Abstract:
A waveguide retroreflector consists of an end cap with curved output surface attached to a waveguide such as optical fiber. The radius of curvature of the output surface of the end cap matches the length of the end cap so as to retro-reflect a substantial portion of radiation exiting the waveguide, back into the waveguide. A method of fabricating the waveguide retroreflector includes steps of splicing an end cap to a waveguide, heating the free flat surface of the end cap, so that surface tension changes the shape of the end cap to a convex shape due to surface tension, monitoring amount of light reflected off the surface being heated, and stopping applying the heat when the amount of the reflected light approaches a maximum value.

Description:
FIELD OF THE INVENTION 
   The invention relates to fiber lasers, and more specifically, to fiber laser cavity mirrors that provide a region for beam expansion, as well as a surface for retroreflection of at least a portion of the laser radiation. 
   BACKGROUND OF THE INVENTION 
   A fiber laser resonator cavity has a reflector at each end of a length of an optical fiber that includes a doped core surrounded by one or more cladding layers. Generally, one reflector is a high reflector, having a reflectivity of close to 100% at the lasing wavelength, and the other reflector serves as the output coupler and typically has a reflectivity between 0.5% and 50% at the lasing wavelength. Reflectors can be formed by simply cleaving or polishing the ends of the fiber near perpendicular to the fiber axis and, if necessary, applying a coating to achieve a desired reflectivity. In most fiber lasers the desired output-coupler reflectivity is in the 1-10% range. The precise value has insignificant impact on the fiber laser performance; therefore, one very inexpensive, robust, and frequently-used option for the output coupler is to utilize the normal-incidence Fresnel reflectivity of the uncoated surface of around 4%, depending upon the refractive index of the fiber core. 
   In fiber lasers operating at high average power or high peak power, it can be deleterious for the unexpanded beam from the fiber core to impinge directly on the fiber end surface, whether coated or uncoated. Most often, the fiber core has a diameter between 5 microns and 30 microns, with a correspondingly small surface area; therefore at power levels of hundreds of Watts, the power density can approach 1 GW/cm 2 , which is near the damage threshold of most fiber materials such as silica, particularly in the event of any slight surface imperfection or contamination. 
   A common technique to reduce this high power density at a fiber end is to splice a short length of coreless fiber or rod onto the fiber end. Such a short length of fiber or rod is often referred to as a fiber end cap or a beam expander. In operation a beam emitted from the fiber core, upon entering the end cap, ceases to be confined and expands as it traverses the end cap, exiting through the end cap surface with an increased beam diameter and correspondingly lower power density. Typically the end cap is 0.1-5 millimeters long and increases the beam diameter up to 50-300 microns. Since the power density scales as the inverse square of the beam diameter, a 5-10 times increase in diameter will lower the power density by a factor of 25-100 times, greatly improving the reliability of the fiber tip. 
   In order to operate a fiber laser at high power levels with one or more fiber-end reflectors, either coated or uncoated, it would be desirable to incorporate a fiber end cap into the fiber end in order to reduce the power density. However, it is neither sufficient nor practicable to simply attach a conventional end cap to a reflective flat output surface. Indeed, the reflected light in this case would continue to expand as it passes back through the end cap, and the beam would not be coupled efficiently back into the fiber core. 
   For example, if for an output coupler end cap, a 10% reflective surface is used with 5% coupling efficiency, then 0.5% of the light incident on the end cap surface will be reflected and fed back into the oscillator, 9.5% of the light will be reflected and lost, and 90% of the light will be transmitted. For typical applications, the coupled fraction of the backreflected light should be at least 4-5%, otherwise the system would have insufficient feedback. Thus, the application of prior art end caps as output couplers for a high power fiber laser is inefficient resulting in a considerable amount of wasted light and poorly controlled lasing due to insufficient feedback. 
