for a 1 second treatment with a 1 KHz, 1 mJ system, would 
be: 
E.sub.inc =E.sub.0 .nu..sub.0 t= 
(1 mJ) (1000 pulses/sec) (1 sec)=1 J 
(E.sub.inc =1 J) 
which yield a maximum left-over energy of only 
E.sub.tlo-max =0.33 J=330 mJ 
at .nu.=750 Hz 
Since the actual amount of per-pulse energy transformed to heat is only 10% 
to 30%, the total left-over energy in the target is in the range of 30 to 
100 mJ per interaction. Also note that because of the self-heat removal 
described by the principle of operation of the present invention--this 
total amount of left-over energy is constant regardless of the length of 
overall operation time. This feature is a unique characteristic of the 
operation of the present invention. 
Quasi-Dynamic Relationship between the Ablation Front and the Thermal 
Diffusion Front 
As we saw from the discussion above, all of the thermal energy deposited in 
the target material prior to the last cross-over time interval txo, is 
completely removed from the material by subsequent pulse ablation. An 
interesting question however, is how much ahead of the ablation front can 
the thermal energy from each pulse get? 
The answer is given again by FIGS. 5a and 11. For each pulse, the distance 
"diffusion front to ablation front is given by: 
EQU .DELTA.X=Xdiff-Xabl=(K.sup.1/2 t.sup.1/2 -(a.sub.r .nu.)t (31) 
Up to the point where .DELTA.X becomes negative (i.e., when all heat is 
removed by the ablation front). 
If we wish to find the maximum distance .DELTA.X as a function of time we 
simply take the derivative with respect to time then: 
EQU d(.DELTA.X)/dt=1/2(K.sup.1/2 /t.sup.1/2)-(a.sub.r .nu.)t (32) 
Which gives a value of: 
EQU t.sub.max =k/(2a.sub.r .nu.).sup.2 =t.sub.xo /4 (33) 
i.e., the maximum distance that the thermal energy diffusion front gets 
ahead of the ablation front occurs at one fourth of the cross-over-time. 
Substituting this in the expression for .DELTA.X above gives: 
EQU .DELTA.X.sub.max =k/4(a.sub.r .nu.) (34) 
For our exemplary 1 KHz 1 .mu.m/pulse water-like system this means about 40 
.mu.m ahead of the ablation front. 
.DELTA.X.sub.max .about.40 .mu.m 
For a 100 KHz system: 
.DELTA.X.sub.max .about.0.4 .mu.m 
A 100 Hz system on the other hand will result in a distance of 400 .mu.m 
For a 10 Hz system: 
.DELTA.X.sub.max .about.4 mm 
While a 10 Hz system with ablation rate of 10 .mu.m per pulse will yield 
.DELTA.X.sub.max .about.0.4 mm 
The calculation above also holds for the distance that each one of the last 
M-.nu.t.sub.xo pulses has reached ahead of the ablation front when the 
system is turned off. The time t in equations 31-34 above simply 
corresponds to pulse number M-t.nu. where M is the last pulse in the pulse 
train. 
Thus, the pulse whose heat has diffused the furthermost from the ablation 
front when the laser is turned off is given by pulse number: M-t.sub.max 
.nu. 
Where M is the last pulse and t.sub.max is given by equation (33). 
A more elaborate way for describing the interaction is provided by the 
additional discussion below: 
A) A SINGLE PULSE INTERACTION: 
Light is deposited within an optical deposition zone, .delta.. Note, 
however, that the optical deposition zone changes with Wavelength, 
material type, and the light intensity. It is, for example, different for 
low intensity pulses as compared to high intensity pulse. .delta. may also 
change within a single pulse as the leading edge of the pulse modifying 
the optical properties of the target material. 
Depending on how the incident pulse optical energy E.sub.0 is deposited in 
the material (i.e., the optical energy distribution and coupling to the 
matter as a function of time and spatial location), some of the material 
will be ejected (e.g., to a depth X=a.sub.r) and some will be permanently 
modified, (e.g., to a depth X.sub.ir) while the rest of the material will 
either not be irreversibly modified or may be unaffected by the incident 
energy at all. 
