Abstract:
Apparatus and methods of measuring optical waveforms are described. In one aspect, an optical waveform measurement apparatus includes a light wave source, a mixer, a down converter, and a controller. The light wave source is operable to provide an adjustable frequency light wave with a frequency that is adjustable over a target frequency range. The mixer is operable to mix a target modulated optical signal with the adjustable frequency light wave to obtain a mixed signal. The frequency down converter is operable to down convert the mixed signal to obtain a down-converted signal. The controller is operable to extract from the down-converted signal amplitude and phase information relating to the target modulated optical signal and to cause the light wave source to incrementally adjust the frequency of the adjustable frequency light wave over the target frequency range.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   Under 35 U.S.C. § 119 this application claims the benefit of co-pending Japanese Patent Application No. 2002-091809, which was filed Mar. 28, 2002, and is incorporated herein by reference. 
   BACKGROUND 
   The goal of optical waveform measurement is to measure the variations of a waveform in time. Optical waveforms may be characterized in the time domain by an intensity and a phase. Optical waveforms also may be characterized in the frequency domain by taking the Fourier transform of the time domain representation. In the frequency domain, an optical waveform may be characterized by a spectral intensity (or spectrum) and a spectral phase. The derivative of the spectral phase with respect to frequency may be computed to obtain the “group delay,” which represents the delay in the arrival time of a particular slice of the spectrum at a frequency at a particular location. If the group delay is constant, all frequencies arrive at the same time, and the pulse is as short as possible. 
   Many different techniques for measuring optical waveforms have been proposed. If the waveform variations are sufficiently slow, a waveform may be measured directly using electronic equipment, such as oscilloscopes, photodiodes, and streak cameras. For faster waveform variations, intensity autocorrelation waveform measuring techniques may be used to determine some aspects of an optical waveform. Such techniques involve crossing a waveform and a delayed replica of the waveform in a nonlinear medium, such as a second-harmonic-generation crystal or a two-photon absorber, and detecting the output optical energy as a function of delay. Time-frequency domain optical waveform measurement techniques also have been proposed. In these techniques, the intensity variations over time are measured for different spectral slices of an optical waveform. More complex waveform measurement methods, such as frequency-resolved optical gating techniques, also have been proposed. In these techniques, the spectrogram of an optical waveform pulse is measured. The gating occurs in time, rather than frequency, followed by measurement of the spectrum of each time slice. Typically, the optical waveform is gated with itself. The resulting spectrogram is a spectrum of the autocorrelation. 
   SUMMARY 
   The invention features apparatus and methods of measuring optical waveforms. 
   In one aspect, the invention features an optical waveform measurement apparatus that includes a light wave source, a mixer, a down converter, and a controller. The light wave source is operable to provide an adjustable frequency light wave with a frequency that is adjustable over a target frequency range. The mixer is operable to mix a target modulated optical signal with the adjustable frequency light wave to obtain a mixed signal. The frequency down converter is operable to down convert the mixed signal to obtain a down-converted signal. The controller is operable to extract from the down-converted signal amplitude and phase information relating to the target modulated optical signal and to incrementally adjust the frequency of the adjustable frequency light wave over the target frequency range. 
   In another aspect, the invention features an optical waveform measurement method. In accordance with this inventive method, an adjustable frequency light wave is provided. A target modulated optical signal is mixed with the adjustable frequency light wave to obtain a mixed signal. The mixed signal is down converted to obtain a down-converted signal. Amplitude and phase information relating to the target modulated optical signal is extracted from the down-converted signal. The frequency of the adjustable frequency light wave is incrementally adjusted over a target frequency range. The steps of mixing, down converting, and extracting are repeated after each frequency adjustment of the adjustable frequency light wave. 
   Other features and advantages of the invention will become apparent from the following description, including the drawings and the claims. 

