Abstract:
An external cavity laser includes a lasing cavity and an optically coupled feedback cavity having differently spaced resonant lasing and feedback mode frequencies. The lasing modes can be collectively or individually matched to selected feedback modes. For example, a current driving the lasing cavity can be adjusted to shift individual lasing modes into alignment with the selected feedback modes.

Description:
FIELD OF INVENTION 
       [0001]    Tunable external cavity lasers include a lasing cavity having resonant modes for amplifying a range of beam frequencies and a feedback cavity optically coupled to the lasing cavity and having resonant modes subject to selection for tuning the beam frequency output of the lasers. 
       DESCRIPTION OF RELATED ART 
       [0002]    Light resonates within laser cavities between front and back surfaces in distinct frequency modes at which standing waves are produced by complete round trips taken by integer numbers of wavelengths between the surfaces. The potential for gain within the laser cavities varies as a distribution function of frequency, and the optical power tends to concentrate in the frequency mode experiencing the highest gain or, conversely, the lowest loss. Beyond encounters with a lasing medium within the laser cavities, most other encounters of the light within the laser cavities entail losses, and the mode frequency experiencing the lowest loss is generally the one most amplified by the laser. 
         [0003]    Frequency tuning of laser sources generally involves adjusting the conditions under which light is oscillated within the laser cavity to alter the nominal frequency that experiences the lowest loss. One way this is done is by coupling the output of the laser to an adjoining cavity that further participates in the oscillation of light. The external cavity includes the original cavity, which is filled with the gain medium and is referred to as “the lasing cavity”, and the adjoining cavity, which is not so filled and is referred to as “the feedback cavity”. 
         [0004]    According to a so-called “Littrow” cavity configuration, the feedback cavity includes an adjustable output mirror or coupler in the form of a diffraction grating that diffracts one portion of the light (through a first order) on a path of retroreflection back toward the lasing cavity and reflects another portion of the light (through the zero order) in a second direction as the laser output. The lasing and feedback cavities are coupled together through a collimating lens, which collimates the light emitted through an active area on the front surface of the lasing cavity. The angle at which light is diffracted from the grating varies as a function of frequency. Of the diffracted light, only a limited band of frequencies is sufficiently aligned with the path of retroreflection to be focused by the collimating lens onto the active area of the front surface for reentry into the lasing cavity. By controlling the inclination of the diffraction grating, the frequencies capable of being retroreflected back into the lasing cavity can be adjusted. 
         [0005]    The frequencies available for diffraction by the diffraction grating are limited to those that are amplified and emitted from the lasing cavity. The effect of returning any of the emitted frequencies to the lasing cavity is to alter the relative amounts of gain and loss experienced among the emitted frequencies. A larger effect on the loss profile is produced by returning frequencies that are also capable of oscillating in the coupled lasing and feedback cavities. Losses are further reduced by the more limited set of frequencies that satisfy a condition that they accrue a phase of exact integer multiples of 2 π per round trip as they propagate between ends of the feedback cavity (i.e., between the front surface of the lasing cavity and the diffraction grating). The frequency modes of the feedback cavity are generally more closely spaced than those of the lasing cavity. 
         [0006]    The frequency output of the external cavity lasers can be controlled, i.e., tuned, over a continuum of the range of frequencies subject to amplification within the lasing cavity or by discrete steps corresponding to combined resonant frequencies of the lasing and feedback cavities. Spectrally pure frequency outputs favoring a single output frequency depend on a matching of resonant modes within both the lasing cavity and the feedback cavity. Ideally, the frequency retroreflected by the frequency-selective element (e.g., diffraction grating) of the feedback cavity should match a resonant (mode) frequency of the feedback cavity as well as a resonant (mode) frequency of the lasing cavity. If the frequency subject to resonation within the feedback cavity does not match one of the frequencies favored for resonance within the lasing cavity, the spectral purity of the output beam is reduced. The resulting output beam can contain multiple frequencies and, thus, be less coherent. In addition, the nominal frequency of the output beam can be displaced from a natural mode frequency of the lasing cavity. Instabilities can develop if the mode frequency supported by the feedback cavity lies between two modes of the lasing cavity or even if the mode frequency of the lasing cavity lies between two modes of the feedback cavity. Either or both of the straddling mode frequencies can be amplified. 
