Patent Publication Number: US-2006007970-A1

Title: Coherence reduction of diode lasers

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
      The present invention claims priority from U.S. Provisional Patent Application No. 60/585,083 filed Jul. 6, 2004, entitled “Coherence reduction of diode lasers”, which is incorporated herein by reference. 
    
    
     TECHNICAL FIELD  
      The present invention relates to methods for reduction of coherence of laser radiation, and to laser devices for emitting laser radiation with reduced coherence for use in laser metrology.  
     BACKGROUND OF THE INVENTION  
      Lasers are commonly used for optical probing of materials and devices because of their ability to provide almost monochromatic optical radiation at a well-defined wavelength with low beam divergence and sufficient intensity. Laser diodes have proven to be very useful in such applications as laser spectroscopy and in testing of optical characteristics of fiber-optic and other optical components. However, a typically very narrow optical spectrum of lasers is associated with a high degree of coherence of the laser radiation, which can lead to undesirable noise-like interference effects during optical test measurements.  
      Therefore, in some applications of diode lasers it is desirable to effectively reduce the coherence of the laser, to minimize the interference effects. An example is a fiber optic loss meter, where power-calibrated laser diode radiation is transmitted through a fiber-optic component, and the transmitted radiation is detected by a power meter to obtain a power reading. During the measurement, interference effects between fiber connectors can cause variations in the power readings. A known solution to this problem is to effectively reduce the laser coherence by modulating the laser wavelength with a triangle or sinusoidal wave pattern to cause averaging of the interference effect by a light-detecting device used in the measurement.. For diode lasers, wavelength modulation can be accomplished by modulating the laser drive current, for example with a triangle wave pattern.  
      It is known in the art that a diode laser&#39;s wavelength varies with the drive current for several reasons, including changing refractive index of the laser diode chip due to changing chip temperature, and changing the refractive index due to injected free carriers. Modulating the laser current therefore has the effect of varying the laser wavelength over time, effectively broadening the laser spectrum and hence reducing the laser coherence, so that a power reading averaged over a time greater than the modulation period will have reduced interference effects.  
      This method is effective for fiber optic components with fiber pigtails, where the optical path differences (OPD) causing the interference effects are typically greater than 1 meter due to the length of the fiber pigtails. However, in some applications interference effects from surfaces only a few centimeters apart must be minimized. In these applications, simple modulation functions such as a triangle wave or a square wave may not provide satisfactory results.  
      It is therefore an object of the present invention to provide a method of modulating of a drive current of a laser diode using a modulation function optimized for reducing coherence of laser diode radiation.  
     SUMMARY OF THE INVENTION  
      In accordance with the invention, a method of modulation of a drive current of a laser diode is provided for obtaining laser radiation having a target time-averaged spectral profile, the laser radiation having a frequency or a wavelength dependent on said drive current, the method comprising the steps of: (a) determining a modulation function for the drive current, and (b) modulating the drive current of the laser diode using said modulation function; wherein step (a) comprises determining a shape of the modulation function from the target time-averaged spectral profile using the dependence of the frequency parameter on the drive current.  
      In accordance with one feature of this invention, the target spectral profile is substantially Gaussian for optimally reducing a coherence of the laser radiation.  
      In accordance with another aspect of the present invention, a method is provided for coherence reduction of time-averaged radiation of a laser diode having a central wavelength and a power dependent on a drive current. The method comprises the step of determining a modulation function of the drive current for obtaining a pre-determined spectral profile of the time-averaged radiation, the pre-determined spectral profile being substantially Gaussian, and the step of modulating the drive current of the laser diode using said modulation function, wherein the step of determining a modulation function comprises performing the steps of i) selecting a set of drive current values, ii) determining an inverse modulation function by first determining, for each drive current value from the set of the drive current values, a fraction of time parameter using the pre-determined spectral profile and values of the central wavelength and the power corresponding to said drive current value, and then determining a time value corrresponding to the drive current value using said fraction of time parameter, and iii) determining the modulation function from the inverse modulation function.  
      Another feature of the present invention provides a laser apparatus for emitting optical radiation with a time-averaged spectral profile having a target spectral shape. The laser apparatus comprises a laser having a wavelength dependent on a drive current, a current source for supplying the drive current to the laser, and modulating means for modulating the drive current using a pre-determined modulation function, wherein the modulation function is determined from the target spectral shape using a pre-determined dependence of the laser wavelength on the drive current. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
      The invention will be described in greater detail with reference to the accompanying drawings which represent preferred embodiments thereof, wherein:  
       FIG. 1  is a diagram of a prior-art fiber-optic component meter.  
       FIG. 2A  is a diagram of time dependence of the drive current, optical power, and wavelength for a laser diode modulated with a triangle waveform;  
       FIG. 2B  is a diagram of an averaged optical spectrum for the laser diode modulated with the triangle waveform shown in  FIG. 2A .  
       FIG. 3A  is a graph showing coherence functions corresponding to spectral profiles shown in  FIG. 3B ;  
       FIG. 3B  is a graph showing a Gaussian and a trapezoidal spectral profiles of a laser radiation;  
       FIG. 4  is a block diagram of the method of the present invention for determining a modulation function for the laser drive current;  
       FIG. 5  is a graph showing the modulation function of the present invention used for simulating the Gaussian spectral profile shown in  FIG. 3B ;  
       FIG. 6  is a block diagram of the laser apparatus according to the present invention.  
    
