A METHOD OF MEASURING A MODE PARTITION CHARACTERISTIC OF A LASER DIODE AND AN APPARATUS OF THE SAME

Abstract: An apparatus and a method for measuring a mode parti­ tion characteristic of a laser diode with a so-called k-value (k factor), in which the PN (Pseudo Noise) pulse pattern is used for modulation of laser diode to be measured on the occasion of measuring various parameters required for cal­ culation of the k value.

Description: The present invention relates to a method of measuring a mode partition characteristic of a laser diode and an apparatus thereof. Investigations for practical use of a high speed optical transmission system utilizing laser diode (LD) is recently progressing rapidly and therefore evaluation for optical transmission system is more and more considered as an important subject from the point of view of system design, etc. In general, output optical signal of a laser diode include a plurality of wavelength elements, for example, λ₀, λ₁, λ₂ ..., as illustrated in Fig. 1(b) which shows the spectra of output optical signal of a laser diode at times t₀, t₁, t z . Each wavelength element is called a longitudial mode. In case an LD outputs the optical signals at the times t₀, t₁, t₂ corresponding to the data having a mark as illustrated in Fig. 1(a), if the three modes λ₀, λ₁, λ₂ exist, the total power P t of an optical signal is partitioned in such a manner as P₀ % for λ₀, P₁ % for λ ₁, and P₂ % for λ₂, ( P₀ + P₁ + P₂ = 100 ) (Mode partitioning). However, when condsidering individual optical signals corresponding to each binary data such as the PCM data, power P₀, P₁, P₂ of each longitudial mode are respectively different for each optical signal at the time t₀, t₁, t₂, and are dispersed along a certain distribution curve around the average values of P ₀, P ₁ and P ₂. This optical power partition to each longitudial mode generates the noise called a mode partition noise. This noise is caused by fluctuation of the reaching time of each longitudial mode at the receiving side. Namely, refractive index in the optical fiber is different in accordance with the wavelengths, λ₀, λ₁, λ₂,.... and therefore the reaching time at the receiving side is different for each wavelength. So the power ratio of each longitudinal mode is changed, received waveform sways, and after all data error rate increases. (When λ ₁ < λ ₂, the refractive index of λ ₂ becomes larger and the reaching time becomes longer) Therefore, it is very important for system design to know the degree of mode partition. Particularly fluctuation of said reaching time is not negligible for high speed data transmission, for example, of 405 Mb/s, 810Mb/s or optical transmission path with longer repeater spacing. On the contrary, data transmission rate or repeater spacing can be limited in accordance with the mode partition. A sign for determining the mode partition character is so-called a k-value (k factor). The k-value is determined uniquely for each LD. This k-value is defined as follows. When P T is total power, P i is optical power partitioned to the longitudial mode of wavelength λ i and P i is a mean value of P i , the following relation can be obtained. (P i ²) -( P i )² = P T ² x(ζ) a i (1-a i ) (P i ² - P i ²); dispersion where, x(ζ) = 1/(1+ζ) = K² , P i = a i P T , and ζ is mode partition constant. Namely, a k-value is related to dispersion of optical power partitioned to each longitudial mode. Therefore, partition of optical power to each longitudial mode along the partition curve defined by this k-value changes for each laser pulse. According to introducing a k-value, a ratio of the continuous spectrai element W cont (f) (mode partition noise element) and line spectral element W line (f) of received signal is given by the following equation (1). W cont (f)/W line (f) = k² ((1-a i )/a i ).T,Δf (1) In the above equation (1). (1) k is a k-value of LD (2) a i is an average relative intensity of i-th longitudial mode in the spectrum of 1D output optical signal (therefore, (3) T is a period of fixed pulse pattern (4) Δ f is a band width of selective level meter for measuring spectral element Here, W cont (f), W line (f) and a i are respectively measured by measuring instruments and a wanted k-value is obtained by substituting such values into above equation (1). Example of the practical values is as follows. k-value Relative strength of vertical mode 0.36 0.55 0.29 0.12 0.25 0.071 As explained above modulation of LD is carried out with the fixed pattern in the conventional mode partition character measuring system. Namely, LD is driven using a fixed pulse pattern generator. As this fixed pulse pattern, "100100100...", for example, is used. One fixed pulse pattern is set, as explained above, based on the fact that above equation (1) can be guided easily and the line spectrum and continuous spectrum can be isolated very easily. Such a system is known from the IEEE Journal of Quantum Electronics, Vol. QE-18, No. 12, December 1982, pages 2000 - 2004 in the article by K. Iwashita