Highly-sensitive measurement technique of relative intensity noise and laser characterization Julien Poette, Pascal Besnard, Laurent Bramerie and Jean-Claude Simon FOTON-ENSSAT, 6 rue de kerampont BP 80518, 22300 Lannion cedex, France ABSTRACT A sensitive technique to measure the relative intensity noise of a laser is described. Such experiment is a useful tool for laser characterizations, allowing direct measurement of physical parameters like relaxation oscillation frequencies and damping factor. Examples of determination of such parameters are given. Keywords: Relative intensity noise, laser, characterization

1. INTRODUCTION Noise properties play a key role in laser physics. Standard techniques have been early introduced1 in order to characterize the statistics associated to the generation of photons. The relative intensity noise RIN of a laser2 is an indicator of the laser intensity stability, which is crucial to numerous applications such as optical communication or metrology. In this paper, we describe variant techniques of the RIN measurement. In a ﬁrst part, a standard method of relative intensity noise measurement is presented.1, 3, 4 Such recall is helpful in order to show what quantities are measured to get the RIN and in order to understand the diﬃculties associated to optical precision measurement. In the following part, a more sensitive measurement bench is described. Both experimental acquisitions and data treatments are detailed, such as the required electronic and optical calibrations, which are necessary to reach a desired precision. The use of referenced low-Rin laser sources enables the transfer function of the whole set-up to be qualiﬁed. This determination makes measured physical parameters independent from the detection system. In a third part, a theoretical modeling is introduced to describe both 2, 3 and 4 levels laser5 such as ﬁber laser6, 7, 9 and semiconductor laser.10–14 After having rewritten the expression obtained for each case, intensity noise may be expressed in a single formula, which explicitly contains the relaxation frequency and the damping factor. These last parameters may be hard to determine, especially in the case of a continuous emission. Generally a pump modulation is used to directly observe them in the temporal domain. We show that a strong discrepancy exists between results brought by these two methods for a single frequency ﬁber laser. Noise measurement is also realized on semiconductor continuous laser. Finally, laser parameters are retrieved from these noise measurements.

2. RELATIVE INTENSITY NOISE MEASUREMENT Like all physical parameters, laser intensity is not free of noise. If most of the time, optical signal degradation comes from ambient noise of the propagation medium or of the environment, there is a fundamental limitation of any optical system induced by the laser source itself. For high performance measurement system like in high speed optical telecommunications or optical metrology, for which many parameters inﬂuence its performance, source noise must be estimated and measured. Further author information: Send correspondence to julien Poette Julien Poette: E-mail: [email protected], Phone: +33 (0)2 96 46 90 27 Noise and Fluctuations in Photonics, Quantum Optics, and Communications edited by Leon Cohen, Proc. of SPIE Vol. 6603, 66031R, (2007) 0277-786X/07/$18 · doi: 10.1117/12.724880 Proc. of SPIE Vol. 6603 66031R-1

2.1. Deﬁnition of the Relative Intensity Noise Relative intensity noise represents the variation of laser photon ﬂow, normalized over the mean value of the squared ﬂow < Φ2 >: < δΦ2 > (1) RIN (f ) = < Φ2 > These ﬂuctuations of optical intensity are measured as function of frequency in a given bandwidth, so that the measured value is given per unit of frequency. Most of the time, the numerical value for relative intensity noise is expressed in decibel per Hertz. Unfortunately, there is still no system that can estimate directly optical power. An electrical conversion is necessary thanks to a photodetector, which will deliver a current. This process will generate, in case of optical noise measurement, additional noises on the ﬁnal measured current noise. The electron excitation due to the ambient temperature creates small local current responsible for thermal noise. Furthermore, the energy carried out by the electrons created from photon absorption inside the detector is not a continuous parameter because of the discrete charge linked to an electron. Such quantiﬁcation creates the shot noise. If thermal noise can be reduced by cooling the detection system, Shot noise is a physical limitation. Its origin lies in the random process associated to the creation of electrons due to photon absorption. It follows that the total noise is made of three contributions, which originates from diﬀerent phenomena. The important property is that they are not correlated. The relative intensity noise is the part due to optical laser ﬂuctuations. The physical parameter that contains all the information is the total electrical noise spectral density Nelec . It can be written as follows : Nelec (f ) = NT n + NSn + NOn

(2)

where NT n represents the thermal noise, NSn the shot noise and NOn the optical noise that is related to the RIN. The goal of the experiment is to determine the Rin value from the measurement of the total noise Nelec . The Rin (1) can be written as an expression more adapted to the electrical measured parameters : RIN (f ) =

NOn < Pelec >

(3)

with Pelec is the electrical power on the photodetector.

2.2. Relative Intensity Noise Measurement As suggested by the previous part, the Rin can be deduced from spectral density of optical noises and electrical power measurement. The diﬀerent contributions have to be distinguished from each other. Thermal noise can be easily discriminated from the total electrical noise by measuring the photocurrent when there is no light onto the detector. This discrepancy is made possible because thermal noise is totally independent from the detected light power. The shot noise is more diﬃcult to take into account. There are several ways to estimate its contribution. Firstly, for very noisy systems, shot noise doesn’t need to be measured as it becomes negligible. Two diﬀerent methods exist to go beyond this physical limitation. One is based on the use of balanced receivers which consists on two identical photodiodes. The intensity noise is the same on both detectors while shot noise, created during the production of photo-electrons is diﬀerent in the two systems (but have the same statistical properties). The substraction of the two photo-currents gives directly the shot noise contribution. The main drawback of such method is the high degree of similarity needed between both detection systems and the quality of the electronic diﬀerence between the currents. Such limitation induces limited bandwidth, which is below 1 GHz. The shot noise determination that we use, is adapted for high frequency measurements, and consists in realizing noise characterization using a source designed to have a very low intensity noise compared to the shot noise. Two lasers of reference have been employed. One of them is a solid state laser with an electronic loop controlling the current of the pumping diode in order to reduce the intensity noise. Such device has negligible

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Rin for frequencies higher than the relaxation frequency. In our case, Relative Intensity Noise is totally negligible for frequencies higher than 10 MHz. To measure Rin under this frequency, another reference laser must be used. The second laser is a Dfb laser. Its frequency is stabilized thanks to a gas cell and its Rin is estimated lower than −160 dB.Hz −1 . The thermal noise may be removed due to the independence between the three diﬀerent noise contributions. It follows that the linear relation between the Shot Noise and the current enables the noise power spectral density (P SD) measured on a reference laser to be expressed as : P SDref (f ) = |H(ω)|2 . (2qRI)