   
     DESCRIPTION OF DRAWINGS 
       FIG. 1  is diagrammatic view of an apparatus for generating a target modulated optical signal and a reference clock optical signal. 
       FIG. 2  is a diagrammatic view of an apparatus for measuring a waveform of a target modulated optical signal. 
       FIG. 3  is a block diagram of an exemplary down converter for the optical waveform measurement apparatus of FIG.  2 . 
       FIG. 4  is an exemplary frequency-domain plot of a target modulated optical signal. 
       FIG. 5  is a block diagram of an exemplary controller for the optical waveform measurement apparatus of FIG.  2 . 
       FIG. 6  is a flow diagram of a method of measuring an optical waveform. 
       FIG. 7  is a block diagram of the waveform measuring apparatus of  FIG. 2  incorporated into a sampling light oscilloscope that is coupled to evaluate and inspect temporal response characteristics of a light source system incorporating components of the modulated optical signal apparatus of FIG.  1 . 
   

   DETAILED DESCRIPTION 
   In the following description, like reference numbers are used to identify like elements. Furthermore, the drawings are intended to illustrate major features of exemplary embodiments in a diagrammatic manner. The drawings are not intended to depict every feature of actual embodiments nor relative dimensions of the depicted elements, and are not drawn to scale. 
     FIG. 1  shows an embodiment of an apparatus  10  for generating a target modulated optical signal  12  and a reference clock optical signal  14  that includes a source  16  of a carrier light wave  18 , a source  20  of a modulation signal  22 , and a reference clock extractor  24 . In the illustrated embodiment, carrier light wave source  16  is a laser-based local oscillator that generates an unmodulated carrier light wave that is characterized by an angular frequency of ω l  and a phase θ l . Modulation signal source  20  is implemented in the form of any one of a wide variety of known modulation signal sources. Modulation signal  22  (s(t)) is characterized by a DC amplitude component S[ 0 ] and N harmonic components each characterized by a respective harmonic angular frequency kω r  and respective amplitude S[k] and phase θ[k] components, where k has an integer value from 1 to N. Modulation signal  22  may be expressed as follows: 
               s   ⁡     (   t   )       =       S   ⁡     [   0   ]       +       ∑     k   =   1     N     ⁢           ⁢       S   ⁡     [   k   ]       ·     cos   ⁡     (       k   ⁢           ⁢     ω   r     ⁢   t     +     θ   ⁡     [   k   ]         )                     (   1   )               
where ω r  is the fundamental harmonic frequency (or repeating frequency). Accordingly, modulation signal s(t) includes multiple harmonic components extending from ω r  to ω max =Nω r . The modulation signal  22  is mixed with the carrier light wave  18  in a mixer (or modulator)  26  to obtain target modulated optical signal  12  (f(t)), which may be expressed as follows:
   f ( t )=cos(ω l   t+θ[k ])· s ( t )  (2) 
   Reference clock extractor  24  generates a reference clock signal  28  from the modulation signal  22  (s(t)) using any one of a wide variety of known square wave signal processing techniques. For example, modulation signal  22  (s(t)) may be made square using a nonlinear electronic device (e.g., a diode), a bandpass filter, or a phase-locked loop. Reference clock signal  28  (s′(t)) is a repetitive signal that is synchronized with modulation signal  22  (s(t)) and is characterized by an angular frequency ω r . A portion of carrier light wave  16  is split by an optical splitter  30  and is mixed with reference clock signal  28  (s′(t)) by a modulator  32  (e.g., a known high-speed lithium niobate optical modulator) to obtain reference clock optical signal  14  (f′(t)). 
     FIG. 2  shows an embodiment of an apparatus  40  for measuring the waveform of target modulated optical signal  12  (f(t)) includes an adjustable frequency light wave source  42 , an optical mixer  44 , a down converter  46 , and a controller  48 . Light wave source  42  is implemented in the form of any one of a wide variety of known laser-based local oscillators (e.g., a known variable-wavelength laser) that generates an unmodulated adjustable frequency light wave  50  that is characterized by an angular frequency ω m  and a phase θ m . Mixer  44  may be a known heterodyne mixer that is implemented by a nonlinear optical device that mixes target modulated optical signal  12  and adjustable frequency light wave  50  to obtain a mixed signal  52  (g(t)), which may be expressed as follows:
   g ( t )=cos(ω m   t+θ   m ) f ( t )=cos(ω m   t+θ   m )cos(ω l   t+θ   l ) s ( t )  (3) 
Mixed signal  52  may be rewritten as: 
               g   ⁡     (   t   )       =         1   2     ⁡     [       cos   ⁡     (         ω   s     ⁢   t     +     θ   s       )       +     cos   ⁡     (         ω   d     ⁢   t     +     θ   d       )         ]       ·     s   ⁡     (   t   )                 (   4   )               
where ω d =ω m −ω l , ω s =ω m +ω l , θ d =θ m −θ l , and θ s =θ m +θ l . In the illustrated embodiment, the various angular frequencies are related as follows:
 ω r &lt;ω d &lt;ω max &lt;&lt;ω l &lt;ω m   (5) 
   Mixed signal  52  (g(t)) is down-converted by down converter  46  to obtain a down-converted signal  54  (h(t)). In the example shown in  FIG. 3 , down converter  46  is implemented as a heterodyne detection circuit that includes a photodetector  56  and a low pass filter  58 . Down converter  46  selectively passes the low-frequency components of mixed signal  52 . Down converter  46  is characterized by a low-frequency passband with an angular frequency bandwidth of Δω. In some embodiments, the passband of down converter  46  is narrower than the difference ω d  between the angular frequency ω l  of the carrier light wave  18  of the target modulated optical signal  12  and the angular frequency ω m  of the adjustable frequency light wave  50  (i.e., Δω&lt;ω d ). The resulting down-converted signal  54  may be expressed as follows: 
               h   ⁡     (   t   )       =       ∑     k   =     N   L         N   H       ⁢       1   4     ⁢           ⁢     S   ⁡     [   k   ]       ⁢     cos   ⁡     (         (       k   ⁢           ⁢     ω   r       -     ω   d       )     ·   t     -     θ   d     +     θ   ⁡     [   k   ]         )                   (   6   )             
 