The exact interaction path may be thermally dominated (e.g., vaporization 
or rapid vaporization of matter and water, leading to explosive ejection 
of material), mechanically dominated (generation of shock wave, mechanical 
transient, or spallation), chemical alteration of the material (changes in 
chemical properties of the target matter are effected), or plasma-mediated 
(e.g., either multiphoton ionization or thermo-ionization of the material 
and the material and the creation of an ion/electron plasma which, in 
turn, alter pulse energy coupling, reflection, or transmission into the 
material). 
The complex dependence of .delta., and a.sub.r both static and dynamic 
properties of the beam and targeted material can, according to this 
invention, be simplified. Using experimental technique one can observe the 
ablation rate a.sub.r (i.e., the amount of ablated material per pulse), 
the depth of the zone of irreversible modification (created by a single 
pulse), optical deposition depth .delta.. 
If a.sub.r and .delta. are known, the mount of energy left by a single 
pulse, E.sub.lopp, can then be estimated: 
EQU E.sub.lopp =E.sub.0 (1-a.sub.r /.delta.) (35) 
Where E.sub.0 is the incident energy of each pulse. The amount of energy 
left over in the tissue after each single pulse is proportional to a.sub.r 
/.delta.. Thus, as a.sub.r /.delta. is diminished (either because a.sub.r 
becomes larger or because .delta. becomes smaller) E.sub.lopp diminishes 
and becomes smaller as well. 
The optical energy in the pulse-initially deposited in the optical 
deposition zone .delta., begins to diffuse deeper into the tissue with a 
characteristics diffusion rate given by: 
EQU dZ/dt=(k/t).sup.1/2 (36) 
where k is the material thermal diffusivity coefficient (for example, for 
water, k=1.4 10.sup.-7 m.sup.2 /sec. 
Depending on the pulse duration, the thermal diffusion into the material 
will take place either already during the pulse (during the optical 
deposition time) or mostly after the optical energy deposition has been 
coupled. 
If the pulse duration .tau. is such that: 
EQU .tau.&lt;.delta..sup.2 /k (37) 
when heat does not diffuse out of the optical deposition zone during the 
pulse duration and the optical deposition process is known as "thermally 
confined". 
For a dielectric with water-like thermal diffusivity, k=1.4 E-7 m.sup.2 
/sec and thermal energy diffuses about a single .mu.m within a .mu.s time 
duration. If we consider pulses shorter than 100 microsecond the diffusion 
distance is only 10 micrometer. IN 10 ms, thermal energy diffusion is 
limited to 100 micrometer. For most practical situations the optical 
deposition is greater than at least 1 .mu.m and more likely between 1 and 
several tens .mu.m. Thus, for most practical situations under 
consideration of this invention, heat does not substantially diffuse out 
of the optical zone during the optical energy deposition cycle. 
The situation can thus be approximated by the picture depicted in FIG. 14 
where the horizontal axis depicts the time axis and the vertical axis 
depict the depth to which pulse energy has reached (either through optical 
or through thermal diffusion). 
Optical energy is deposited to an optical deposition depth .delta., 505. 
The curved line 506 represents additional energy penetration due to 
thermal diffusion. The line 507 represents the propagation of the ablation 
front due to subsequent pulses removal of material. It shows that 
ultimately all the first pulse energy will be removed from the material. 
We begin by calculating the time required for complete removal--by 
subsequent ablation pulses--of the entire amount of thermal energy 
deposited by the first pulse (or any arbitrarily selected pulse N in an 
incoming pulse train of M pulses). 
The time, termed by the inventor cross-over time t.sub.xo, is found by 
setting the distance reached by the thermal diffusion front, Z.sub.thrm : 
EQU Z.sub.thrm =.delta.+(kt).sup.1/2 (38) 
equal to the ablation front term: 
EQU Z.sub.abl =a.sub.r .nu.t (39) 
Which leads to: 
EQU kt=(a.sub.r .nu.t-.delta.).sup.2 (40) 
Which may be expanded to: 
EQU a.sub.r.sup.2 .nu..sup.2 t.sup.2 -(2.delta..nu.a.sub.r -k)t+.delta..sup.2 
=0(41) 
Defining the coefficient in front of the t.sup.2 term as .alpha., and the 
one in front of the t-term as .beta. we have a simple quadratic equation 
with a solution: 
EQU t.sub.1/2 =[-.beta.+/-(.beta..sup.2 -4.alpha..delta..sup.2).sup.1/2 
]/(2.alpha.) (42) 
If we substitute .alpha. and .beta. in Equation (42) we obtain: 
##EQU6## 
Equation (43) shows that the cross over time, the time at which the 
progressing ablation front will completely eliminates the thermal energy 
deposited by a single pulse of energy, is a complex function of k, ar, 
.nu. and .delta.. 
