LASER SYSTEMS

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of priority to U.S. Provisional Patent Application No. 62/084,783, entitled "Systems and Methods to Control Depth of Treatment in Dental Laser Systems," filed November 26, 2014, the disclosure of which is incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

[0002] The present disclosure relates generally to a laser-based dental laser treatment system and, more specifically, to a system in which one or more laser parameters and/or one or more system parameters are controlled so as to provide an increased depth of treatment capability.

BACKGROUND

[0003] Lasers are increasingly being shown to be useful in a multitude of hard and soft tissue dental procedures, including removing decay, cutting, drilling or shaping hard tissue, and removing or cutting soft tissue. A tooth has three layers. The outermost layer is the enamel which is the hardest and forms a protective layer for the rest of the tooth. The middle and bulk of the tooth includes dentin, and the innermost layer includes pulp. Enamel includes roughly at least 70% mineral by weight, which generally includes carbonated hydroxyapatite. The enamel and dentin are similar in composition, with dentin having significantly less hydroxyapatite. The pulp includes vessels and nerves. Lasers of a wavelength in the 9.3 - 9.6 micrometer range are well absorbed by the hydroxyapatite that forms a significant portion of tooth and bone, making these lasers efficient in the removal of hard dental tissue.

[0004] Lasers have also been found to be useful in the removal of dental material without needing a local anesthetic that is required when a similar procedure is performed using a drill. Further, lasers generally do not make the noises and vibrations that are associated with dental drills. At least for these reasons, it is the hope of many in the dental industry that lasers may replace the drill, and remove, or at least lessen, the anxiety and fear from dental treatment.

[0005] In several dental laser systems, the laser is housed in a console and transmitted to a handpiece through an articulated or flexible arm, via an optical system for beam delivery which may include mirrors, lenses and fiber optic cables. The arm generally attaches to a

handpiece/main chamber assembly. For the ease of cleaning and servicing, the handpiece can be detachable. Differently configured detachable handpieces may be used for different dental procedures. Within an end portion of the arm or within the handpiece/main chamber assembly, there is generally a beam guidance system which may be used to precisely guide the laser beam out of the end or beam exit of the handpiece/main chamber assembly and to a treatment area. Generally, the handpiece/main chamber assembly beam exit is small for improved ergonomics and easier manipulation within a person's mouth, and the laser beam path typically passes approximately through the center of the beam exit. The beam guidance system generally includes a pair of galvanometers (e.g., galvo or servo-controlled rotatable mirrors), which can be relatively small and inexpensive.

[0006] In order to ablate dental tissue, the laser must provide sufficient energy density at the treatment surface. Energy density may be referred to as fluence, which may be expressed in units of joules per square centimeter (J/cm ² ). For each specific frequency of radiation, typically there exists a fluence threshold (also called an ablation threshold) for effectively ablating dental tissue, including hard tissue such as enamel and dentin. For example, at 9.3 μιη a threshold for surface modification occurs at approximately 2 J/cm ² and a threshold for ablation occurs at approximately 10 J/cm ² . If the laser beam is pulsed, the fluence is defined as the energy per pulse divided by the cross-sectional area of the beam at the treatment location (e.g., beam spot size).

[0007] Dental laser systems often include one or more focusing elements such as lenses. The focusing element may serve to concentrate the laser beam into a spot of a smaller diameter than the diameter of the beam incident upon the focusing element, so as to increase the fluence (J/cm ² ) at the laser beam focused spot by reducing the target area upon which the beam impinges. Typically, such a laser beam has an hourglass profile, where the region of minimum diameter and highest fluence is referred to as the waist. The distance from the focusing element to the waist may be called the focal length of the focusing element. From either side of the waist, the laser beam diameter generally diverges and consequently the fluence decreases. In general, a depth of treatment is described as the total distance before, at, and after the waist where the laser beam fluence is equal to or exceeds the material (e.g., tissue) treatment threshold. The treatment threshold may be equal to a tissue ablation threshold for ablative treatments. The depth of treatment for a pulsed laser system can be described as the distance before, at, and after the focused waist diameter, where the energy per pulse per a cross- sectional area of the laser beam exceeds the absorption threshold of the material being treated. Laser beam equations usually call the waist radius ω ₀ and thus the waist diameter is 2ω ₀ . In many conventional systems, the laser beam diverges from the waist at an angle so large that the depth of treatment is typically just a few millimeters.