(4)

where NSn = 2qRI is the shot noise, I is the measured photocurrent, R the charge impedance, q the electron charge and H(ω) is the transfer function of the detection system. This last term takes into account the gain of the whole detection system, which includes ampliﬁcation and attenuation. An ampliﬁer is added to increase the signal power, so that it modiﬁes the thermal noise term. The measurement on the device under test (dut) gives, using the Rin deﬁnition (3): RINdB P SDdut (f ) = |H(ω)|2 . 2qRI + RI 2 .10 10

(5)

where RINdB is the numerical value of the intensity noise expressed in decibel. The comparison between (P SDref ) and (P SDdut ) allows to ignore the unknown transfer function of the detection system. By suppressing the contribution of the thermal noise, the Rin value can be extracted from the ratio between the two measurements : RINdB (f ) = 10.log10

2q I

P SDdut (f ) −1 P SDref (f )

(6)

As the shot noise depends on the optical power on the detector, the more diﬃcult point with such a method is to have the same contribution of the shot noise on the reference laser and on the device under test. Usually it is made by realizing the measurement on the reference laser and on the device under test at the same time and at the same power.

2.3. Characterization of the Laser of Reference An optical source can be a reference laser when the relative intensity noise contribution can be neglected in comparison to the shot noise term. A good way to evaluate such properties is to normalize the measurement by the detected current. This treatment also responds to the need of an estimation of the shot noise contribution to the photocurrent, measured on the source under test. Thanks to the equation (5), it can be easily noticed that the normalized spectral density of a laser (i.e. P SDdut divided by I) is independent of the photo-current only when the relative intensity noise can be neglected. This property helps to know wether a laser can be a reference source. The ﬁgure 1 shows normalized spectral densities of the reference laser for diﬀerent powers on the detector and for frequencies higher than 10 MHz. As observed on this ﬁgure, the determination of the shot noise contribution is more precise for higher photo-current. Furthermore, it shows the possibility of a shot noise measurement, which is independent on the optical power. In other words, it is not necessary to make the reference laser measurements in the same conditions than the device under test. A storage of P SDref frees the experiment from the drawbacks of repeating measurements on the reference laser. In a practical way, reference measurements are done only once at a high photocurrent and then compare to measurement on sources to be studied. The diﬀerent measurement do not need to be realized the same day.

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I = 0,151 mA I = 2,59 mA

-1

DSPNorm(dBm.Hz .A )

-40

-1

-60

-80

-100

-120 0,1

1

10

Frequency (MHz)

100

1000

Figure 1. Normalized spectral density of a reference laser.

3. SENSITIVE INTENSITY NOISE MEASURE IMPROVEMENT Diﬀerent solutions exist to measure lower power spectral density of intensity noise. The ﬁrst one consists in realizing the measurement at high optical power. As shown on the expression (5), the intensity noise contribution increases faster than the shot noise one along with the photo-current. Then, the Rin is easier to estimate as the optical power is bigger. When it is not possible or desirable, the only way of estimating low intensity noise is to increase the precision of the measurement. In our case, we use two improvements detailed in the following.

3.1. Power Spectral Density Measurement The ﬁrst solution consists in increasing the precision of the power spectral density (Psd) measurement. This can be done by a synchronous detection.15 A spectrum analyzer, the most often used to measure Psd, is employed in our case as a tunable electronic ﬁlter. The setup is shown on ﬁgure 2.

Ampere meter

Laser

Optical Attenuator

DC Block

RF Amplifier

ESA

Synchronous Detection

Figure 2. Experimental setup.

The output from the spectrum analyzer is then sent towards a synchronous detection, which is combined to an optical chopper. Then crenels can be seen on the screen of the spectrum analyzer, as shown on ﬁgure 3. When the light is blocked by the chopper, only thermal noise is measured and determines the low level (1). When the light is detected, all noises are measured as indicated in equation (5). It corresponds to the higher level (2) of crenels. From the amplitude α of the crenels, expressed in decibel, shot noise and intensity noise can be retrieved: α(f ) = (NT n (f ) + NSn (f ) + NOn (f )) |dB − (NT n (f )) |dB (7)

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-125 (2)

-1

DSP (dBm.Hz )

-130 -135

a

-140 -145

(1)

-150 -155

0

5

10

15

20

25

30

Time (ms)

Figure 3. Measurement of Power Spectral Density when the light is chopped at a frequency of 1 GHz.

A more useful parameter is deﬁned by the diﬀerence between noises due to optical detection and thermal noise: = (NSn (f ) + NOn (f )) |dB − (NT n (f )) |dB α = 10log10 10 10 − 1

γ(f )

(8) (9)

Thanks to this deﬁnition, the Relative Intensity Noise of the source at a given frequency can be determined thanks to the measurement of this last parameters on both the device under test and the reference laser using: γ −γ dut ref 2q 10 10 RIN (f ) = 10log10 −1 (10) I

3.2. Synchronous detection improvement The synchronous detection allows very small signal to be measured, even if the power noise contribution is higher than the signal power. This can be realized with an important ﬁltering of the signal near a deﬁnite frequency, equal in our case to the chopping frequency. A voltage that corresponds to the mean amplitude of the crenels 20

10 5

15

g (dB)

a (dB)

0 10

5

-5 -10 -15 -20

0

0

20

40

60

80

1E-5

100

1E-4

1E-3

Photocurrent (mA)

Vds (V)

a. Determination of the factor k.

b. Low noise measurement example.

Figure 4. Electrical calibration of the synchronous detection.

is used on a synchronous detection. That voltage Vds is calibrated with respect to the crenels amplitude α. This calibration is done with the generation of a signal sent to the spectrum analyzer and with the help of a programmable electrical attenuator. A proportionality factor k is then obtained: α = k.Vds

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(11)

k is extracted from a linear interpolation of curves like the one presented on the ﬁgure 4.a. From such characterization, the factor k can be determined and is equal to 185 dB.V −1 . This method increases the sensitivity of the system. Noises, for which PSD is 20 dB lower than the thermal noise, can be easily measured. An example of such measurement of the γ parameter is given on the ﬁgure 4.b.