    
     DETAILED DESCRIPTION  
      This invention provides a method of modulation of a wavelength λ of a laser diode, and a laser apparatus realizing it, for obtaining a target time-averaged spectral profile of the laser radiation. The target spectral profile can be pre-determined, or it can be a spectral profile that is suited for a particular application, and can be selected during the laser diode operation based on the application. In a preferred embodiment of the invention, the target time-averaged spectral profile is a spectral profile optimized for reducing coherence of laser radiation at small to medium optical path differences (OPD). Quantitative definition of the term “small to medium OPDs” depends on a particular application; in an embodiment considered herein, it is used to mean distances from about 10 mm to about 500 mm.  
      The laser wavelength λ is understood herein as a central wavelength of an optical spectrum of the laser diode radiation for a particular value of a drive current of the laser diode.  
      The method can be used for suppressing undesirable noise-like interference effects in laser-based devices for optical measurements of components and materials. It can also be used for other purposes when a particular shape of time-averaged spectral profile is required. By way of example only, the method of the present invention will be described with reference to an optical loss meter.  
      Operation of such a device is illustrated in  FIG. 1 , which shows a light beam  15 , emitted by a laser diode  10 , impinging on a photodiode  30  after passing through a device under test (DUT)  20 , for example a transmissive or reflective fiber optic component having an input and an output port, such as a WDM filter or an attenuator. The DUT  20  has an internal unwanted reflection plane  35 , for example an optical fiber facet or a lens facet, which causes internal reflection in the DUT  20  to occur, resulting in a small portion of the beam  15  experiencing multiple reflections within the DUT  20 , as schematically illustrated by an S-shaped arrow  40 . As a result, a portion  50  of the laser beam  15  which is output from the DUT  20  includes two components: a first component  25  which has passed through the DUT  20  without unwanted reflections, and a second component  45  which experienced the unwanted reflections within the DUT  20 . Interference of these two components of the optical beam  50  at the photodiode  30  gives rise to an unwanted noise-like interference component, caused by interference fringes, in a power reading of the photodiode  30 . Intensity of this noise-like component is proportional to the interference fringe contrast, which is determined by a normalized coherence function Γ t  (τ) of the laser beam  15 , where τ is an optical delay time corresponding to an OPD value l equal to an optical length of the multi-path trajectory  40 , i.e. for τ=l/c, where c is the speed of light. The coherence function Γ t  (τ), represented as a function of the OPD l, will be denoted hereinbelow as Γ (l).  
      It has been known in the art to reduce the undesirable interference effect within the DUT on the power reading by modulating the laser wavelength with a triangular waveform. The method has been applied to wavelength-tunable lasers in general, and to semiconductor laser diodes in particular, where a wavelength modulation is especially easily achieved by modulating their drive current. The method is based on recognition that each power reading can be collected, and often is collected and thereby averaged over a relatively large period of time T m , and that the undesirable effect of the interference fringes can be at least partially obviated by the time averaging, provided that the laser wavelength λ is modulated with a characteristic period, which is at least several times smaller than the duration of the power reading measurement. The time T m  over which one power reading is averaged, typically between a few psec and one second, is hereinafter also referred to as a measurement time T m .  
      In mathematical terms, the coherence function Γ t (τ) that affects an amplitude of the undesirable interference component of the power reading, is a time-averaged coherence function, i.e. the coherence function which is averaged over a time period of the measurement. For a typical cw-pumped laser diode, Γ t (τ) is an exponentially decreasing function of the time delay τ, which is characterized by a coherence time t c  corresponding to a coherence length l c =ct c  between tens of centimeters to tens of meters. On the other hand, the coherence function is the Fourier transform of the optical spectrum of the laser, and the time averaged coherence function Γ t (t) is a Fourier-transform of a time-averaged optical spectrum S(ω), where ω=2πν=2πc/λ is a cyclic optical frequency corresponding to the laser wavelength λ. The time-averaged optical spectrum S(ω) can also be represented as a function S ν (ν) of the optical frequency ν, and a function S λ (λ) of the laser wavelength.  
      Because of the intrinsic properties of the Fourier transform, the coherence time t c  is inversely proportional to a spectral width Δν of the laser radiation: 
 