[0008] Research performed at University of California San Francisco, by researchers such as Featherston, Fried, and Rechmann, has shown that 9.3 μιη and 9.6 μιη laser wavelengths are well suited for treatment of dental hard tissue. According to techniques that describe the thermal relaxation time as an indicator of the pulse duration for laser treatment, pulses having a duration in the range of 5 μ8 to 130 μ8 may be desirable for ablation. Pulse widths in the range of 5 μ8 to 20 μ8 may prevent accumulation of heat and may minimize the risk of pulp damage. The pulp of the tooth may be irreversibly damaged if it undergoes a temperature rise of 5° C or more.

[0009] A relatively small depth of treatment in a dental laser treatment system can limit the distance over which dental tissue can be treated, the options for interproximal treatment, and the user flexibility of the system. Several known laser-based dental treatment techniques suffer from one or more of the following disadvantages: depth of treatment is just a few millimeters, need for overly large focusing elements, overly large laser beam waist, operation at a wavelength that is not efficiently absorbed by dental tissue, and insufficient fluence to treat dental hard tissue.

SUMMARY

[0010] In order to facilitate improved treatment, e.g., faster and/or more efficient treatment, various embodiments of a dental laser treatment system described herein provide for a relatively large depth of treatment (e.g., about 5 mm or greater) for treatment of dental tissue (e.g., enamel and dentin) while maintaining a sufficiently high fluence, and minimizing or avoiding damage to the dental tissue that is not to be treated. Providing a larger (e.g., longer) depth of treatment can allow for interproximal cutting of teeth and can simplify the use of the dental laser. For example, with a sufficiently large depth of treatment, small deviations in the distance of the laser beam delivery device from the treatment surface (e.g., the standoff distance between the beam exit of a handpiece and the treatment surface), that may be caused by inadvertent movement of the handpiece or the treatment site (e.g., a patients head/mouth), may have no significant effect (e.g., less than 1%, less than 5%, less than 10%, etc.) on the fluence at the treatment surface.

[0011] To this end, one aspect of the present disclosure includes a dental laser treatment system featuring a laser source providing a laser beam and a subsystem focusing element adapted to shape the laser beam to have a waist and to provide a depth of treatment of at least 5 mm, centered about the waist. The laser source may be adapted to provide at the depth of treatment an energy density at least equal to a minimum energy density desired to perform treatment upon hard dental tissue.

[0012] In various embodiments, the waist may be in the range of 50 μιη to 500 μιη. The laser beam may have a wavelength in the range from 9 μιη to 12 μιη. In some instances, the focusing element is adapted to provide a laser beam having a Gaussian beam profile or a top- hat beam profile. The focusing element may be adapted to form the waist of the laser beam at a focal distance of at least 25 mm (e.g., up to 135 mm). The focusing element may include at least one lens. In certain implementations, the dental laser treatment system may also include a beam guidance system located, for example, between the laser source and the focusing element. The beam guidance system may include at least one galvometer. The dental laser treatment system may also include a handpiece assembly downstream from the focusing element. In some instances, a turning mirror and/or the focusing element may be disposed within the handpiece assembly. In certain cases, the laser source is configured to provide a laser beam having a diameter (e.g., within a range from 0.06 mm up to 5 mm) based at least in part on the waist and a focal length of the focusing element.

[0013] In general, in another aspect, embodiments of the disclosure feature a method for performing a laser dental treatment that includes the steps of: providing a laser beam from a laser source; shaping the laser beam using a subsystem focusing element, such that the laser beam has a waist and provides a depth of treatment of at least 5 mm, centered about the waist; and providing at the depth of treatment an energy density at least equal to a minimum energy density required to perform treatment upon hard tissue. [0014] In various embodiments, the waist may be in the range from 50 μιη to 500 μιη. The laser beam may have a wavelength in the range from 9 μιη to 12 μιη, and have a Gaussian or top-hat beam profile. In some instances, the shaping step may include using the focusing element (e.g., a lens) to form the waist of the laser beam at a focal distance of at least 25 mm (e.g., up to 135 mm). The method may also include turning a laser beam using a turning mirror disposed within a handpiece assembly. In some instances, the handpiece assembly is disposed downstream from the focusing element. In other instances, the focusing element is disposed within the handpiece assembly. In certain instances, providing the laser beam from the laser source includes adjusting a diameter of the laser beam (e.g., within a range from 0.06 mm up to 5 mm) based at least in part on the waist and a focal length of the focusing element.

[0015] In general, in another aspect, embodiments of the disclosure feature a dental laser treatment system that includes a laser source providing a laser beam having a waist, a focus element including at least one lens to provide a focal distance for the laser beam, and a beam guidance system including at least one galvanometer located between the laser source and the focus element. The waist may be in the range of 50 μιη to 500 μιη and be present at the focal distance. The laser beam may have a wavelength in the range of 9 μιη to 10 μιη. The laser beam may provide a depth of treatment of at least 5 mm and centered about the waist. In some cases, the depth of treatment has an energy density of at least a minimum energy density required to perform treatment upon dental tissue.

