**3.3. Selection of diffraction grating for ECDL**

of the ECDL are 75, 173, 296 and 481 mW with injected current of 330, 450, 600 and 850 mA, respectively. In the *p*-polarized mode, the maximum output powers are 56, 161 and 293 mW with injected current of 330, 550 and 850 mA, respectively. The output power is relatively

**Figure 8.** Output power of the ECDL at different wavelengths and operating currents, operated in *s*-polarized mode (red

**Figure 7.** Optical spectra of the green ECDL system operates in (a) *s*-polarized mode and (b) *p*-polarized mode. The

output power is around 290 mW for both operation modes.

10 Laser Technology and its Applications

signs) and *p*-polarized mode (black signs).

With the highest injected current, that is, 850 mA, the maximum output powers for the *s*- and *p*-polarized mode operation are 481 and 293 mW. This means that 75 and 46% of the output power in freely running condition is extracted in the ECDL system for the *s*- and *p*-polarized

constant in the tunable range at each injected current for both operating modes.

Both the blue and green tunable ECDL systems show the efficiency (output power) of the ECDL system is higher when the zeroth-order diffraction efficiency of the grating used in the laser system is higher, such as the conditions for the holographic grating in the blue diode laser system and the *s*-polarized mode operation for the green diode laser system. However, the tunable range of the ECDL system with higher efficiency is narrower since a higher firstorder diffraction efficiency of the grating is needed to achieve a wider tunable range. Thus, there is a compromise between the output power and the tunable range of the ECDL system since the sum of the zeroth- and first-order diffraction efficiencies is around unity.

To understand this compromise between the efficiency (output power) and tunable range further, a theoretical analysis is given below based on rate equations of the diode laser. The rate equations describing the carrier density *N* and the photon density *N*ph in the diode laser cavity are given as [15, 17]:

$$\frac{dN}{dt} = \frac{\eta\_i j}{qd} - \frac{N}{\overline{\tau}} - \upsilon\_{yr} \,\mathrm{g}\,\mathrm{NJ}\,\mathrm{N}\_{ph'} \tag{1}$$

$$\frac{dN\_{ph}}{dt} = \upsilon\_{gr} \, \Gamma g \text{(N)} \, N\_{ph} - \frac{N\_{ph}}{\tau\_{ph}} + \alpha\_m \upsilon\_{gr} \, K N\_{ph} (t - t\_0) \tag{2}$$

where *j* is the inject current density, *η*<sup>i</sup> is the internal efficiency, *q* is the elementary charge of an electron, *d* is the thickness of the active region, *τ* is the carrier lifetime, *v*gr is the group velocity of the photons, *g*(*N*) is the material gain, *Г* is the confinement factor, *τ*ph is the photon lifetime, *α*m is the mirror loss, *K* is the feedback strength of the grating (the first-order diffraction efficiency in our case, here the other loss in the cavity is neglected.), *t* 0 is the time delay of the external cavity. In particular 1/*τ*ph = *v*gr(*α*<sup>i</sup> + *α*m), where *α*<sup>i</sup> is the internal loss; and the gain *g*(*N*) = *g*N(*N*−*N*tr), *g*N is the differential gain coefficient and *N*tr is the transparency carrier density. When the diode laser system is steady-state operated, rearrange Eqs. (1) and (2), we obtain:

$$dN/dt = \eta\_i/\eta d - N/\pi - v\_{gr}g\_N(N - N\_u)N\_{ph'} \tag{3}$$

$$d\mathbf{N}\_{ph}/dt = \boldsymbol{\upsilon}\_{gr}\boldsymbol{\Gamma}\,\mathbf{g}\_{\text{N}}(\mathbf{N}-\mathbf{N}\_{\text{tr}})\,\mathbf{N}\_{ph} - \boldsymbol{\upsilon}\_{gr}\left[\boldsymbol{a}\_{i} + (\mathbf{1}-\mathbf{K})\,\boldsymbol{a}\_{\text{m}}\right]\mathbf{N}\_{ph}.\tag{4}$$

Eq. (4) shows the effect of the feedback is to reduce the mirror loss from *α*m to (1−*K*)*α*m.

