Читать книгу VCSEL Industry - Babu Dayal Padullaparthi - Страница 26

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 λ /(2n) in the medium:

(1.7)

Now, in a laser cavity with a resonator length L longer than the wavelength, waves of many wavelengths with slightly different lengths can resonate. These modes are called longitudinal modes. On the other hand, the modes in the perpendicular direction are called the transverse modes.

Considering a normal semiconductor laser, if λ is 1.3 μm, n = 3.5, and L = 3 μm, then q = 16.

Therefore, even if q differs by 1, the resonance wavelength changes only slightly as Δλ. With |Δ λ | ≪̸ λ in mind, if λ → λ ₀ + Δλ , q → q + 1, then we obtain,

(1.8)

This |∆ λ | is called free spectral range (FSR) and is inversely proportional to cavity length, L.

Here, n_eff is the effective index considering the dispersion of the medium and is given by the following expression:

(1.9)

Since ∂n/∂ λ < 0 in ordinary semiconductors, n_eff is usually larger than n. In the above example, n_eff = 4.0 and |∆ λ | = 70 nm.