[0016] In various embodiments, the laser beam may have a Gaussian or a top-hat beam profile. The dental laser treatment system may further include a handpiece assembly disposed between the focus element and the depth of treatment. In some instances, the dental laser treatment system may also include a turning mirror disposed within the handpiece assembly, for example, between the focus element and the depth of treatment.

[0017] In general, in another aspect, embodiments of the disclosure feature a dental laser treatment system that includes a laser source providing a laser beam having a waist and a focal distance, and a depth of treatment centered about the waist. The laser beam may include pulses having a duration greater than 50 μ8. The depth of treatment may have an energy density of at least a minimum energy density required to perform treatment upon hard dental tissue. In some cases, the depth of treatment in combination with the focal distance permit laser dental treatment to be performed without the need for standoff distance regulation interdisposed between the dental laser treatment system and the dental tissue. [0018] In various embodiments, the laser beam may have a Gaussian or a top-hat beam profile. The dental laser treatment system may include a system for cooling material within the depth of treatment. The system for cooling material may include fluid (e.g., water or water mist) delivered to the material within the depth of treatment. In some instances, the dental laser treatment system also includes a handpiece assembly, where the fluid is delivered to the material through the handpiece assembly. In some cases, the waist may be in the range of 50 μιη to 500 μιη. The laser beam may have a wavelength in the range of 9 μιη to 12 μιη. In certain implementations, the dental laser treatment system includes at least one focus element that provides a focal distance (e.g., at least 25 mm, e.g., up to 135 mm) for the laser beam. In some cases, the waist is present at the focal distance. In certain implementations, the dental laser treatment system also includes a beam guidance system, which may be located between the laser source and the focus element. In some instances, the handpiece assembly may be disposed between the focus element the depth of treatment. The focus element may include at least one lens. The beam guidance system may include at least one galvanometer. In certain implementations, the dental laser treatment system may feature a turning mirror disposed within the handpiece assembly, in which the turning mirror is disposed between the focus element and the depth of treatment.

[0019] In general, in another aspect, embodiments of the disclosure feature a dental laser treatment system that includes a laser source providing a laser beam having a waist and a focal distance, a focal element including at least one lens, and a beam guidance system including at least one galvanometer. The waist may be in a range of 50 μιη to 500 μιη. The laser beam may have a wavelength in a range of 9 μιη to 10 μιη. In some instances, the laser beam includes pulses having a duration of approximately 50 μ8. In some instances, the focal element provides a focal distance for the laser beam, in which the waist is present at the focal distance, and the depth of treatment is centered about the waist. The beam guidance system may be located between the laser source and the focus element. The depth of treatment may have an energy density of at least a minimum energy density required to perform treatment upon dental tissue. In certain implementations, the depth of treatment in combination with the focal distance and/or the pulses permit laser dental treatment to be performed without the need for a standoff distance regulation interdisposed between the dental laser treatment system and the dental tissue. [0020] In various embodiments, the laser beam may have a Gaussian or a top-hat beam profile. The dental laser treatment system may also include a system for cooling material within the depth of treatment. The system for cooling may include fluid (e.g., water or water mist) delivered to the material within the depth of treatment. In some instances, the laser dental treatment system may also include a handpiece assembly, in which fluid is delivered to the material through the handpiece assembly. The handpiece assembly may be disposed between the focus element and the depth of treatment. In some cases, a turning mirror is disposed within the handpiece assembly between the focus element and the depth of treatment. BRIEF DESCRIPTION OF THE FIGURES

[0021] Various aspects this disclosure will become more apparent in view of the attached drawings and accompanying detailed description. The embodiments depicted therein are provided by way of example, not by way of limitation, wherein like reference numerals generally refer to the same or similar elements. In different drawings, the same or similar elements may be referenced using different reference numerals. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating aspects of the invention. In the drawings:

[0022] FIG. 1 schematically depicts the waist of a laser beam and depth of treatment regions, according to various embodiments;

[0023] FIGS. 2A-2C depict three different laser waists and depth of treatment regions, according to various embodiments;

[0024] FIG. 3 is a depiction of a laser beam path and a resultant beam waist and depth of treatment, according to various embodiments;

[0025] FIG. 4 depicts a portion of a laser beam handpiece/main chamber assembly and a depth of treatment, according to various embodiments;

[0026] FIG. 5 is a chart showing example minimum, maximum, and nominal operating parameters of a laser system, according to various embodiments;

[0027] FIG. 6 is a schematic graph showing an example laser pulse train including both a signal pulse and a laser pulse, according to various embodiments;

[0028] FIG. 7 depicts a Gaussian beam profile and a top-hat beam profile that may be used for treatment, according to various embodiments; and [0029] FIG. 8 is a chart showing example values of laser pulse width, energy per pulse, and corresponding temperature rises in hard dental tissue, according to various embodiments.

