2. Extended-cavity diode laser development 2.1. The spacing between longitudinal modes (δν) is governed by the following equation (Demtröder 2003):
( ( ) )
2 1
c
nd n dn d
δν = + ν ν (2.10)
Here, n is the refractive index of the cavity material, d is the cavity length, ν is the laser frequency, and c is the speed of light in a vacuum. Note a more complicated expression is given here because the dispersion (dn dν), a term that can normally be neglected, is unusually high for GaN (Tisch et al. 2001).
2. Extended-cavity diode laser development configuration extended (or external) cavity diode laser (ECDL). Although the Littrow scheme is most widely used, other extended-cavity geometries, such as the Littman-Metcalf configuration (Littman and Metcalf 1978) have also been implemented (Harvey and Myatt 1991).
Figure 2.2 Littrow-configuration ECDL
The Littrow configuration ECDL involves the use of optical feedback from a grating positioned at an angle so that the minus-one diffraction order is retro-reflected into the diode (MacAdam et al. 1992; Ricci et al. 1995). The grating angle determines the feedback wavelength, and thus also the output wavelength of the ECDL, according to the grating equation:
(sin m sin )i
d θ − θ =mλ (2.11)
Here, d is the grating groove spacing, m is the diffraction order, λ is the laser wavelength, θi is the incident angle and θm is the angle of the m order diffraction fringe. For the retro-reflected beam, the condition θi = -θm is fulfilled and m = -1, so Eqn. 2.11 can be simplified to:
2dsinθ = λ (2.12)
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2. Extended-cavity diode laser development
The zero order diffraction from the grating forms the output beam. In addition to the internal Fabry-Perot cavity formed by the facets of the diode, there is also an extended cavity formed between the grating and the back facet of the diode.
This leads to the existence of extended-cavity modes in addition to the Fabry-Perot diode modes. These modes are represented schematically in Fig. 2.3 along with the grating feedback profile and the diode gain curve. The spectral profile of the grating feedback is narrower than the diode gain curve and its width (FWHM) can be approximated by considering the resolution of the grating (Boggs et al. 1998):
g cos i
dc
ν D θ
∆ = λ (2.13)
Here, D is the width of the diode laser beam. As an example, let us consider the blue ECDLs used during this project, whose approximate characteristics are summarised in Table 2.1.
2. Extended-cavity diode laser development
ECDL 1 ECDL 2
Wavelength λ 451 nm 410 nm
Beam diameter D 5 mm 5 mm
Grating angle θi 24.0º 21.7º
Grating lines per mm 1800 1800
Grating period d 556 nm 556 nm
Grating feedback width ∆νg 70 GHz 80 GHz
Extended cavity length 24 mm 25 mm
Extended cavity mode spacing 6 GHz 6 GHz Diode cavity length (assumed) 0.7 mm 0.7 mm
GaN refractive index n 2.52 2.56
GaN dispersion dn dν 9.8 x 10-16 Hz -1 12.0 x 10-16 Hz -1 Diode mode spacing (predicted) 45 pm 35 pm
Table 2.1. General characteristics of the extended-cavity diode lasers constructed during this research.
The width of the grating feedback profile was calculated from Eqn. 2.13. In estimating the extended-cavity mode spacing from Eqn. 2.7, it was assumed that the refractive index of air is nair=1. It should be noted that the diode cavity length shown here is an assumed value from literature and has not been measured. The diode mode spacing was estimated from Eqn. 2.10, based on an assumed chip length of 0.7 mm (Nakamura et al. 1997), and using the values for the refractive index and dispersion of GaN from plots in the literature (Tisch et al. 2001).
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2. Extended-cavity diode laser development The emission wavelength of the ECDL corresponds to the position at which a longitudinal mode of the extended cavity matches a Fabry-Perot diode laser mode that lies close to the peak of the grating wavelength feedback profile (Yan and Schawlow 1992).
Figure 2.3 Schematic representation of mode competition in an ECDL.
