Design The Single Mode Laser Biology Essay

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The design of a laser is strongly related to the material used to fabricate it. This is because every material is unique in its own way, like structure of the layer and optical characteristics (refractive index, gain spectrum, etc.). The choice of the material to be used depends on the range of frequencies that the device is expected to work in. It is necessary to ensure that the operating frequency lies close to the center of the gain spectrum of the material chosen. Thus maximizing the gain obtained from the material.

As described earlier, the frequencies used in this project are 795 nm and 1550 nm. The material description of each of the lasers is given below.

1.55µm Material Structure

A commercially available AlGaInAs/InP ( IQE Ltd. Product IEGENS-13-17) compound was used in a multiple quantum well (MQW) structure. The figure shows the layer structure of the wafer.

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It is to be noted that Aluminum(Al) is used as the quaternary element instead of Phosphorous(P), i.e. AlGaInAs is used instead of InGaAsP. This is because recent studies have shown that an Al-quaternary device provides a significant advantage over the norm[1]. That is, the conduction band offset of AlGaInAs is much larger than that of InGaAsP. In the case of AlGaInAs, the 72% of the offset lies within the conduction band (i.e. ΔEc = 0.72ΔEg), as compared to 40% in the case of InGaAsP (i.e. ΔEc = 0.40ΔEg). This leads to a better carrier confinement and a higher characteristic temperature of the device[2].

Waveguide

Core

Figure 2: Epitaxial layer structure of the material IQE-IEGENS-13-17, used for the fabrication of the 1550nm device.

All the layers were grown by Metal Organic Chemical Vapor Deposition (MOCVD). The MQW region consists of five layers of Al0.07Ga0.22In0.71As wells which are compressively strained (12000ppm) and 6nm thick each. There six 10 nm thick Al0.224Ga0.286In0.71As layers of barriers which are tensely strained (3000ppm). Two 60nm thick AlGaInAs GRINSCH (i.e., GRaded INdex Separate Confinement Heterostructure) layers are used to confine the carriers to the quantum wells. The GRINSCH is chosen over the standard SCH (Separate Confinement Heterostructure) because it allows a lower threshold current density and a larger differential gain. The upper and lower claddings used were an 800nm InP lower cladding and a 1720nm InP upper cladding layers. The structure is finally completed by a highly doped (1.5 Ã- 1019 cm-1) GaInAs contact layer. All layers were lattice matched to the n-type InP substrate layer. Zn and Si were used as the p-type and n-type dopants respectively.

795nm Material Structure

Similar to the 1.55µm device, the material used for 795nm is a commercially available AlGaAs ( IQE Ltd. Product COST01-36-1) compound with an MQW structure. The figure shows the epitaxial wafer's layer structure.

Figure 2: Epitaxial layer structure of the material IQE-COST01-36-1, used for the fabrication of the 795nm device.

The MQW structure is made of three strained 7 nm thick AlGaAs layers and two 10nm inner barriers (between the quantum wells) along with two 40nm outer barriers (at the top and bottom of the MQW). All the layers are lattice matched to an n-type GaAs substrate.

Lateral Confinement

To maximize the output of the laser, it is necessary to confine the photons in the laser in both the vertical and lateral direction. The multilayered structures discussed above have a core refractive index that is higher than the cladding refractive indices. This ensures the vertical confinement of the photons within the device. Now the lateral confinement is achieved by using the etched ridge waveguide technique. In this technique a ridge shaped waveguide (also called mesa-structure) is formed by etching down from the top most layer in order to produce lateral index guiding and transversal current confinement. There are two types of waveguides that can be formed (shown in figure 2.3), they are shallow etched waveguide and deep etched waveguide.

Figure 2: The cross section of shallow etched and deep etched waveguide

Shallow etched waveguide

They are formed by etching down to the top edge of the active layer and not through it. The lateral confinement provided by this type of waveguide is comparatively low, due to the small effective refractive index difference (Δneff = neff - nc) between the etched and non-etched region of the structure. But it is enough to ensure that only a single transverse mode is sustained within the waveguide. Furthermore, since the etching is not done through the active region, the carrier recombination at the sidewalls is minimized along with the back reflections from the sidewalls.

Deep etched waveguide

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These are made by etching all the way through the active layer. This type of waveguide ensure a strong carrier confinement as the effective refractive index difference (Δneff = neff - nc) between the etched and non-etched region is high. They are very useful in curved structures with a small radius. But the interaction of the optical mode with the side walls may lead to large back reflections and scattering effects if the sidewall roughness is not small. There is also a problem of reduced performance due to the non-radiative recombination that occurs at the interface of the active layer and air (i.e., at the edge). This can also lead to overheating of the device and reduced lifespan.