et. al. entitled "Mode Partition noise characteristics in high-speed modulated laser diodes". However, such single fixed pulse pattern is too intentional and is not practical. Therefore, here arises a problem that a k-value to be obtained is not always a believable value. It is accordingly an object of the present invention to provide a measuring apparatus and a method for measuring a mode partition characteristic of a laser diode under the condition near the actual drive condition. The objects of the invention are solved by an apparatus for measuring a mode partition characteristic of a laser diode comprising: a first means driven by a clock signal of period T, for generating an N-bit-length pseudo noise pattern; an opto-electric conversion means including a laser diode to be measured, for outputting optical signal modulated by said pseudo noise pattern, second means for separating a particular longitudinal mode from said optical signal, third means for detecting power P i of said particular longitudinal mode, fourth means for detecting a line spectral element W line (f) and continuous spectral element W cont (f)' of said particular longitudinal mode, and processing means for calculating a coefficient which indicates a mode partition characteristic by obtaining a relative power a i of said particular longitudinal mode with respect to total longitudinal mode power, a ratio of line spectral elements to continuous spectral elements and a coefficient defined by a number of N-bits of pseudo noise. The objects of the invention are also solved by a method of measuring a mode partition characteristic of a laser diode comprising the following steps; modulating said laser diode by pseudo noise having a period NT, measuring relative intensity of a particular longitudinal mode with respect to all longitudinal modes of an output optical signal of said laser diode, measuring the line spectral element and the continuous spectral element of said particular longitudinal mode and calculating a coefficient which indicates a mode partition characteristic of said laser diode from measured values and a coefficient defined by N-bits of pseudo noise. Brief description of the drawings; Fig. 1 is a pictorial presentation for explaining the mode partition of an L.D., Fig. 2(a) is a block diagram of an apparatus for measuring a mode partition characteristic of a laser diode to which the present invention pertains, Fig. 2(b) is a flow chart for explaining control steps of Fig. 2(a), Fig. 3 illustrates an example of the PN pulse pattern generator. Fig. 4 indicates power spectral density of the received optical output modulated by the PN pattern, Fig. 5 illustrates result of measuring k-value, Fig. 6 illustrates result of measuring k-value, Fig. 7 illustrates optical signal for all longitudinal modes, Fig. 7(A) is a graph measured in the time domain, while Fig. 7(B) is a graph measured in the frequency domain, Fig. 8 illustrates optical signal for particular longitudinal modes, Fig. 8(A) is a graph measured in the time domain, while Fig. 8(B) is a graph measured in the frequency domain, Fig. 9 is a pictorial presentation for explaining a ratio of continuous spectral intensity to line spectral intensity, Fig. 10 is an example of the optical signal waveform of the particular longitudinal mode i, Fig. 11 is a power spectrum of a mode partition nose in the PN modulation, Fig. 12 illustrates the PN impulse series, Fig. 13 illustrates a self-correlation function of the PN impulse series, Fig. 14 illustrates a power spectral density of the PN impulse series, Fig. 15 illustrates the PN series of ordinary waveform, Fig. 16 illustrates the PN series of ordinary waveform by disassembling it into sum of the PN impulse series, Fig. 17 is outline of power spectral density of PN series of RZ pulse. Fig. 18 is a self-correlation function when a number of stages of PN is infinitive, Fig. 19 is a diagram for explaining the development of equation, Fig. 20 illustrates transfer from the line spectrum to continuous spectrum for the RZ output waveform. Fig. 1 illustrates a block diagram of an apparatus for measuring a mode partition characteristic of a laser diode, where a PN pulse pattern is used for the LD modulation signal. Namely, an LD has been modulated by the fixed pulse pattern for measuring of k-value in the existing method, but in Fig. 1, the PN (Pseudo Noise) pulse pattern is utilized of an LD modulation signal. Use of PN pulse pattern reproduces the environment more similar to the actual data pattern and the k-value thus obtained is sufficiently believable. It should be noted here that the PN pulse pattern has been introduced as the pulse pattern in place of simple random pulse pattern and fixed pulse pattern. Accordingly, in the mode partition characteristic measuring system, an LD modulated by the PN pulse pattern generator is remarkably unique. In the mode partition characteristic measuring system to which the present invention pertains, as will be explained complementarily in greater detail, a