A standard Fabry-Perot diode laser in Littrow configuration can be coarsely tuned over its gain bandwidth through rotation of the grating. However, such coarse tuning involves discrete jumps, which occur when the number of standing wave nodes in the laser cavity changes abruptly. To avoid this, the length of the extended cavity must be simultaneously adjusted (Favre et al.
1986). With reference to Figure 2.3, rotation of the grating causes the grating feedback curve to move to one side. An expression for the shift in the central wavelength of the grating feedback profile is obtained by differentiation of Eqn 2.12. For small changes in grating angle:
2 cosd
λ θ θ
∆ = ∆ (2.14)
Similarly, scanning the cavity length causes the comb of extended-cavity modes to shift in wavelength. The magnitude of this change can be
2. Extended-cavity diode laser development determined by considering the number of standing waves in the extended cavity:
2nlC N ν
δν λ
= = (2.15)
Here, lC is the extended-cavity length. By differentiation, we obtain (for small cavity length changes):
C C
l l λ λ
∆ = ∆ (2.16)
The grating rotation and cavity length change must be performed in the correct proportion so that mode-hops are avoided.
The most common way of achieving the optimum ratio between grating angle and cavity length is to mount the grating on a lever arm in contact with a single piezoelectric crystal and to rotate it around a pivot-point (de Labachelerie and Passedat 1993; Trutna and Stokes 1993). Considerable effort has been spent on the theoretical prediction of where the optimal pivot-point should lie; see for example (Nilse et al. 1999). An alternative is to use a multiple-piezo actuator optical mount to achieve the same relation between grating rotation and translation during tuning (Mellis et al. 1988; Laurila et al.
2005). A key advantage of this approach is that the requirement for accurate mechanical positioning of the pivot point is replaced by a simple balancing of the electrical signals driving the piezo-actuators. Furthermore, this strategy avoids the need to construct a precision pivot-point grating mount: a standard
53
2. Extended-cavity diode laser development kinematic mount may be used instead. Since the extended-cavity length and the grating angle may be adjusted independently in the multiple-piezo scheme, it is also possible to optimise the initial overlap between the active extended-cavity mode and the grating feedback centre-wavelength at the beginning of the wavelength scan. Such an optimisation would be more difficult to achieve with the conventional pivot-arm design.
The issue of mode-competition from the internal Fabry-Perot cavity has commonly been addressed by applying a high-quality anti-reflection coating to the front facet (Boshier et al. 1991). By removing the reflectivity of the front facet, the internal cavity should, in theory, be eliminated, leaving only a single cavity formed between the grating and the back diode facet. In practice, however, it is still necessary to match the lengths of the extended cavity and the Fabry-Perot cavity in order to achieve a large tuning range, even with antireflection coated diodes (Hildebrandt et al. 2003). This appears to suggest that the residual reflectance is generally not low enough to suppress entirely the Fabry-Perot mode structure of the diode. Another disadvantage of the anti-reflection coating approach is that such treatment of the diode is a complex and expensive process, which risks damaging the device. As a result of this there is limited commercial availability of anti-reflection coated laser diodes.
It has been reported, however, that the need for anti-reflection coating can be avoided by modulating the laser diode injection current (Ricci et al. 1995).
This causes temperature variations in the active region of the diode, which lead in turn to changes in both the length and refractive index of the diode cavity. It should be noted that the temperature change also causes a shift in the central wavelength of the diode gain curve (at a higher rate); since the gain curve is very broad, however, this effect is not normally of significance.
2. Extended-cavity diode laser development The shift in the wavelength of the diode mode is given by (Demtröder 2003):
1 1
d d
dl
dn dn dL
T T
n dT l dT n dT L dT
λ λ
λ ∂ ∂ λ⎛
∆ = ∂ ∆ +∂ ∆ = ⎜⎝ + ⎠
⎞⎟ (2.17)
The idea of the concept is to tune the laser diode injection current in synchronisation with the extended-cavity tuning, thus matching the wavelength shifts of the cavity modes. This then allows wide mode-hop free tuning ranges to be achieved using standard uncoated laser diodes, therefore resulting in low-cost ECDL systems.