This complicated relation can be simplified if we consider the two 
extremes: 
A) (2.delta..nu.a.sub.r)&lt;&lt;k 
(Thermal diffusion dominates the energy diffusion process) 
(e.g., If the ablation per pulse is on the order of the optical penetration 
which is on the order of a micrometer, and if with pulse repetition rate 
of about 1000 Hz, the term (2.delta..nu.a.sub.r) is on the order of 
10.sup.-9 while k is on the order of 10.sup.-7.) 
In this case equation (43) reduces to the cross over times: 
EQU t.sub.1 =k/(.nu.a.sub.r).sup.2 (44) 
and to the non-practical solution is t.sub.2 =0. 
If on the other hand: 
B) (2 .delta..nu.a.sub.r)&gt;&gt;k 
(for example if the optical penetration depth is on the order of a few 
millimeters or more) 
Then, in this case the cross-over time is given by: 
EQU t.sub.1/2 .fwdarw.t.sub.1 =.delta./.nu.a.sub.r (45) 
B) Multiple-Pulse Effects: 
An important contribution of the present invention is that after a time 
period equal to the cross-over time, t.sub.xo, no thermal energy due to 
the pulse N under consideration remains in the target material. This is so 
due to the ablative removal by subsequent pulses. 
FIG. 14 shows the relationship between the thermal diffusion front due to 
pulse number N and the progressing ablation front due to subsequent 
pulses. The inventor has recognized that the same figure may also 
represent the amount of heated material left in the target after an energy 
deposition by each of the N pulses (between pulse L and the last pulse M) 
due to the action of subsequent remaining pulses M-N that follow each 
pulse N. 
FIG. 15 depicts the position of the thermal diffusion front (relative to 
the position of the original surface) for each pulse at the time of pulse 
train termination, and also the position of the ablation front (relative 
to the position of the original surface) for each pulse at the time of 
pulse train termination. 
The total amount of left-over energy due to a pulse train of M pulses (N=1, 
2, 3, . . . L . . . M. Where M is the last pulse in the pulse train, and L 
is the pulse arriving at a time t=t.sub.xo before the pulse train 
termination) can be calculated. 
As was mentioned above the thermal energy due to the first pulses in the 
train, (if the pulse train total time duration, T is longer than t.sub.xo, 
i.e., T&gt;t.sub.xo) will be ablated away. This is the case if these pulses 
occur at times t such that T-t&gt;t.sub.xo. (i.e., if these pulses interact 
with the target in times earlier than the cross over time t.sub.xo prior 
to the end of the pulse train. 
For the last few pulses (from pulse L to pulse M occurring at times t such 
that T-t&lt;.sup.t.sub.xo, the situation is different. These pulses do no 
have enough subsequent pulses behind them to have their own heat 
completely removed. 
With the aid of FIG. 15, we can estimate the amount of total energy left 
over by these last pulses, (which is also the total amount of left over 
thermal energy E.sub.tlo, due to the entire pulse train. 
##EQU7## 
Where the summation is carried over the last M-L pulses. Since the 
incremental number of pulses in the sum is given by #=.nu. dt the 
summation can be written as an integral of the corresponding interval of 
time, i.e., the time from T to T=.sub.txo. 
Since the integration is invariant to the direction in time, we can simply 
integrate from t=0 to t=txo. Equation (46) thus becomes: 
EQU E.sub.tlo =.nu.E.sub.pp .intg.1-[t.nu.a.sub.r /(.delta.=(tk).sup.1/2)]dt(47 
) 
Where the integration is from t=0 to t=t.sub.xo. 