3.3. Statistical determination of the RIN value The use of the synchronous detection helps in measuring with a good precision (lower than 0.1 dB), the power spectral density at a given frequency, even for signal under the thermal noise value. Another way of increasing the precision of the Rin measurement is to reduce the interval of conﬁdence thanks to statistical studies. The noises from diﬀerent origins don’t have the same behavior as the optical power changes. As seen on the expression (5) of the total measured PSD, the thermal noise is independent from optical power while shot noise varies proportionally to the photo-current. Moreover, optical noise contribution increases as the square of this current. From this consideration, if the diﬀerent contributions have the same order of magnitude, the noises can be distinguished and a simple polynomial formula can be established using the equations (5) and (8): γ

10 10 = aI + bI 2

(12)

where a and b are respectively the polynomial coeﬃcients linked to the shot noise contribution and the intensity noise. The Rin value can be extracted from their expression and is equal to: b RIN = 10.log10 2q (13) a This expression gives several information about the eﬀectiveness of the measurement. First of all, the thermal noise contribution does not appear. As the measurement of noise under the thermal noise ﬂoor is possible, its determination is useless. In spite of such improvement, we have to keep in mind that thermal noise is still a limitation (as a matter of fact, noises 20 dB under the thermal ﬂoor cannot be measured). Consequently its level is critical on the choice of the detection components. On the other hand, when shot noise measurement is possible, this contribution will not be a limiting factor. 2,5

Simulation Experimantal data

g - Shot noise (dB)

2,0 1,5 1,0 0,5 0,0 -0,5

0,01

0,1

Photocurrent (mA)

Figure 5. Experimental and Simulation of Noise measurement for a Rin of −152.57 dB.Hz −1 .

The sensitivity of the rin measurement is deﬁned by the possibility to discriminate the intensity noise from the shot noise. Thanks to the reference laser measurement, the coeﬃcient a can be determined. The characterization of the source under test will then give the value of b. Remark that it is important to vary externally the optical power of a laser instead of changing its pump power in order to keep the Rin constant. A good trick to estimate the accuracy of the measurement is to observe the diﬀerence between the intensity noise and the shot noise. It helps in the observation of small contribution of Rin. The ﬁgure 5 shows an

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example of such measurement and also a simulation of the noise contribution thanks to the measured value of −157.57 dB.Hz −1 . The precision of this measurement, linked to the standard deviation, is estimated to be lower than 0.01 dB.Hz −1 .

3.4. Very low Intensity Noise estimation If the relative intensity noise contribution is smaller, the precision needed for the shot noise estimation increases. Error of 0.1 dB on the shot noise estimation can be critical for noise intensity under −160 dB.Hz −1 . Such variation generally comes with thermal noise modiﬁcation from the measurement on the reference and on the laser. Without any numerical improvement, measurement, similar to the one presented on ﬁgure 5, cannot be anymore ﬁtted with our numerical model in order to extract the right value for the small Rin as shown in the ﬁgure 6.a. The consequence is an overestimation of the Rin value around here −164.76 dB.Hz −1 .

g - Shot noise (dB)

0,25

0,30

Measurement Simulation

0,25

g - Shot noise (dB)

0,30

0,20 0,15 0,10 0,05 0,00 -0,05

0,20 0,15 0,10 0,05 0,00 -0,05

1E-4

Measurement with correction Simulation

Courant (mA)

1E-4

Courant (mA)

a. Low noise measurement.

b. Corrected Shot noise estimation.

Figure 6. Electrical calibration of the synchronous detection.

For very low intensity noise measurement, corresponding to those that need a really good shot noise estimation, it is possible to use a correction factor obtained directly from the laser measurement. For such case, the evolution of the optical power on the detector gives a variation large enough to estimate the two parameters of the polynomial expression 12. To get the value of the correction factor, the equation 12 is modiﬁed to take into account the modiﬁcation of the thermal noise variation between the two measurements. The measurement of γ is interpolated thanks to the following expression : γ+Correction 10 10 = aI + bI 2 (14) Using this modiﬁcation, the previous measurement presented on the ﬁgure 6.a. can be better ﬁtted by the model. The Rin value extracted from that corrected model change from −164.76 dB.Hz −1 without correction to −170.98 dB.Hz −1 . This represents a variation higher than 5 dB and an increase in the precision of the measurement. The sensitivity of the noise estimation is ﬁxed by the required precision. As the Rin decreases, at a given photo-current, the error on its measurement increases. The limits are given by the smallest distance between the intensity noise and the shot noise. The precision has been ﬁxed to 0.1 dB. For example, the maximum deviation in ﬁgure 6.b. is 0.08 dB. Using all these improvements, the lower value of relative intensity noise that can be measured is −170 dB.Hz −1 for an optical power of 1 mW on the detector. The precision is less than 0.4 dB on the Rin value for such value and falls under 0.1 dB for value higher than −165 dB.Hz −1 . Considering the bandwidth, Shot noise measurement have already been made at frequencies as high as 22 GHz.

4. LASER NOISE MODEL To extract physical parameters from such measurements, a model has been developed to study Relative Intensity Noise evolution of laser against frequency.

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4.1. Four levels laser model The ﬁrst model developed shows the noise behavior of classical four levels system thanks to the useful rate equations: ∂D ∂t ∂φl ∂t

= − (σl φl + γ2 ) D + σp φp N ωl 1 = − + LD φl τc 0

(15) (16)

D represents the population diﬀerence, t the time, σl the emitting cross section, φL the laser photon ﬂow, γ2 the inverse of the upper level lifetime, σp the absoption cross section, φp the pumping photon ﬂow and N is the carrier density. In the second equation τc is the cavity lifetime, ωl is the laser pulsation, 0 is the vacuum permittivity and ﬁnally L takes into account the frequency-lorentzian shape of the gain. Using such equations, steady state solutions can be easily found. A small signal approach introduces the relaxation pulsation ωr and the damping factor Γ: Γ = ωr2

=

σl φ0 + γ2 2 2 1 (σl φ0 + γ2 ) σl φ0 − τc 4

(17) (18)

By introducing Langevin noise sources fd and fφ respectively in the small signal equations of the population diﬀerence and of the photon ﬂow,16–18 noise ﬂuctuations can be taken into account. They are linked respectively to the random spontaneous emission of photon, the absorption and the pump noise. Finally thanks to a Fourier transform, the theoretical expression for the Rin of a continuous four levels solid laser can be expressed using the following deﬁnitions (1):

|δφ|2 A + Bω 2 RIN (ω) = = (19) 2 2 φ0 (ωr2 + Γ2 − ω 2 ) + 4ω 2 Γ2 Where A and B are quantities depending on the mean value of the square of the Langevin force fd and fφ and of their product.