         [0007]    The resonant mode frequencies of feedback cavities having a fixed length tend to be evenly spaced, since most of the propagations between end surfaces take place through air, which exhibits little dispersion (i.e., frequency dependence of the refractive index). However, the resonant mode frequencies of lasing cavities also having a fixed length, such as those of laser diodes, can undergo some variation in spacing over the range of amplified frequencies, since the lasing mediums are generally dispersive. Accordingly, if the spacing between the lasing cavity modes and the feedback cavity modes are matched at one frequency, such as the peak frequency of amplification, the spacing between the lasing cavity modes and the feedback cavity modes becomes progressively less matched at higher or lower frequencies. Particularly where the nominal spacing between lasing cavity modes corresponds to an integer multiple of the feedback cavity modes, the spacing of the lasing cavity modes can vary so much as to transition through a different integer multiple of feedback cavity modes. Frequency outputs are especially unstable within the regions of transition, where mode hops and multiple lasing frequencies are observed. 
         [0008]    Generally, single-mode semiconductor diode lasers operate at a single wavelength and, if tuned, the lasers are generally tuned over a more limited range short of any regions of transition. Temperature variations and other disturbances can shift the mode frequencies further, limiting the frequency ranges that still safely avoid the regions of transition. 
       SUMMARY OF INVENTION 
       [0009]    An expanded range of frequency tuning with improved spectral purity can be achieved by the invention, which includes arrangements providing discrete tuning choices throughout a range of lasing frequencies. The invention in one or more of its preferred embodiments provides for making predetermined frequency-sensitive optical path length adjustments to match at least initially unevenly spaced resonant modes of lasing cavities to selected resonant modes of optically coupled feedback cavities. Finer adjustments can be made to more precisely align the modes of the lasing and feedback cavities or to maintain desired alignments under changing conditions. 
         [0010]    One version of the invention as a mode-matching system for tunable external cavity lasers, includes both a lasing cavity having a set of initial lasing cavity modes favoring amplification of unevenly spaced beam frequencies and a fixed-length feedback cavity optically coupled to the lasing cavity and having a set of feedback cavity modes favoring feedback of more evenly spaced beam frequencies to the lasing cavity. A nonlinear optical path length adjuster relatively alters the frequencies of the lasing cavity modes to match selected frequencies of the feedback cavity modes. 
         [0011]    The initial lasing cavity modes can be of the type that have a frequency spacing that varies as a function of the frequencies that are amplified within the lasing cavity. The feedback cavity modes can have a frequency spacing that remains substantially constant over a range of the frequencies that are amplified within the lasing cavity. The fixed length of the feedback cavity is preferably set so that a predetermined multiple of the substantially constant frequency spacing between feedback cavity modes at least approximately matches the frequency spacing between at least one pair of the lasing cavity modes. The nonlinear optical path length adjuster can be used at a base setting to more finely match the spacing between the at least one pair of lasing cavity modes with a predetermined multiple of the spacing between the feedback cavity modes. 
         [0012]    The lasing cavity can include a lasing medium that exhibits a refractive index dispersion profile in which the refractive index of the lasing medium varies nonlinearly with the amplified beam frequencies. The nonlinear optical path length adjuster displaces the refractive index dispersion profile by varying amounts to move individual lasing cavity modes into alignment with the selected feedback cavity modes. For example, the nonlinear optical path length adjuster can be arranged to vary a current applied to the lasing cavity for displacing the refractive index dispersion profile of the lasing cavity. 
         [0013]    The uneven frequency spacing of the lasing cavity modes is generally predictable, and the nonlinear optical path length adjuster can be prearranged to align the lasing cavity modes with the selected feedback cavity modes. In addition, a spectral frequency or purity monitor can be used to provide feedback to the nonlinear optical path length adjuster to more precisely or dynamically align the lasing and feedback cavity modes where the spectral purity is highest. Optical path length adjustments made in response to the spectral condition of the output beam can be used to compensate for environmental influences including temperature variations. 