The steady-state solution of Eqs. (3) and (4) can be obtained as:

$$N = N\_{\rm tr} + \frac{1}{\Gamma g\_{\rm N} \tau\_{\rm ph}} - \frac{K a\_{\rm m}}{\Gamma g\_{\rm N}} = N\_{\rm th}(0) - \frac{K a\_{\rm m}}{\Gamma g\_{\rm N}} \tag{5}$$

$$N\_{ph} = \frac{\eta\_i \Gamma \tau\_{ph}}{qd} [j - j\_\text{in}(\text{K})] \frac{1}{1 - K \alpha\_m / (\alpha\_i + \alpha\_m)'} \tag{6}$$

$$j\_{\rm th}(\text{K}) = j\_{\rm th}(0) - q dK \,\alpha\_{\rm m}/\eta\_{\rm l} \,\tau \Gamma \,\mathcal{g}\_{\rm N} \tag{7}$$

The theoretical analysis above mentioned is in agreement with our experimental results obtained from the blue and green ECDL systems; where the green laser system in *p*-polarized mode (high first-order diffraction efficiency) has a much wider tunable range but less output power compared with the laser system in *s*-polarized mode (low first-order diffraction efficiency). The experimental results in Refs. [18, 19] also show that wider tunable ranges and low output powers of the ECDLs were achieved with gratings with higher first-order diffraction efficiencies. From both the theoretical and experimental results, we can conclude that the compromise between the output power and the tunable range of an ECDL is a general condi-

**Figure 9.** Schematic diagram of the gain and threshold with and without grating feedback. The grating feedback profile

Tunable High-Power External-Cavity GaN Diode Laser Systems in the Visible Spectral Range

http://dx.doi.org/10.5772/intechopen.79703

13

Considering the results obtained from the blue ECDL system using two different diffraction gratings, the ECDL system with the holographic grating has a narrower spectral bandwidth and a larger suppression of ASE when the output power of the ECDL with the two gratings are comparable. We believe the reason is that the holographic grating has a larger groove density compared with ruled grating, that is, 2400 lines/mm for the holographic grating versus 1800 lines/mm for the ruled grating, meaning that the holographic grating has a higher

Both the experimental results and the theoretical analysis here provide a general guide to the selection of gratings for ECDL systems. Two main parameters of a diffraction grating are considered when a grating is used to build an ECDL system: the groove density and the first-order diffraction efficiency. A grating with a larger groove density leads to a narrower spectral bandwidth and a higher suppression of ASE compared with a grating with a small groove density. If a higher output power of a laser system is prioritized, a grating with a lower first-order diffraction efficiency should be selected. If a wider tunable range of a laser system is the high priority, a grating with a higher first-order diffraction efficiency should be selected. Thus, there is a compromise between the output power and the tuning range of an ECDL system. This is the main consideration for selecting a diffraction grating to build

tion and irrelevant to the geometry of the external cavity.

spectral resolution.

is also shown.

an ECDL system.

where *N*th(0) is the threshold carrier density without feedback, and *j* th(0) = *qdN*th(0)/*η*<sup>i</sup> *τ* is the threshold current density without feedback. Eq. (7) shows the threshold current density *j* th(*K*) is decreased with the feedback strength *K*. Eq. (6) shows the photon density increases with *K*.