The integral (47) can be executed in parts leading to the following 
expression: 
EQU E.sub.tlo =t.sub.xo .nu.E.sub.pp -.nu..sup.2 E.sub.pp a.sub.r 
.intg.tdt/(.delta.+(tk).sup.1/2) (48) 
With the same limits of integration as in (47) 
The integral in equation (48) is an indefinite integral and can be 
performed using Equation 19 on page 929 in the tables of indefinite 
integral given by Korn an Korn: 
It is given by: 
EQU E.sub.tlo =t.sub.xo .nu.E.sub.pp [1-.nu..sup.2 a.sub.r (1/txo)(.zeta.)](49) 
Where: 
EQU .zeta.=(1/k.sup.2)[Y.sup.3 /3+(3/2).delta.Y.sup.2 +(3.delta..sup.2 
Y)-.delta..sup.3 lnY]- (50) 
EQU -.delta..sup.3 (29/6-ln.delta.)/k.sup.2 
and where 
Y=.delta.+(kt.sub.xo).sup.1/2 
Equation (49) is the general expression for the left-over energy E.sub.tlo. 
Considering the limiting cases can simplify equation (48): 
Limit i) THERMAL CONDUCTION DOMINATES ENERGY PROPAGATION 
.delta./t&lt;&lt;(k/t).sup.1/2 
In this case Equation (48) yields: 
EQU E.sub.tlo =E.sub.lopp k/(3.nu.a.sub.r.sup.2)=Einc/3 (51) 
Where: 
E.sub.inc =E.sub.lopp txo .nu. 
In this limit the cross over time is given by: 
t.sub.xo =k/(a.sub.r.sup.2 .nu..sup.2) 
In The Other Limit: 
Limit ii) OPTICAL DEPOSITION DOMINATES ENERGY PROPAGATION 
.delta./T&lt;&lt;(k/t).sup.1/2 
In this case equation 48 becomes: 
EQU E.sub.tlo =t.sub.xo E.sub.lopp .nu.[1-.nu.a.sub.r t.sub.xo 
/(2.delta.)]=E.sub.inc /2 (52) 
Where: 
E.sub.inc =E.sub.lopp txo .nu. 
In this limits the cross over time as given by: 
t.sub.xo =.delta./(a.sub.r .nu.) 
C) Left-Over Energy And Damage Zones Due To Multiple Pulse Action. 
Table 1 summarizes the cross-over time t.sub.xo, the thermal diffusion 
depth corresponding to t.sub.xo, and the total incident energy, total left 
over thermal energy and the realistic values for E.sub.tlo (since only 
about 10-30% of the incident energy couples to the target 
material)--during t.sub.xo. Finally the table also shows the expected 
depth of zones of irreversible damage. 
The following system parameters are assumed for the example in table 1: 
Optical penetration depth, .delta.=1 .mu.m, ablation depth per pulse 
a.sub.r =1 .mu.m thermal diffusivity, k=1.4 10.sup.-7 m.sup.2 /sec, and 
the incident energy per pulse Einc is assumed at 1 mJ. 
TABLE 1 
__________________________________________________________________________ 
E.sub.tlo -realistic 
(only 10% 
Z.sub.damg 0.1 
.nu. t.sub.xo (Sec) 
(tk).sup.1/2 (m) 
E.sub.inc (mJ) 
E.sub.tlo (mJ) 
coupled) 
mJ/.mu.m 
__________________________________________________________________________ 
100 10 1.2 E-3 
1000 330 33 330 .mu.m 
Diffusion 
Dominates 
300 1 4 E-4 
300 100 10 100 
1 KHz 
0.1 E-4 100 33 3.3 33 
3000 0.01 
4 E-5 
30 10 1 10 
10 KHz 
0.001 
E-5 10 3.3 0.3 3 
30,000 Hz 
10.sup.-4 
4 E-6 
3 1 0.1 1 
.delta.-Zdiff 
"optical 
deposition 
dominates" 
100 KHz 
10.sup.-5 
E-6 1 0.3 0.03 0.3 
__________________________________________________________________________ 
In the above a damange energy threshold of approximately 0.1 mJ per .mu.m 
was assumed. 
Thus, for optical deposition depth .delta. of 1 micrometer one need not 
worry about .delta. in the expression for E.sub.tlo until a pulse 
repetition rate of over 10 KHz. 
For this regime .delta.&lt;&lt;(tk).sup.1/2 
and t.sub.xo =k/(ar .nu.).sup.2 
and E.sub.tlo =k E.sub.0 /(3 a.sub.r.sup.2 .nu.)=E.sub.inc /3 
For the regime .delta.&gt;&gt;(tk).sup.1/2 
t.sub.xo =.delta./(ar .nu.) 