The above mentioned problems with the deep etched waveguide leads us to conclude that shallow etched structure is to be chosen for the design of the device.

In the case of the 1.55µm device, the etching is done upto 1920nm of depth from the top surface, i.e. upto the first Al-quaternary layer lying at the top of the core structure. Similarly in the case of the 795nm device, the etching is done till a depth of 1.65 µm depth, i.e. until the topmost layer of the MQW core structure. To ensure that only a single transverse mode existed within the device, the waveguide width was chosen to be 3µm or lower. The method given in [3] and a dedicated site called Luxpop [4] were used to find the refractive index of each of the layers from their corresponding refractive indices.

There are some considerations to be taken care of while making the output of the waveguide. The back reflections from the edges of the waveguide has to be minimized in order to avoid the creation of sub Fabry-Perot cavities (i.e., a miniature Fabry-Perot cavity within the device). There are two effective methods of reducing the back reflections:

Anti-reflective coating :

This is formed by depositing multiple layers of thin films on the cleaved facet where the waveguide interacts with air. The thickness of each layer has to be carefully monitored so as to create destructive interference of the reflected waves and constructive interference of the transmitted waves.

Tilting of the output waveguide:

In this method the output of the waveguide is tilted to an angle of 100 to the direction of propagation of the wave. This ensures that the back reflections do not go back to the gain medium of the device. In this case the output wave emerges from the device at an angle of 330 to the direction of propagation of the waveguide. This can be got from Snell's law as shown below.

Due to the time requirement and complexities involved in the making of the anti-reflective coating, the tilting of the output waveguide is preferred.

Distributed Feedback (DFB) Design

A laser has two main types of modes. They are:

Longitudinal modes: These are related to the length of the laser. Since the length is usually much larger than the wavelength, multiple longitudinal modes can exist within the cavity.[5]

Transverse modes: These modes are formed due to the electromagnetic fields along the plane perpendicular to that of the p-n junction. [5]

Figure 2: Output spectra for multimode lasers: (a) with multitransverse modes; (b) with single transverse mode (reference: [6])

Figure 2.4 (a) shows the effect of multiple transverse modes on the spectra of the device. This can be avoided by limiting the width of the waveguide in the device, in order to give only a single transverse mode. [6]

A Fabry-Perot laser will have multiple longitudinal modes in its output spectrum. This is because the reflectivity of the mirrors used is not wavelength selective, hence all modes close to the lasing threshold will appear in the output spectrum.

In a single mode of operation there will be only one longitudinal and one transverse mode. The single transverse mode may be obtained by adjusting the width of the waveguide. The next step is to obtain a single longitudinal mode. The typical spectrum of a single mode laser is shown in figure 2.5.

Figure 2: Spectrum of a single mode laser (Reference[6])

One of the ways of achieving this is by adjusting the mode spacing so that only one of the modes exists within the gain curve. The mode spacing is given by δf c/2nL. [7] But the problem with this method is that lasers with very small cavity lengths require large currents, this in turn could form other longitudinal modes. Another way to attain single mode is by using an external LASER for light injection. In this case the modal loss becomes frequency depended, due to the interference while tuning the two LASERs[8]. Thus the oscillating mode is limited.

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The best amongst these techniques is by adding additional structures to the device. These are called diffraction gratings. These are called Bragg reflectors. In this section, the basic theory behind Bragg reflectors is discussed along with some design options so as to obtain a single wavelength of operation.

The Wave Equations

In November 1912 W.L. Bragg published his discovery[9] that it is possible to induce coupling between orthogonal modes of a waveguide by using refractive index perturbations. These perturbations are made to be periodic along the direction of propagation so that the forward and backward moving waves are coupled. This effect is known as "backward Bragg scattering". It produces coherent coupling only between fields that satisfy the Bragg condition, which is defined by the following equation.

(2.1)

Where,

m is the order of the grating.

neff is the effective refractive index

λb is the Bragg wavelength (the wavelength at which the peak occurs)

Λo is the grating period (the distance between two consecutive gratings)

This condition is satisfied by only those modes that exist at a particular wavelength called the Bragg wavelength (λb). All other modes in the device get attenuated and reduce in amplitude, thus forming a single mode of operation.

The refractive index perturbations can be described by first looking at the general wave equations as given by the Maxwell's equations at a wavelength of λb and a propagation constant ko= 2π/ λb. The equation is as given below[10].