k-value can be obtained from the following equations (2) and (3). Each letter and symbol have the same meaning as those in the equation (1) (where, T is bit period) and N is newly introduced. N is a bit length of one period of the PN pulse pattern. G(f) is the Fourier transform of received waveform of modulated optical signal. Here. W cont (f), W line (f) and a i are measured resepectively by the specified measuring instrument and a k-value can be obtained by substituting these values into the equation (2) or (3). In comparison of the conventional equation (1) with above equations (2), (3) in relation to the present invention, it can be seen that there is no distinctive modification in the equations themselves in spite of the fact that the PN pulse pattern which is more complicated than the conventional fixed pulse is employed. This is because of focusing on periodicity of the self-correlation of the PN pulse pattern in the present invention and the equations (2), (3) which are not largely different from the equation (1) can be obtained by utilizing this periodicity. It will be proved later theoretically. Fig. 2(a) shows an apparatus for measuring a mode partition character of a laser diode in detail. In this figure, 12 is a spectro-photometer , 13 is an optical attenuator , 14 is an optoelectric converter, 15 is a selective level meter, 21 is a PN pulse pattern generator and LD is a laser diode. In order to assemble a measuring apparatus, an oscillator (OSC) 20 is first necessary. The oscillator 20 drives the PN pulse pattern generator 21. An example of this generator 21 is illustrated in Fig. 3 described later. A laser driver (DRV) 22 receives the PN pulse pattern and drives the laser diode LD to be measured, causing it to generate optical signal modulated by PN pattern. This optical signal inputs a first optical switch (SW) 23 and it is herein switched to the first direction (arrow mark of solid line) or the second direction (arrow mark of dotted line). The optical signal divided to the first direction inputs to a spectro-photometer 12 and only the light element of particular longitudinal mode is output therefrom. L1, L2 provided in the preceding and succeeding stages of such spectro-photometer are optical systems such as lens, etc. Meanwhile, the PN modulated optical signal divided to the second direction is input to the optical attenuator 13. The optical signal from the spectro-photometer 12 (first direction) and the optical attenuator 13 (second direction) are both arranged in the direction 1 by a second optical switch 24. The optical signal from the second optical switch 24 is directed again to the first and second directions. Namely, the third optical switch 25 guides the optical signal directed to the first direction (arrow mark of dotted line) to an optical power meter (PWM) 26, and also guides the optical signal directed to the second direction (arrow mark of solid line) to the opto-electric converter (OR) 14. The opto-electric converter 14 receiving the optical signal converts it into an electrical signal and then applies it to the selection level meter (SLM) 15. Except for said laser diode LD to be measured and the opto-electric converter 14, said various units (20,21, 22, 23, 24, 25, 26, 12, 13, 15) are all driven and controlled by the specified timing by a controller 28. Particularly the drive timing control for first, second and third optical switches 23, 24, 25, optical power meter 26, spectro-photometer 12, optical attenuator 13 and selective level meter 15 is important for obtaining the required data. Namely, on the occasion of guiding a k-value with the arithmetic operations from said equations (2) and (3), necessary data W cont (f), W line (f) and a i are obtained under the control of controller 28. The data W cont (f) is finally obtained from the selective level meter 15, but since thermal noise and shot noise are subtracted from the continuous spectrum element of the output of the opto-electric converter 14, attenuation level is adjusted so that an input level at the converter 14 through the spectro-photometer 12 becomes equal to an input level at the converter 14 through optical attenuator 13. In this case, the drive timing control is required for the units 23, 24, 25, 26, 12 and 13. Moreover, on the occasion of attaining the data a i (defined freely as i = k), the drive timing of the units 23, 12, 24, 25 and 26 is controlled in order to read the first, second ...., k-th, ...n-th optical powers P₁, P₂, ..., P k , .....P n with power meter 26, respectively. Finally, a k can be obtained from P k /(P₁ + P₂ + ..... P k + .....P n ). This arithmetic operation is carried out by the data processing unit 27 indicated in the right lower part of Fig. 2(a). This data processing unit 27 is given W cont (f) and W line (f) as the input data and calculates a k value. Therefore, it is preferable that the data processing unit 27 comprises a microprocessor. Fig. 2(b) is a flowchart for explaining operations of the controller 28 and the processor 27. In