   An external bulk optic mirror can be used as an output coupler in a fiber laser. However, such a mirror has to be aligned with a high precision in angular, as well as in linear sense; moreover, the high accuracy of alignment would have to be maintained over the operational temperature range of the laser. A high degree of alignment stability is difficult to achieve, especially in high power lasers which generate large temperature gradients during normal operation. Moreover, when an external output coupler, such as an external concave mirror, is used for providing feedback into the fiber laser, there is an additional interface that the light has to go through in order to reflect off that external coupler and couple back into the fiber. Such an interface would exhibit a potential point of failure due to high optical power densities at the interface as has been explained above. Therefore, it is preferable that an output coupler of a fiber laser has no air gaps, or voids, for the laser light to go through in its way from the fiber core towards the output coupler reflective surface; ideally, the output coupler would have to be bonded to the fiber directly, such that the laser light does not encounter a significant change of the index of refraction as it travels from the fiber core and towards the output coupler reflective surface. 
   Further, in some of prior art applications of beam expanders, an output surface of an end cap is sometimes lensed, so as to collimate the output beam exiting a fiber. However, such a fiber collimator is not practical as an output coupler because, in order for a lensed surface to collimate a diverging optical beam through refraction, a nonzero, or non-normal angle of incidence of a ray onto said surface is required; therefore, a ray reflected off such a surface would be deviated from going back, such that the entire reflected beam would be defocused upon retroreflection and, therefore, would not couple back into fiber with a required efficiency. 
   It is an object of this invention to provide a monolithic end cap that will ensure that a sufficient fraction of the radiation reflected from the output surface of the end cap is coupled back into the fiber core. 
   It is also an object of the invention to provide an end cap with an efficiency that would couple at least 50% of the backreflected light back into the fiber core. This high coupling efficiency is achieved without having to rely on often difficult and tedious alignment of external optical elements. Prior to this invention, it would have been very difficult to achieve the required precision in transverse, longitudinal, and angular alignment of an external bulk optic mirror to achieve efficient coupling of the reflected light back into the laser core. 
   It is also an object of the invention to provide a method which incorporates an efficient reflector onto the end surfaces of a fiber end cap using conventional equipment in a novel way. 
   The method, which will be described in more detail below, has additional benefit of yielding a surface that is extremely clean and free of micro-cracks and other defects typical of a surface prepared by conventional processes such as polishing or cleaving. 
   SUMMARY OF THE INVENTION 
   In accordance with the invention there is provided a waveguide retroreflector, comprising: 
   an optical waveguide having an end face; 
   an optical element bonded to said optical waveguide end face, 
   wherein the optical element is substantially free of voids and/or air spaces in a light transmitting region thereof, 
   wherein said light transmitting region of the optical element has a length along a direction of light propagation in said region; 
   wherein the optical element has a convex end face having a radius of curvature at an end of the light transmitting region; 
   wherein said radius of curvature is between 80% and 120% of the length of the light transmitting region of the optical element, such that at least 5% of a light reflected from said convex end face is coupled back into the optical waveguide. 
   In accordance with the invention there is further provided a method for fabricating a waveguide retroreflector, comprising: 
   providing an end cap affixed to an optical waveguide, wherein said end cap contains substantially homogeneous material, wherein said end cap has a length between two first and second opposing and substantially flat end faces, and wherein the first end face is fused to an end of said waveguide; 
   irradiating a second end of the waveguide with light such that the light is transmitted by the waveguide into the end cap; 
   measuring a fraction of said light reflected from the second end face of the end cap and coupled back into the waveguide; 
   applying sufficient amount of heat to said second end face, so that surface tension changes the shape of the flat second end face so as to form a convex shaped end having a radius of curvature; 
   repeating steps c) and d) until the radius of curvature of said convex shape becomes between 80% and 120% of the length of the end cap; 
   g) wherein proximity of said radius of curvature to said length of the end cap is determined from the value of said fraction of light, as compared to a maximum value of said fraction of light. 