DETAILED DESCRIPTION

[0030] FIG. 1 shows a portion of an example laser beam 12 that is generated in various embodiments. The laser beam 12 has a waist 14 having a diameter of 2ω ₀ . The area of the waist 14 is Ao, where Ao = πω ₀ ² , and the area at a point n along the laser beam 12 is A _n = πω _η ² . For a pulsed laser beam, the energy per pulse is described as E and the fluence or the energy density is described as F. Thus, the fluence at any given point n along the laser beam 12 is F _n = E/A _n . The fluence threshold 15, or the required minimum energy density of the laser beam 12 for a particular dental treatment is FT. For ablative treatments the treatment threshold is equal to the minimum energy density needed for ablation of dental tissue. In some embodiments, a sub- ablative operation may be performed on the dental hard tissue in which the temperature of the surface of the enamel is increased by about 400° C, so as to remove carbonate therefrom.

Carbonate removal may occur in enamel with a 9.3 μιη laser having a fluence typically between 0.5-5 J/cm ² . Due to carbonate removal, the tooth can become more resistant to formation of caries. The fluence threshold 15 or FT is generally determined by the waist 14 diameter 2ω ₀ , a distance from the waist along the beam, the energy per pulse E, the absorption of the laser energy by the material being treated, and the treatment to be performed. The absorption of the laser energy is a function of the wavelength of the laser beam 12 and of the material being treated. For absorption of laser energy in dental hard tissue the wavelength range is generally from about 9 μιη to about 12 μη , e.g., about 9.3 μιη to about 9.6 μιη.

[0031] In general, the farther the point n is from the waist 14, the larger ω _η will generally be. As ω _η increases, F _n decreases. This occurs in both directions from the waist 14. Thus, on either side of the waist 14, typically there exists a point where F _n = FT, with the beam diameter 2ω _η . As such, any further increase in the beam diameter may fail to treat dental tissue at the given energy per pulse of the laser beam 12. A depth of treatment 16 can thus be described as the distance between the two points, one on each side of the waist 14, at which the fluence is approximately equal to FT. The depth of treatment 16 is typically centered around the waist 14.

[0032] The size of the waist 14 can have a strong effect on the depth of treatment 16. With reference to FIGS. 2A-2C, for a given level of E, a moderate waist 14 (shown, e.g., in FIG. 2A) with a low beam taper can maximize the depth of treatment 16. A smaller waist 14 (shown, e.g., in FIG. 2B), although providing a higher F at the waist 14, in combination with a higher beam taper may result in a greater rate of increase in ω _η and, thus, may result in a smaller depth of treatment 16. A larger waist 14 (shown, e.g., in FIG. 2C), no matter how low the beam taper, generally yields an energy density below the fluence threshold 15 generally required for treatment of hard dental tissue. While the waist 14 is the minimum beam diameter, the actual beam diameter at the point of contact on the treatment surface is generally called the spot size. Spot sizes less than 50 μιη typically can be formed with a relatively short a depth of treatment 16, while spot sizes larger than 1000 μιη typically do not have enough fluence even at longer pulse widths.

[0033] With reference to FIG. 3, in various embodiments an example dental laser treatment system 10 includes a laser beam 12 provided by a laser source 1 1 that follows a path formed by a beam guidance system 18. In some embodiments, the beam guidance system 18 includes two galvanometer mirrors 20 driven by galvanometer actuators 22, and a focusing element 24. In various other embodiments, any other beam guidance devices, e.g., optical fibers, waveguides, etc. can be used. Generally, one or more lenses form at least one focusing element 24. The laser source 1 1 generally outputs the laser beam that is subsequently transmitted through an articulated arm, one or more fiber optic cables, a combination of an articulated arm and one or more fiber optic cables, or any other devices for transmitting a laser beam over a distance.