t c ˜a/Δν,   (1) 
 
      where a is a constant parameter. Equation (1) is equally applicable to the time-averaged values of the coherence time and the laser spectral width, thereby enabling at least partial suppressing the time-averaged interference effects by modulating the laser wavelength to widen the time-averaged optical spectrum.  
      The prior art method for reducing the undesirable interference effects by reducing the time-averaged coherence of the laser diode radiation is illustrated in  FIGS. 2A and 2B . The laser diode drive current J is modulated around a steady-state operating value J 0  with a triangular waveform  110  having a period T, so that the drive current of the laser diode changes piece-wise linearly within a drive current interval ΔJ=J max −J min , also referred to hereinafter as the current modulation span, between a minimum value J min  and a maximum value J max . This triangular modulation leads to a periodic modulation of the laser output power P between a minimum power value P min  and a maximum power value P max , and also to a periodic modulation of the laser wavelength λ between a minimum value λ min  and a maximum value λ max , since the laser diode output power and the laser wavelength are known to depend on the laser drive current. Typically, both the laser diode power P and the laser wavelength λ change linearly for relatively small changes of the drive current: 
 
 P ( J )= P   0   +k   p ( J−J   0 ),   (2) 
 
λ( J )=λ 0   +k   λ ( J−J   0 ),   (3) 
 
      Coefficients k p  and k □ in equations (2), (3) are typically known, either from a supplier specification or pre-determined by a laser diode calibration procedure. The coefficient k p  is typically referred to as the laser slope efficiency. Accordingly, the triangular modulation of the drive current gives rise to a triangular modulation  120  of the laser power P, and a triangular modulation  130  of the laser wavelength λ.  
      A resulting time-averaged optical spectrum S □ (□) of the modulated laser diode is represented in  FIG. 2B  by a line  140 . The spectrum has a trapezoidal shape, and a width in the wavelength domain 
 
Δλ=(λ max −λ min )= k   80    J   max   −J   min ).   (4) 
 
      In writing equation (4), it has been assumed that the laser linewidth at each particular moment during the modulation remains much smaller than the spectral width Δλ averaged over one or more periods of the modulation. In a frequency domain, the averaged laser spectrum has a width Δν≈cΔλ/λ 0   2 , where a relationship Δλ&lt;&lt;λ 0  has been taken into account.  
      The trapezoidal spectral profile of the time-averaged laser diode spectrum, although leading to a reduced coherence time t c =aλ 0   2 /cΔλ and a correspondingly reduced coherence length l c =t c /c=aλ 0   2 /Δλ . . . is not optimal when suppression of the interference fringes beyond the coherence length is desired. With reference to  FIG. 3A , a normalized coherence function Γ(l)  310 , calculated from the trapezoidal spectral profile  140  and referred to in the figure as the fringe contrast, has a series of peaks of decreasing amplitude beyond the coherence length l c . These peaks of the fringe contrast at OPD values exceeding the coherence length I,c although relatively small in amplitude, extend far towards large OPD values, and can cause measurable errors when the laser diode&#39;s radiation is used for optical probing of a component or a material.  
      The present invention improves on the prior art by providing an optimized modulation function to reduce interference effects for OPD values beyond the coherence length l c .  
      The method starts by recognizing that the slow decay of the fringe contrast with increasing OPD for the prior-art modulation waveforms stems from large discontinuities of the averaged spectral profile  140  of the laser radiation at the edges λ min  and λ max  of the wavelength modulation span. To obtain a coherence function which falls off rapidly with increasing OPD, we need to avoid these large discontinuities in the optical spectrum. A spectral profile which has the Fourier transform falling off most rapidly is a Gaussian profile. Therefore, the objective is to modulate the laser in such a way that the time-averaged frequency spectrum S ν (ν) has a target spectral profile that approximates a Gaussian profile, i.e. the following relation holds:  
                   S   v     ⁡     (   v   )       ≅     exp   ⁡     (     -       (       v   -     v   0         δ   ⁢           ⁢     v   /   2         )     2       )         ,           (     5   ⁢   a     )             
 