4.2. General laser RIN expression By using the same approach for three and two levels system, the ﬁnal Rin expression can be put in the same form as the one given in the equation 19. Rate equations of semiconductor laser have also been studied and similar ﬁnal expressions have been found. The expressions for the diﬀerent coeﬃcients A, B, the relaxation pulsation ωr and the damping factor Γ are of course diﬀerent in the 4 cases. This model describes the intensity noise behavior of any kind of single mode continuous laser source. To check its validity, measurement on codoped Erbium-Ytterbium ﬁber laser that represents the three levels case, were interpolated using the general expression (19). It permits the four parameters introduced in the equation to be ﬁtted. An example is given on the ﬁgure 7.a. This example shows a good agreement between the experiment and the model. The relaxation frequency and the damping factor are deduced and are equal respectively to 662 kHz and 40.8 ms−1 . To extend the intensity noise expression to semiconductor devices, measurement on a commercial single mode Dfb laser has also been realized as shown on the ﬁgure 7.b. In this case, the relaxation occurs at the frequency of 1.11 GHz with a damping factor of 1.32 ns−1 . Using these models, it is also possible to study simultaneously the relaxation and the damping of every mode of a multimode laser.9 Such method is particularly adapted for solid laser parameters determination. Indeed, relative intensity noise measurement are realized with continuous pumping while more classical method use pump modulation. This last method induces thermal eﬀects that considerably modify the laser behavior.

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-90

Measurement Interpolation

-100

-120 -130 -140 -150 -160 -170 -180

1

10

100

Frequency (MHz)

Measurement Interpolation

-80

RIN (dB/Hz)

-1

RIN (dB.Hz )

-110

-100

-120

-140

-160

1

a. Fibre laser.

10

100

Frequency (MHz)

1000

10000

b. Semiconductor laser.

Figure 7. Measurement and interpolation for single-frequency lasers.

5. CONCLUSION Relative intensity noise measurement method has been presented. Diﬀerent improvements in the measurement and also in the data treatment permit to increase by more than 20 dB the precision of standard measurement. Intensity noise as low as −170 dB.Hz −1 can be measured for optical powers of 1 mW on the detector with a precision of 0.4 dB. As the power increases, it is possible to measure lower rin. Thus, for a power of 2 mW , −173 dB.Hz −1 can be reached. The actual bandwidth covers the range from 100 kHz to 22 GHz and allows studies of solid laser but also of semiconductor sources. The general model enables physical laser parameters to be estimated while operating continuous-wave regime and in their conditions of use. It has already been modiﬁed to study lasers submitted to optical injection.19 Some recent experiment on autopulsating semiconductor lasers have shown the possibilities of measuring the damping factor and the relaxation frequency of non-continuous-wave laser. The model has then to be adapted to take into account the laser behavior.

REFERENCES 1. D. McCumber, ”Intensity Fluctuations in the Output of Cw Laser Oscillators”, Physical Review, vol. 141, pp. 306-322, January 1966. 2. K. Petermann, ”Laser Diode Modulation and Noise” Kluwer Academic Publishers, 1988. 3. H. Shi, D. Cohen, J. Barton, M. Majewski, L. Coldren, M. Larson, and G. Fish, ”Relative intensity noise measurements of a widely tunable sampled grating DBR laser”, PTL, vol. 14, pp. 759-761, June 2002. 4. M.C. Cox and al., Proc.-Sci. Meas. Tech., vol. 145, n. 4 (1998) 5. Siegman, ”Lasers”. university science books ed. 6. E. Rnnekleiv, ”Frequency and intensity noise of single frequency ﬁber bragg grating lasers”, OFT, vol. 7, pp. 206-232, 2001. 7. S. Taccheo, P. Laporta, O. Svelto, and G. D. Geronimo, ”Theoretical and experimental analysis of intensity noise in a codoped Erbium-Ytterbium glass-laser,” APL, vol. 66, pp. 19-26, 1998. 8. S. Lvseth and D. Stepanov, ”Dynamic analysis of multiple wavelength DFB ﬁber laser”, JQE, vol. 37, pp. 1237-1245, October 2001. 9. J. Potte, S. Blin, G. Brochu, L. Bramerie, R. Slavik, J-C. Simon, S. Larochelle, P. Besnard ”Relative Intensity Noise of Multi-wavelength Fiber Laser”, Electronics Letters, Vol. 40, issue 12, pp. 724-726, juin 2004. 10. H. Haug, ”Quantum-Mechanical Rate Equations for Semiconductor Lasers”, Physical Review, vol. 184, pp. 338-348, August 1969. 11. G.P. Agrawal and N.K. Dutta, ”Long Wavelength semiconductor lasers”, Von Nostrand Reinhold Company, New York (1986) 12. D. Marcuse, ”Computer Simulation of Laser Photon Fluctuations: Single Cavity Laser Results”, IEEE Journal of Quantum Electronics, vol. 20, pp. 1148-1155, October 1984.

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13. I. Maurin, ”Etude Du Bruit Quantique Dans Les Lasers Semi-Conducteurs (VCSELs et Diodes Laser)”. PhD thesis, Universit Paris VI, 2002. 14. M.-B. Bibey, ”Transmission Optique D’un Signal Hyperfrquence Haute Puret Spectrale”, PhD thesis, Universit des Sciences et Technologies de Lille, 1998. 15. P. Doussire, ”Contribution l’tude et la ralisation d’ampliﬁcateurs optiques semiconducteur”, PhD thesis, Universit de Nice, 1989. 16. M. Lax, ”Formal Theory of Quantum Fluctuations from a Driven State”, Physical Review, vol. 129, pp. 2342-2348, March 1963. 17. M. Lax, ”Fluctuations from the Nonequilibrium Steady State”, Reviews of modern physics, vol. 32, pp. 25-64, January 1960. 18. M. Lax, ”Classical Noise IV : Langevin Methods”, Reviews of Modern Physics, vol. 38, pp. 541-566, July 1966. 19. J. Poette, O. Vaudel and P. Besnard, ”Relative Intensity Noise of an injected semiconductor laser”, ICONO/LAT2005, St-Petersbourg, May 2005, Proceedings of SPIE Vol. 6054

