Material with
thermal conductivity k
d
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heats up it becomes larger due to the increased kinetic energy of its
constituent molecules. However, there are some rare exceptions where
there is an inverse relationship between temperature and length, such as
water, where its CTE becomes negative below 3,983°C and causes it to
expand as the temperature drops below 3,983°C.
The CTE is given in units of 1/°C. When selecting an optic for your application,
CTE is important to consider because changes in the optic’s
size may influence alignment and stresses on the component. In environments
involving swings in temperature, users need to be cognizant that
their optic will expand when heated. An optic that is 25 mm at room
temperature may be 25,1 mm at 300°C, which could break the mounting
or skew light in an unwanted direction, thereby affecting pointing stability
and laser alignment; this is generally why a small CTE is desired. Fused
Silica has a low CTE and is often used to reduce thermal expansion.
Section 8.3: Temperature Coefficient
of Refractive Index
The temperature coefficient of refractive index (dn/dT) is a measure of
the change in refractive index with respect to temperature. The dn/dT
of most IR materials is orders of magnitude higher than those of visible
glasses, creating large changes in the refractive index. The density of a
substance is almost always inversely proportional to temperature, meaning
that a material’s density will decrease as the temperature increases.
Therefore, refractive index decreases as the temperature increases,3
The full equation for a material’s dn/dT is given by:
8.2
Where:
T0 is the reference temperature (20°C)
T is the temperature in °C
ΔT is the temperature difference with T0
λ is the wavelength of light
D0 ,D1 ,D2 ,E0 ,E1 , and λTK are material constants
dn/dT is irrelevant for reflective optics, except for minor performance
variations due to changes in the refractive index of the coating. However,
dn/dT is an important property for transmissive optics as it helps
determine their stability under temperature variations. There will always
be some absorption with a high power laser beam incident on an optic,
leading to an increase in temperature; dn/dT determines how much this
affects performance (Figure 8.3).
Section 8.4: Thermal Conductivity
The thermal conductivity (k) of a material is a measure of the ability of
the material to transfer heat via conduction (Figure 8.4). It is commonly
measured in W/(m ⋅ K) or Btu/(hr ⋅ ft ⋅ °F) and is used to define the rate
of thermal conduction:
8.3
Q represents the amount of heat transferred in time t, and the units of
Q/t are J/s, or W. A is the cross-sectional area of the substrate, ΔT is the
temperature difference between one side of the material and the other,
and d is the material’s thickness.
Materials with high thermal conductivities, like metals, are able to dissipate
heat much quicker than materials with low thermal conductivities,
such as glasses or plastics. Because one of the primary effects of
transmitting laser radiation through an optic is the conversion of the
radiative energy to thermal energy, knowing the thermal conductivity of
a material is important in order to evaluate the energy balance around
the optic. Materials that do not reflect or transmit specific wavelengths
f
Figure 8.3: The change in an optical component’s refractive index with
temperature (dn/dT) can lead to a shift in a lenses focal length (Δf ),
changing the focus position
T2
Q
T1
T2 > T1
Area A
Figure 8.4: The thermal conductivity of a material (k) defines its ability
to transfer heat (Q) through a given thickness (d)
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