   In accordance with another aspect of the invention there is provided a fiber laser resonator cavity, comprising: 
   an optical waveguide, having: first, an active section, and second, an end face; 
   an optical element bonded to said end face of the optical waveguide; 
   wherein the optical element is substantially free of voids and/or air spaces in a light transmitting region thereof; 
   wherein the optical element has an end face located at an end of the light transmitting region; 
   wherein said end face of the optical element is shaped to be perpendicular to the ray fan of a light emitted by the active section of the optical waveguide, said light impinging onto the end face of the optical element after having passed through the light transmitting region thereof. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Exemplary embodiments of the invention will now be described in accordance with the drawings, in which: 
       FIGS. 1A and 1B  are schematic views of a prior-art fiber laser resonator cavity, wherein  FIG. 1A  is a cross section taken along the line A-A through  FIG. 1B ; 
       FIG. 2  is a schematic view of a prior-art fiber end cap; 
       FIG. 3A  is a schematic view of beam propagation and retroreflection in a prior-art fiber end cap with flat output surface; 
       FIG. 3B  is a schematic view of beam propagation and retroreflection in a prior art end-cap beam collimator; 
       FIG. 4A  is a schematic view of waveguide retroreflector of present invention; 
       FIG. 4B  is a diagram for illustrating relationship between length and radius of curvature of output surface of the waveguide retroreflector of present invention; 
       FIG. 5  is a block diagram illustrating a method of fabrication of said waveguide retroreflector. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Referring to  FIG. 1A  a prior art optical fiber, having a core  102  and cladding  104 , is shown.  FIG. 1A  is a cross section taken along the line A-A through  FIG. 1B . 
   Referring to  FIG. 1B  a prior art fiber laser cavity is shown wherein an optical fiber  100  is cleaved at ends  106  and  108 . A high reflector coating  110  is applied to the end  106 , and the end  108  is left uncoated. 
   Referring to  FIG. 2  a prior art fiber end cap is shown consisting of a fiber section  200  and end cap section  206 . The fiber section  200  consists of a fiber core  202  and fiber cladding  204 . An expanding optical beam  208  propagates inside the end cap section  206 . In operation, the optical beam  208  exits the end cap section  206  and continues to propagate in free space, as is schematically illustrated by arrows  210 . 
     FIG. 3A  illustrates a prior art fiber laser output coupler consisting of a fiber section  300  and an end cap section  306 . The fiber section  300  consists of fiber core  302  and fiber cladding  304 . An expanding optical beam  308  propagates inside the end cap section  306 . The optical beam  308  splits at the end of the end cap section  306  into outwards propagating beam  310  and retroreflected diverging beam  312 . 
   In  FIG. 3B  a prior art fiber collimator is shown wherein a fiber section  300  consists of fiber core  302  and fiber cladding  304 . An end cap section  306  contains an expanding optical beam  308 . The optical beam  308  splits at the end of the end cap section  306  into outwards propagating collimated beam, represented by parallel lines  310 , and quickly converging retroreflected beam  312  which propagates through intermediate focus  314  and diverges before reaching fiber section  300 . 
   Turning now to  FIG. 4A  a waveguide retroreflector of the present invention is shown having a waveguide section  400  and end cap section  406 . The waveguide section  400  has a core  402  and cladding  404 . In operation, an expanding optical beam  408  propagates inside the end cap section  406 . The sections  400  and  406  can be bonded together using a variety of methods, such as splicing, fusing, glass soldering, epoxying, optical contacting, or other methods known to those skilled in the art. Whichever method of bonding is used, it is important that sections  400  and  406  are joined directly, i.e. without a spacer or other external structure leaving an air gap in the light transmitting region between sections  400  and  406 . Fusing is a preferable bonding method because of its high yield, low cost, and lack of external bonding materials such as epoxy or glass solder, in the light transmitting region between sections  400  and  406 . 
   During normal operation, the optical beam propagating within the waveguide  400  splits at the convex end surface  409  of the end cap section  406  into the outwards propagating beam  410  and the retroreflected converging beam  412 , such that a sufficient fraction of the reflected radiation, for example at least 5%, is coupled back directly into the fiber core. The curved convex end surface  409  can be coated or uncoated, depending on whether the uncoated reflectivity of about 4% is adequate for the user&#39;s needs. 
