Distributed Feedback Laser ECE 464. Tin Nguyen

Transcription

1 Distributed Feedbac Laser ECE 464 Tin Nguyen La Rosa, Spring 2008

2 Abstract In recent year, distributed feedbac laser was one of the hot topics that have been study for many years. It was introduced and developed by Kogelni and Shan. Since that model release, people are now realizing distributed feedbac laser are important to human need. How many people now distributed feedbac laser are important role or useful item in the optic world? What is does do? What is DFB using for? What are advantages of using distributed feedbac laser? What are disadvantage of using distributed feedbac laser? What are methods that analyze the dephased complexcoupling of DFB? Distributed feedbac laser is one type of laser diode or quantum cascaded laser where the whole laser resonator that contain periodic structure as diffraction grating when Bragg reflection occurs the change. Distributed feedbac laser are useful item in society or the world because it is provide the phase difference between the gain and the index grating based on using power series method to solve the couple-wave equation that reflect the calculation of the threshold gain margin which located in complex-couple distributed feedbac laser. Introduction I decide to choose distributed feedbac laser as my research project because I was surprise that using power series method can lead me analyzed the dephase of complex-coupled of distributed feedbac laser which introduced the method of calculation the threshold gain margin as function and ability to see the phase change between the index and the gain rating. I discover whenever the effect stay on facet reflectivity (both magnitude and phase) impact on the gain margin of complex coupled of distributed feedbac laser will cause gain margin slowly and potential of large variation of phase function increase. I also figured out using LED can pump polymer whenever people spend a lot of money expensive laser to pump. In this paper, I will illustrate the method of calculation the threshold gain margin that play important role in the optic world. In addition, I also present how DFB play important role in optic world and the advantage or disadvantage of using DFB. Content

3 1) How many people now distributed feedbac laser are important role or useful item in the optic world? 2) What is does do? 3) What is using for? Wal in the distributed feedbac laser world, I definitely see the future of distributed feedbac laser are grow dramatically and also DFB play important role in the optic world because DFB are now using for optical communication and also use for bipolar field effect transistor laser (BICFET laser). BICFET laser has produce single modes, tunable laser and stable. Just thining about possible way that the electrical pump require expensive laser to pump polymer laser by using tunable laser to produce the reflection wavelength of the grating structure and out coming output laser of the wavelength. One of the new by optic organization announced that using Nitride LED can pump polymer laser will reduce low-cost tunable visible source, simple to mae, and easy to compact. In order to pump polymer, LED pumping is required high expectation of carefully DFB design that are capable to have laser which include thin 350nm fluorene copolymer film will be placed on top of a corrugated silica substrate. When is come to design, the thin polymer layer has to provide the gain and the corrugation has to provide the feedbac. Figure 1: LED Pump Laser

4 4) What are advantages of using DFB? In the world we live in now, everything is technology. Now is optical communication system coming along? The advantage of using DFB is better dynamic-single stability and low noise operation, and distributed feedbac laser are fast to transmit data in optical communication world. Based on using DFB laser array, there a lot of advantage lie tunable vertical cavity surface emitting laser (VCSELs), tunable distributed Bragg reflector (T- DBR), and grating assisted co directional coupler with sampled rear reflector (GCSR) because these advantage have high power outputs, wave stability, reliability and manufacturing seem to be complexity than conventional single DFB laser. 5) What are disadvantages of using DFB? Disadvantages of using DFB are hard to get current density in gain and laser arrangement. Without using safety rule can cause the person blind whenever distributed feedbac laser is on your body. 6) What are methods that analyze the dephased complex-coupling of DFB? Power series is another method that analyzes the dephased complexcoupling of DFB. When it come to introduce the power series method, we have to now the bacground of complex-coupled DFB laser because both index coupling gain and gain coupling will play important role of reflection because impact of the power series method. In addition, complex-coupled DFB laser usually define as single-mode operation that have lasing mode will maintain exactly level of the Bragg wavelength. Most of distributed feedbac laser is including either optic fiber or semiconductor to operate sing-mode. The figure 2 below will demonstrated of DFB interact. Figure 2: DFB fiber laser include fiber Bragg grating with phase change by doped fiber.

5 Whenever we increase the complex laser, it will be harder to do calculation based on solved the coupled-wave because the phased difference between gain grating and the index grating have to be set as 0 or pi in order to see change of in-phase or anti-phase change. In this paper, you will have opportunity to see the new century of power series method that solved coupled-wave equation by analyzed aperiodic structure and studied the behavior of threshold gain margin of a dephased complex-couple DFB laser in order to see outcome of the phase occur the change between the gain and index grating. Figure 3: This is schematic of diphase complex-coupled DFB laser diagram. Based on figure 3, you will have opportunity to see the square signal waveform of gain grating have same length with the index grating. The only difference between gain grating and index grating is gain grating stay the same position but other hand the index grating is move to the right so this will cause the change of delta and also change the Z. In theory, complex-coupled DFB structures are normally assuming uniform sinusoidal perturbation because the impacts of coupled-wave equation are given below. Equation 1A:

