Theory of Relative Intensity Noise(RIN)

RIN peak is a good show of the relaxation frequency of the device. The driving force not input current is the Langevin force (F

s, F

n and F_φ) of the field due to the spontaneous emission. The Langevin force is assumed to be irrelative white Gaussian noise [14]. The relative intensity noise (RIN) spectrum is frequency dependence. The former can be derived from the rate equations.

The intrinsic relative intensity noise(RIN) of a device is defined as

P

small-signal analysis of the rate equations for a single-mode laser, we can derive the noise spectrum of the device. The relative intensity noise spectrum of external light injected locked device can be derived using the follow rate equations [15].

Eq 2-3.1

S ,  and N are the photon number, the phase and the carrier number inside the slave laser cavity. G0 is the gain coefficient, N0 is the transparency carrier number, τp

is the photon lifetime, τ_n is the carrier lifetime, I is the slave laser bias current, ε is the gain compression factor, and α is the linewidth enhancement factor. Fs , Fφ and Fn are the noise terms. Δω is the detuning between the master and slave laser. S is the _inj

photons injection into the slave laser. k_c is the coupling coefficient, which determined by the photon injected into the cavity-round trip time.

We based model of injection-locked rate equation is usually used to describe the interaction between photons and carriers inside a laser cavity. When an additional light source is injected into the cavity, the system preserves the general form of the original equations, but with extra terms describing the effects of the injection.

t

Substituting into the injection-locked rate equation

 

For the phase part:

Finally, for the carrier part:

 

( )

Equations (2-3.3), (2-3.4), (2-3.5) are written in matrix form:

 considering I as the small signal modulation current.

 

The modulation response transfer function will be

) (

) ) (

( ¹



 

I H  S

The light injected into the cavity of the slave laser and depletes the carrier density. It makes the spontaneous emission rate reduced and more photons are coupled in phase into the amplified injection field. The more photons in phase and the relaxation frequency should enhance. The RIN spectrum shows that the relaxation frequency peak becomes higher with injections. At a lower injection level directly adds photons into the slave laser cavity by using more carriers, compensating the gain saturation and enhances the relaxation peaks of the slave laser. Under the stronger injections condition, the injected photons deplete the most of the available carriers, saturate the signal and decrease the relaxation peaks finally. It prevents the further improvement of the relaxation frequency.

References

[1] S. Kobayashi and T. Kimura,"Coherence on injection phase-locked AlGaAs semiconductor laser," Electronics Letters, vol. 16, pp. 668-670, 1980

[2] Lukas Chrostowski, Xiaoxue Zhao and Connie J. Chang-Hasnain, “50 GHz Directly-Modulated Injection-Locked 1.55 μm VCSELs,” Optical Society of America, 2005

[3] Erwin K Lau,"High-Speed Modulation of Optical Injection-Locked Semiconductor Lasers," Electrical Engineering and Computer Sciences University of California at Berkeley, 2006

[4] S. Mohrdiek, H.Burkhard, and H. Walter, "Chirp reduction of directly modulated semiconductor lasers at 10 Gb/s by strong CW light injection," J. Lightw.

Technol., vol. 12, no. 3, pp. 418-424, Mar. 1994.

[5] R. P. Braun, G. Grosskopf, R. Meschenmoser, D. Rohde, F. Schmidt, and G.

Villino,"Microwave generation for bidirectional broadband mobile communications using optical sideband injection locking," Electron. Lett., vol. 33, no.

16, pp. 1395-1396, Jul. 1997.

[6] X. Lixin, W. H. Chung, L. Y. Chan, L. F. K. Lui, P. K. A. Wai, and H. Y. Tam,

"Simultaneous all-optical waveform reshaping of two 10-Gb/s signals using a single injection-locked Fabry-Perot laser diode," IEEE Photon. Technol. Lett., vol. 16, no. 6, pp. 1537-1539, Jun. 2004.

[7] M. W. Fleming and A. Mooradian, “Fundamental line broadening of single-mode(GaA1)As diode lasers,’’ Appl. Phys. Lett., vol. 38, p. 511, 1981.