         [0014]    For purposes of selective tuning, a frequency adjuster can be used to select among the feedback cavity modes for shifting a lasing frequency output to a corresponding altered lasing cavity mode. The nonlinear optical path length adjuster is preferably responsive to the selections effected by the frequency adjuster so that shifts in lasing frequency output between the relatively altered lasing cavity modes correspond to frequency shifts between the selected feedback cavity modes. 
         [0015]    Another version of the invention as a frequency tuning system for an external cavity laser includes a lasing cavity containing an amplifying medium for amplifying a range of frequencies and having a length favoring certain initial resonant lasing frequencies. The amplifying medium exhibits a nonlinear variation in refractive index over the range of amplified frequencies, which has the effect of unevenly spacing the initial resonant lasing frequencies. A feedback cavity, which is optically coupled to the lasing cavity, has a fixed length favoring certain initial resonant feedback frequencies having a different spacing pattern than the initial resonant lasing frequencies. A frequency selector selects among the resonant feedback frequencies for favoring amplification of correspondingly spaced resonant lasing frequencies. A nonlinear resonant frequency adjuster relatively alters the resonant lasing frequencies with respect to the resonant feedback frequencies to individually match the relatively altered resonant lasing frequencies to the selected resonant feedback frequencies. 
         [0016]    Preferably, the initial resonant feedback frequencies of the feedback cavity are substantially evenly spaced, and the nonlinear resonant frequency adjuster alters the resonant lasing frequencies to match the selected resonant feedback frequencies. For example, the nonlinear resonant frequency adjuster can be used to alter the refractive index of the amplifying medium, such as by altering a current that is applied to the lasing cavity to produce photons by stimulated emission. In addition, alternations in the temperature of the amplifying medium or in the physical length of the lasing cavity also be used to individually match the resonant lasing frequencies to the selected resonant feedback frequencies. 
         [0017]    Alternatively, the nonlinear resonant frequency adjuster can be arranged to alter the resonant feedback frequencies of the fixed-length feedback cavity to match the resonant lasing frequencies of the lasing cavity. For example, the nonlinear resonant frequency adjuster could be formed by an optical medium within the feedback cavity exhibiting a refractive index that varies nonlinearly over the range of amplified frequencies. The nonlinear variation in the refractive index of the optical medium within the feedback cavity can be arranged to correspond to the nonlinear variation in refractive index of the amplifying medium within the lasing cavity over the range of amplified frequencies. 
         [0018]    The output frequencies of the laser can vary in spectral purity as a function of the relative alignment between the resonant lasing frequencies and the selected resonant feedback frequencies and a spectral purity monitor is used to monitor these variations. The nonlinear resonant frequency adjuster can be made responsive to a measure of the spectral purity of the output frequencies for performing the desired alignments. 
         [0019]    Another version of the invention as a method of mode matching between a lasing cavity and a feedback cavity within an external cavity laser, includes optically coupling a feedback cavity having resonant feedback modes that are substantially evenly spaced to a lasing cavity having resonant lasing modes that are unevenly spaced over a range of frequencies amplified within the lasing cavity. The optical path length of the feedback cavity is set to relate an integer multiple of the spacing between feedback cavity modes to the spacing between one or more pairs of lasing cavity modes within the lasing cavity. Selections are made among the feedback cavity modes for coupling to the lasing cavity; and relative adjustments are made to the other lasing cavity modes to match the selected feedback cavity modes. 
         [0020]    Preferably, the relative adjustments include making individual adjustments to the lasing cavity modes in association with the feedback cavity modes coupled to the lasing cavity. For example, current to the lasing cavity can be adjusted in association with the selection among feedback frequencies for changing a refractive index of an optical medium within the lasing cavity. 
         [0021]    The optical path length of the feedback cavity is preferably set to relate the integer multiple of the spacing between feedback cavity modes to the spacing between the one or more pairs of lasing cavity modes located near a center of the range of frequencies amplified within the lasing cavity. The adjustments to the uneven spacing between the lasing cavity modes include making progressively larger adjustments for lasing cavity modes that increasingly depart from the center of the range of frequencies amplified by the lasing cavity. 