E.sub.tlo =E.sub.0 /(2 a.sub.r)=E.sub.inc /2 
at 100 KHz, .delta..about.1 .mu.m, the left-over energy is approximately 
0.5 mJ, which corresponds to Z.sub.damage of about 5 .mu.m. 
It is worth noting that at 1 KHz the total left over energy is 33 mJ 
(regardless of how long the laser has been on. This should be contrasted, 
for example, with conventional Nd, Ho, or Er:YAG lasers with pulse energy 
on the order of 300 mJ per single pulse. (i.e., this KHz system E.sub.tlo 
is only 1% of the se lasers.) 
D) Combined Effect Due To High a.sub.r /.delta. Ratio And High PRR 
i) Thermal Conduction Dominates Energy Propagation .delta./T&lt;&lt;(K/T).sup.1/2 
Here E.sub.tlo becomes: 
EQU E.sub.tlo =(1-a.sub.r /.delta.)E.sub.0 
k/(3.nu.a.sub.r.sup.2)=(1/3)E.sub.inc (1-a.sub.r /.delta.)(53) 
Where E.sub.0 is the per-pulse incident energy or 
EQU E.sub.tlo =E.sub.0 k/(3.nu.a.sub.r.sup.2)-a.sub.r /E.sub.0 
k/(3.nu..delta.a.sub.r) (54) 
Thus, from equation (54) if a.sub.r approaches .delta. then the left-over 
energy (regardless of the pulse repetition rate) becomes negligible. 
Also, if .nu. becomes very large then the left over energy becomes 
negligible. 
Thus, if either, a.sub.r appreciates .delta. or .nu. becomes very large, 
then the total left-over energy becomes negligible. 
On the other hand, if a.sub.r is very small or k is very large then the 
E.sub.tlo becomes larger. 
i.e., if 
a.sub.r .fwdarw.0 
or k.fwdarw.infinity 
then 
E.sub.tlo .fwdarw.infinity 
ii) Optical Deposition Dominates Energy Propagation .delta./t&gt;&gt;(k/t).sup.1/ 
2 
E.sub.tlo =(1/2) .delta. E.sub.0 /a.sub.r -(1/2)E.sub.0 
thus, 
if a.sub.r .fwdarw..delta. 
E.sub.tlo .fwdarw.0 
But if 
.delta.&gt;&gt;a.sub.r 
Then 
E.sub.tlo .fwdarw.(1/2)E.sub.0 .delta./a.sub.r 
This means that in cases where optical penetration is very large (e.g., 
A.sub.r.sup.+ ion laser of .about./cm) and ablation is small (e.g. 
.about./.mu.m) (then the ratio (a.sub.r /.delta.) is on the order of 
10.sup.-4, and the total left-over energy is E.sub.tlo =(1/2) .nu. 
t.sub.xo E.sub.0 (1-ar/.delta.), 
which approaches: 
E.sub.tlo .fwdarw.(1/2) .nu.t.sub.xo E.sub.0 =(1/2) E.sub.inc 
This is reasonable since only negligible ablative removal takes place. 
As became clear from the above, part of the practice of the present 
invention is based on the requirement of removal of portion of the pulse 
energy by subsequent pulses. It is, therefore, important in the practice 
of the present invention to identify failure of at least some of the 
pulses to accomplish such ablative removal of heat so that the number of 
pulses may be reduced until operating parameters allow ablative removal of 
heat to be restored. 
To identify an ablative event by a an electromagnetic pulse at least some 
luminescence emission is collected from the interaction site and delivered 
to a detector which then compare the emission intensity and spectral 
content to a predetermined reference characteristic ablative emission. 
FIG. 16a shows a typical emission spectrum from an ablative interaction 
followed by the formation of plasma. While the peaks 1604 are 
characteristic to the exemplary type of tissue ablated (Dentin) and to the 
Calcium atoms and ions generated by this interaction, the broad spectral 
continuum 1606 is a general characteristic of all ablation-induced plasmas 
and is indicative of ablative interaction. For comparison, the 
luminescence emission from ablative interaction of 193 nm beam with 
corneal tissue is also shown in FIG. 16b. While in this case, the 
characteristic tissue-specific Calcium peaks are absent and instead a 
single OH.sup.- peak at 660 nm is the main dominating spectral structure, 
as was indicated above, the background emission is always present. In the 
absence of ablative interaction, no background emission can be detected. 