6 da( z) dz = i ΔβΑ ( z) + ik ab Β ( z) Equation 1A is the coupling equation that describe A(z) are the amplitude of forward- traveling wave. Equation 1B: da( z) dz = iδβα( z) + ik abβ ( z) Equation 1B is the coupling equation but this time is describe B(z) are the amplitude of bacward-traveling wave. Equation 2A: Κ ab = Κ g + iκ n Equation 2A will describe ab is the result of g (gain coupling constant) plus n ( index coupling constant) in order to see the coupling constant change based on respective of forward and bacward-traveling wave. Equation 2B: Κ ba = Κ g * + iκ n * Equation 2B will describe ba is the result of g prime(gain coupling constant) plus n prime( index coupling constant) in order to see the coupling constant change from respective of bacward-traveling wave to forward-traveling wave. Equation 3A: d 2 A( z) dz 2 = pa( z)

7 Based on decoupling Equation 1A, I received Equation 3A s Equation 3B: d 2 B( z) dz 2 = pb( z) In order to get Equation 3B, I have to decoupling Equation 1B Equation 4: ( 1) a z 2 = p a z By using solution of Equation 3A, I have opportunity to use power series to see the reflection of sum coupling constant in respective of power. Equation 5: a pa = 2 ( = ( 1) 2,3,...). By the observe Equation 5, I receive the outcome of two linearly independent series. One is defines as arbitrary of a0 and another is defines as arbitrary of a1. Both arbitrary equal to zero. Equation 6: a z + A( z) = α1 α1 Based on observe the general solution Equation 3A will help me receive outcome of A(z) as the amplitudes of forward-traveling wave. Equation 7: b z a a, b, b = p 2 2 = ( ( 1) 2,3,...).

8 In order to get a and b arbitrary, we have to use power series by assign (coupling constant) to start from 2 to 100 to see how is the arbitrary occur change. Equation 8: B( z) = 1 i ab [ α 1 a z 1 iδβ a z ) + b l 1 iδβ b z )] In order to get output of B(z) as the amplitudes of bacward-traveling wave, I have to use substitution method of substituting Equation 6 in to Equation 1A to get output of B(z) as the bac-ward traveling wave. Equation 9: i( ab + r Δβ ) a a l i( Δβ + ab r 2 ) a l Κ b l 1 i( Δβ + ab r 2 ) b l Κ ][ α1]/[ α 2] = 0 Equation 9 is basically describing determinant that using Equation 8 and Equation 6 must receive output as zero. Equation 10: 1 Κ 1 i( ab + r1 Δβ ) bl i( Δβ + abr2 ) bl ] + r1b 1 al i( Δβ + abr2 ) a l Κ ] By solved Equation 10, I have to use Newton s method to calculate the threshold gain. To be honest, Equation -1 through Equation-10 is useful coupled-wave equation because it was using on measurement the distributed feedbac laser. In the simulation part, the author (Muhammad Arif and Mohmmad A.Karim) went into five steps that analyze a dephased complex-coupled distributed feedbac laser by applying the power-series method

9 1) Effects of Dephasing on δ l and gl 2) Effects of the Ratio g / n on δ l and gl 3) Effects of facet reflectivity 4) Effects of dephasing and g / n on Spatial Hole Burning 5) Chirped Grating Distributed Feedbac Laser In my point of view, this is five great step helps me now how to analyze a dephased of complex-couple of DFB because it help me calculated the threshold gain margin of DFB. The author simulation help me identify effect of the phase and gain coupling and index coupling constant and see behavior of each change. The figure 4 is determined how the normal-gain behavior in AR coated complex coupled DFB laser which represent for three coupling. From figure 4, the graph on the author (Muhammad Arif and Mohmmad A.Karim) simulation is about normal-gain versus with dephased in pi but this time the gain become larger and high in gain coupling constant.

10 The figure 5 is described about δ l is a function of diphase that call up several facet reflectives. From figure 5, the graph on the author (Muhammad Arif and Mohmmad A.Karim) simulation seem lie the lasing mode tae over AR coated facets. The figure 6 is illustrated the gain versus with several facet reflective. From figure 6, the graph on the author (Muhammad Arif and Mohmmad A.Karim) simulation will be described about δ l continue decrease as the gain and Bragg wavelength laser will increase.

11 From step one, the author names Muhammad Arif and Mohmmad A.Karim just went into effect of dephasing δ l and gl by dephasing angle Δ θ from 0 to 2π for gain coupling constant of l equal to 0.1, 0.5 and 1 and index coupling constant equal 1. When the author chosed delta=0. I see the laser show a mode that have degeneracy of the AR-coated facet and lasing mode start from negative 1 to positive 1. Figure 7 is illustrated the function the plot of δ l as the function of the ratio over three coupling coefficient. From figure 7, I see the function of gain coupling constant over index coupling constant are decrease whenever δ l begin. By observe the figure 7, the author (Muhammad Arif and Mohmmad A.Karim) simulation seem that the function of ratio is about gain coupling constant divide by index coupling constant seem to be decrease. On the other hand, δ l liely to be increase.