   By way of example, using typical values, if the fiber core  402  has a diameter of 15 microns and a numerical aperture (NA) of 0.07, and the laser wavelength is 1.1 microns, it can be calculated that a 1.5 mm long fused silica end cap  406  will expand the beam diameter from 15 microns to 98 microns. This represents an increase in cross-sectional area of 43×, which greatly improves the reliability of the end cap  406  as desired. In order to couple the laser beam efficiently back into the core  402 , the output surface of the end cap  406  should be approximately spherical with a radius of curvature slightly longer than the length of the end cap, specifically 1.54 mm. The precision of this radius of curvature relative to the end cap length must be +/−0.12 mm in order for the reflected beam to focus within one Rayleigh range of the fiber core, at which point approximately 50% of the reflected beam will overlap with the fiber core and can be coupled thereinto. By contrast, if a flat output surface is used, as is shown in prior art  FIG. 3A , the beam diameter will expand to 194 microns at the point where it returns to the fiber core  302 , and approximately 0.6% of the beam will overlap with the core  302  resulting in very poor coupling. 
   In order to couple the reflected light into the core efficiently, it is also important to control the centration (or equivalently the angular orientation) of the curved output surface  409 . The splice between the laser fiber  400  and the end cap  406  is one factor that will affect the centration of the output surface. This splice can typically be made with a centration of +/−1 micron, which will create a displacement of +/−2 microns in the reflected beam, and an angle of +/−1.5 milliradian, resulting in a displacement of +/−5 microns in the reflected beam. Since both of these displacements are small compared to the core diameter of 15 microns, it can be seen that current splicing technology is adequate to generate the desired high coupling efficiency. 
   The centration with which the curved output surface  409  is fabricated is similarly important. It is preferably centered to a precision of +/−4 microns or more in order to provide a displacement of +/−8 microns or more at the fiber core  402 , which is required for efficient coupling. Equivalently, the angular orientation is preferably controlled within +/−2.7 milliradian. In this manner, efficient coupling can be achieved. 
   Referring now to  FIG. 4B  a relationship between the length L of the end cap section  406  and radius of curvature R of the end cap output surface  409  is further illustrated, such that a critical difference from the prior art collimator, shown in  FIG. 3B , can be better understood. The waveguide section  400  consists of core  402  and cladding  404 . The expanding optical beam  408  propagates inside the end cap section  406 . The rays  414  of the beam  408 , when continued backwards as straight lines, originate from substantially the same point  416  as is symbolically shown by dashed lines  418 . The common point of origin  416  lies on axis of symmetry  418  of the end cap section  406 . The concave surface  409  is arranged to be substantially perpendicular to rays  414  of the beam  408 , such that, firstly, rays  414  will retrace backwards along their own respective paths, and secondly, substantially no refraction-caused deviation of output rays can occur. In order for the concave surface  409  to satisfy said requirement of perpendicularity to rays  414  over its area, it has to be spherical with center of the surface located at point  416 . Furthermore, as it follows from the near-Gaussian nature of the expanding beam  408 , the point  416 , from which all the rays originate when projected backwards, or to the left from surface  409  as straight lines  418 , is located close to the interface between waveguide section  400  and end cap section  406 . Thus, the radius of curvature R should be approximately equal to the length L of the end cap section  406 . In a preferred embodiment, the radius of curvature R differs from the length L by less than 20%, or 0.8L&lt;R&lt;1.2L. This 20% difference accounts mostly for manufacturing tolerances. 
   Referring now to  FIG. 5 , a system, or a kit, for making the waveguide backreflector of the present invention is shown wherein a light source  500  is coupled to the input port  502  of a splitting/combining element  504 . The function of said splitting/combining element  504  is to couple light from light source  500  into waveguide  506  through one of the two ends of the waveguide  506 . An end cap  508  is attached to the other end of the waveguide  506 . A light coupled into the waveguide  506  is reflected off the end surface  509  of the end cap  508 , propagates back through the waveguide  506  and splitting/combining element  504 , and is coupled, through its output port  510 , to a backreflection sensor  512 . The signal from the backreflection sensor  512  is applied to heating control circuit  514 . The function of heating control circuit  514  is to control a heating element  516  for heating the surface  509  of the end cap  508 . The dotted arrows  518  symbolize the heat provided by the heating element  516 .  FIG. 5  also shows optional filter  520  for rejecting thermal radiation generated by heated tip  509 . 