[0034] The distance from the focusing element 24 to the waist 14 is referred to as the focal distance 28. In some embodiments, the focusing element 24 is located between the beam guidance system 18 and the waist 14, and the beam guidance system 18 may be located between the laser source and the focusing element 24. The laser source 11 and/or the focusing element 24 are configured such that a waist 14 having a diameter in the range from about 50 μιη up to about 500 μιη can be formed. In various instances, the waist 14 diameter may be, e.g., 50 μιη, 75 μιη, 100 μιη, 150 μιη, 200 μιη, 250 μιη, 300 μιη, 350 μιη, 400 μιη, 450 μιη, 500 μιη, etc. In order to have a low enough beam taper so as to provide a suitable depth of treatment 16 of about 5 mm or more, the focal distance 28 in some embodiments is at least about 25 mm. For example, the focal distance 28 may be, e.g., 25mm, 35mm, 45mm, 55 mm, 65 mm, 75 mm, 85 mm, 95 mm, 105 mm, 120 mm, 135 mm, 150 mm, 165mm, 175 mm, 185 mm, 200 mm, etc. With a proper selection of focal distance 28, waist 14 diameter, laser wavelength, and energy per pulse, a depth of treatment 16 of at least about 5 mm, 10 mm, 15 mm, 20 mm, 25 mm, 30 mm, 35 mm, 40 mm, 45 mm, or even 50 mm can be achieved. In some instances, as shown for example in the embodiment of FIG. 3, the focal distance 28 and the depth of treatment 16 are approximately equal.

[0035] With reference to FIG. 4, in some embodiments a handpiece/main chamber assembly 26 is configured for directing the laser beam 12 to treat a hard tissue, e.g., portion of a tooth 30. The handpiece portion of the handpiece/main chamber assembly 26 is disposed downstream from the focusing element 24 (which is located within the main chamber). Optionally, the handpiece/main chamber assembly 26 may contain a turning mirror (not shown) that is disposed downstream from the focusing element 24 and that guides the laser beam 12 at an angle to the main axis of the handpiece/main chamber assembly 26 in order to improve ergonomics. In some embodiments, the focusing element 24 is located within the handpiece.

[0036] When the example handpiece/main chamber assembly 26 is used, the focal distance 28 in one embodiment may be approximately 135 mm. At a wavelength of about 9.3 μιη and with a size of the beam incident upon the focusing element 24 of about 7 mm in diameter this focal distance can produce a waist of about 250 μιη. High fluence and a long focal distance 28 aid in providing a relatively large depth of treatment 16. One benefit of a large depth of treatment is the lack of need for any mechanical distance regulator between the laser system (generally the handpiece/main chamber assembly) and the dental tissue being treated. Conventional distance regulation devices may include gauges, scales, spacers, standoff devices, or any other means for regulating a distance between the dental laser treatment system and the dental surface to be treated. With a sufficiently large depth of treatment, laser dental treatment may be performed without any distance regulation, since the laser beam energy density remains at or above the fluence threshold despite the distance variations expected in using a manually controlled tool (e.g., caused by movements of a dentist's hand and/or patient's head/mouth).

[0037] Many laser-based treatment systems are configured to minimize wasted laser energy which, if not used for treatment, can cause damage to tissue portions that are not to be treated. To this end, various systems are configured such that laser-based ablation and/or other treatment occurs at a region where the laser beam is focused, e.g., at the waist of the laser beam. The focal region can be at a tissue surface or below the tissue surface, but the laser beam is generally targeted such that the desired treatment occurs at or very close to the focal region. Thus, if the focal region is at the tissue surface, the treatment generally occurs at the tissue surface. If the focal region is below the tissue surface, the treatment may occur beneath the tissue surface. Such systems are often described as "optically fast" systems. [0038] In "optically fast" systems, a focusing optic having a relatively short focal length (e.g., 5 mm, 10 mm, 12 mm, 15 mm, etc.), is used to taper a laser beam over a relatively short beam- propagation distance so as to concentrate the energy thereof within the focal region. If an operator intentionally or inadvertently moves the beam-directing instrument, such as a handpiece, in a Z direction (i.e., a direction normal to tissue surface and along the beam), the tissue portion to be treated may no longer be at the focal region. As such, the tolerance of such systems in the Z direction is generally low, e.g., 1 mm, 0.5 mm, or even less. The standoff between the tip of the beam-directing instrument and the tissue surface is also relatively low, e.g., 2 mm, 5 mm, etc. Due to the short standoff, a slight movement of the beam-directing instrument, whether intentional or inadvertent, may cause the laser beam spot to move a relatively small distance in the X and/or Y directions along the tissue surface.