      with a corresponding wavelength spectrum  
                   S   λ     ⁡     (   λ   )       ≅     exp   ⁡     (     -       (       λ   -     λ   0         δλ   /   2       )     2       )         ,           (     5   ⁢   b     )             
 
      with each of the spectral widths δν and δλ=cδν/ν 2  defined here as a full width of the corresponding Gaussian spectral profile at a l/e˜0.37 level thereof. Note that the Gaussian shape of the wavelength spectral profile δ λ (λ) defined by equation (5b) results from the Gaussian shape of the frequency spectral profile δ ν (ν) defined by equation (5a), provided that Δλ&lt;&lt;λ, which is typically the case.  
      The target Gaussian wavelength spectral profile S λ (λ) is shown in  FIG. 3B  by a solid line labeled “ 321 ”, where it is given in comparison with the trapezoidal spectral profile  140  of the prior art. The wavelength spectral width δλ for the Gaussian profile  321  is selected here to be about one half of the full wavelength modulation span Δλ, which satisfies equation (4). It is not possible to match the Gaussian profile exactly, because the Gaussian function extends to plus and minus infinity, whereas there is only a finite wavelength tuning range available through current modulation of the diode laser. Nevertheless, we can generate a reasonable approximation.  
      Turning back to  FIG. 3A , the coherence function  320  corresponding to the Gaussian averaged spectral profile  321  is shown to roll off much faster than the prior-art coherence function  310  at medium to large OPD values, beyond approximately 2 l c , where l c  is a characteristic time-averaged coherence length for the prior-art triangular wavelength modulation waveform  130 . The coherence function  320  has an approximately Gaussian shape defined by equation (6b), with a characteristic coherence length l gc , as defined at l/e level of the coherence function, satisfying equation (6a): 
 
 l   gc =2 c /(πδν)=2λ 2 /(πδλ),   (6a) 
 
Γ gλ ≈exp[−(l/l gc ) 2 ]  (6b) 
 