In our experiment, when we rotate the grating further to operate the laser system outside of the tunable ranges, the freely running emission appears and dominates the laser output, this means the competition of the freely running lasing at the gain center *λ*<sup>0</sup> and the lasing at wavelength *λ* (with a distance from the gain center) with feedback determines the tunable range of the external-cavity diode laser system. **Figure 9** shows a schematic diagram of the gain and the threshold of the diode laser system; the grating feedback profile is also shown. The grating feedback decreases the threshold current density at λ from *j* th(λ, 0) to *j* th(λ, *K*). When *j* th(λ, *K*) is less than the freely running threshold current density at *λ*<sup>0</sup> , that is, *j* th(λ<sup>0</sup> , 0), the laser system lases at *λ*, and vice versa. Since the decrease of the threshold current density by the feedback is proportional to *K*, a higher value of *K* causes a wider tunable range of the external-cavity diode laser system.

The output power *P* of an external-cavity diode laser system can be expressed as:

$$P \propto N\_{ph}(1 - K) = \frac{\eta\_i \Gamma \tau\_{ph}}{qd} \left[ j - j\_m(K) \right] \frac{1 - K}{1 - K \alpha\_m / (\alpha\_i + \alpha\_m)}.\tag{8}$$

The slope efficiency of the laser system decreases with the feedback strength *K* due to the last term in Eq. (8). Thus, the output power decreases with *K*, when the laser system is operated far above the threshold; although the threshold of the laser system also decreases with the feedback strength *K*.

Tunable High-Power External-Cavity GaN Diode Laser Systems in the Visible Spectral Range http://dx.doi.org/10.5772/intechopen.79703 13

the external cavity. In particular 1/*τ*ph = *v*gr(*α*<sup>i</sup> + *α*m), where *α*<sup>i</sup>

The steady-state solution of Eqs. (3) and (4) can be obtained as:

*<sup>N</sup>* <sup>=</sup> *<sup>N</sup>*tr <sup>+</sup> \_\_\_\_\_\_\_\_ <sup>1</sup>

*<sup>N</sup>*ph <sup>=</sup> *<sup>η</sup>*<sup>i</sup> <sup>Γ</sup> *<sup>τ</sup>* \_\_\_\_\_ph

*j*

12 Laser Technology and its Applications

external-cavity diode laser system.

feedback strength *K*.

*<sup>P</sup>* <sup>∝</sup> *<sup>N</sup>*ph(1 <sup>−</sup> *<sup>K</sup>*) <sup>=</sup> *<sup>η</sup>*<sup>i</sup> <sup>Γ</sup> *<sup>τ</sup>* \_\_\_\_\_ph

When *j*

*g*(*N*) = *g*N(*N*−*N*tr), *g*N is the differential gain coefficient and *N*tr is the transparency carrier density. When the diode laser system is steady-state operated, rearrange Eqs. (1) and (2), we obtain:

*dN*/*dt* = *η*<sup>i</sup> *j*/*qd* − *N*/*τ* − *v*gr *g*N(*N* − *N*tr) *N*ph, (3)

*dN*ph/*dt* = *v*gr Γ *g*N(*N* − *N*tr) *N*ph − *v*gr[*α*<sup>i</sup> + (1 − *K*) *α*m] *N*ph. (4)

<sup>−</sup> *<sup>K</sup> <sup>α</sup>* \_\_\_\_m Γ *g*<sup>N</sup>

th(*K*) ]

threshold current density without feedback. Eq. (7) shows the threshold current density *j*

is decreased with the feedback strength *K*. Eq. (6) shows the photon density increases with *K*. In our experiment, when we rotate the grating further to operate the laser system outside of the tunable ranges, the freely running emission appears and dominates the laser output,

at wavelength *λ* (with a distance from the gain center) with feedback determines the tunable range of the external-cavity diode laser system. **Figure 9** shows a schematic diagram of the gain and the threshold of the diode laser system; the grating feedback profile is also shown.

the laser system lases at *λ*, and vice versa. Since the decrease of the threshold current density by the feedback is proportional to *K*, a higher value of *K* causes a wider tunable range of the