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1. INTRODUCTION Noise properties play a key role in laser physics. Standard techniques have been early introduced1 in order to characterize the statistics associated to the generation of photons. The relative intensity noise RIN of a laser2 is an indicator of the laser intensity stability, which is crucial to numerous applications such as optical communication or metrology. In this paper, we describe variant techniques of the RIN measurement. In a ﬁrst part, a standard method of relative intensity noise measurement is presented.1, 3, 4 Such recall is helpful in order to show what quantities are measured to get the RIN and in order to understand the diﬃculties associated to optical precision measurement. In the following part, a more sensitive measurement bench is described. Both experimental acquisitions and data treatments are detailed, such as the required electronic and optical calibrations, which are necessary to reach a desired precision. The use of referenced low-Rin laser sources enables the transfer function of the whole set-up to be qualiﬁed. This determination makes measured physical parameters independent from the detection system. In a third part, a theoretical modeling is introduced to describe both 2, 3 and 4 levels laser5 such as ﬁber laser6, 7, 9 and semiconductor laser.10–14 After having rewritten the expression obtained for each case, intensity noise may be expressed in a single formula, which explicitly contains the relaxation frequency and the damping factor. These last parameters may be hard to determine, especially in the case of a continuous emission. Generally a pump modulation is used to directly observe them in the temporal domain. We show that a strong discrepancy exists between results brought by these two methods for a single frequency ﬁber laser. Noise measurement is also realized on semiconductor continuous laser. Finally, laser parameters are retrieved from these noise measurements.

2. RELATIVE INTENSITY NOISE MEASUREMENT Like all physical parameters, laser intensity is not free of noise. If most of the time, optical signal degradation comes from ambient noise of the propagation medium or of the environment, there is a fundamental limitation of any optical system induced by the laser source itself. For high performance measurement system like in high speed optical telecommunications or optical metrology, for which many parameters inﬂuence its performance, source noise must be estimated and measured. Further author information: Send correspondence to julien Poette Julien Poette: E-mail: [email protected], Phone: +33 (0)2 96 46 90 27 Noise and Fluctuations in Photonics, Quantum Optics, and Communications edited by Leon Cohen, Proc. of SPIE Vol. 6603, 66031R, (2007) 0277-786X/07/$18 · doi: 10.1117/12.724880 Proc. of SPIE Vol. 6603 66031R-1

2.1. Deﬁnition of the Relative Intensity Noise Relative intensity noise represents the variation of laser photon ﬂow, normalized over the mean value of the squared ﬂow < Φ2 >: < δΦ2 > (1) RIN (f ) = < Φ2 > These ﬂuctuations of optical intensity are measured as function of frequency in a given bandwidth, so that the measured value is given per unit of frequency. Most of the time, the numerical value for relative intensity noise is expressed in decibel per Hertz. Unfortunately, there is still no system that can estimate directly optical power. An electrical conversion is necessary thanks to a photodetector, which will deliver a current. This process will generate, in case of optical noise measurement, additional noises on the ﬁnal measured current noise. The electron excitation due to the ambient temperature creates small local current responsible for thermal noise. Furthermore, the energy carried out by the electrons created from photon absorption inside the detector is not a continuous parameter because of the discrete charge linked to an electron. Such quantiﬁcation creates the shot noise. If thermal noise can be reduced by cooling the detection system, Shot noise is a physical limitation. Its origin lies in the random process associated to the creation of electrons due to photon absorption. It follows that the total noise is made of three contributions, which originates from diﬀerent phenomena. The important property is that they are not correlated. The relative intensity noise is the part due to optical laser ﬂuctuations. The physical parameter that contains all the information is the total electrical noise spectral density Nelec . It can be written as follows : Nelec (f ) = NT n + NSn + NOn

(2)

where NT n represents the thermal noise, NSn the shot noise and NOn the optical noise that is related to the RIN. The goal of the experiment is to determine the Rin value from the measurement of the total noise Nelec . The Rin (1) can be written as an expression more adapted to the electrical measured parameters : RIN (f ) =

NOn < Pelec >

(3)

with Pelec is the electrical power on the photodetector.

2.2. Relative Intensity Noise Measurement As suggested by the previous part, the Rin can be deduced from spectral density of optical noises and electrical power measurement. The diﬀerent contributions have to be distinguished from each other. Thermal noise can be easily discriminated from the total electrical noise by measuring the photocurrent when there is no light onto the detector. This discrepancy is made possible because thermal noise is totally independent from the detected light power. The shot noise is more diﬃcult to take into account. There are several ways to estimate its contribution. Firstly, for very noisy systems, shot noise doesn’t need to be measured as it becomes negligible. Two diﬀerent methods exist to go beyond this physical limitation. One is based on the use of balanced receivers which consists on two identical photodiodes. The intensity noise is the same on both detectors while shot noise, created during the production of photo-electrons is diﬀerent in the two systems (but have the same statistical properties). The substraction of the two photo-currents gives directly the shot noise contribution. The main drawback of such method is the high degree of similarity needed between both detection systems and the quality of the electronic diﬀerence between the currents. Such limitation induces limited bandwidth, which is below 1 GHz. The shot noise determination that we use, is adapted for high frequency measurements, and consists in realizing noise characterization using a source designed to have a very low intensity noise compared to the shot noise. Two lasers of reference have been employed. One of them is a solid state laser with an electronic loop controlling the current of the pumping diode in order to reduce the intensity noise. Such device has negligible

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Rin for frequencies higher than the relaxation frequency. In our case, Relative Intensity Noise is totally negligible for frequencies higher than 10 MHz. To measure Rin under this frequency, another reference laser must be used. The second laser is a Dfb laser. Its frequency is stabilized thanks to a gas cell and its Rin is estimated lower than −160 dB.Hz −1 . The thermal noise may be removed due to the independence between the three diﬀerent noise contributions. It follows that the linear relation between the Shot Noise and the current enables the noise power spectral density (P SD) measured on a reference laser to be expressed as : P SDref (f ) = |H(ω)|2 . (2qRI)