(2.2)

Where, E: sum of the forward and backward propagating waves

βo = n(z).ko, where n(z) is the refractive index along the direction of propagation.

The general solution for the differential equation is given by[11]:

(2.3)

Here the fast changing phase terms have been included in the exponential terms, hence the R(z) and S(s) terms vary slowly along z. The amount of coupling between the two counter propagating fields is given by the coupling coefficient (κ) of the device. By assuming a rectangular index perturbation profile and a 0.5 duty cycle (shown in figure 2.6), the coupling coefficient (κ) of the device is given by:

(2.4)

Where, neff : refractive index of the propagating mode

n1, n2 : refractive index of the waveguide and grating recess

Γx,y : confinement factor of the mode to the propagating area

Figure 2: Index profile for a rectangular refractive index perturbations within a waveguide (reference [12])

Substituting equation 2.3 in 2.1 and later solving them gives us the following equations[10].

(2.5)

(2.6)

Where, Δβ: detuning factor around βo, with Δβ << βo

The equations 2.5 and 2.6 relate the forward traveling wave with the backward traveling wave. These are called the coupled wave equations. From the equations it can be seen that when the coupling coefficient (κ) becomes zero, the equations represent two completely independent waves, i.e. the counter propagating waves become de-coupled.

Consider the periodic structure shown in figure 2.6. The reflection coefficient 'r' of the first discontinuity can be got from the Fresnel equation as given below.

(2.7)

Where, Δn = n1 - n2. The reflection coefficient of the next discontinuity is negative of the equation 2.7 (i.e., - r). This is because in the second discontinuity the wave is traveling from a high index region to a low index one.

For a mode whose wavelength is equal to that of the Bragg wavelength, the phase difference between the forward and back ward traveling wave within one section of the grating is given by βoΛo=π. Thus the field reflectivity per unit length is given by[12]:

(2.8)

Design of the Bragg grating

The design of the grating comprises of two main steps. Firstly the Bragg wavelength must be chosen. The Bragg wavelength (λb) is selected by varying the grating period (Λo) and the order (m) of the grating.

For the 1.55µm device, a first order grating with a period of 0.242µm was chosen. The index profile shown in figure 2.6 was chosen with a duty cycle (D) of 0.5.

The 795 nm laser cannot be made in the first order as the gap between gratings become too small, thus making it difficult to fabricate. Hence, in this case, a third order grating is chosen with a period of 0.36µm. The index profile and the duty cycle chosen were the same as that of the 1.55 µm device (i.e. rectangular profile with D=0.5).

When the grating order is increased (as in the case of 795nm device) the coupling coefficient decreases. This decrease in coupling coefficient can be found using the equation 2.9

(2.9)

Where,

(2.10)

The figure 2.7 gives the variation of the fred function with varying duty cycles at different grating orders. From the figure it can be clearly seen that the first order gratings gives the highest value of coupling coefficient along with the minimizing its dependence on duty cycle (D). Hence ideally the order of the grating should be one until and unless the first order is not a physically feasible one (like in the case of the 795nm device).

Figure 2: Coupling coefficient reduction factor (fred) as a function of duty cycle (D) at different grating orders (m) [Reference [12]]

The second step for the grating design is the design of the reflection spectrum. The main spectral properties that have to be designed are the stop band of the grating (width of the maximum reflectivity peak) and the peak reflectivity at the Bragg wavelength. From the equations 2.5 and 2.6 the wavelength dependence of the Bragg grating can be written as[12]:

(2.11)

Where, (2.12)

(2.13)

From the equations 2.11 to 2.13 it can be clearly seen that the previously mentioned spectral properties strongly depend on the values of the coupling coefficient (κ) and the grating length (L)

The variation of the reflectivity spectrum of the grating (1.55µm device grating) with varying values of κ and L were studied using a series of MATLAB codes.

Figure 2: Plot for the variation of the reflection spectrum for a varying κ value at L=400µm

Figure 2: Reflectivity spectrum for all values of κ at L=400µm

Figure 2.8 shows the varying reflectivity spectrum calculated using the equation 2.11 at three values of κ and a constant L=400µm. it can be clearly seen that as the value of κ increases the reflectivity and the stop-band width increases. This continues up to a particular value of κ after which the reflectivity saturates at 1 for a wide range of wavelengths. The figure 2.9 gives the variation in the reflectivity spectrum over all values of κ in the range of 0 to 200.