*qd* [*<sup>j</sup>* <sup>−</sup> *<sup>j</sup>*

The slope efficiency of the laser system decreases with the feedback strength *K* due to the last term in Eq. (8). Thus, the output power decreases with *K*, when the laser system is operated far above the threshold; although the threshold of the laser system also decreases with the

th(*K*) ] \_\_\_\_\_\_\_\_\_\_\_\_ <sup>1</sup> <sup>−</sup> *<sup>K</sup>* 1 <sup>−</sup> *<sup>K</sup> <sup>α</sup>*m/(*α*<sup>i</sup> <sup>+</sup> *<sup>α</sup>*m)

<sup>=</sup> *<sup>N</sup>*th(0) <sup>−</sup> *<sup>K</sup> <sup>α</sup>* \_\_\_\_m

\_\_\_\_\_\_\_\_\_\_\_\_ 1 1 <sup>−</sup> *<sup>K</sup> <sup>α</sup>*m/(*α*<sup>i</sup> <sup>+</sup> *<sup>α</sup>*m)

Γ *g*<sup>N</sup>

th(0) − *qdK α*m/*η*<sup>i</sup> *τ*Γ *g*N, (7)

Eq. (4) shows the effect of the feedback is to reduce the mirror loss from *α*m to (1−*K*)*α*m.

Γ *g*<sup>N</sup> *τ*ph *v*gr

*qd* [*<sup>j</sup>* <sup>−</sup> *<sup>j</sup>*

th(*K*) = *j*

this means the competition of the freely running lasing at the gain center *λ*<sup>0</sup>

The grating feedback decreases the threshold current density at λ from *j*

th(λ, *K*) is less than the freely running threshold current density at *λ*<sup>0</sup>

The output power *P* of an external-cavity diode laser system can be expressed as:

where *N*th(0) is the threshold carrier density without feedback, and *j*

is the internal loss; and the gain

, (5)

, (6)

th(0) = *qdN*th(0)/*η*<sup>i</sup>

*τ* is the

th(λ, *K*).

th(λ<sup>0</sup> , 0),

and the lasing

th(λ, 0) to *j*

, that is, *j*

. (8)

th(*K*)

**Figure 9.** Schematic diagram of the gain and threshold with and without grating feedback. The grating feedback profile is also shown.

The theoretical analysis above mentioned is in agreement with our experimental results obtained from the blue and green ECDL systems; where the green laser system in *p*-polarized mode (high first-order diffraction efficiency) has a much wider tunable range but less output power compared with the laser system in *s*-polarized mode (low first-order diffraction efficiency). The experimental results in Refs. [18, 19] also show that wider tunable ranges and low output powers of the ECDLs were achieved with gratings with higher first-order diffraction efficiencies. From both the theoretical and experimental results, we can conclude that the compromise between the output power and the tunable range of an ECDL is a general condition and irrelevant to the geometry of the external cavity.

Considering the results obtained from the blue ECDL system using two different diffraction gratings, the ECDL system with the holographic grating has a narrower spectral bandwidth and a larger suppression of ASE when the output power of the ECDL with the two gratings are comparable. We believe the reason is that the holographic grating has a larger groove density compared with ruled grating, that is, 2400 lines/mm for the holographic grating versus 1800 lines/mm for the ruled grating, meaning that the holographic grating has a higher spectral resolution.

Both the experimental results and the theoretical analysis here provide a general guide to the selection of gratings for ECDL systems. Two main parameters of a diffraction grating are considered when a grating is used to build an ECDL system: the groove density and the first-order diffraction efficiency. A grating with a larger groove density leads to a narrower spectral bandwidth and a higher suppression of ASE compared with a grating with a small groove density. If a higher output power of a laser system is prioritized, a grating with a lower first-order diffraction efficiency should be selected. If a wider tunable range of a laser system is the high priority, a grating with a higher first-order diffraction efficiency should be selected. Thus, there is a compromise between the output power and the tuning range of an ECDL system. This is the main consideration for selecting a diffraction grating to build an ECDL system.