[8] CHARLES H. HENRY, “Theory of the Linewidth of Semiconductor Lasers,’’

IEEE journal of quantum electronics, vol. QE-18, no. 2, February 1982

[9] Yasunari Miyake and Masahiro Asada, “Spectral Characteristics of Linewidth

Enhancement Factor α of Multidimensional Quantum Wells, “ Japanese journal of applied physics, vol 28 pp1280-1281, 1989

[10] MAREK OSINSKI and JENS BUUS, “Linewidth Broadening Factor in semiconductor Lasers-An Overview” Quantum Electronics, IEEE Journal of, 1987 [11] G. Liu, X. Jin, and S. L. Chuang,“Measurement of Linewidth Enhancement Factor of Semiconductor Lasers Using an Injection-Locking Technique” IEEE photonics technology letters, VOL. 13, NO. 5, MAY 2001

[12] C. H. Henry, ``Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers,'' J. Lightwave Technol., LT-4, 288-297 (1986).

[13] B. Tromborg, H. Olesen, and X. Pan, ``Theory of linewidth for multi-electrode laser diodes with spatially distributed noise sources,'' IEEE J. Quantum Electron., QE-27, 178-192 (1991).

[14] X. Jin and S. L. Chuang , “Relative intensity noise characteristics of injection-locked semiconductor lasers, “APPLIED PHYSICS LETTERS, vol 77, NUMBER 9 , 28 AUGUST (2000)

[15] Lukas Chrostowski, “Optical Injection Locking of Vertical Cavity Surface Emitting Lasers,” Fall (2003)

Chapter 3.

Simulation Result of the Self-pulsation Laser

3.1 Background on design

In this section a single gapped FP laser diode will be introduced which forms the basis for our platform.The single gap laser is fabricated by etching into the waveguide of the FP laser diode. The gaps act as reflection centers and produce a modulation of the reflection and transmission spectra dependent on the characteristics of the slot such as gap position, gap depth to which it is etched and slot width. Even if the gap is not etched into the active regions it will still interact with the mode of the electric field of the waveguide as the mode profile is not fully confined to the active region and will expand into the surrounding cladding regions. The 1D first order electric field mode profile modeled using the finite difference time domain technique for a simple laser structure with active region depth of 1 µm, upper cladding region of 1 µm and lower cladding of 1 µm with active region refractive index of 3.55 and cladding region refractive index 3.41, which are normal values for an InGaAsP active region sandwiched between InP cladding regions, are shown below in Fig. 3.1.1.

Figure. 3.1.1 Mode profile of the fundamental mode and refractive index profile through the laser structure.[1]

From Fig. 3.1.1 the fundamental mode is seen to penetrate into the cladding region so any perturbation in this area will influence the mode profile. The scattering matrix method is a easy and accurate technique which can be used to determine the reflection and transmission from gaps etched into the laser cavity.Numerous texts deal with the SMM of which is a good introduction.Of particular importance in a laser structure is the ability to determine loss using the method. This is an important advantage of the SMM over that transmission matrix method (TMM). A FP laser with one etched slot can be described as three cavities with different interface reflections and transmissions as described below in Fig 3.1.2.

Figure 3.1.2. Schematic description of single slot laser diode.[1]

In fig. 3.1.2, n_i refers to the effective refractive index in these section of the laser structure, while ri refers to the reflection from the interfaces as shown above. Each section can be described as a separated cavity and the total reflection and transmission is then found.The back section amplitude reflection from the left side and right side is described as

   

the back section cavity length. The back section amplitude transmission from the left side is described as

giving a power reflection and transmission is Rbl = rbl2

and Tbr = tbr2

respectively. The reflection and transmission of the back section and gap region is found by including the back section reflection and transmission in the SMM calculation as follows

 

 

Figure 3.1.3 Calculated reflection spectrum of a single gap laser (1550 nm).

3.2 Wave intensity distribution analysis

To solve this problem, initially we took an finite difference technique [4] for the start. The variation in the third dimension is assumed to be uniform for now. When we simulate the device structure, the pumped region was indexed a little higher to mimic the optical source field. Fig. 3.2.1 shows the two dimensional field distribution.

When calculating the axial field intensity, we can find out a sharp increase of confinement when the D_gap increases more than 2um as shown in Fig. 3.2.2.