the step 2, the period T of clock generated by the OCS 20 and a number of stages Z of PNPPG21 (a number of stages of FF illustrated in Fig. 3) are set to the processor 27. In the step 5, a wavelength band of spectro-photometer 12 is adjusted and only the particular longitudinal mode ai of wavelength λ i is extracted from the output optical signal of LD. In the step 6, the switches SW23, 24 are controlled to output the optical signal to the solid line side, while SW25 to the dotted line. In the step 7, through above switching control, an optical power P i of the particular longitudinal mode a i having passed the spectro-photometer 12 is measured by PWM26. In the step 8, the switches SW23, 24 are switched to the dotted line side. In the steps 9 and 10, attenuation level of ATT 13 is adjusted so that the level of the optical power P t of total longitudinal modes of LD having passed ATT13 become equal to that of P i . In the step 11, the switches 23, 24, 25 are switched again to the solid line side. In the step 12, band of SLM15 is adjusted so that the frequency K/NT which is equal to the K-times (K is integer) of the PN pattern frequency 1/NT can be set within the frequency band Δf of SLM15. In the step 14, a measured value of SLM15 at the frequency K/NT is obtained. This measured value is the line spectral intensity W line of the longitudinal mode a i . In the step 15, the band SLM15 is deviated by +Σ (+Σ is a small value) from K/NT in order to obtain the continuous spectral intensity W cont ' near the line spectrum element. In the step 16, a measured value of SLM15 near the frequency K/NT is obtained. This measured value becomes the continuous spectral intensity W cont ' of the longitudinal mode a i , but this value contains the spectrum of thermal noise and shot noise of OR14. In step 17, the switches SW23, 24 are switched to the dotted line side so that all the longitudinal modes of output optical signal of LD can pass through ATT13 adjusted in the step 10. In the step 18, a measured value of SLM15 at the frequency K/NT + Σ can be obtained. This measured value is the continuous spectral intensity W cont '' of total longitudinal modes and ATT13 is adjusted so that P i = P T . In general, since the continuous general spectrum element for all longitudinal modes results form thermal noise and shot noise, W cont k given by W contk = W cont ' - W cont '' becomes the continuous spectrum element of longitudinal mode a i from which those of the thermal noise and shot noise are eliminated. In the step 19, said W cont k is calculated and a ratio W k of continuous spectral intensity W cont k and line spectral intensity W line is also calculated. Measured values of a plurality of line spectral intensities for vertical mode a i can be obtained by executing the processing at each frequency (1/NT, 2/NT, ......, k/NT, ......n/NT) and also at the neighboring frequencies (1/NT + Σ, 2/NT + Σ, ......K/NT + Σ, ...... n/NT + Σ ) and thereby measured values of a plurality of continuous spectral intesities for the longitudinal mode a i can be obtained. Then, a mean value W of W k is obtained. In this case, measurement is executed at the frequency for W line > W cont '. This is because SLM15 cannot separate the line spectrum and the continuous spectrum when W line < W cont '. Then, a mark ratio M = (N+1)/2N = 2 Z /2 (2 Z -1) of PN pattern corresponding to the equation (3) is obtained (step 21 ). Moreover, above processings are executed for each longitudinal mode (a₁, a₂, ..., a₁, ...., a m ) and thereby relative intensity a i of P i for the power of total modes (step 23 ). In the step 24, a value measured and calculated in each step is substituted into the equation (3) in order to obtain a k-value of the particular longitudinal mode. Fig. 3 is an example of PN pulse pattern generator and is already known. When a period of Pn pulse pattern is N-bit length, the D-flip-flops 31-1, 31-2,......31-m,....,31-Z of Z stages are cascade-connected and each stage is driven by the oscillator (OSC) 20 to form the Z-stage shift register. Moreover, the specified PN pulse pattern output PN out can be obtained by feeding back the output of the m stage and that of the final stage, Z stage, to the initial stage through the EXOR gate 32. Various kinds of patterns of Pn pulse can be selected in accordance with selection of an intermediate stage, m stage, from which output feedback to the gate 32. The Fig. 3 illustrates the structure of primitive polynomial X n + X m + 1 . Fig. 4 is a diagram illustrating power spectral density of output optical signal of LD modulated by PN pattern. The horizontal axis represents frequency, while the vertical axis power spectral density. Various conditions for obtaining this diagram are that the PN pattern is RZ (return to zero), a number of stages of shift register Z in Fig. 3 is 3 (PN3) and frequency (f b ) of PN pattern is 405 Mb/s. Therefore, T of said equation (2), (3) is 1/f b . In addition, f b /N in the lower left in Fig. 4 is an interval f b /N per bit. N is a