         [0022]    In addition, the spectral purity of output lasing frequencies can be monitored as a feedback for further adjusting or maintaining individual lasing modes in alignment with the selected feedback modes. The further adjustments can compensate for environmental influences to maintain or enhance the spectral purity of the output beam. 
         [0023]    The invention is particularly useful as a tunable light source for frequency shifting interferometers, which make distance measurements including measurements of surface height variations by determining a rate at which individual points cycle through conditions of constructive and destructive interference with changes in illuminating beam frequency. The rate increases with distance. Accuracy can be increased by incrementally varying beam frequency over a larger range. Accordingly, expanded tuning ranges are particularly beneficial to frequency shifting interferometers. Measures of contrast or phase can also be used as feedback for measuring spectral purity and frequency drift. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS  
         [0024]      FIG. 1  is a diagram of an external cavity laser in accordance with the invention having fixed length lasing and feedback cavities. 
           [0025]      FIG. 2  is a diagram showing optical path lengths of the lasing and feedback cavities of a laser with matching modes within both cavities. 
           [0026]      FIG. 3  is a plot illustrating a refractive index dispersion profile of the lasing cavity. 
           [0027]      FIG. 4  is a plot of gain over a domain of frequency for a lasing cavity schematically showing the available frequency modes under a curve of potential gain. 
           [0028]      FIG. 5  is a diagram showing a progressive mismatch of lasing cavity modes to feedback cavity modes from a center position of alignment. 
           [0029]      FIG. 6  is a diagram showing a control system for selecting among the feedback cavity modes and for matching the lasing cavity modes to the selected feedback cavity modes. 
           [0030]      FIG. 7  plots the effects of current manipulations on the laser frequency response over three different domains of the frequency response. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0031]    As shown in  FIG. 1  a laser  10 , which is preferably a semiconductor diode laser, includes a lasing cavity  12  and an adjoining feedback cavity  14  aligned along a common optical axis  16 . Together, the cavities  12  and  14  form an external cavity  18 . 
         [0032]    The lasing cavity  12  contains a lasing medium (an active layer)  15  sandwiched between two electrically biased regions  13  and  17  (e.g., p and n regions) and has a fixed length along the optical axis  16  between a reflective back surface  20  and a reflective front surface  22  located at opposite ends of the lasing cavity  12 . The gain is such for conventional laser diodes that the front surface  22  requires only a small reflectivity (e.g., approximately 4 percent) to support resonant frequency modes. The feedback cavity  14 , which is filled with air, has a fixed length between the front surface  22  of the lasing cavity  12  and a pivotable reflective surface  24  located at an opposite end of the feedback cavity  14 . A collimating lens  28  forms an optical coupling  30  between the lasing and feedback cavities  12  and  14  through an active area  32  of the front surface  22 . Combined, the lasing cavity  12  and the feedback cavity  14  form an external cavity having a fixed overall length L. 
         [0033]    The pivotable surface  24  includes a diffraction grating  34  that diffracts one order, preferably the first order, back toward the lasing cavity  12  and that diffracts another order, preferably the zero order, beyond the feedback cavity  14  as the laser output beam  38 . Within the preferred first order of diffraction, the diffraction grating  34  angularly disperses incident light according to its frequency, such that a single frequency of light is retroreflected back along the optical axis  16  to the optical coupling  30 . However, the diffraction grating  34  is pivotable as a part of the surface  24  about a pivot axis  36  through a pivot angle α so that a range of different frequencies can be retroreflected along the optical axis  16 . A folding mirror (not shown) moves together with the diffraction grating  34  to maintain a single output direction for the laser output. Such folding mirrors are shown in U.S. Pat. No. 6,690,690, entitled TUNABLE LASER SYSTEM HAVING AN ADJUSTABLE EXTERNAL CAVITY, which is hereby incorporated by reference. 