For the detailed 2D E-field distribution, we need to use a more elaborated way to simulate this problem.The basic equations used to describe the semiconductor device behavior are Poisson’s equation and the current continuity equations from Maxwell’s equations for electrons and holes:

, where V is electrical potential, n and p are electron concentration and hole concentration, N_D and N_A are doping of shallow donors(D) and shallow acceptors(A),fD and fA are occupancy of donor (D) and acceptor(A) levels, Ntj is density of j th deep trap,f_tj is occupancy of the j th deep trap level , J_n and J_p are current flux densities,Rntj and Rptj are electron and hole recombination rate for quantum well, Rsp is spontaneous recombination rate, Rst is stimulated recombination rate, R_au is auger recombination rate.

Figure 3.2.1. 2-dimensional simulation of pumped dual-section cavity

Figure 3.2.2. Calculation of confinement of E-field in the quantum well axial direction.

99.0%

99.2%

99.4%

99.6%

99.8%

100.0%

100.2%

0 0.5 1 1.5 2 2.5 3 3.5

D_gap (m)

Confinement of E-field (%)

Figure 3.2.3. (a) Field distribution: W_gap=5μm, but with no air gap; (b) Field distribution on Wgap=5μm,Dgap=5 μm

Wgap Dgap =1μm Dgap =3μm Dgap =5μm

2μm 50.3% 90.1% 90.4%

3μm 49.7% 90.8% 93%

5μm 55.4% 93.4% 94%

Table 2. Field intensity ratio on the pumped cavity

By solving the above equation sets, we could calculate more precisely the field distribution within the cavity. First of all, we started the simulation under R₁=R₂=0.32 and I2 off .We focus now on the wave intensity distribution with an air gap of different depths and widths.Figure 3.2.3(a) shows the E-field distribution without any gap. Figure 3.2.3(b) shows that the wave intensity is re-distributed when the depth of the air gap is increased to 5μm, the field is hardly penetrated into the right section.

We calculated the wave intensity distribution ratio of the pumped cavity versus the overall field intensity shown at the Table 1. When there is no depth on the chip, the left field intensity is about 50.3% at width of gap is 2μm and is 55.4% at the width of the air gap is 5μm. There is little difference of intensity ratio between the two cases.

However, once we start increase Dgap, and widen Wgap, the obvious partition of field intensity can be observed. The detailed 2 dimensional calculation is summarized in table 1. As we could see, the influences of the air gap is profound. Most of the excited E-field is confined in the pumped region, however, some of them will leak into the other un-pumped (or cold) cavity. This leakage is the source of interference of the other section of laser and usually we don’t know, to what extent, this leakage will disturbing the operation of the other laser unless we can quantify it. Using this method, we can estimate the possible feedback or coupling between multiple sections of semiconductor lasers.

3.3 Two-Section Laser dynamic characteristics with

different slot depth

3.3.1 L-I curve

When we put a air slot in the middle section of the two-section laser, the basic performances such as laser power, current distribution or leakage current , which could be influenced to what extent by different D_gap.Therefore,we have to do some simulation and measurement about the basic performances after the focus ion beams process.

0 5 10 15 20 25 30 35 40

0 5 10 15 20

Laser Power(mW)

Laser Current(mA) Dgap=5um

No gap

Figure 3.3.1.L-I curve (a) simulation results with air gap Dgap=5um and with no gap(b) measurement result with Dgap=5um

0 10 20 30 40 50 60 70 80 90 100 110 0.0

0.2 0.4 0.6 0.8 1.0 1.2

Laser Power(mW)

Laser Current(mA)

The figure 3.3.1(a) shows the L-I simulation result of un-FIB laser, which is normal average performance on the two-section laser. The figure 3.3.1(b) shows the L-I measurement result under different bias current. In addition, the threshold current is matches, while the power is decrease at 91mA due to large bias current which leads to the spatial hole burning.

If we etch the laser to Dgap=5um,the threshold current could increase and the laser power decrease a little. Hower,etching to the active layer, we can see not only the threshold current will increase more but also the laser power will fall down sharply. We could have the most moderate D_gap to etch the two section laser.

3.3.2 Leakage current

Our monolithic two-section laser is not composed of two independent lasers.However,the two sections have a common laser grating and an optical cavity originally. After the FIB etching process, the monolithic laser has two asymmetric laser cavities, but it still have common active layers.So,the other characteristic what we want to know is the laser current distribution after FIB process.

Because the pumped cavity current could leak through the cold cavity, it might give rise to some influence on cold cavity. From the figure 3.3.2(a), we can see that some leakage current inject through the active layer on the cold cavity with an air gap.However,figure 3.3.2(b) shows that if we cut through the active layer,the pumped cavity current will almost not leak out to the active layer of the cold cavity.

