VCSEL Industry. Babu Dayal Padullaparthi

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      Consider that the light wave in the resonator travels in the z direction from z = 0 and is reflected by the reflector r₂ at z = L; then it goes backward by the length of L and returns to the starting point z = 0. If the electric field is sustainable, we should have:

(1.1)

      By comparing the imaginary and real parts, we have:

(1.2a)

(1.2b)

For the threshold gain g_th required for oscillation, use ln, the natural logarithm; from Eq. (1.2b),

      (1.3)

      The first term is absorption by the medium, and in GaAs, absorption by the free carrier has a magnitude of about 10 cm⁻¹. In the second term, the reflectance of a reflector made by cleaving the surface of a semiconductor is

      (1.4)

      Therefore, in the case of a GaAs edge‐emitting laser (n = 3.5) with L = d = 300 μm, it is about 39 cm⁻¹. To oscillate, a threshold gain of 10 + 39 = 49 cm⁻¹ or more is required.

      The electric field E_out of the output light, with E₀: field at the end of cavity, is given by:

      (1.5)

      1.1.5.2 Resonant Wavelength

Now, if λ denotes the wavelength and n the equivalent refractive index, from Eq. (1.2a) we have:

      (1.6)

      When the phase shift is 0 and the reflector is at the fixed end, for example, the standing wave is as shown in Figure 1.8b. The total length L is an integer q times the half wavelength СКАЧАТЬ