(4)

where NSn = 2qRI is the shot noise, I is the measured photocurrent, R the charge impedance, q the electron charge and H(ω) is the transfer function of the detection system. This last term takes into account the gain of the whole detection system, which includes ampliﬁcation and attenuation. An ampliﬁer is added to increase the signal power, so that it modiﬁes the thermal noise term. The measurement on the device under test (dut) gives, using the Rin deﬁnition (3): RINdB P SDdut (f ) = |H(ω)|2 . 2qRI + RI 2 .10 10

(5)

where RINdB is the numerical value of the intensity noise expressed in decibel. The comparison between (P SDref ) and (P SDdut ) allows to ignore the unknown transfer function of the detection system. By suppressing the contribution of the thermal noise, the Rin value can be extracted from the ratio between the two measurements : RINdB (f ) = 10.log10

2q I

P SDdut (f ) −1 P SDref (f )

(6)

As the shot noise depends on the optical power on the detector, the more diﬃcult point with such a method is to have the same contribution of the shot noise on the reference laser and on the device under test. Usually it is made by realizing the measurement on the reference laser and on the device under test at the same time and at the same power.

2.3. Characterization of the Laser of Reference An optical source can be a reference laser when the relative intensity noise contribution can be neglected in comparison to the shot noise term. A good way to evaluate such properties is to normalize the measurement by the detected current. This treatment also responds to the need of an estimation of the shot noise contribution to the photocurrent, measured on the source under test. Thanks to the equation (5), it can be easily noticed that the normalized spectral density of a laser (i.e. P SDdut divided by I) is independent of the photo-current only when the relative intensity noise can be neglected. This property helps to know wether a laser can be a reference source. The ﬁgure 1 shows normalized spectral densities of the reference laser for diﬀerent powers on the detector and for frequencies higher than 10 MHz. As observed on this ﬁgure, the determination of the shot noise contribution is more precise for higher photo-current. Furthermore, it shows the possibility of a shot noise measurement, which is independent on the optical power. In other words, it is not necessary to make the reference laser measurements in the same conditions than the device under test. A storage of P SDref frees the experiment from the drawbacks of repeating measurements on the reference laser. In a practical way, reference measurements are done only once at a high photocurrent and then compare to measurement on sources to be studied. The diﬀerent measurement do not need to be realized the same day.

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I = 0,151 mA I = 2,59 mA

-1

DSPNorm(dBm.Hz .A )

-40

-1

-60

-80

-100

-120 0,1

1

10

Frequency (MHz)

100

1000

Figure 1. Normalized spectral density of a reference laser.

3. SENSITIVE INTENSITY NOISE MEASURE IMPROVEMENT Diﬀerent solutions exist to measure lower power spectral density of intensity noise. The ﬁrst one consists in realizing the measurement at high optical power. As shown on the expression (5), the intensity noise contribution increases faster than the shot noise one along with the photo-current. Then, the Rin is easier to estimate as the optical power is bigger. When it is not possible or desirable, the only way of estimating low intensity noise is to increase the precision of the measurement. In our case, we use two improvements detailed in the following.

3.1. Power Spectral Density Measurement The ﬁrst solution consists in increasing the precision of the power spectral density (Psd) measurement. This can be done by a synchronous detection.15 A spectrum analyzer, the most often used to measure Psd, is employed in our case as a tunable electronic ﬁlter. The setup is shown on ﬁgure 2.

Ampere meter

Laser

Optical Attenuator

DC Block

RF Amplifier

ESA

Synchronous Detection

Figure 2. Experimental setup.

The output from the spectrum analyzer is then sent towards a synchronous detection, which is combined to an optical chopper. Then crenels can be seen on the screen of the spectrum analyzer, as shown on ﬁgure 3. When the light is blocked by the chopper, only thermal noise is measured and determines the low level (1). When the light is detected, all noises are measured as indicated in equation (5). It corresponds to the higher level (2) of crenels. From the amplitude α of the crenels, expressed in decibel, shot noise and intensity noise can be retrieved: α(f ) = (NT n (f ) + NSn (f ) + NOn (f )) |dB − (NT n (f )) |dB (7)

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-125 (2)

-1

DSP (dBm.Hz )

-130 -135

a

-140 -145

(1)

-150 -155

0

5

10

15

20

25

30

Time (ms)

Figure 3. Measurement of Power Spectral Density when the light is chopped at a frequency of 1 GHz.

A more useful parameter is deﬁned by the diﬀerence between noises due to optical detection and thermal noise: = (NSn (f ) + NOn (f )) |dB − (NT n (f )) |dB α = 10log10 10 10 − 1

γ(f )

(8) (9)

Thanks to this deﬁnition, the Relative Intensity Noise of the source at a given frequency can be determined thanks to the measurement of this last parameters on both the device under test and the reference laser using: γ −γ dut ref 2q 10 10 RIN (f ) = 10log10 −1 (10) I

3.2. Synchronous detection improvement The synchronous detection allows very small signal to be measured, even if the power noise contribution is higher than the signal power. This can be realized with an important ﬁltering of the signal near a deﬁnite frequency, equal in our case to the chopping frequency. A voltage that corresponds to the mean amplitude of the crenels 20

10 5

15

g (dB)

a (dB)

0 10

5

-5 -10 -15 -20

0

0

20

40

60

80

1E-5

100

1E-4

1E-3

Photocurrent (mA)

Vds (V)

a. Determination of the factor k.

b. Low noise measurement example.

Figure 4. Electrical calibration of the synchronous detection.

is used on a synchronous detection. That voltage Vds is calibrated with respect to the crenels amplitude α. This calibration is done with the generation of a signal sent to the spectrum analyzer and with the help of a programmable electrical attenuator. A proportionality factor k is then obtained: α = k.Vds

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(11)

k is extracted from a linear interpolation of curves like the one presented on the ﬁgure 4.a. From such characterization, the factor k can be determined and is equal to 185 dB.V −1 . This method increases the sensitivity of the system. Noises, for which PSD is 20 dB lower than the thermal noise, can be easily measured. An example of such measurement of the γ parameter is given on the ﬁgure 4.b.