FIG. 17 shows a typical collection and diagnostic setup with feedback means 
for monitoring ablation and controlling the Electromagnetic beam source. A 
source of electromagnetic radiation conforming with the principles of 
operation of the present invention (for example a pulsed laser source) 
1702, emits a beam which is directed to a Pockels cell 1704. The Pockels 
cells acts as a shutter in response to instructions from the 
controller/computer 1714. In its normal operating condition the beam would 
be allowed to propagate through a beam splitter 1706 and into a focusing 
lens 1708. The focusing lens send the beam either directly into the target 
1712 or through delivery fiber or hollow wave guide 1710 to the target 
1712. Following the ablative interaction, luminescence emission from the 
ablated target site is collected by the same delivery system (for example, 
the fiber and imaging lens). The collected emission is then reflected by 
the beam splitter 1706 to the diagnostic/feedback/controller unit 1714. 
The unit 1714 consists for example, of a detector to detect the intensity 
level of the collected luminescence emission (or, alternatively, of a 
spectrometer to detect and evaluate both intensity and spectral 
distribution of the collected luminescence emission), of a computer 
processor to analyze and compare the collected radiation to that expected 
from ablation luminescence emission, and finally, means to feedback a 
signal to the control unit of the beam source so that adjustment to the 
source pulse repetition rate may be made. 
If the diagnostic unit 1714 does not detect sufficiently high level of 
luminescence emission, the feed back circuit instructs the source control 
unit to slow the pulse rate to 10 pulses per second (or any exemplary X 
pulses per second pulse repetition rate, sufficiently low to avoid 
significant deposit of energy within the "linear" interaction regime). 
This process is shown in FIG. 18: here, the operating pulse repetition 
rate of Y Pulses per second is shown in 1810. The luminescence emission 
level corresponding to ablative interaction is shown for pulse number 1 
through N-1 in 1812. When a decrease in luminescence emission level is 
detected for pulse N and N+1 in 1812, the corresponding pulse repetition 
rate is automatically changed to lower rate of X Pulses per second as 
shown in 1814. The lower repetition rate must be sufficiently low to bring 
non-ablative thermal deposition to a fraction of the value for threshold 
of irreversible material damage. Meanwhile, luminescence emission is 
continued to be monitored while the laser parameters are changed (either 
automatically through computer control or through actions taken by the 
operator). When Luminescence emission is restored following the action of 
pulse M as shown in 1816, the pulse repetition rate is restored to its 
original frequency as shown in 1814. 
Ablative interaction is restored through one of the following adjustments: 
Increasing pulse energy or beam power 
Decreasing spot size (e.g. optically, or by moving the fiber/HWG/delivery 
arm etc. closer or further away from the target). 
Decreasing time scale 
Changing wavelength (e.g. through OPO/OPA nonlinear crystal insertion) to a 
more absorbing wavelength. 
Alternatively, in the practice of the present invention and the use of an 
ablation detection feedback, the luminescence emission signal may be 
replaced by a transducer detector for detecting the presence of a 
mechanical recoil momentum, shock waves, thermoelastic stresses or any 
other transient mechanical or thermal effects which uniquely characterize 
an ablative interaction of the beam with the targeted material. Such a 
transducer feedback means may, in a manner similar to that described 
above, further provide a control signal in response to a change in the 
transducer detector output signal so that the electromagnetic source pulse 
repetition rate may be slowed down to an interrogative pulse repetition 
rate (or operation may be completely terminated) in response to such a 
feedback signal. 
Such a transducer feedback means carrying a response signal which is a 
consequence of phenomena which occur only during an ablative event (such 
as, mechanical recoil momentum, shock waves, thermoelastic stresses or any 
other transient mechanical or thermal effects caused by the ablative 
interaction of the beam with the targeted materia) shall further provide a 
control signal. In response to such changes in the transducer detector 
output, the electromagnetic source pulse repetition rate may be slowed 
down or operation may be completely terminated. 
Those skilled in the art will appreciate that the foregoing examples and 
descriptions of various preferred embodiments of the present invention are 
merely illustrative of the invention as a whole, and that variations in 
wavelength, pulse duration, pulse repetition rate, as well as beam energy 
density, may be made within the spirit and scope of the invention. 
Accordingly, the present invention is not limited to the specific 
embodiments described herein, but rather is defined by the scope of the 
appended claims.