bit length of a period of PN pulse pattern as described previously (in this case, N = 2³ - 1 = 7). Fig. 5 illustrates measuring result of k-value, particularly searching dependency on number of stages of PN. PN3, PN4, ... given to the data marked by block circle indicates three stages, four stages,.... In addition, measuring frequency of selective level meter is ranged from 135 MHz to 175 MMHz. Meanwhile, the data with white circles and triangles have been obtained by the conventional method (fixed pulse pattern) and the data with white circle has been obtained using the fixed pattern of (100100.....) while the data with triangle obtained using the fixed pattern of (10001000....). As indicated in this figure, these data are smaller than the data obtained using the fixed pattern irrespective of a number of stages of PN. This means that a value of k which is a little larger than the actual k-value has been measured in the conventional method. Fig. 6 illustrates a result of measurement of k-value. Particularly, variations of measured value in case the measuring frequency (frequency of selective level meter) is changed have been search for PN10. The white circle data and triangle data in the same figure are similar to that in Fig. 5. Hereinafter, the concept of the present invention will be explained in greater detail in comparison with the conventional method. A k-value can generally be measured by the method in the time domain or by the method in the frequency domain. The former is difficult because a particular unit such as sampling unit is necessary. Accordingly it is preferable to measure the k-value by the latter method. The measuring system of the present invention (Fig. 1) corresponds to the latter method. Discussion will be made hereinafter to the conventional method where the PPG output is employed as the fixed pattern and the method of present invention where it is employed as the PN pattern. Method by fixed pulse pattern (conventional method) For simplification, considered here is the case where PPG output is set to the fixed pulse pattern to which the mark ("1") of 1 bit is entered within one period. In this case, the pulse amplitude of all longitudinal modes optical output of LD does not change with time, but when only the optical output of a particular longitudinal mode is extracted, the pulse amplitude thereof as a whole sways. The continuous spectrum by such swaying element is indicated as the curve 2 of Fig. 8(B) described later. Fig. 8 and Fig. 7 indicate comparison of optical outputs for the fixed pulse pattern (100100.....). Fig. 7 illustrates optical outputs of all longitudinal modes; (A) is a graph measured in the time domain while (B) in the frequency domain. Fig. 8 illustrates optical outputs of particular longitudinal mode; (A) is a graph measured in the time domain while (B) in the frequency domain. The perpendicular arrow mark of Fig. 8(B) is the line spectrum by means element of the particular longitudinal mode level. When thinking in the frequency domain, only the line spectrum element exists in the optical outputs of all longitudinal modes, but the continuous spectrum element by the sway is also added to such line spectrum in the optical outputs of the particular longitudinal modes. A value of k can be obtained as described below by measuring a ratio of such line spectrum element and the continuous spectrum element. The line spectrum element W line (f) and continuous spectrum element W cont (f) in case that only the i-th longitudinal mode among the N-longitudinal modes of optical signal spectrum is extracted can be obtained as indicated by the following equations where the Probability P (a i ; α i , β i ) for optical level of i-th longitudinal mode to become a i times (normalized intensity of i-th longitudinal mode, 0 < a i < 1) of the optical levels of all longitudinal modes is considered as the coefficient of delta function indicating the line spectrum. a i ; a mean value of a i . δ(f - (n/T)) ; a delta function and indicates the line spectrum corresponding to frequencies 1/T, 2/T, ....n/T in Fig. 7. G₁(f); Fourier's transform of optical output waveforms of all longitudinal modes Ga i (f); Fourier's transform of optical output waveforms when optical output of i-th longitudinal mode is a i times of the optical outputs of all longitudinal modes, Ga i (f) = a i · G₁(f) In addition, Wherein, α i = ζ a i β i = ζ (1 - a i ) ζ : mode partition constant (k² = 1/(ζ +1)) Therefore, the equation (4) indicates the line spectrum W line (n/T) in Fig. 7. Meanwile, the continuous spectral element can be obtained as the dispersion of G ai , and Here , a i ² - (a i ) ² indicates dispersion of a i . Moreover, from the property of beta distribution, Therefore, as illustrated in Fig. 9, taking a ratio of the line spectral intensity of the particular line spectral frequency n/T to the neighboring continuous spectral intensity from said equations (4),(5), Here, Δf is the bandwidth of selective level meter (SLM) and ε is frequency deviation of selective