3.3. Statistical determination of the RIN value The use of the synchronous detection helps in measuring with a good precision (lower than 0.1 dB), the power spectral density at a given frequency, even for signal under the thermal noise value. Another way of increasing the precision of the Rin measurement is to reduce the interval of conﬁdence thanks to statistical studies. The noises from diﬀerent origins don’t have the same behavior as the optical power changes. As seen on the expression (5) of the total measured PSD, the thermal noise is independent from optical power while shot noise varies proportionally to the photo-current. Moreover, optical noise contribution increases as the square of this current. From this consideration, if the diﬀerent contributions have the same order of magnitude, the noises can be distinguished and a simple polynomial formula can be established using the equations (5) and (8): γ

10 10 = aI + bI 2

(12)

where a and b are respectively the polynomial coeﬃcients linked to the shot noise contribution and the intensity noise. The Rin value can be extracted from their expression and is equal to: b RIN = 10.log10 2q (13) a This expression gives several information about the eﬀectiveness of the measurement. First of all, the thermal noise contribution does not appear. As the measurement of noise under the thermal noise ﬂoor is possible, its determination is useless. In spite of such improvement, we have to keep in mind that thermal noise is still a limitation (as a matter of fact, noises 20 dB under the thermal ﬂoor cannot be measured). Consequently its level is critical on the choice of the detection components. On the other hand, when shot noise measurement is possible, this contribution will not be a limiting factor. 2,5

Simulation Experimantal data

g - Shot noise (dB)

2,0 1,5 1,0 0,5 0,0 -0,5

0,01

0,1

Photocurrent (mA)

Figure 5. Experimental and Simulation of Noise measurement for a Rin of −152.57 dB.Hz −1 .

The sensitivity of the rin measurement is deﬁned by the possibility to discriminate the intensity noise from the shot noise. Thanks to the reference laser measurement, the coeﬃcient a can be determined. The characterization of the source under test will then give the value of b. Remark that it is important to vary externally the optical power of a laser instead of changing its pump power in order to keep the Rin constant. A good trick to estimate the accuracy of the measurement is to observe the diﬀerence between the intensity noise and the shot noise. It helps in the observation of small contribution of Rin. The ﬁgure 5 shows an

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example of such measurement and also a simulation of the noise contribution thanks to the measured value of −157.57 dB.Hz −1 . The precision of this measurement, linked to the standard deviation, is estimated to be lower than 0.01 dB.Hz −1 .

3.4. Very low Intensity Noise estimation If the relative intensity noise contribution is smaller, the precision needed for the shot noise estimation increases. Error of 0.1 dB on the shot noise estimation can be critical for noise intensity under −160 dB.Hz −1 . Such variation generally comes with thermal noise modiﬁcation from the measurement on the reference and on the laser. Without any numerical improvement, measurement, similar to the one presented on ﬁgure 5, cannot be anymore ﬁtted with our numerical model in order to extract the right value for the small Rin as shown in the ﬁgure 6.a. The consequence is an overestimation of the Rin value around here −164.76 dB.Hz −1 .

g - Shot noise (dB)

0,25

0,30

Measurement Simulation

0,25

g - Shot noise (dB)

0,30

0,20 0,15 0,10 0,05 0,00 -0,05

0,20 0,15 0,10 0,05 0,00 -0,05

1E-4

Measurement with correction Simulation

Courant (mA)

1E-4

Courant (mA)

a. Low noise measurement.

b. Corrected Shot noise estimation.

Figure 6. Electrical calibration of the synchronous detection.

For very low intensity noise measurement, corresponding to those that need a really good shot noise estimation, it is possible to use a correction factor obtained directly from the laser measurement. For such case, the evolution of the optical power on the detector gives a variation large enough to estimate the two parameters of the polynomial expression 12. To get the value of the correction factor, the equation 12 is modiﬁed to take into account the modiﬁcation of the thermal noise variation between the two measurements. The measurement of γ is interpolated thanks to the following expression : γ+Correction 10 10 = aI + bI 2 (14) Using this modiﬁcation, the previous measurement presented on the ﬁgure 6.a. can be better ﬁtted by the model. The Rin value extracted from that corrected model change from −164.76 dB.Hz −1 without correction to −170.98 dB.Hz −1 . This represents a variation higher than 5 dB and an increase in the precision of the measurement. The sensitivity of the noise estimation is ﬁxed by the required precision. As the Rin decreases, at a given photo-current, the error on its measurement increases. The limits are given by the smallest distance between the intensity noise and the shot noise. The precision has been ﬁxed to 0.1 dB. For example, the maximum deviation in ﬁgure 6.b. is 0.08 dB. Using all these improvements, the lower value of relative intensity noise that can be measured is −170 dB.Hz −1 for an optical power of 1 mW on the detector. The precision is less than 0.4 dB on the Rin value for such value and falls under 0.1 dB for value higher than −165 dB.Hz −1 . Considering the bandwidth, Shot noise measurement have already been made at frequencies as high as 22 GHz.

4. LASER NOISE MODEL To extract physical parameters from such measurements, a model has been developed to study Relative Intensity Noise evolution of laser against frequency.

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4.1. Four levels laser model The ﬁrst model developed shows the noise behavior of classical four levels system thanks to the useful rate equations: ∂D ∂t ∂φl ∂t

= − (σl φl + γ2 ) D + σp φp N ωl 1 = − + LD φl τc 0

(15) (16)

D represents the population diﬀerence, t the time, σl the emitting cross section, φL the laser photon ﬂow, γ2 the inverse of the upper level lifetime, σp the absoption cross section, φp the pumping photon ﬂow and N is the carrier density. In the second equation τc is the cavity lifetime, ωl is the laser pulsation, 0 is the vacuum permittivity and ﬁnally L takes into account the frequency-lorentzian shape of the gain. Using such equations, steady state solutions can be easily found. A small signal approach introduces the relaxation pulsation ωr and the damping factor Γ: Γ = ωr2

=

σl φ0 + γ2 2 2 1 (σl φ0 + γ2 ) σl φ0 − τc 4

(17) (18)

By introducing Langevin noise sources fd and fφ respectively in the small signal equations of the population diﬀerence and of the photon ﬂow,16–18 noise ﬂuctuations can be taken into account. They are linked respectively to the random spontaneous emission of photon, the absorption and the pump noise. Finally thanks to a Fourier transform, the theoretical expression for the Rin of a continuous four levels solid laser can be expressed using the following deﬁnitions (1):

|δφ|2 A + Bω 2 RIN (ω) = = (19) 2 2 φ0 (ωr2 + Γ2 − ω 2 ) + 4ω 2 Γ2 Where A and B are quantities depending on the mean value of the square of the Langevin force fd and fφ and of their product.