where the angular frequency range of h(t) is constrained as follows:
 
ω d   −Δω&lt;N   L ω r   ≦kω   r   ≦N   H ω r &lt;ω d +Δω  (7)
 
The angular frequency relationships of Equation (7) are illustrated graphically in FIG.  4 . In one exemplary embodiment, Δω is on the order of about 1 GHz, ω r  is on the order of about a few MHz, ω max  is on the order of about 1 THz, and ω l  and ω m  are on the order of about 200 THz. In some embodiments, ω r  is less than or equal to 2Δω.
 
   As seen from Equation (6), down-converted signal  54  (h(t)) includes all of the amplitude and phase components of modulation signal  22  (s(t)) between the angular frequencies N L ω r  and N H ω r . Therefore, in order to obtain all of the amplitude and frequency information for modulation signal  22  (s(t)) between ω r  and ω max =Nω r , ω m  should be swept over an angular frequency range encompassing angular frequencies from about ω l +ω r  to about ω l +Nω r  such that ω d  is swept over the angular frequency range from about ω r  to about ω max . In some embodiments, the down-converted signal  54  (h(t)) is measured, while ω m  (and hence ω d ) is adjusted in increments of 2Δω or less. 
   As shown in  FIG. 5 , in some embodiments, controller  48  includes a signal recorder  60  and a data processor  62 . The down-converted signal  54  (h(t)) is measured and recorded by controller  48 . The signal measurements are synchronized with the reference clock optical signal  14 . Data processor  62  may compute the amplitude and phase components of h(t) by computing Fourier transforms of the recorded data signals as follows: 
               ∫   0   T     ⁢       h   ⁡     (   t   )       ⁢     cos   ⁡     (       kω   r     -     ω   d       )       ⁢     t   ·     ⅆ   t                 (   8   )                 ∫   0   T     ⁢       h   ⁡     (   t   )       ⁢     sin   ⁡     (       kω   r     -     ω   d       )       ⁢     t   ·     ⅆ   t                 (   9   )             
 
In this way, the amplitude components S[k] and the phase components θ[k]−θ d  may be obtained. In some embodiments, the integration period, T, is selected so that kω r T and ω d T are integral multiples of 2π, which allows errors to be reduced.
 