      The current invention provides a method of modulation of the drive current of a laser diode for obtaining laser radiation having a target time-averaged spectral profile, by first determining a modulation function for the drive current, including determining a shape of the modulation function from the target time-averaged spectral profile, and, second, by modulating the drive current of the laser diode using said modulation function. In a preferred embodiment, the target time-averaged spectral profile is substantially Gaussian, as required for the optimal reduction of the laser coherence.  
      We note here that the conventional methods of laser coherence reduction, e.g. the aforedescribed triangular modulation method, do not include the step of determining the shape of the laser modulation function from a target time-averaged spectral profile. Instead, the prior art methods typically start with defining the drive current modulation waveform, e.g. the triangular waveform or a sinusoidal waveform, and then proceed to determine the current modulation span ΔJ required for obtaining a certain spectral width Δλ, e.g. using equation (4) or a similar equation for the current dependence of the laser wavelength, for providing a sufficiently small coherence length l as required for a particular application.  
      Opposite to the prior art methods, the determining of a shape of the current modulation function J(t), or the current modulation waveform, lies in the heart of the method of the present invention.  
      A preferred embodiment of the method of modulation of a drive current of a laser diode for obtaining laser radiation having a target time-averaged spectral profile will now be discussed with reference to  FIG. 4 , showing a block diagram of the method embodiment, and to  FIG. 6 , showing an exemplary embodiment of a laser apparatus realizing said method.  
      With reference to  FIG. 4 , in a first step  420  of the method, the laser diode characteristics relevant for the laser diode modulation method of the present invention are determined within an operating range of the laser diode, namely the dependences λ(J) and P(J) of the laser wavelength and output power, resepectively, on the laser diode drive current J. This step is optional; for example, in some embodiments these dependences may be pre-determined at an earlier calibration stage, stored in a memory device and provided to the method therefrom.  
      In a next step  420 , the target spectral profile of the time-averaged spectrum is selected. In the preferred embodiment of the method, the target profile is selected for optimally reducing the time-averaged coherence function as described hereinabove, and within the wavelength modulation span (λ min , λ max ) approximates the Gaussian profile, as described by equation (5a) in the wavelength domain, and by equation (5b) in the frequency domain. Hereinafter in this specification, the subscripts “ν” and “λ” of the spectral profile functions S λ (λ) and S ν (ν) will be for simplicity omitted.  
      For certainty, herein in this specification we chose to described the method in terms of the wavelength, although those skilled in the art would appreciate that the method can be both described and computationally implemented using either of the following parameters, which will be hereinafter referred to as frequency parameters: the laser wavelength λ, the laser frequency ν, and the laser cyclic frequency ω.  
      Continuing the description of the method steps, step  420  also includes selecting the width Δλ=(λ max −λ min ) of the wavelength modulation span determining the total width of the target time-averaged laser spectrum S(λ), and selecting a characteristic spectral width δλ thereof at a pre-determined intensity level. In the preferred embodiment, the characteristic spectral width δλ is the full width of the Gaussian function at the l/e level as defined by equation (5a). Particular values of the parameters Δλ and δλ≦Δλ are selected depending on requirements of a particular application, taking into account an allowable value of the modulation span ΔJ of the drive current, and a target suppression of the fringe contrast for OPD values relevant for the application. Generally, increasing the ratio δλ/Δλ leads to a faster initial roll-off of the coherence function Γ(l) , at the expense of a less steep coherence roll-off at larger OPDs beyond the coherence length, as in the case of the triangular modulation. Decreasing of this ratio, on the contrary, widens the central peak of the coherence function, but enhances the suppression of the Γ(l) “tail” for larger OPD values.  
      By way of example, selecting the target time-averaged profile S(λ) so to satisfy equation (5a) with δλ˜0.5 Δλ for λ min &lt;λ&lt;λ max , and to equal zero outside of this interval, leads to relatively small, less than 2%, discontinuities of the averaged spectrum at the edges thereof, and to a reasonably high suppression of the coherence function at large OPD values. In practice, physical limitations of a current source and a modulator require that S(λ) to be above a certain minimum value over the range λ min &lt;λ&lt;λ max , otherwise the rate of change of the drive current would exceed capabilities of the current source and modulator. Thus, the truncated Gaussian profile for S(λ) is appropriate for minimizing the coherence of the laser as well as matching the physical requirements of the apparatus.  
      Once the target spectral profile is selected and the current modulation span ΔJ is identified, the drive current modulation waveform J(t), also referred to herein as the modulation function, can be determined using the dependences P(J) and λ(J) as follows.  
      In the preferred embodiment, the modulation function J(t) is periodic with a period, which will be denored hereinafter as 2T, with T being half of the period. Particular value of the period depends on the application, but it must be short enough compared to the averaging time T m , i.e. T&lt;T m .  
      In a next step  425 , a plurality {J j } of N drive current values J j , j=0 . . . N−1, is selected, the plurality spanning the drive current interval (J min , J max ). For example, the N drive current values can be uniformly spaced within the drive current interval, satisfying a relation J j =J min +j·ΔJ/N for j=0 . . . N−1. The integer number N is preferably in the range between 20 and 1000.  
      In a step  430 , a fraction of time η(J j ), when the drive current has a particular value J j  during one modulation period, is determined for each drive current from the plurality {J j }, using the known dependences λ(J) and P(J) of the laser wavelength on the drive current, and the laser optical power on the drive current, respectively.  
      This fraction of time, or time fraction η(J j ) satisfies the following equation (7):  
               η   ⁡     (     J   j     )       =         S   ⁡     (     λ   ⁡     (     J   j     )       )       ⁢       ⅆ   λ       ⅆ   J           P   ⁡     (     J   j     )                 (   7   )             
 
      Computationally, the plurality of time fraction values η(J j ), j=0, . . . ,N−1, can be obtained by performing the following steps: 
      i) determining a first plurality of optical power values {S j } from the target spectral shape S(□) and the pre-determined dependence of the laser wavelength on the drive current □(J), e.g. using the equation  
           S   j     =       S   ⁡     (     λ   ⁡     (     J   j     )       )       ⁢       ⅆ   λ       ⅆ   J           ,     j   =   0     ,         …   ⁢           ⁢   N     -   1     ;   and     ,       
    ii) dividing the first plurality of optical power values by a second plurality of optical power values {P j }, determined from the laser power dependence on the drive current P(J) as P j =P(J j ). This step can be omitted if P(J)=const.    