         [0034]    Although other frequencies are reflected in the general direction of the optical coupler  30 , only light that is substantially collimated along the optical axis  16  is coupled to the lasing cavity  12  through the limited active area  32 . Neighboring frequencies that are angularly dispersed by the diffraction grating  34  from the optical axis  16  converge elsewhere, not upon the limited active area  32  of the optical coupler  30 . The resolution of the diffraction grating  34  is preferably large enough to feedback each frequency within the tunable range of the laser  10  by positioning the grating  34  at a unique angle α for each frequency. 
         [0035]    The pivot axis  36 , which extends through a reflective face of the diffraction grating  34 , intersects the optical axis  16  so that angular movement of the diffraction grating  34  about the pivot axis  36  does not change the length of the feedback cavity  14 . Thus, the diffraction grating  34  can be pivoted through a range of angles α for controlling the frequency of light that is retroreflected along the optical axis  16  within the feedback cavity  14 . The optical coupler  30  limits the coupling of light from the feedback cavity  14  to the lasing cavity  12  to retroreflections along the optical axis  16 . Together, the pivotable diffraction grating  34  and the optical coupling  30  control the frequencies that can be returned to the lasing cavity  12 . 
         [0036]    The fixed length of the feedback cavity  14  as shown in  FIG. 2  supports the resonance of certain among the tunable frequencies as standing waves  40 . The resonant frequencies or modes of the feedback cavity  14  correspond to frequencies whose wavelengths evenly divide the round-trip optical path length of the feedback cavity  14 . Since most of the feedback cavity  14  is filled with air as the propagating medium, the optical path length is close to the physical path length of the feedback cavity  14  and is relatively insensitive to changes in beam frequency. Accordingly, twice the optical path length equals an integer multiple N 2  of the wavelengths of the resonant frequencies or modes of the feedback cavity  14 . The propagation of other frequencies within the feedback cavity  14  is suppressed by interference. Thus, among the frequencies diffracted back by the angular position of the diffraction grating  34 , the resonant frequencies or modes of the feedback cavity  14  propagate at the highest amplitudes. 
         [0037]    The frequency spacing between modes of the feedback cavity  14  is given as follows. 
         [0038]    where c is the speed of light, is the average refractive index of the feedback cavity (nearly  1 ), and is the physical length of the feedback cavity  14 . Since both the nominal refractive index of the air and the cavity length remain substantially constant over the range of beam frequencies, the frequency spacing also remains substantially the same over the range of beam frequencies. For example, a feedback mode spacing of 10 GHz arises from a feedback cavity length of approximately 15 millimeters assuming a refractive index close to 1.0. 
         [0039]    The fixed length of the lasing cavity  12  supports resonance among certain frequencies ν that are subject to amplification by the lasing medium  15  as standing waves  42 . The resonant frequencies or modes of the lasing cavity  12  correspond to frequencies v whose wavelengths evenly divide the round-trip optical path length of the lasing cavity  12 . However, the lasing medium  15  has a refractive index that is subject to a nonlinear variation with beam frequency ν. 
         [0040]    The frequency spacing between modes of the lasing cavity  12  is given as follows. 
         [0041]    The refractive index of the lasing cavity  12  is subject to a nonlinear variation with beam frequency ν as follows: where is a nonlinear function of ν. A graph in  FIG. 3  plots a typical nonlinear refractive index variation  17  over the range of frequencies amplified by the lasing cavity  12 . The result is an uneven spacing between the modes of the lasing cavity  12 , which is emphasized by  FIG. 5 . For a lasing medium  15  having a nominal refractive index of approximately 3.5, a nominal lasing mode spacing of 50 GHz arises from a cavity length of approximately 1 millimeters. Overall, the external cavity of the exemplary laser  10  can have a length L of approximately 16 millimeters. 
         [0042]      FIG. 4  plots resonant frequencies or modes  43 ,  44 ,  45 ,  46 ,  47 ,  48 , and  49  with gains the exceed a lasing threshold  50  for gain from the lasing medium  15  in the lasing cavity  12 . The modes  43 ,  44 ,  45 ,  46 ,  47 ,  48 , and  49  vary in amplitude according to their potential for amplification within the lasing cavity  12  (as bounded by the envelope  52 ) and also vary slightly in spacing as a result of the frequency-sensitive refractive index variation of the lasing medium  15 . The result of the latter is a misalignment between the evenly spaced modes of the feedback cavity  14  and the unevenly spaced modes of the lasing cavity  12 . 