12 Figure 8 is illustrated the function of the ratio that represent three coupling coefficient. By observe figure 8 from the author (Muhammad Arif and Mohmmad A.Karim) simulation, I see the function of ratio about gain coupling constant divide by index coupling constant seem to be increase. On other hand, the threshold gain will be decrease. Figure 9 is illustrated the δ l versus with the function of the ratio that deal with several cleaved facet. From Figure 9 from the author (Muhammad Arif and Mohmmad A.Karim) simulation, it is ind of corresponding of the gain margin from positive 3 to negative 3.

13 Figure 10 is illustrated the gain margin as the function of the ratio that deal with cleaved facets. From figure 10 from the author (Muhammad Arif and Mohmmad A.Karim) simulation, I see the function of ratio about gain coupling constant divide by index coupling constant seem to be increase. On other hand, the threshold gain decrease. When it is start function of ratio is increase and also spread out from other facets. From step two, the author names Muhammad Arif and Mohmmad A.Karim who just went into AR-coated facet by explore the effect of three coupling constant and define formula of coupling constant as g + n and let delta equal to π. From the author graph, I see whenever we decrease δ l, the lasing wavelength that go into Bragg wavelength definitely increase coupled gain. Another author graph, I see whenever the ratio increase, it will let threshold gain decrease.

14 Figure 11 is indicated δ l as the function of the phase facet of reflectivity of r1. By observe figure 11 from author (Muhammad Arif and Mohmmad A.Karim) simulation, I see the lasing mode just switch from positive one to negative one. Figure 12 is indicated gain margin represent as the function of facet reflectivity of r1. By observed figure 12 from author (Muhammad Arif and Mohmmad A.Karim) simulation, I see there are two line. First line is started out from 0.4 of normalized gain continue to decrease at 0.7 of the phase at left facet in π will start bac up and continue to decrease. Second lines is start out from 0.75 of normalized gain decrease and touch the first line during 0.2 of normalize gain.

15 From step three, the author names Muhammad Arif and Mohmmad A.Karim who just went into effect of facet reflectivity. I guess author just thin facet phase are important because it will play important role in cleaved-facet DFB laser and In addition, the magnitude of reflectivity in the two facet will be the same because the phases. I see whenever we increase the phase, the gain margin to be smaller. Based on my observation from the author simulation, both gain margin andδ l in face reflectivity are less than sensitive from magnitude than the phase. Figure 13 is variation of δ l indicate as function of facet reflectivity of r1. By observed figure 13 from author (Muhammad Arif and Mohmmad A.Karim) simulation, the graph indicated gain margin will continue to decrease r2. In addition, the phase of r1 and r2 will be zero.

16 Figure 14 will indicate the gain margin as the function of facet reflectivity of r1. Figure 15 is showing us how to dephasing the gain coupling constant is 0.5 and the index coupling constant is 1.

17 Figure 16 will demonstrated us on dephasing the gain coupling constant which start from 1 and the index coupling constant should be 2. From step fourth, the author names Muhammad Arif and Mohmmad A. Karim who just went into effect of dephasing on Spatial hole Burning. They are team up together by study and observe the effect of phase and ratio on SHB behavior which located inside complex-coupled DFB laser cavity. The author go direct in CF quantity measurement is the change of delta. It s nown as minimum power versus with maximum power that occur the change in DFB laser cavity. When author find out SHB (spatial hole burning) are minimum of delta = n, n=0 and maximum is delta equal pi/2 and delta= 3pi/2. From there, I see SHB decreases and K (gain coupling constant) are decrease and also asymptotically reach minimum point. Whenever I apply the SHB behavior, I see the power series methods are effective to use on this case.

18 Figure 17 will be normalizing threshold gain versus with four laser chirping of CF DFB. Final step, the author names Muhammad Arif and Mohmmad A. Karim who change their style of simulation by chirped grating distributed feedbac laser in order to prove the power series method are useful method to analyze linear single-section chirping and the period of the grating must not be constant. Conclusion Before the experiment, I didn t understand how to analyze the dephased complex-coupled distributed feedbac laser. Now I now there is method of analyzed the dephased complex-coupled distributed feedbac laser based on using power series. Before the experiment, there are a lot of question I have in mind that unsolved lie this following questions. 1) How many people now distributed feedbac laser are important role or useful item in the optic world? What is does do? What is DFB using for?

19 2) What are advantages of using distributed feedbac laser? 3) What are disadvantage of using distributed feedbac laser? What are methods that analyze the dephased complex-coupling of DFB? During the experiment, I got clear response and all the question that I have in my mind are solved it. I learn LED will pump polymer and be useful for electrical pump. Furthermore it is reduced cost. In addition, I also learn advantage of distributed feedbac laser (DFB) are high output power, wave stability, reliability and manufacturing seem to be complexity than conventional single DFB laser. Definitely I learn gain grating and index grating has same pulse but index grating shift to the right. Reference: Y=DESC Y=DESC C1AF4FB6C787F648_44488.pdf?da=1&id=44488&seq=0&CFID= &CFTOKE N=

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