   In order to obtain values for the phase components θ[k] of the target modulated optical signal  12 , the phase component values for θ d  are computed. In the embodiment shown in  FIG. 2 , the phase component values θ d  are determined by mixing the reference clock optical signal  14  with adjustable frequency light wave  50  in a mixer  63  to obtain a mixed signal  64  (g′(t)), which may be expressed as follows:
 
 g ′( t )=cos(ω m   t+θ   m ) f ′( t )=cos(ω m   t+θ   m )cos(ω l   t+θ   l ) s ′( t )  (10)
 
where f′(t) is the reference clock optical signal  14  and s′(t) is the reference clock signal  28 . Mixed signal  64  may be rewritten as: 
                 g   ′     ⁡     (   t   )       =         1   2     ⁡     [       cos   ⁡     (         ω   s     ⁢   t     +     θ   s       )       +     cos   ⁡     (         ω   d     ⁢   t     +     θ   d       )         ]       ·       s   ′     ⁡     (   t   )                 (   11   )             
 
where ω d =ω m −ω l , ω s =ω m +ω l , θ d =θ m −θ l , and θ s =θ m +θ l . In the illustrated embodiment, the various angular frequencies are related as indicated in Equation (7).
 
   Mixed signal  64  (g′(t)) is down-converted by down converter  66  to obtain a down-converted signal  68  (h′(t)). In one embodiment, down converter  66  may be implemented as a known heterodyne detection circuit that includes a photodetector and a low pass filter. Down converter  66  selectively passes the low-frequency components of mixed signal  64 . Down converter  66  is characterized by a low-frequency passband with an angular frequency bandwidth of Δω. In some embodiments, the passband of down converter  66  is smaller than the difference between the angular frequency of the carrier light wave  18  of the reference clock optical signal  14  and the angular frequency of the adjustable frequency light wave  50  (i.e., Δω&lt;ω d ) The resulting down-converted signal  68  may be expressed as follows: 
                 h   ′     ⁡     (   t   )       =       ∑     k   =     N   L         N   H       ⁢       1   4     ⁢           ⁢       S   ′     ⁡     [   k   ]       ⁢     cos   ⁡     (         (       k   ⁢           ⁢     ω   r       -     ω   d       )     ·   t     -     θ   d     +       θ   ′     ⁡     [   k   ]         )                   (   12   )             
 
As seen from equation (12), down-converted signal  68  (h′(t)) includes all of the amplitude and phase components of reference clock optical signal  14  (s′(t)) between the angular frequencies N L ω r  and N H ω r . Therefore, in order to obtain all of the amplitude and frequency information for reference clock optical signal  14  (s′(t)) between ω r  and ω max =Nω r , ω m  should be swept over an angular frequency range encompassing angular frequencies from about ω l +ω r  to about ω l +Nω r  such that ω d  is swept over the angular frequency range from about ω r  to about ω max . In some embodiments, the down-converted signal  68  (h′(t)) is measured, while ω m  (and hence ω d ) is adjusted in increments of 2Δω or less.
 
   The down-converted signal  54  (h′(t)) is measured and recorded by controller  48 . The signal measurements are synchronized with the reference clock optical signal  14 . Data processor  62  may compute the amplitude and phase components of h′(t) by computing Fourier transforms of the recorded data signals as follows: 
               ∫   0   T     ⁢         h   ′     ⁡     (   t   )       ⁢     cos   ⁡     (       k   ⁢           ⁢     ω   r       -     ω   d       )       ⁢     t   ·     ⅆ   t                 (   13   )                 ∫   0   T     ⁢         h   ′     ⁡     (   t   )       ⁢     sin   ⁡     (       k   ⁢           ⁢     ω   r       -     ω   d       )       ⁢     t   ·     ⅆ   t                 (   14   )             
 
In this way, the amplitude components S′[k] and the phase components θ′[k]−θ d  may be obtained. In some embodiments, the integration period, T, is selected so that kω r T and ω d T are integral multiples of 2π, which allows errors to be reduced.
 