      In a next step  440 , the plurality of time fractions η(J j ) is used to determine an inverse modulation function t(J) by determining a plurality of time values {t j }, t j =t(J j ), j=0, . . . N−1, corresponding to the plurality of drive current values {J j }. For continuous functions, this inverse modulation function t(J) can be computed by integration of a function η(J j ):  
           t   ⁡     (   J   )       =       t   0     +       T       J   max     -     J   min         ⁢       ∫     J   min     J     ⁢       η   ⁡     (   i   )       ⁢           ⁢     ⅆ   i               ,       
 
 where t 0  is an arbitrary time offset. Using the computed discrete function η j =η(J j ), the plurality of time values {t j =t(J j )} is determined using the following equation (8):  
                 t   j     =       t   ⁡     (     J   j     )       =         t   0     +       ∑     k   =   0     j     ⁢       η   k     ⁢           ⁢   for   ⁢           ⁢   j         =   0         ,       …   ⁢           ⁢   N     -   1.             (   8   )             
 
      Equation (8) defines the discrete inverse modulation function t(J j ) as the plurality of pairs {t j , J j }, j=0, . . . N−1, of the time and drive current values. In a next step  460 , the discrete-valued inverse modulation function t(J j ) is inverted to determine the modulation function J(t). This can be done, for example, by saving the plurality of pairs {t j , J j } in a two-column look-up table, and then inverting the column order. However, the resulting discrete-valued modulation function J j (t j ) is defined for the plurality of time values {t j } that are not equally spaced in time. This problem can be easily solved by interpolating the discrete-valued modulation function J j (t j ) computed from equation (8) to any target time moment t between t 0  and (t 0 +T), and thereby computing a first half of the modulation waveform J(t) defined for the first modulation half-period (t 0 , t 0 +T).  
      Finally, in the last step  470 , a first half of the modulation waveform J(t) is symmetrically extended into a second modulation half-period (T+t 0 , 2T+t 0 ), to obtain the modulation waveform J(t). The laser drive current is then modulated by periodically repeating the modulation waveform J(t) in time with the period 2T, which is preferably between few microseconds and tens of milliseconds, depending on application, but can also be outside of this range.  
      By way of example,  FIG. 5  shows the modulation function  520  computed by the aforedescribed method of the present invention for obtaining an averaged spectral profile  321  shown in  FIG. 3B , in comparison with the conventional triangular modulation waveform  510 . The modulation waveform  520  was computed assuming typical linear dependences of the laser power P(J) and the laser wavelength λ(J) on the drive current, as described by equations (2) and (3), and was normalized by the maximum drive current J max .  
      Turning now to  FIG. 6 , a laser apparatus  200 , implementing the aforedescribed method of the present invention for emitting optical radiation with a time-averaged spectral profile having a target spectral shape, will now be described.  
       FIG. 6  shows the block diagram of the laser apparatus  200 . Various blocks shown in FIG. 6  are to be understood as functional blocks rather than as separate pieces of equipment unless stated otherwise, and can be realized in hardware or software or a combination thereof, depending on a particular implementation, and may include one or more integrated circuit (IC) chips and one or more additional optical components. Best embodiment of each block shown in  FIG. 6  may depend on particular application and would be known to those skilled in the art after reading this specification.  
      The laser apparatus  200  includes a laser diode  210  which emits laser radiation via an output optical fiber  215 , a current source  250  for supplying a drive current to the laser, and modulating means  220  for modulating the drive current using a modulation function J(t), which is determined from the target spectral profile S(t) using the aforedescribed method of the present invention.  
      The laser diode  210  has a wavelength λ of the laser diode radiation, which is dependent on the drive current J of the laser  210  in a known manner, and an optical power P, which is also dependent on the laser drive current in a known manner. These dependences P(J) and λ(J) can typically be approximated by linear functions given by equations (2), (3); the linear approximation is however not a requirement for the present invention.  
      The current source  250  has a modulation input for receiving a periodic analog or digital modulation signal  252 , and an output for supplying the drive current  253  to the laser diode  210 . It has also an optional input for receiving a power feedback signal  254  from an optional power sensor  240 . The drive current  253  is a continuous, or analog, signal formed as a periodical extension of the modulation function J(t).  