4.2. General laser RIN expression By using the same approach for three and two levels system, the ﬁnal Rin expression can be put in the same form as the one given in the equation 19. Rate equations of semiconductor laser have also been studied and similar ﬁnal expressions have been found. The expressions for the diﬀerent coeﬃcients A, B, the relaxation pulsation ωr and the damping factor Γ are of course diﬀerent in the 4 cases. This model describes the intensity noise behavior of any kind of single mode continuous laser source. To check its validity, measurement on codoped Erbium-Ytterbium ﬁber laser that represents the three levels case, were interpolated using the general expression (19). It permits the four parameters introduced in the equation to be ﬁtted. An example is given on the ﬁgure 7.a. This example shows a good agreement between the experiment and the model. The relaxation frequency and the damping factor are deduced and are equal respectively to 662 kHz and 40.8 ms−1 . To extend the intensity noise expression to semiconductor devices, measurement on a commercial single mode Dfb laser has also been realized as shown on the ﬁgure 7.b. In this case, the relaxation occurs at the frequency of 1.11 GHz with a damping factor of 1.32 ns−1 . Using these models, it is also possible to study simultaneously the relaxation and the damping of every mode of a multimode laser.9 Such method is particularly adapted for solid laser parameters determination. Indeed, relative intensity noise measurement are realized with continuous pumping while more classical method use pump modulation. This last method induces thermal eﬀects that considerably modify the laser behavior.

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-90

Measurement Interpolation

-100

-120 -130 -140 -150 -160 -170 -180

1

10

100

Frequency (MHz)

Measurement Interpolation

-80

RIN (dB/Hz)

-1

RIN (dB.Hz )

-110

-100

-120

-140

-160

1

a. Fibre laser.

10

100

Frequency (MHz)

1000

10000

b. Semiconductor laser.

Figure 7. Measurement and interpolation for single-frequency lasers.

5. CONCLUSION Relative intensity noise measurement method has been presented. Diﬀerent improvements in the measurement and also in the data treatment permit to increase by more than 20 dB the precision of standard measurement. Intensity noise as low as −170 dB.Hz −1 can be measured for optical powers of 1 mW on the detector with a precision of 0.4 dB. As the power increases, it is possible to measure lower rin. Thus, for a power of 2 mW , −173 dB.Hz −1 can be reached. The actual bandwidth covers the range from 100 kHz to 22 GHz and allows studies of solid laser but also of semiconductor sources. The general model enables physical laser parameters to be estimated while operating continuous-wave regime and in their conditions of use. It has already been modiﬁed to study lasers submitted to optical injection.19 Some recent experiment on autopulsating semiconductor lasers have shown the possibilities of measuring the damping factor and the relaxation frequency of non-continuous-wave laser. The model has then to be adapted to take into account the laser behavior.

REFERENCES 1. D. McCumber, ”Intensity Fluctuations in the Output of Cw Laser Oscillators”, Physical Review, vol. 141, pp. 306-322, January 1966. 2. K. Petermann, ”Laser Diode Modulation and Noise” Kluwer Academic Publishers, 1988. 3. H. Shi, D. Cohen, J. Barton, M. Majewski, L. Coldren, M. Larson, and G. Fish, ”Relative intensity noise measurements of a widely tunable sampled grating DBR laser”, PTL, vol. 14, pp. 759-761, June 2002. 4. M.C. Cox and al., Proc.-Sci. Meas. Tech., vol. 145, n. 4 (1998) 5. Siegman, ”Lasers”. university science books ed. 6. E. Rnnekleiv, ”Frequency and intensity noise of single frequency ﬁber bragg grating lasers”, OFT, vol. 7, pp. 206-232, 2001. 7. S. Taccheo, P. Laporta, O. Svelto, and G. D. Geronimo, ”Theoretical and experimental analysis of intensity noise in a codoped Erbium-Ytterbium glass-laser,” APL, vol. 66, pp. 19-26, 1998. 8. S. Lvseth and D. Stepanov, ”Dynamic analysis of multiple wavelength DFB ﬁber laser”, JQE, vol. 37, pp. 1237-1245, October 2001. 9. J. Potte, S. Blin, G. Brochu, L. Bramerie, R. Slavik, J-C. Simon, S. Larochelle, P. Besnard ”Relative Intensity Noise of Multi-wavelength Fiber Laser”, Electronics Letters, Vol. 40, issue 12, pp. 724-726, juin 2004. 10. H. Haug, ”Quantum-Mechanical Rate Equations for Semiconductor Lasers”, Physical Review, vol. 184, pp. 338-348, August 1969. 11. G.P. Agrawal and N.K. Dutta, ”Long Wavelength semiconductor lasers”, Von Nostrand Reinhold Company, New York (1986) 12. D. Marcuse, ”Computer Simulation of Laser Photon Fluctuations: Single Cavity Laser Results”, IEEE Journal of Quantum Electronics, vol. 20, pp. 1148-1155, October 1984.

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13. I. Maurin, ”Etude Du Bruit Quantique Dans Les Lasers Semi-Conducteurs (VCSELs et Diodes Laser)”. PhD thesis, Universit Paris VI, 2002. 14. M.-B. Bibey, ”Transmission Optique D’un Signal Hyperfrquence Haute Puret Spectrale”, PhD thesis, Universit des Sciences et Technologies de Lille, 1998. 15. P. Doussire, ”Contribution l’tude et la ralisation d’ampliﬁcateurs optiques semiconducteur”, PhD thesis, Universit de Nice, 1989. 16. M. Lax, ”Formal Theory of Quantum Fluctuations from a Driven State”, Physical Review, vol. 129, pp. 2342-2348, March 1963. 17. M. Lax, ”Fluctuations from the Nonequilibrium Steady State”, Reviews of modern physics, vol. 32, pp. 25-64, January 1960. 18. M. Lax, ”Classical Noise IV : Langevin Methods”, Reviews of Modern Physics, vol. 38, pp. 541-566, July 1966. 19. J. Poette, O. Vaudel and P. Besnard, ”Relative Intensity Noise of an injected semiconductor laser”, ICONO/LAT2005, St-Petersbourg, May 2005, Proceedings of SPIE Vol. 6054

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