level meter from line spectral frequency corresponding to the continuous spectrum to be obtained. This is because the band width of selective level meter must be deviated by Σ from the line spectral frequency on the occasion of measuring the continuous spectrum since the line spectrum and continuous spectrum are indicated in overlap and these cannot be discriminated in the selective level meter. From the equation (6), a k-value can be obtained since other parameters may be obtained by measurement. Fig. 9 is a pictorial presentation for explaining a ratio of continuous spectral intensity to line spectral intensity. Only one mark is given in the one period of pattern, the formula (1) can be adopted. For example, the formula (6) can be adopted for the patterns such as 100100100..... 101010.... 1111..... In actual measurement, since thermal noise and shot noise are added to the continuous spectrum, these must be separated. This purpose can be satisfied by obtaining difference of continuous spectrum elements in the cases where the optical output of all longitudinal modes are applied in the same optical input level and the optical input of single longitudinal mode is applied. Method by PN pulse pattern (present invention) The method of measuring k.value by the fixed pulse pattern provides a problem that the measurement is carried out under the condition different from that of actual use. Namely, the data modulating LD is random pattern under the actual condition for use. Therefore, measurement utilizing the PN pulse pattern will then be discussed in detail. the principle is the same as the case where the fixed pulse pattern is used. For guidance of the equation (6) using the fixed pattern, a i has been treated as the single dimensional numerical value corresponding to a number of wavelength spectrum because only one mark is given to the one period, but when the PN pattern is used, above equation (6)cannot be used because a number of marks in the one period of PN pattern is not always one. With reference to Fig. 10 which illustrates an example of the optical output waveform of the particular longitudinal mode i, NT corresponds to the one period of PN pulse pattern (N bit length, N = 2 Z - 1 in the case of Z-stages of flip-flop circuits). The optical output waveform of the particular vertical mode i is given in Fig. 10 and in this case the waveform of the one period of PN is defined as PNAi(t). Where A i indicates a pair of (a i1 , a i2 , ......., a iN ). Here, the power partition of each bit is considered to be independent as in the case of the fixed pattern. Moreoever, definition is made as follows. In this case, power spectral density w(f) of optical output waveform is given by the following equation. Next, each term of the equation (7) is calculated as follow. Here, b ℓ : 1 when the ℓ-th bit is mark or 0 when the ℓ-th bit is space g ℓ (t -ℓT): optical output waveform of all longitudinal modes of ℓ-th bit From above relation, Here, since the power partition can be thought to be independent for any bit, a il ² - ( a il )² = a i ² - ( a i )² Since is a mark rate (M) of one period of PN pattern, if is defined as M, On the other hand, the line spectral element w line (f) is Where, Wherein and the nth order complex Fourier's expansion coefficient of PN(t). Fig. 11 illustrates power spectrum of mode partition noise in the PN modulation. Where, the RZ pulse is used. The concept of w cont (f) and w line (f) can be attained from Fig. 11. As in the case of the fixed pulse pattern, when a ratio of line spectral intensity w line (f) of line spectrum frequency f line to the continuous spectral intensity near f line is obtained, from above equations (8) and (9), Above equation (11) is an approximate value when the number of stages of PN is infinite . This equation (11) will be proved later. Next, a power spectral density (line spectrum) of the PN series (PN pulse pattern) is obtained and when a number of stages of PN series is large, it comes close to the power spectral density of the perfectly random binary code series (actual data) and may be reviewed as the actual data by using the PN series and above equation (11) is also effective when a number of stages of PN is finite. As illustrated in Fig. 3, it is here considered that an output is obtained from the Q side of the shift register which is formed in accordance with the primitive polynomial as the PN series. In this case, a mark ratio M of output is defined by the following relation when a number of bits of one period is considered as N. N = 2 Z - 1 Where, Z is a number of stages of flip-flops. M = (N + 1)/2N (P ≈ 1/2 when N » 1) For better outlook, the PN series forming an output as the impulse is considered and then the PN series of the desired output waveform is also considered (Fig. 3 is the PN series of the NRZ output waveform). The majority of the result obtained here can also be adopted to the PN series of desired mark ratio when a number of stages of PN is large. (b) PN impulse series Here, the period of one bit