      The modulating means  220  can be embodied as an arbitrary signal generator; it includes: a modulator block  270  for generating the periodic modulating signal  252  using the modulation function J(t), the periodic signal  252  used by the current source  250  for periodically modulating the laser drive current  254 ; a first memory block  265  for storing the modulation function J(t) in a digitized form. In some embodiments, the modulating means  220  includes means  275  for adjusting the modulation function J(t) in response to a change in the drive current dependence of one of the laser power P(J), and the laser wavelength λ(J). The means  275  are formed by processing means  255 , and a second memory block  260  for storing the target spectral shape S(λ). The processing means  255 , hereinafter also referred to as a processor  255 , can be embodied using a micro-processor, a digital signal processor, and/or an FPGA device.  
      In some embodiments, the modulation function J(t) is pre-determined at a stage of calibration of the laser apparatus  200  from the target time-averaged spectral shape S(λ), using the method of the present invention as described hereinabove with reference to  FIG. 4 , and the pre-determined dependencies P(J) and λ(J) for the laser diode  200 , e.g. by performing the steps of:  
      A) for a plurality of drive current values {J j } within a drive current interval ΔJ, determining a first plurality of optical power values {S j } from the target spectral shape S(λ) and the pre-determined dependence λ(J) of the laser wavelength on the drive current;  
      B) dividing the first plurality of optical power values by a second plurality of optical power values {P(J j )} determined from the laser power dependence P(J j ) on the drive current, by dividing each power value S j  from the first plurality by a corresponding power value P(J j ) from the second plurality, to obtain a plurality of time fraction values {η(J j )=S j /P(J j )};  
      C) determining a plurality of time values {t j } corresponding to the plurality of drive current values {J j } from the plurality of time fraction values {η(J j )} to obtain a discrete time versus current function t j =t(J j ); and  
      D) inverting the discrete time versus current function.  
      In the preferred embodiment, the drive current interval ΔJ is chosen by first determining the wavelength modulation span Δλ to provide a suitably reduced coherence length l gc  as described hereinabove in the specification, and then by calculating the drive current interval ΔJ from the pre-determined laser characteristics.  
      By way of example, the laser diode  210  is a Hitachi 7859MG laser diode having following nominal characteristics: lasing wavelength λ˜780 nm, slope efficiency k p ˜0.65 mW/mA, wavelength vs. current coefficient k λ ˜0.003 nm/mA, wavelength vs. temperature coefficient k T ˜0.3 nm/deg C. The target spectral profile is the Gaussian function defined by equation (5a), with δλ=Δλ/2. An application requires the coherence length of the time-averaged coherence function l gc ≦2 cm. Using equation (6a), the modulation wavelength span Δλ=2δλ≧0.04 nm, and the required current interval ΔJ of the modulation is calculated as ΔJ=Δλ/k λ ≧13.3 mA.  
      In some embodiments, the laser apparatus  200  may also include optional optical sensing means  245  coupled to the fiber-optic laser output  215 , the optical sensing means  25  including one or more of the following optical sensors: an optical power sensor  245 , a mode hope sensor, and a wavelength sensor, with the later two shown in  FIG. 6  combined in a single mode hop and wavelength sensor  230 . These sensors have a function of monitoring the drive current dependences of the laser power P(J) and the laser wavelength λ(J) during the laser operation for sensing a change in either the P(J) or λ(J). They provide feedback information to the processor  255  for suitably updating the modulation function J(t), e.g. if a change in the P(J) or λ(J) characteristic is detected.  
      The laser diode  210  may experience mode hops when the drive current deviates outside a mode hop free range; these mode hops tend to reduce the effectiveness of the optimized modulation of the drive current according to the method of the present invention. To overcome this potential problem, the laser apparatus  200  includes a mode hop sensor  230 , which is optically coupled via a tap  212  to the fiber-optic laser output  215  for receiving a portion of the laser radiation, an electrically coupled to a thermo-electric controller (TEC)  280  of the laser diode. The TEC  280  provides means for adjusting the central laser wavelength λ 0  by adjusting the laser diode temperature.  