[0039] Unlike conventional "optically-fast" systems, various embodiments described herein feature optical subsystems that can be described as "optically slow" systems. FIG. 5 is a chart showing example minimum, maximum, and nominal values for various parameters of an example laser system described herein. Such "optically slow" systems include a focusing optic having a relatively long focal length, e.g., greater than about 25 mm and up to about 200 mm, e.g., 25 mm, 35 mm, 45 mm, 55 mm, 65 mm, 75 mm, 85 mm, 95 mm, 105 mm, 120 mm, 135 mm, 150 mm, 165 mm, 175 mm, 185 mm, 200 mm, etc., each limit having a tolerance of, e.g., 0.5%, 1%, 2%, 5%, 10%, 20%, etc. The standoff between the tip of the beam-directing instrument and the tissue surface may be, e.g., 0.1 mm, 1 mm, 5 mm, 10 mm, 15 mm, 20 mm, 30 mm, 40 mm, 50 mm, etc. In instances in which the standoff is relatively large, a small angular movement of the instrument that can cause the laser-beam spot to move in X and/or Y directions along the tissue surface can cause a relatively large movement of the beam spot, e.g., by 0.2 mm, 0.5 mm, 1 mm, or more. To minimize the risk that the laser beam is directed to a portion of the tissue not to be treated due to such X and/or Y direction movement, various embodiments of this disclosure include an automated, feedback-controlled beam-guidance system for scanning a region of the tissue to be treated. The operator thus need not manually move the beam-directing instrument to move the beam in the X and/or Y directions.

[0040] Moreover, in various embodiments, the focus element 24 can taper a laser beam over a relatively long propagation distance so as to concentrate the energy thereof within the focal region. In various embodiments, the taper angle relative to a normal to the tissue surface may be, e.g., 0.5°, 0.75°, 1°, 1.25°, 1.75°, 2°, 5°, 7°, 10°, etc. Due to this, the depth of treatment 16 (e.g., a distance in a Z direction about the beam waist 14 at which the fluence is effective for treatment (e.g., ablation, removal of carbonate, etc.) may be, e.g., 5 mm, 10 mm, 15 mm, 20 mm, 25 mm, 30 mm, 35 mm, 40 mm, 45 mm, 50 mm, etc., with a tolerance of, e.g., 0.5%, 1%, 5%, 10%, 20%, etc. In such systems, the fluence at the waist 14 may be, e.g., 10 J/cm ² , 12 J/cm ² , 15 J/cm ² , 20 J/cm ² , 25 J/cm ² , 30 J/cm ² , 40 J/cm ² , 50 J/cm ² , etc. The fluence at the extremes of the depth of treatment 16 (F _T ) may be, e.g., 5 J/cm ² , 7 J/cm ² , 10 J/cm ² , 12 J/cm ² , 15 J/cm ² , 17 J/cm ² , 20 J/cm ² , etc. Therefore, various embodiments allow for a greater tolerance of about 5 mm up to about 15 mm in the movement of the beam-directing instrument in the Z direction, whether such movement is inadvertent or intentional. In various instances, the spot size generated by such systems may be, e.g., 50 μιη, 75 μιη, 100 μιη, 150 μιη, 200 μιη, 250 μιη, 300 μιη, 350 μιη, 400 μιη, 450 μιη, 500 μιη, 600 μιη, 700 μιη, 800 μιη, 900 μιη, 1000 μιη, etc.

[0041] In general, the diameter of the laser beam that is incident upon a focusing element also affects the diameter of the waist (the spot size at the focal distance from the focusing element). The relationship between the diameter of the incident beam and the waist diameter is generally given by:

M ²

waist diameter = 1.27 * f * wavelength *—

where /is the focal length of the beam- focusing element, M is a constant associated with the beam profile (such as Gaussian, top hat, etc.), and D is the diameter of the incident beam. Thus, for a laser having a certain wavelength (e.g., 9.3 μιη, 9.6 μιη, etc.) and a beam profile, a beam having a suitable waist diameter can be formed by controlling the focal length / of the focusing element and/or diameter D of the incident beam. For a specified focal length the waist diameter (also called the waist) is inversely proportional to the incident-beam diameter Ζλ

[0042] In various embodiments, the waist diameter is selected such that the fluence per pulse at the waist and at any cross-section of the laser beam within the depth of treatment is adequate for the selected treatment such as ablation of dental hard tissue, a subablative treatment such as removal of carbonate from enamel, etc. To this end, in some embodiments, initially the wavelength of the laser, the beam profile, and focal length / of the focusing element are selected. In order to provide a waist diameter within a suitable range, e.g., from about 50 μιη up to about 500 μιη, the laser is configured to transmit to the focusing element a laser beam having a suitable diameter. If such a beam is not provided, the selected waist diameters and spot sizes within the depth of treatment may not be achieved.

[0043] To illustrate, if a focusing element having a focal length of 25 mm is used, to achieve a waist diameter of 50 μιη, the laser is configured to provide a beam having a diameter of about 0.6 mm. To achieve waist diameters of 250 μιη and 500 μιη, however, the laser is configured to provide beams having diameters of about 0.6 mm and 0.06 mm, respectively. If a focusing element having a focal length of 200 mm is used instead, to achieve a waist diameter of 50 μιη, the laser is configured to provide a beam having a diameter of about 5 mm. To achieve waist diameters of 250 μιη and 500 μιη, the laser is configured to provide beams having diameters of about 0.95 mm and 0.48 mm, respectively.

