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7 雷射線寬(Linewidth)及啁啾(chirp)量測 • Measurement of the intensity dynamics can be carried out using a photodetector and a appropriate electronic receiver. • Using the optical mixing and interference techniques,the phase noise and frequency dynamics of optical sources can be measured. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.1 Coherence Time and Linewidth • The coherence time, c , of a laser is measure of the spectral purity of the laser frequency over time. • In two-path interferometers, an optical wave interferes with a time-delayed portion of itself. • The degree of interference depends on the coherence time of the wave with respect to the optical delay. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.1 Coherence Time and Linewidth • Coherence time is reduced by random events, such as spontaneous emission in the laser cavity, which alter the phase or frequency of the laser-output field. • In Fig 7.1(a), the coherence time is longer than that of (b) , since the phase is predictable during the of time . T1 interval T2 T1 (a) T1 T2 T2 E (t) time (b) E (t) Fig.7.1 Concept of coherence time 教育部顧問室光通訊系統教育改進計畫 time Phase jumps 台科大 師大 淡江 東南 萬能 7.1 Coherence Time and Linewidth • The coherence time, c ,varies inversely with laser linewidth, . • It is defined as 1 c for spectra with Lorentzian line shapes 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.1 Coherence Length and Linewidth • The coherence length is the coherence time multiplied by velocity of light: Lc vg c c v • g ng is the group velocity • ng is the refractive index, ( approximately 1.47 in optical fiber) 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.2 Linewidth and Chirp • The phase noise and frequency noise cause spectral broadening in single-longitudinalmode lasers. • Random phase noise is created when spontaneous-emission,originating in the laser cavity gain media,changes the phase of the free running laser frequency. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.2 Linewidth and Chirp • The effective amplitude-phase coupling factor, eff shows the link between power changes in the laser cavity to phase changes of the emitted light. • A large value of eff results in increased laser linewidth. • It results in a broadening of the laser spectral linewidth. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.2 Linewidth and Chirp Frequency Chirp • Laser frequency chirp results in significant spectral broadening when the laser injection current is modulated. • The unwanted frequency modulation (chirp) can broaden the laser spectrum. • The magnitude of the chirp is proportional to the amplitude-phase coupling factor. eff . 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.2 Linewidth and Chirp E(t) time CW optical field E(t) time Chirped optical field Lower frequency region Fig7.2 Optical field with and without frequency chirp 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.3 Methods of Linewidth Measurement • Neither OSA nor wavelength meters have sufficient wavelength resolution to display each longitudinal mode of a laser. • Heterodyne and homodyne measurements can be used to study the intensity dynamics. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.3 Methods of Linewidth Measurement Heterodyne measurements: • The unknown signal is combined with a narrow-linewidth local oscillator (LO) laser. • The LO must have the same polarization as the unknown signal. • The intermediate frequency (IF) signal is analyzed with an electronic signal analyzer such as a spectrum analyzer. S o u rc e U nder T est (L O ) L ocal O s c illa to r 教育部顧問室光通訊系統教育改進計畫 C a lib ra te d R e c e iv e r E le c tric a l S p e c tr u m A n a ly z e r Fig 7.3 Measurement configuration for Heterodyne spectrum analysis 台科大 師大 淡江 東南 萬能 7.3 Methods of Linewidth Measurement Homodyne measurements: • Homodyne techniques are similar to heterodyne analysis except that the LO is a time-delayed version of itself. • If an optical signal is delayed in time by more than the inverse of the source spectral width (measured in Hz), the signal becomes phase independent of the original signal, allowing it to be an effective LO. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.3 Methods of Linewidth Measurement (a)Heterodyne 0 P o w e r (d B m ) P o w e r (d B m ) • The asymmetries of the RB =1 M Hz Fig 7.4 optical spectrum can’t been seen in homodyne (a) Intensity modulation measurement. sideband for -5 0 • The information about 0 .7 5 2 + 3 .2 5 a DFB laser. F req u e n cy D iffe re n c e (G H z ) the center wavelength of (b)Homodyne (b) Unmodulated a laser is not shown in 0 Linewidth R B = 0 .1 M H z homodyne method. measurement -3 d B of a DFB • Both methods can be U n m o d u la te d laser. D F B la s e r used to characterize laser lin e w id th -2 0 chirp . 0 .5 100 F re q u e n c y (M H z ) 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.4 Delayed Self-Heterodyne Linewidth Measurement • The delayed self-heterodyne technique can perform linewidth measurements without the requirement of a separate local oscillator laser. i (t ) Es (t ) E (t ) 0 教育部顧問室光通訊系統教育改進計畫 Fig7.5 Delayed self-heterodyne Optical measurement setup Frequency Shifter (AO) 台科大 師大 淡江 東南 萬能 7.4 Delayed Self-Heterodyne Linewidth Measurement • Incident light is split into two paths by the interferometer. • The optical frequency of one arm is offset with respect to the other. • If the delay, 0 ,of one path exceeds the coherence time, c , of the source, the two combining beams interfere as if they are originated from two independent lasers offset in frequency by i(t) Es(t) frequency shift Fig7.6 Equivalent circuit when the interferometer delay time is larger than the signal Coherence time( 0 c) 教育部顧問室光通訊系統教育改進計畫 E (t ) Es (t ) 台科大 師大 淡江 東南 萬能 7.4 Delayed Self-Heterodyne Linewidth Measurement • The incoherent mixing requires a minimum delay requirement of the interferometer with respect to the laser’s linewidth: 0 1 • When this condition is satisfied, the mixing becomes independent of the phase of the interfering light and the measurement is stable. • The delayed self-heterodyne photocurrent consists of direct detection as well as the desire mixing point: Si ( f ) R 2 S d ( f ) 2S s ( ) S s ( ) (ESA=>direct direction + self-heterodyne spectrum) 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.5 Delayed Self-Heterodyne Linewidth Measurement S E ( ) • is the shift frequency applied to the field traversing one arm of the interferometer and R is the usual detector responsivity. • The displayed lineshape will always be symmetrical,even if the original lineshape had important asymmetries. s S E ( ) ~ 200THz convolution s Si ( f ) 2 0 80MHz frequency Fig 7.7 The delayed self-heterodyne mixing of the laser field with a frequency shifted replica. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.4 Delayed Self-Heterodyne Linewidth Measurement • For the case of a Lorentizan-shaped field spectrum, the displayed lineshape will be twice of the actual linewidth. • Laser sources exhibiting frequency jitter or 1/f noise will yield larger measured linewidths. • A larger delay yields a larger linewidth. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.4 Delayed Self-Heterodyne Linewidth Measurement • The frequency shift in delayed selfheterodyne linewidth measurements can be obtained a verity of devices including acousto-optic frequency shifters, phase modulators, and intensity modulators. • The frequency shift should be larger than the spectral content of the laser under study. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.4 Delayed Self-Heterodyne Linewidth Measurement An Example (from “Fiber Optic Test and Measurement”, edited by D. Derickson) • An acousto-optic frequency provide an 80 MHz shift frequency for a delayed self-heterodyne linewidth measurement as shown in Fig. • The preamplifier following the photodiode provided high gain(~30dB)to reduce the effects if the ESA noise on the sensitivity of the electronic spectrum analysis. Fiber delay PS Fig 7.8 Optical self-heterodyne input for laser linewidth Es (t ) measurement . 80MHz 0 PC E (t ) SMF AOFS G ESA photodiode Diffracted beam AOFS=acousto-optic Frequency shifter Undiffracted beam stop Power oscillator amplifier 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.5 Delayed Self-Homodyne Linewidth Measurement • The delayed self-homodyne technique can measure the linewidth of an unmodulated laser. • This method has high resolution afforded by using optical interferometers with low-loss fiber optic delays. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.5 Delayed Self-Homodyne Linewidth Measurement • Several optical circuit implementations for the delayed selfhomodyne method are shown in Fig.7.9 input (from “Fiber Optic Test and input Measurement”, edited by D. Derickson) (a)Mach-Zehnder interferometer Fiber delay 0 PS E (t ) SMF i(t) ESA photodiode PC Fiber delay PS (b)Michelson interferometer i(t) 0 E (t ) SMF PC mirror ESA photodiode Fig 7.9 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.5 Delayed Self-Homodyne Linewidth Measurement • The photocurrent spectrum for the delayed selfhomodyne technique consists of direct detection as well as the desired mixing product but without the frequency shift: 2 Si ( f ) R Sd ( f ) 2 Ss () Ss () (ESA=>direct direction + self-homodyne spectrum) • The displayed lineshape will always be symmetrical,even if the original lineshape had important asymmetries. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.5 Delayed Self-Homodyne Linewidth Measurement • The translation of linewidth information from the optical spectrum to electrical spectrum is illustrated in Fig. • For the case of laser lineshapes described by Lorentzian or Gaussian functions,the displayed electrical power spectrum will have identical functional shapes to the actual optical spectrum. S E ( ) s S E ( ) convolution s Si ( f ) 2 Fig 7.10 The delayed self-homodyne mixing of the laser field. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 frequency 淡江 東南 萬能 7.6 Laser Chirp Measurement • Measurement of chirp provides the dynamics of the laser frequency excursions during intensity modulation. • The time dependence of frequency chirp can be characterized using optical discriminators to convert optical frequency variations into detectable intensity variations. • A linear optical component with wavelengthdependent transmission characteristics may serve as a discriminator. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.6 Laser Chirp Measurement • An interferometer circuit for measuring laser chirp as shown in Fig . (from Fiber Optic Test and Measurement, edited by D. Derickson) • The differential time of flight between the two interference path is denoted by 0 . 教育部顧問室光通訊系統教育改進計畫 Quadrature Feedback circuit lens PZT idc idc PC Computer A SOURCE laser B Es (t ) z collimator modulation scope i(t ) Bias T E (t ) High-speed receiver to:scope trigger Fig 7.11 Time-domain laser chirp measurement using A Mach-Zehnder interferometer followed by A high-speed receiver. 台科大 師大 淡江 東南 萬能 7.6 Laser Chirp Measurement • A feedback circuit maintains quadrature by adjusting the delay 0 . • This delay adjustment is small,on the order of an optical wavelength. • This delay can be realized using piezo-electric(PZT) devices. • The measurements apparatus uses a sampling oscilloscope which is triggered by the laser modulation source. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.6 Laser Chirp Measurement Analysis. • For interferometers with two optical paths,the average output power interferometer is the sum of the path power contributions and an interference term: P (t ) P (t ) P (t ) 2 P (t ) P (t ) cos( (t , ) 2 ) 0 1 2 1 2 0 0 0 0 is the average optical carrier frequency and 0 is the differential interferometer delay. • In the absence of any frequency modulation, (t ) is zero 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能 7.6 Laser Chirp Measurement Interferometer Delay Requirement. • To maintain unambiguous chirp measurement,the peak frequency excursion peak must be less than one-forth the interferometer free-spectral range. • To reduce the effects of noise on the chirp measurement ,the maximum chirp is confined to the approximately linear region of the interferometer characteristic : peak 教育部顧問室光通訊系統教育改進計畫 台科大 師大 FSR 1 8 8 0 淡江 東南 萬能 7.6 Laser Chirp Measurement (a) 1Gb/s 200ps Example. (from “Fiber Optic Test and Measurement”, edited by D. Derickson) (b) 10 . 5 0 Fig 7.12 Optical discriminator used to measure DFB laser.(a) Intensity Modulation.(b)Frequency chirp. 教育部顧問室光通訊系統教育改進計畫 time -5 -10 台科大 time 師大 淡江 東南 萬能 7.6 Laser Chirp Measurement • Since the measurement is made in the time domain, both the magnitude and the phase of the amplitude and frequency modulation are measured. • This technique can also be applied towards frequency domain measurements of the FM response by characterizing laser FM response as a function of modulation frequency applied to the laser. 教育部顧問室光通訊系統教育改進計畫 台科大 師大 淡江 東南 萬能