         [0043]    Although only seven lasing modes  43 ,  44 , 45 ,  46 ,  47 ,  48 , and  49  are depicted in the views of  FIGS. 4 and 5 , many more lasing modes are generally available for purposes of tuning. For example a semiconductor laser diode available from Mitsubishi Electric as a ML6XX34 series laser having a nominal wavelength of 785 nm is capable of amplifying lasing modes nominally spaced at approximately 50 GHz over a bandwidth of approximately 5000 GHz. A total of around 100 different lasing modes are available as discretely tunable frequencies. However, the exact spacing between lasing modes varies over the bandwidth. 
         [0044]      FIG. 5  compares the sample lasing modes  43  through  49  of the lasing cavity  12  with evenly spaced the feedback modes  62   a - d,    63   a - d,    64   a - d,    65   a - d,    66   a - d,    67   a - d,    68   a - d  and  69   a - d  of the feedback cavity  14  over the range of frequencies subject to amplification. The feedback modes  62   a  through  69   d  of the feedback cavity  14  are substantially evenly spaced at a constant spacing over the considered range of frequencies. The individual lasing modes  43  through  49  of the lasing cavity  12  vary in spacing, and tend to decrease as a function of increasing frequency ν. The feedback mode frequencies  63   a,    64   a,    65   a,    66   a,    67   a,    68   a,    69   a,  which are emphasized by slightly increased line width correspond to the selected feedback frequencies for optical coupling with the lasing cavity  12 . Near the median frequency, the lasing mode pairs  45  &amp;  46  and  46  &amp;  47  of the lasing cavity  12  are spaced by an amount approximately equal to an integer multiple of four times the constant spacing between the feedback modes  60   a  through  69   d  and are directly aligned with the selected feedback modes  65   a  &amp;  66   a  and  66   a  &amp;  67   a.  Approaching the ends of the illustrated frequency range, the lasing mode pair  43  &amp;  44  is spaced by a larger amount and the lasing mode pair  48  &amp;  49  is spaced by a smaller amount. As a result of the spacing variation, the lasing modes  44  and  48  have drifted out of alignment with the selected feedback modes  64   a  and  68   a.  In fact, the lasing modes  43  and  49  have drifted so far out of alignment with the selected feedback modes  63   a  and  69   a  that they have aligned with alternative feedback modes  62   d  and  68   d.  Frequency instability and reduced spectral purity can result from such misalignments between selected feedback modes and the nearest lasing modes, especially where the misalignments approach alternative feedback modes. 
         [0045]    The invention as preferably embodied deals with such misalignments, such as by altering the frequencies of the lasing modes that depart from the selected frequencies of the feedback modes, e.g.,  63   a,    64   a,    65   a,    66   a,    67   a,    68   a,  and  69   a.  Generally, the feedback cavity  14  is expected to be longer than the lasing cavity  12 , so that the mode spacing of the feedback cavity  14  is finer than the mode spacing of the lasing cavity  12 . The length of the feedback cavity  14  is preferably set so that an integer multiple of the feedback mode spacing is equal to a nominal spacing of the lasing cavity modes, which can be considered as an average spacing or a spacing located at the center or elsewhere of the amplified frequencies.  FIG. 5  shows a preferred alignment of the selected feedback cavity modes  65   a,    66   a,    67   a  with the lasing modes  45 ,  46 , and  47  about the center (median) frequency. 
         [0046]    A laser control system depicted in  FIG. 6  provides for tuning the output  38  of the external cavity laser  10  through discrete steps that correspond to overlapping modes of the lasing and feedback cavities  12  and  14 . A motor (or voice coil)  82  pivots the diffraction grating  34 , and conventional feedback system  84  (e.g., a rotary encoder) is used in conjunction with a motor driver  86  for monitoring and controlling the rotational position of the motor  82  to effect the desired inclination of the diffraction grating  34  through angle α (see  FIG. 1 ). Variations are made to the angle α to select a desired feedback frequency for choosing among the available lasing modes of the lasing cavity  12 . The changes in angle α are accompanied by a nonlinear optical path length adjustment of the lasing cavity  12  so that the feedback mode linked to the angle α is aligned with a desired lasing mode. 
