3. Fiber-optic temperature sensors with amplitude modulation of light

From the types of fiber-optic sensors being represented in the previous paragraph, sensors with amplitude modulation of light are most suitable for further processing of the output signal from optical fiber. Most of the schemes with amplitude modulation of signals do not require the use of coherent light and therefore do not include specific requirements for emission source (LED) and emission detector (photodiode).

The amplitude modulation of optic signal can be done in several ways: (1) attenuation of light when α absorption coefficient changes; (2) changes in the cross section on the way of light passing; (3) changes in the coefficient of reflection of the medium when refractive index n is changing; (4) receiving additional radiation when the temperature of the sensitive element of sensor is changing; and others.

The operation principle of the first-type fiber-optic sensors is that light passing through a semiconductor material is absorbed in the case when the photon energy hν is greater than the width of the bandgap Eg [14].

With increasing temperature, the width of the bandgap decreases monotonously. In works [5, 15–17], as a temperature sensor, a GaAs crystal was selected. The principle of operation of the sensor is to shift the edge of optic absorption induced by temperature change (Figure 1). From the graph, it is seen that, for example, passing the sample at wavelength λr will be different when temperature changes. Knowing the optic characteristics of a material, one can estimate the transmission characteristic of such a sensor.

Indeed, according to the Beer–Lambert law of absorption

$$I(l,T) = I\_0(\mathbb{1} - R) \exp\left[a(T) \cdot l\right] \tag{1}$$

where:

I<sup>0</sup> is the intensity of the falling light.

I is the intensity of the light passing through the sample.

R is coefficient of reflection.

αð Þ T is the material absorption coefficient at a given temperature and wavelength. As shown in [16], for GaAs.

$$a(T) = \mathbf{A} \cdot \left[ h\nu - \mathbf{E}\_{\mathbf{g}}(T) \right]^{1/4},\tag{2}$$

where:

A is the constant of the material.

Eg ð Þ T is the width of the bandgap at temperature T.

h is Planck's constant.

ν is the light frequency.

In the temperature range of 20–297 K, Egð Þ T can be described by the formula:

$$E\_{\mathbf{g}}(T) = \frac{E\_{\mathbf{g}}(\mathbf{0}) - \chi T^2}{(\beta + T)},\tag{3}$$

where Eg ð Þ 0 is the width of the forbidden zone at 0 K and γ and β are empirical constants.

Figure 1.

The principle of operation of the fiber-optic temperature sensor: (1) spectrum of light source radiation; (2, 3, 4) the dependence of the optic transmittance of the material on the wavelength λ at different temperatures T2 < T3 < T4.

Fiber-Optic Temperature Sensors with Chalcogenide Glass and Crystalline Sensing Element DOI: http://dx.doi.org/10.5772/intechopen.89207

Figure 2. Dependence of the photodiode output voltage from temperature sensor temperature [2].

For GaAs, Eg ð Þ 0 = 1.522 eV, γ = 5.8 � 10-4E/K, β = 300 K, A = 2.446 � 10-4 (cm � eV)�<sup>1</sup> . Proceeding from Eq. (3), we can find the wavelength λ<sup>g</sup> of light on which a given semiconductor will absorb:

$$\lambda\_{\mathbf{g}}(T) = \frac{n\_{\mathbf{c}}}{E\_{\mathbf{g}}(T)} = \frac{n\_{\mathbf{c}}}{\frac{E\_{\mathbf{f}}(0) - \mathbf{y}T^{2}}{(\boldsymbol{\beta} + T)}} \tag{4}$$

Taking into account the Eqs. (2) and (3), the connection between the intensity of light I passing through the sensitive element and its temperature can be written as

$$I(l,T) = I\_0(\mathbf{1} - R) \exp\left\{ A \left[ h\nu - E\_{\rm g}(\mathbf{0}) + \frac{\gamma T^2}{T + \beta} \right]^{\natural\_{\rm f}} \cdot l \right\} \tag{5}$$

Thus, if the light passes through the sample in the region of its absorption, the intensity of light will diminish, with increasing of sample temperature. If the emission detector (photodiode) is chosen in the working range, then change in intensity of light will lead to a decrease in the photodiode voltage (Figure 2).