Figure 2: Plot for the variation of the reflection spectrum for a varying L at κ =60 cm-1

Figure 2: Reflectivity spectrum v/s wavelength for all values of L at κ =60cm-1

From figure 2.10 it can be seen that as the length (L) increases, the reflectivity peak increases while the stop-band width decreases. This effect can be seen over all values of L in the range of 100 to 500µm in figure 2.11

The stop-band width can be said to be the distance between the first zeros of the reflectivity spectrum. This can be got by using equation 2.14, when ΔβL> κL.

(2.14)

When the wavelength (λ) equals the Bragg wavelength (λb) the equation 2.11 reduces to the one given below.

(2.15)

It can be seen from equation 2.15 that the peak reflectivity is directly related to the κL product. This product is called the normalized coupling coefficient. Figure 2.12 shows a plot of the peak reflectivity as a function of the κL product. It is interesting to note that the same value of the product can be got with various values of κ and L, thus allowing a choice of the coupling coefficient and the length. This can be clearly seen in figure 2.13, where every band of colour is a point where the value of the normalized coupling coefficient is the equal.

Since the value of R saturates at 1 after a κL value of 4, it is preferable to have κL to be within the range of 2 to 3.

Figure 2: Peak Reflectivity as a function of the κL product

Figure 2: Peak Reflectivity over all values of κ and L

Side Etched Gratings

The Bragg reflectors can be made vertically with multiple layers of materials (they are called Vertical Cavity Surface Emitting Lasers or VCSELs) as shown in figure 2.14. But for DFB lasers the gratings are made by etching the layers on top of the active layer. This can be done by etching of a layer followed by the regrowth of the remaining layers. This is a highly complicated process and even increases the cost & time required for fabrication. In 1991, L.M. Miller and his colleagues released a paper [13] in which they proposed a post growth lateral etching process for making the Bragg gratings (shown in figure 2.15).

Figure 2: Vertical gratings (Reference [14])

Figure 2: Lateral etched gratings (Reference [13])

This structure is a combination of the lateral confinement of the photons provided by the ridge waveguide and the distributed feedback given by the gratings. The index profile shown in figure 2.6 is formed by making a lateral recess of depth d with a period of Λo on a waveguide of width W. This is illustrated in figure 2.16. The Bragg condition is satisfied by the reflection of the evanescent fields from the periodic lateral corrugations that were made.

Figure 2: Lateral etched grating

This type of design for the grating allows a great flexibility in the choice of the Bragg wavelength and κ. The Bragg wavelength can be changed by varying the period of the grating(Λo) and the formula . Whereas the κ value can be varied by changing the W and d values, since higher ratios of W/d leads to a lower value of κ

Summary and Conclusion

From the detailed design procedure, the following were decided done and decided upon.

The materials to be used in fabrication of each of the lasers were chosen. The material chosen for the 1550nm device was chosen to have Al as the quaternary element.

Shallow etched ridge waveguide was chosen for the lateral confinement of the photons, so as to avoid the non-radiative recombination and sidewall back reflections.

Bragg gratings were selected as the obvious choice for arriving at the single mode operation.

Side etched gratings was found to be highly flexible in terms of designing the grating properties and hence decided upon as the method to be followed.

The variations in reflectivity spectrum and stop-band widths with varying κ and L values were studied using a series of MATLAB programs.

The output of the MATLAB programs showed a trend in the variations of the peak reflectivity and the stop-band width (as can be seen in figures 2.8 to 2.11). The values received can be summarized as shown in table 2.1 and 2.2

The different values of peak reflectivity and stop-band width at L=400µm and varying κ

κ in cm-1

Peak Reflectivity [a.u.]

Stop-Band Width (nm)

160

1

4.2

60

0.968

2.4

20

0.441

2

Table 2: The Values of Peak Reflectivity and stop-band width with varying κ

The different values of peak reflectivity and stop-band width at κ =60 cm-1 and varying L

L in µm

Peak Reflectivity [a.u.]

Stop-Band Width (nm)

400

0.968

2.4

250

0.8193

3.4

120

0.38

6.4

Table 2: The Values of Peak Reflectivity and stop-band width with varying L

It can be clearly seen from the tables 2.1 & 2.2 that :

As κ increases the reflectivity peak and the stop-band width increases.

As L increases the reflectivity peak increases while the stop-band width decreases.

The reasons for this are:

As κ increases, the coupling the occurs between the counter propagating waves increases, thus the gratings can couple waves that propagate at wavelength that are further away from the Bragg wavelength.

As L increases, the number of gratings that are taking part in the Bragg scattering increase, thus the wavelength selectivity of the device is improved. Which means that only those waves that lie closer to the Bragg wavelength are coupled (hence decreasing the stop-band width) while the coupling itself is improved (hence increasing the peak reflectivity).