Figure 3.3.2.Current distribution with different depths of the air gap

References

[1] D. C. Byrne, W. H. Guo, Q. Lu and J. F. Donegan “A Tunable Semiconductor Lased Based on Etched Slots Suitable for Monolithic Integration” School of Physics, Trinity College Dublin ,Ireland

[2] N. A. Pikhtin, A. Yu. Leshko, A. V. Lyutetski , V. B. Khalfin, N. V.

Shuvalova,Yu. V. Il’in, and I. S. Tarasov “Two-section InGaAsP/InP Fabry-Perot laser with a 12 nm tuning range”, Pis’ma Zh. Tekh. Fiz. 23, 10–15 ~March 26, 1997 [3] H. Hillmer, A. Grabmaier, S. Hansmann, H. -L. Zhu, H. Burkhard, and K. Mazagi, IEEE J. of Selected Topics in Quant. Electr. 1, 356 (1995).

[4]Wan Q, Sun C-Z, Xiong B, Wang J and Luo “A novel multisection distributed feedback laser with varied ridge width for self-pulsation generation” Chin. Phys. Lett.

23 2753–5 , (2006)

[5] Larry A. Coldren, and Scott W. Corzine, “ Diode Lasers and Photonic Integrated Circuits”, Wiley Interscience series, New York, (1995).

Chapter4. Experiments Results

4-1. Two-Section Laser Structure

The device is grown on a n⁺InP substrate. The one facet is AR(anti-reflection)and the other is HR(high-reflection).There would be an optical feedback light at the HR side traveling through the z-direction cavity. The feedback wavelength is detuning with the original wavelength .The feedback section at HR side becomes a master laser and the other side becomes a slave laser. An air gap is located in the middle section with adjustable width and depth. There would be some optical injection locking phenomenon in the structure. Therefore, we expect that there would be some modification of dynamic characteristics of the laser, such as relative intensity noise(RIN), chirp frequency under these conditions.

Figure 4.1.1. 1.55μm InGaAsP Fabry-Perot laser with a tunable air gap in the middle section

Figure 4.1.2. Typical experimental setups for edge-emitting laser as a slave laser.

4.2 FIB(focus ion beam) Etching Process

Figure 4.2.1 Dual beam (focused ion beam & electron beam) System (FIB/SEM)

To etch an air gap which we expect in the middle section accurately , we choose the Dual beam (focused ion beam & electron beam) System . Focused ion beam has been widely used for preparing cross-sectional transmission electron microscopy specimens, because of the ease with which a structure having multiple layers of different hardnesses can be etched and the good lateral accuracy. The operating current is about 0.4 nA.If the operating current is too large, the laser device will be damaged.

Figure 4.2.2. SEM figure (Dgap is 5um.)

4.3 Leakage Current Measurement

According to the conventional optical injection locking system , there are two independent lasers and other optical devices ,such as isolator and circulator, so the two lasers do not interfere with each other.But,when we make the two independent lasers monolithic two-section laser ,the current distribution in the common laser cavity will redistribute. If the laser is etched to 5um , the resistance between the two electrodes is 168Ω .A more detailed understanding of this relationship can be gained from Fig.4.3.1 and Table 3.

1 2 3 4 5 6 7

0.0 0.5 1.0 1.5

Voltage(mV)

Current between two top contacts(mA) No gap 1um 3um 5um

Figure 4.3.1. I-V curve between the two top contacts

Table 3.The resistance value between the two top contacts

4.4 Distributed Bragg reflectors on Edge-laser HR facet 4.4.1 Introduction of Distributed Bragg reflectors

Distributed Bragg reflectors (DBRs) served as high reflecting mirror in numerous optoelectronic and photonic devices. It is a periodic structure formed by stacking several pairs of two 1/4-lambda-thick layers with different refractive index. Consider a distributed Bragg reflector consisting of m pairs of two dielectric, lossless materials with high- and low- refractive index n_H and n_L, as shown in Figure 4.4.1. The thickness of the two layers is assumed to be a quarter wave, that is, L1 =λB/4nH and L2

=λB/4nL, where the λB is the Bragg wavelength.

Figure 4.4.1. distributed Bragg reflector

Multiple reflections at the interface of the DBR and constructive interference of the multiple reflected waves increase the reflectivity with increasing number of pairs.