   In some implementations, the resulting computed phase terms θ′[k] all will be zero or may be computed in advance by known binary analysis techniques. After all of the phase terms θ′[k] are determined, the values of θ d  may be computed for each angular frequency value. These values may then be used to obtain the corrected phase terms θ[k] for the target modulated optical signal  12 . 
   In some embodiments, in the process of determining S[k], θ[k]−θ d  and S′[k], θ[k]−θ d , the values of k are constrained by the following condition:
 
| kω   r −ω d |&lt;Δω  (15)
 
   Referring to  FIG. 6 , in some embodiments, optical waveform measurement apparatus  40  may be programmed to operate as follows. The frequency of the adjustable frequency light wave  50  is adjusted to the next frequency within the target frequency range (step  70 ). In some embodiments, controller  48  adjusts light wave source  42  to provide an adjustable frequency light wave  50  with an initial angular frequency of about ω l +ω r . The target modulated optical signal  12  is mixed with adjustable frequency light wave  50  to obtain mixed signal  52  and the reference clock optical signal is mixed with the adjustable frequency light wave  50  to obtain mixed clock signal  64  (step  72 ). The mixed signal  52  and the mixed clock signal  64  are down-converted (step  74 ). In some embodiments, the target modulated optical signal  12  and the adjustable frequency light wave  14  may be mixed and down-converted simultaneously. Amplitude and phase information relating to the modulation signal  22  is extracted from the down-converted signals  54 ,  68  (step  76 ). If the adjustable frequency light wave  50  has been swept across the entire target frequency range (step  78 ), the waveform measurement process is terminated (step  80 ). In some embodiments, the final frequency of adjustable frequency light wave  50  is equal to about ω l +Nω r . If the adjustable frequency light wave  50  has not been swept across the entire target frequency range (step  78 ), the process is repeated for the next frequency within the target frequency range (steps  70 - 76 ). In some embodiments, the frequency of the adjustable frequency light wave  50  is adjusted in increments of 2Δω or less. 
   Referring to  FIG. 7 , in one implementation, the waveform measuring apparatus  40  of  FIG. 2  is incorporated into a sampling light oscilloscope  90  that is coupled to evaluate and inspect temporal response characteristics of a light source system  92  that incorporates components of the modulated optical signal apparatus  10  of FIG.  1 . In this implementation, modulator  32  is incorporated within sampling light oscilloscope  90 . Modulator  32  is coupled to optical splitter  30  and optical mixer  44  is coupled to mixer  26  by respective external optical transmission lines. The external optical transmission lines are optical fibers, and the optical transmission lines within sampling light oscilloscope  90  and light source system  92  are optical fibers or spatial optical connections. Modulator  32  is coupled to reference clock extractor by electrical connections. The external electrical connection  94  is an electrical cable and the internal electrical connections  96 ,  98  are circuit board electrical connections. Controller  48  is coupled to adjustable frequency light wave source  42  and a display  100  by respective control and data lines  102 ,  104 . An optical divider  106  splits the adjustable frequency light wave  50 , and respective optical transmission lines  108 ,  110  (e.g., optical fibers) carry the split light wave signals to mixers  44  and  63 , respectively. In some implementations, reference clock extractor  24  may be incorporated in sampling light oscilloscope rather than in light source system  92 . 
   Other embodiments are within the scope of the claims. 
   The systems and methods described herein are not limited to any particular hardware or software configuration, but rather they may be implemented in any computing or processing environment, including in digital electronic circuitry or in computer hardware, firmware, or software.