in the PN series is defined as T and a bit length as N. In this case, the PN impulse series can be developed to the Fourier's series where the frequency is an integral multiple of 1/NT. Fig. 12 illustrates the PN impulse series. The one period of PN impulse series is written as PN i (t) and is expressed by the following equation Here, a i ; 1 when the i-th time slot is mark 0 when the i-th time slot is space δ (t); Delta function of Dirac When the equation (12) is expanded into the Fourier's series, the nth expanded coefficient C n is expressed as follows. The power spectrum density w PNi (f) of the PN impulse series can be obtained as indicated below. Here, Cn* is the conjugate complex of Cn. Next, the power spectrum density is obtained using the self-correlation function of the PN series. The self-correlation function  ii (τ) is indicated in Fig. 13 due to the property of PN series. Namely, Where, T is the period of one bit of PN. Therefore,  ii (τ) can be expanded into the Fourier's series where the frequency is an integral multiples of 1/NT. Here, the section (0, NT) of one period of PN is replaced with (- ε, NT -ε) for integration of the delta function. From the formula of reverse conversion of the Fourier's integral, Depending on the theory of Wiener-Khintchine, the power spectrum density w PNi (f) is equal to the Fourier's transform of the self-correlation function  ii (τ). Accordingly, Here, the power spectrum density of PN impulse series is illustrated in Fig. 14. In comparison with the equation (14), C n ·Cn* = f n Namely, Namely, the equation (11) has been proved. (c) PN series of ordinary waveform Fig. 15 is the PN series of ordinary waveform. Here, one bit of of mark waveform is considered as g(t), the PN(t) of one period of PN is expressed as follow. The nth order Fourier's expansion coefficient h n is expressed as follow. Where, G(f) ≡ F{g(t)} and the intersymbol interference is considered not to exist. From the equations (17) and (15), h n = c n ·G(n/NT) (18) Therefore, power spectrum density w PN (f) is expressed as follow. Above equation(18) can be understood direclty by thinking it as illustrated in Fig. 16. Fig. 16 illustrates the PN series of ordinary waveform in such a form as disassembled sums of the PN impulse series. From Fig. 16, Said formula (18) can be guided immediately from above relaiton. From above formulae (18), (20), w PN (f) = |G(f)|² w PNi (f) (21) Fig. 17 illustrates outline or power spectrum density of the PN series of RZ pulse. Where, this figure corresponds to the case of three stages of PN. (d) A number of stages of PN → Infinitive(check of result) In this case, the self-correlation function  ii (τ) of the PN impulse series is as indicated in Fig. 18. Fig. 18 illustrates the self-correlation function when the stages of PN is considered as infinitive. Since this is a sum of the (M²/T) x δ(τ) train of the period T and the (M(1-M)/T) x δ(τ) train of the period NT, In the right side of above formula, the first item is the timing element (corresponding to the short arrow mark group D between the arrow marks A to C of Fig. 18) and the second item is the element to be transfered to the continuous spectrum. It can be expressed by the Fourier's sereis as indicated below. Therefore, Accordingly, Here, if N is considered as infinite (refer to Fig. 19), therefore, In the case of PN series of the ordinary waveform, above relation can be transformed as follow using said formula (20). This is equal to power spectrum density of independent binary code series. (e) In case N is finite: Relation of power spectrum density when a number of stages of PN transfers to infinite from finite for the PN series of RZ pulse is illustrated in Fig. 20. In Fig. 20(A), the number of stages of PN is finite and in Fig. 20(B), it is perfectly random. As illustrated in Fig. 20, the area C' by the perfectly random continuous spectrum in the section (n/NT, n+1/NT) (n ≠ KN, k is an integer) is almost equal to the area C surrounded by the line spectrum at n/NT and n+1/NT in case the number of stages of PN is finite. Here, if Δf = 1/NT, from the formula (24), Also from the formula (21), Therefore, following relation must be obtained. When following calculation is carried out actually to each PN series, following result can be obtained as summarized in the following table (comparison of power spectrum density). Accordingly, the approximate power spectrum density of the finite PN series can be obtained using that of the power spectral density of the perfectly random code. Therefore, the formula (1) is approximated by the power spectrum density in case the number of stages of PN is infinite but it has a high accuracy even as the power spectrum density of the PN series in each number of stages. When a number of stages of PN is infinite such power spectrum density can also be reviewed as the binary code series. Therefore, a k-value obtained from the formula (11) matches in the condition to the case where LD is modulated by the perfectly random binary code series.