The reflectivity has a maximum at the Bragg wavelength λ_B. The reflectivity of a DBR with m quarter wave pairs at the Bragg wavelength is given by

L

₁

L

₂

n

_H

n

_L

1 2 .. .. .. .. .. .. .. .. .. m

effective reflector

L

_pen

n

_s

su b strate

n

_o

L

₁

L

₂

n

_H

n

_L

1 2 .. .. .. .. .. .. .. .. .. m

effective reflector

L

_pen

n

_s

su b strate

n

_o

2

2

1 ( )

1 ( )

s L

o H

s L

o H

p

p

n n R n n

n n n n

  

 

  

  

 

where the no and ns are the refractive index of incident medium and substrate.

The high-reflectivity or stop band of a DBR depends on the difference in refractive index of the two constituent materials, ∆n (nH - n_L). The spectral width of the stop band is given by

2

B stopband

eff

n n

 



  

where neff is the effective refractive index of the mirror. It can be calculated by requiring the same optical path length normal to the layers for the DBR and the effective medium. The effective refractive index is then given by

1 1

1

2( )

H L

n

eff

n n

 



4.4.2 Reflectance simulation of T

i

O

2

/SiO

2

DBRs

To determine how many pairs DBRs are required for the laser, the realization of reflectivity spectra of DBR is inevitable and necessary. In the following, we simulate and discuss the reflectance of reflectors we used, TiO2/SiO2 DBRs, to understand the DBR pairs we required at least to deposit for a laser facet. Reflectivity spectra of DBR structures here were simulated using the transfer matrix method. The incident angle of illumination and wavelength of the reference light were set to be 0^o (the direction normal to the sample surface) and 1550nm, respectively.

Dielectric mirror has the advantage of the large refractive index contrast between two different dielectric materials so it only needs a few pairs of DBR to form high reflectivity mirror. In most dielectric DBRs, SiO2 is usually used as the low refractive index material due to its some advantaged characteristics such as relative low refractive index than many other dielectric materials. It is easy and cheap to get, hard to decompose, and high transparent window from the wavelength of 180 nm to 8 µm.

As to the high refractive index material, TiO₂ is a proper selection owing to benefits of low absorption and high transparency in IR ray. The refractive index of SiO2 and TiO₂ at wavelength of 1550 nm, used as the parameters in the simulation, are n _SiO2 = 1.463 and n TiO2 = 2.5. The 8 pairs of TiO2/SiO2 mirror can have a high reflectivity of 98% and the wide stop band about 200 nm. Therefore, we use at least 8 pairs of TiO₂/SiO₂ DBR as the mirror in the following experiments.

200 400 600 800 1000 1200 1400 1600 1800 2000 0

20 40 60 80 100

Reflectance (%)

Wavelength (nm)

Simulation

200 400 600 800 1000 1200 1400 1600 1800 2000 0

20 40 60 80 100

R ef lec ta nc e

Wavelength (nm)

1.55 um

Figure 4.4.2(a) TFCalc simulation for 1.55um(b) reflectivity measurement on the HR facet(200nm~2000nm)

4.5 Optical Spectrum and RF Measurement

4.5.1 Experimental Setup

We setup our system which can test our sample non-packaged device . The scheme of the measurement system, which illustrates in Fig 4.5.1, including two DC power supplies, single-mode fiber, optical spectrum analyzer (OSA, AQ6317B), electrical spectrum analyzer, and semiconductor optical amplifier (SOA).The optical spectrum data were collected using a floppy disk and the RIN data were collected using a GPIB card and Labview software.

Figure 4.5.1. experimental setup for measurement

4.5.2 Optical Spectrum Measurement Without FIB Process

First of all, before the FIB process , we measure the optical spectrum of the coated lasers and uncoated lasers, which are biased on the slave laser section. These presents that the uncoated lasers have more clearly DFB modes. We choose the coated lasers to do following experiments. In addition, the lasers are dual-modes lasing rather than single-mode lasing. It might because of the asymmetric two laser cavities .

First of all, before the FIB process , we measure the optical spectrum of the coated lasers and uncoated lasers, which are biased on the slave laser section. These presents that the uncoated lasers have more clearly DFB modes. We choose the coated lasers to do following experiments. In addition, the lasers are dual-modes lasing rather than single-mode lasing. It might because of the asymmetric two laser cavities .

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