      Once the mode-hop sensor  230  senses, or detects, a mode-hop event, a signal is sent to the TEC  280  for controlling the laser temperature so that the laser operates in a region free of mode hops. The TEC  280  may receive this signal either directly from the mode-hop sensor  230  as shown in  FIG. 6 , in which case the mode hop detector  230  may include a TEC control circuit, or via the processor  255 . The mode-hop sensor  212  can be embodied using a Fabry-Perot etalon or other wavelength-dependent optical element, followed by a photodiode and a differentiator circuit. Such a mode-hop sensor is described, for example, in a Canadian Patent Application CA—2,222,002, in the name of the inventor of the current invention, which is included herein by reference. A large positive or negative spike from the differentiator circuit would indicate that a laser mode hop had occurred. By identifying the timing of the mode hop relative to the modulation signal, it can be deduced whether the laser temperature should be increased or decreased to avoid the mode hop. By suitable changing the laser temperature, the temperature dependence of the laser diode wavelength is exploited for adjusting the wavelength modulation span Δλ to be centered in the mode-hope free wavelength region.  
      The laser diode  210  may also experience changes in the pre-determined laser characteristics P(J) and λ(J), e.g. due to changing environmental conditions or laser aging. Such changes would make the pre-determined modulation function J(t) no longer optimal, i.e. not providing the target time-averaged spectral profile S(λ). To overcome this problem, the laser apparatus  200  includes a power sensor  240  coupled to the fiber-optic laser output  215  via a second tap  214 , and a wavelength sensor, which monitor for changes in the drive current dependence of the laser power, and the laser wavelength, respectively. In the embodiment shown in  FIG. 6 , the wavelength sensor function is provided by the mode-hop detector  230 , which is in this case functions as a wavelength meter, and may include a Fabry-Perot etalon, an optical splitter and two photodetectors, as known in the art.  
      In one embodiment, the power sensor  240  and the wavelength sensor  230  monitor the output optical power P and the laser wavelength λ during operation as the laser drive current is modulated, and provide information related to the time dependence of the output power P(t) and the laser wavelength λ(t) to the processor  255 , for example, in a form of digitized signals proportional to P(t) and λ(t). The processor  255  then relates the digitized signals to the time dependence of the modulated drive current to determine the dependences P(J) and λ(J) of the laser power and the laser wavelength on the drive current, and computes the modified modulation signal J′(t) from the target spectral profile S(λ) stored in the memory  260 , using the aforedescribed method of the present invention. In some embodiments, this in-operation computing of the modulation function can be done at a pre-determined time fractions during the laser operation. In other embodiments, the processor  255  adjusts the modulation function J(t) in response to a change in the drive current dependence of at least one of the laser power and the laser wavelength, as detected using the signals received from the power sensor  240  and/or the wavelength sensor  230 .  
      The power sensor  240  may provide a feedback signal to the current source  250  for maintaining a time-averaged output optical power of the laser apparatus  200  at a constant level.  
      In the embodiments wherein the mode-hope sensor  230  provides the real-time wavelength monitoring function, it can be used for direct estimating of the time-averaged wavelength spectral profile S(λ) by integrating the detected wavelength in time; this function can be performed by the processor  255  and/or by the wavelength sensor  230  itself. In other embodiments, the wavelength sensor  230 , instead of providing a real-time wavelength monitoring at the laser modulation frequency ƒ= ½T, may be embodied as an averaging spectrometer, e.g. using a grating and a photo-receiver array as known in the art, to provide to the processor 255 spectral information for determining an estimated time-averaged spectral profile S   e (λ), for comparing thereof with the target spectral profile S(λ) stored in the memory  260 , and for adjusting the modulation function J(t) as required.  
      The embodiments described hereinabove in this specification are given for illustration purposes only and are not meant to limit the scope of the invention, as defined by the appended claims. For example, although the preferred mode of carrying out the invention has been described in relation to the drive-current modulation of laser diodes, the method of the present invention can also be applied to other types of current-tunable lasers or voltage-tunable lasers. Of course numerous other embodiments may be envisioned without departing from the spirit and scope of the invention.