         [0047]    The lasing cavity  12  is supplied with current from a laser diode driver  90  for inducing the stimulated emission of photons within the lasing cavity  12 . One example of such drivers ia available from Thorlabs, Inc. of Newton, N.J. as laser diode driver number LD1255. An external control feature of the laser diode driver  90  accepts a control voltage to adjust the current supplied to the lasing cavity  12 . Variations in the current supplied to the lasing cavity  12  tend to displace the refractive index dispersion profile such as shown by phantom line  19  in  FIG. 3 . The current can be varied by voltage regulation, so that the refractive index profile of the lasing medium  15  remains constant or varies linearly with changes in the beam frequency propagating through the medium  15 . A different amount of current can be supplied for each different beam frequency intended for amplification by the lasing cavity so that the lasing modes are individually matched to the selected feedback modes. 
         [0048]    If selected feedback modes separated by an integer multiple number of feedback modes are matched at a particular current value (e.g. a base current) to similarly spaced lasing modes, such as lasing mode parings near the median of the amplified frequencies, the remaining lasing modes can be matched to other similarly spaced feedback modes by adjusting the current applied to the lasing cavity  12 . The amount of current correction can be expected to increase as the lasing modes depart from the frequency (e.g., the median frequency) at which they are initially matched to the selected feedback modes. 
         [0049]    Thus, the amount of current change depends upon the frequency departure from the initially matched frequency and on the amount of nonlinear variation in the refractive index associated with the frequency departure. With different currents associated with different lasing frequencies, the effective mode spacing of the lasing cavity  12  can be matched to a multiple of the mode spacing of the feed back cavity  14 . 
         [0050]    Alternatively, the feedback mode frequencies selected for optical coupling to the lasing cavity  12  can be irregularly spaced such as at different multiples of the feedback mode spacing. Variations in the spacing between the selected feedback modes can be accommodated by altering the effective optical path length of the lasing cavity  12 , such as by the above-described current-induced variation in refractive index, so that a lasing mode is matched to each of the irregularly spaced selected feedback modes. Thus, instead of matching unevenly spaced lasing modes to evenly spaced selected feedback modes, the lasing modes, whether evenly or unevenly spaced, can also be matched to unevenly spaced selected feedback modes. The uneven spacing between the selected feedback modes can be as a result of an uneven mode spacing or as a result of an unequal number of even mode spacings between the selected feedback modes. 
         [0051]    The uneven spacing between lasing modes that result from refractive index variations with lasing frequency, i.e., the refractive index dispersion profile, can be predetermined along with the variations in current required to match the lasing modes to selected feedback modes. However, laser performance as measured by the spectral purity of the output beam  38  can be measured to provide feedback for more finely adjusting the lasing modes to match the selected feedback modes or to compensate for dynamic factors such as environmental influences or system instabilities that can shift or distort the mode positions of either the lasing cavity or the feedback cavity. 
         [0052]    The laser control system depicted in  FIG. 6  includes optical feedback system  88  including a monitor, such as a frequency analyzer, that can be used for monitoring a portion of the output beam  38  diverted by a beamsplitter  92 . An example of such a feedback system is disclosed in co-assigned U.S. application Ser. No. 10/946,691 entitled OPTICAL FEEDBACK FROM MODE-SELECTIVE TUNER, which is hereby incorporated by reference. For example, contrast between interference fringes produced within the feedback system  88  can be used to monitor the spectral purity of the output beam  38 . High contrast is evidence of good spectral coherence and close alignments between the lasing and feedback modes. Low contrast is evidence of poor spectral coherence and misalignments between the lasing and feedback modes. Measures of spectral purity and frequency drift by the feedback system  88  can also be used to make other adjustments including adjustments to the angle α at which the grating  34  is inclined for controlling the feedback frequency. A controller  94  gathers the optical information from the feedback system  88  for controlling both the motor driver  86  and the laser diode driver  90 . 