Claims: An apparatus for measuring a mode partition characteristic of a laser diode comprising: a first means (21) driven by a clock signal of period T, for generating an N-bit-length pseudo noise pattern; an opto-electric conversion means (22) including a laser diode to be measured, for outputting an optical signal modulated by said pseudo noise pattern, second means (12) for separating a particular longitudinal mode from said optical signal, third means (26) for detecting power P i of said particular longitudinal mode, fourth means (15) for detecting a line spectral element W line (f) and continuous spectral element W cont (f)' of said particular longitudinal mode, and processing means (27) for calculating a coefficient which indicates a mode partition characteristic by obtaining a relative power a i of said particular longitudinal mode with respect to total longitudinal mode power, a ratio of line spectral elements to continuous spectral elements and a coefficient defined by a number of N-bits of pseudo noise. An apparatus for measuring a mode partition characteristic of a laser diode according to claim 1, wherein said processor (27) obtains a value of k which indicates the mode partition characteristics by the following equation: where Δ f is the bandwidth of said fourth means (15) and N is 2 n -1. An apparatus for measuring a mode partition characteristic of a laser diode according to claim 2, further comprising means (13) for attenuating the power of the optical signal of all the longitudinal modes so as to match the level of power P i of said particular longitudinal mode, wherein; the continuous spectrum element W cont (f)'' of all the attenuated longitudinal modes is measured by said fourth means (15), and said processing means (27) employs a value obtained by subtracting the continuous spectrum element W cont (f)'' of all said longitudinal modes from the continuous spectral element W cont (f)' of said particular longitudinal mode as a value of continuous spectral element W contk (f). An apparatus for measuring a mode partition characteristic of a laser diode according to claim 2, wherein power P i of each longitudinal mode included in said laser beam is measured by said second means (12) and said third means (26), and said processor (27) obtains said relative intensity a i from a ratio of the sum of powers of each longitudinal mode to the power P i of the particular longitudinal mode. An apparatus for measuring a mode partition characteristic of a laser diode according to claim 2, wherein said fourth means (15) detects the line spectrum W line (f) at the frequency which is an integral multiple of the frequency 1/NT and also detects the continuous spectral element W cont (f)' and W cont (f)'' at a neighbouring frequency differing by a small value (Σ) from the integral multiple of frequency 1/NT. A method of measuring a mode partition characteristic of a laser diode comprising the following steps; modulating said laser diode by pseudo noise having a period NT, measuring relative intensity of a particular longitudinal mode with respect to all longitudinal modes of an output optical signal of said laser diode, measuring the line spectral element and the continuous spectral element of said particular longitudinal mode and calculating a coefficient which indicates a mode partition characteristic of said laser diode from measured values and a coefficient defined by N-bits of pseudo noise. A method of measuring a mode partition characteristic of a laser diode according to claim 6, wherein said continuous spectral element can be obtained by subtracting the continuous spectral element of all the longitudinal modes from the continuous spectral element of the particular longitudinal mode. A method of measuring a mode partition characteristic of a laser diode according to claim 6 or 7, wherein said line spectrum is measured at the frequency integral multiple of 1/NT and said continuous spectral element is measured at a neighbouring frequency differing by a small value (Σ) from that integral multiple of 1/NT.

Inventors: MORI, MASAKAZU, TSUDA, TAKASHI, YAMAE, KAZUO
Applicants: FUJITSU LIMITED
Application year: 1987
Main classification: G01J1
IPC codes: H04B10, H01S5