[0044] In general, if a laser beam having a specified diameter is incident upon a focusing element having a short focus (e.g., less than 25 mm), the waist diameter, which is directly proportional to the focal length, would be relatively small compared to a waist diameter obtained if the same laser beam is directed to a focusing element having a longer focal length (e.g., about 25 mm or more). As such, the taper angle of the beam output from a focusing element having a longer focus would be less than the taper angle produced by a focusing element having a shorter focus. As described above, the smaller taper angle can result in an optically slow system having a relatively greater depth of treatment than an optically fast system. The values of focal length and waist or waist diameter described herein are within a tolerance of, e.g., 0.05%, 0.1%, 1%, 2%, 5%, 10%, 20%, etc.

[0045] FIG. 6 shows an example pulse train according to various embodiments, which includes both a signal pulse 40 and a laser pulse 42 (e.g., a CO ₂ laser pulse). The signal pulse 40 may be a TTY trigger signal. The laser pulse 42 can have shape similar to that of a shark fin and has an ignition delay after the start of the signal pulse. The pulse width (X) 44 and pulse height (Y) 46 of the trigger signal are shown, and may be used to describe the laser pulse. One pulse cycle (R) 48 is also shown, the duration of which together with the pulse ON duration 44 can describe a distance/spacing between two consecutive pulses. Unless operated in a continuous wave mode, a pulse cycle includes ON and OFF durations. The number of pulse cycles 48 in one second represents the pulse repetition rate. In various instances, the pulse ON duration 44 may be, e.g., 5 μ8, 10 μ8, 15 μ8, 20 μ8, 25 μ8, 30 μδ, 40 μ8, 50 μ8, 60 μδ, 70 μ8, 80 μ8, 90 μδ, 100 μ8, 125 μ8, 150 μδ, 175 μ8, 200 μ8, 250 μδ, 300 μ8, etc. In various instances, the pulse cycle period may be, e.g., 30 μ8, 40 μ8, 50 μ8, 100 μδ, 200 μ8, 300 μ8, 500 μδ, 750 μ8, 1000 μ8, 2000 μ8, 5000 μ8, 10,000 μ8, 15,000 μ8, 20,000 μ8, etc. In various instances, the duty cycle (described as a ratio of pulse ON duration to pulse cycle period) may be, e.g., 1%, 5%, 10%, 20%, 30%, 40%, 50%, etc.

[0046] In some embodiments, pulsed lasers emit laser optical energy in bursts of photons. The bursts of photons, or pulses, can be structured into a pulse train. The pulses are typically described in terms of by pulse width, pulse height, and/or pulse energy. The pulse width can represent the pulse ON duration or the pulse cycle period. The pulse train is typically described in terms of the repetition rate or pulse frequency, i.e., a frequency of the bursts of photons. Only certain pulse trains, described by the pulse width, height, and repetition rate, can cut dental tissue, especially dental hard tissue, safely and effectively. Dental hard tissue may include oral osseous tissue as well as the tissue of teeth. The need to have enough energy to exceed the dental tissue's ablation threshold, and not too much energy so as to avoid adverse surface thermal modification, limits the possible combinations of useful laser parameters including pulse and pulse-train parameters. The combination of useful laser parameters are sets of laser parameters that, when used in combination, can result in safe and effective treatment of dental tissue. The laser parameters include pulse shape, pulse width, pulse height, and/or repetition rate. The pulse width and height affect the amount of energy per pulse, and the repetition rate affects the amount of power delivered over time. Additionally, the dental tissue may be cooled to allow for greater pulse energies to be used that, without cooling, may cause thermal shock and may damage the dental tissue. The use of cooling can thus increase the energy that may be safely and effectively directed to the dental tissue per pulse.

[0047] Variation of the pulse shape parameters can result in changes in the pulse energy.

Variation of the repetition rate can result in changes in laser power. The energy per pulse typically affects surface characteristics and can result in cracking or asperities when the energy per pulse is too great. Asperities may be formed by the melting of enamel and/or dentin and the associated mineral modification from a ceramic transitioning to a salt phase. The power delivered over time to the tooth, when too great, may result in pulpal heating. If the temperature of the pulp of the tooth increased by about 5°C there is a chance that the pulp will be damaged and that the tooth may be damaged permanently. In general, the dental tissue is insulating, however, and usually limits the temperature increase in the pulp, even when the tooth surface temperatures are relatively high. Additionally, cooling the tooth surface may reduce the amount of heat conducted into the tooth and may further limit any increase in the pulp temperature.