         [0053]    A change in the base current at which a first pairing of lasing and feed back modes are initially matched tends to shift the frequencies of the lasing modes with respect to the frequencies of the feedback modes similar to a change in the physical length of the lasing cavity  12 . Although also accompanied by a small change in the nominal mode spacing Δν L  of the lasing cavity  12 , the frequency shifts are much more pronounced because they reflect the cumulative effect of the mode spacing change over a number of resonating cycles. This allows the length of the feedback cavity to be set for matching a nominal spacing Δν L  of the lasing modes and the nominal refractive index n L  of the lasing medium  15  to be set for more precisely aligning corresponding lasing and feedback modes on center or elsewhere within their range of overlap. The individual adjustments to current can be made to align the remaining lasing modes to the selected feedback modes. 
         [0054]      FIG. 7  shows in detail frequency effects of current variations, referenced in terms of control voltages at three different sections of the lasing cavity bandwidth. In the middle section of the bandwidth corresponding to lasing modes +2 through −2, the change in optical path length caused by the small variations of current does not effect significant changes in mode frequency until the optical path length difference is sufficient enough to align the lasing cavity modes with a different one of the feedback cavity modes. The desired alignment within the center section of the bandwidth, such as at the diffraction grating setting α 0 , is achieved at an input control signal to the laser diode driver  90  of −0.3 V corresponding to a laser diode current input of 80.2 mA. At one end of the lasing cavity bandwidth corresponding to lasing modes +42 through +47, a control signal of −0.7 V (79.4 mA) is required to achieve the desired alignment at the diffraction grating setting α+45. At slightly less negative voltages (i.e., approaching 0.0 V), the output frequency enters a region of uncertainty, and at slightly more negative voltages (i.e., approximately −1.1 V), the output frequency hops by an amount of the feedback mode spacing Δν F  after passing through a region of uncertainty. At the other end of the lasing cavity bandwidth corresponding to modes −46 through −50, a control voltage of approximately −1.1 V (78.5 mA) is required to achieve the desired alignment at the diffraction grating setting α−48. At slightly less negative voltages (i.e., approximately −0.4 V), the output frequency hops down by the amount of the feedback mode spacing Δν F , and at slightly more negative voltages (i.e., approximately −1.4 V), the output frequency hops up by an amount of the feedback mode spacing Δν F  after passing through regions of uncertainty. Thus both ends of the bandwidth require current adjustments associated with negative voltages for evenly spacing the modes throughout the lasing cavity bandwidth. The resulting current variation to the lasing cavity is within the range of 2 mA. 
         [0055]    Although changes to the optical path length of the lasing cavity  12 , such as by varying the refractive index n L  of its lasing medium  15 , are preferably used for matching the lasing modes to selected feedback modes, changes can also be made to the optical path length of the feedback cavity to effect a similar matching. For example, one or more transmissive mediums, including the optical coupling  30 , can be arranged by choice of material with a refractive index dispersion profile that effectively matches the refractive index dispersion profile of the lasing medium  15 . Even a partial matching of refractive index dispersion profiles could be used to reduce demands for individually matching the lasing modes to the selected feedback modes. 
         [0056]    The invention is particularly applicable to frequency-shifting interferometry in which distances, particularly surface height variations, are measured by producing a series of interference patterns at different measuring beam frequencies. The laser  10  supports the tuning of discrete beam frequencies corresponding to the mode spacing or a multiple of the mode spacing of the lasing cavity. Frequency monitoring is simplified by limiting the measuring beam frequencies to certain frequency steps that can be monitored more easily than changes in beam frequencies over a continuum. 
         [0057]    Although the invention has been described with respect to particular embodiments, those of skill in the art will appreciate that a wide range of variations can be made in the components, configurations, and tuning methods within the overall teaching of the invention. For example, the invention can be practiced with other types of lasers, including gas, dye, and solid-state lasers.