   Splicing is perhaps the most convenient way of attaching end cap  508  to fiber  506 . Preferably end cap  508  is a section of coreless fiber which is spliced onto the tip of the fiber  506  using techniques well established in the art. Further, this coreless fiber should preferably match the diameter of the glass cladding layer of the fiber  506  in order to ensure the good centration and angular alignment. Notwithstanding, with careful accurate splicing, or fusing, it is possible to get acceptable performance with mismatched fibers as well. 
   The coreless fiber is cleaved at normal incidence at the desired length of the end cap  508 . It is difficult to control the cleaved length precisely using current typical cleaving technology, wherein the cleave position can be controlled to about +/−0.1-0.2 mm. Because the length of the end cap  508  will not necessarily be known to within +/−0.12 mm, using the values from the above typical example, the radius of curvature of the output surface  509  will likely need to be individually tailored to the length of the end cap  508 . 
   The cleaving process generally provides an extremely flat and clean surface that can be aligned within 2 milliradians of normal to the fiber axis. The desired curved surface with a well controlled radius of curvature is formed by heating the end cap tip  509  until the material is softened sufficiently that surface tension causes the tip to become rounded. The heat, represented by arrows  518 , may be generated from a variety of sources including a flame, an arc, a laser, or an electric filament such as that used in fusion splicers manufactured by the Vytran Corporation of New Jersey. The heating should preferably be very uniform and well controlled, and it may be desirable for the fiber end cap  508  to be oriented vertically in order to avoid distortion of the softened tip  509  by gravity. Under these circumstances, surface tension generates a very precisely and uniformly curved end surface. 
   As the fiber end surface  509  is heated and softened and begins to take on a curved shape, increasing amounts of light reflected by the output surface  509  will be focused back into the fiber core, and the backreflected signal will be seen to increase. Eventually, when the radius of curvature of the output surface  509  approximately equals the length of end cap  508 , as explained above, a maximum amount of backreflection will be observed, and thereafter as the curvature of the end surface  509  continues to increase, the backreflected signal will begin to lessen. An algorithm for monitoring the backreflected signal and for controlling the heating element  516  may be provided; for example, the algorithm may control the turning off the heating element  516  as the backreflected signal approaches a desired level, which may equal the maximum level or any level less than the maximum. Note that the actual amount of curvature is very small; in the above example of a 1.5 mm long end cap  508 , if the outer diameter of the end cap  508  is 400 micron, then the amount of “sag” required at the edges relative to the center of the surface  509 , assuming a spherical shape of surface  509 , is only about 9 microns. Therefore very little softening of the glass is required, and the heating temperature will be moderate. 
   Preferably, the control software built into heating control circuit  514  should take into account that the fiber tip  509  will not cool instantly, and will therefore continue to deform briefly, after the heating element  516  is turned off. It can control for fiber-to-fiber variations, for example, in splice centration or end-tip angle, which would affect the lateral position of the focused reflection relative to the fiber core; these variations would manifest themselves in differing rates of increase of the reflected signal level as the tip  509  is heated, and the algorithm could take account of the measured rate in order to optimize the time at which to, for example, turn off the heating element  516 . A number of other variations of the heating algorithm can be provided; for instance, it may be desirable to cycle the heater  516  on and off repeatedly during the shaping of the fiber tip  509  in order to prevent it from heating too deeply or reaching too high a temperature. It is also important that the light source  500  and backreflection monitor system be designed with adequate signal-to-noise ratio; for example, the light source  500  should be of adequate power, and an optical filter  520  may be useful at the backreflection monitor, in order to overcome the infrared radiation generated by the heated fiber tip  509 .