[0048] These thermal insulating properties are generally dependent upon the thickness of the tooth between the tooth's surface and its pulp chamber. Therefore, as the tooth surface is worn or removed, the tooth's thermal insulating properties generally have a reduced effect. Pulse energies therefore typically have to be decreased as the tooth tissue thickness to the pulpal chamber decreases. A reduction of tooth thickness, often resulting from wear, erosion, clinical removal, etc., can change the pulse shapes and repetition rates that may be used safely and effectively. As such, in various embodiments, an objective of avoiding undesirable surface modifications and excessive heating of the pulp of the tooth can determine a group of pulse shapes and repetition rates that are safe and practical, or a combination of useful laser parameters. The range of safe and effective laser pulse shapes and repetition rates can be broadened by cooling of the tooth surface and by the insulating properties of teeth.

[0049] With reference to FIG. 7, two different example beam profiles in a single laser axis, X, are shown. The laser beam propagates in a direction normal to the X axis. A Gaussian beam profile 50 has a bell shaped beam profile. A top-hat beam profile 52 is shaped like a square wave. A waist may be defined by a number of standard techniques including: D4o, 10/90 or 20/80 knife-edge, l/e2, full width half maximum (FWHM), and D86. A person of ordinary skill in the art understands the definition and use of these techniques and, as such, use of these techniques is within the scope of various embodiments of this disclosure. The Gaussian beam profile 50 can provide maximum energy at the center of the waist. A near-Gaussian beam profile closely resembles a Gaussian beam profile without being purely Gaussian in shape. The Gaussian beam profile or near-Gaussian beam profiles are typically generated using standard spherical optics and lasers. The top-hat beam profile can be generated using diffractive optics. Diffractive optics for producing a top-hat beam profile are typically designed for each specific application. Near-top-hat beam profiles may be generated using beam homogenizers and lenses. The top-hat beam profile 52 can uniformly provide energy throughout the waist. This may allow the top-hat and near-top-hat beam profiles to be well suited for treatments that do not require a threshold fluence that can only be obtained using a Gaussian or near-Gaussian profile, but can benefit from a substantially even fluence throughout the beam spot. Unlike typical ablative treatments, some laser treatments require that the fluence be within a treatment fluence range, a lower bound of which is greater than (or at least equal to) a lower treatment threshold, and an upper bound of which is smaller than (or at most equal to) a higher treatment threshold. The top-hat beam profile may be used for these treatments to ensure that energy directed to a region of dental tissue is within a selected treatment fluence range. In other embodiments, other beam profiles known in the art may be used (e.g., a donut beam profile).

[0050] FIG. 8 shows example effects of laser pulse width and energy per pulse on the temperature of dental hard tissue (e.g., enamel). Pulse durations greater than 50 μ$ are longer than those typically used for ablative treatment using 9.3 μιη or 9.6 μιη lasers. In some instances, pulse durations significantly greater than the thermal relaxation time of the dental hard tissue can result in heat accumulation, which can damage the pulp of the tooth. These longer pulse durations can also result in poor surface morphology, cracking, and/or asperities. By employing cooling of the dental tissue, however, heat buildup and surface damage can be avoided or at least mitigated, and longer pulse durations can be safely used. For cooling dental tissue, fluid can be delivered to the dental tissue to be treated, and a handpiece/main chamber assembly may provide a subsystem for delivering the fluid/coolant. U.S. Patent Application No. 2013/0323675, describes examples of such cooling systems and methods and is incorporated herein by reference in its entirety. In some instances, the coolant fluid is water or a water mist. Pulse durations that are greater than 50 μ$ can, in some cases, provide greater energy per pulse (E), and thus allow for a greater depth of treatment 16.

[0051] The terms and expressions employed herein are used as terms and expressions of description and not of limitation, and there is no intention, in the use of such terms and expressions, of excluding any equivalents of the features shown and described or portions thereof. In addition, having described certain embodiments of the invention, it will be apparent to those of ordinary skill in the art that other embodiments incorporating the concepts disclosed herein may be used without departing from the spirit and scope of the invention. The structural features and operational functions of the various embodiments may be arranged in various combinations and permutations, and all are considered to be within the scope of the disclosed invention. Accordingly, the described embodiments are to be considered in all respects as only illustrative and not restrictive. Furthermore, the configurations, materials, and dimensions described herein are intended as illustrative and in no way limiting. Similarly, although physical explanations have been provided for explanatory purposes, there is no intent to be bound by any particular theory or mechanism, or to limit the claims in accordance therewith.