Two-Photon Absorption

Electrical current is generated in a standard semiconductor photodetector when incident photons with an energy greater than the band gap of the active region are absorbed. These absorbed photons each excite an electron from the ground state, or valance band, to the excited state, or conduction band, creating an electron-hole pair. When an electric field is present across the active region of the photodetector, each electron-hole pair is separated, resulting in a flow of photocurrent in an external circuit.

Incident photons that have an energy less than the band gap of the photodetector do not generate an electron-hole pair and as a result, do not contribute to the photocurrent gener- ated. However, under certain operational conditions, two incident photons can be absorbed simultaneously to produce a single electron-hole pair. This nonlinear optical-to-electrical conversion process is called two-photon absorption and was proposed in 1931 [12] and ex- perimentally demonstrated in 1961 [13].

The TPA process occurs when a photon with energy Eph is incident on an active region

with a band gap energy Eg, where Eph < Eg < 2Eph. Under these conditions, a sin-

gle photon does not possess enough energy to produce an electron-hole pair. However, an electron-hole pair can be generated by the simultaneous absorption of two photons, were the combined energy of both photons is greater than the energy of the band gap. This two- photon absorption process can be explained through the use of a virtual state between the conduction band and the valence band and is shown in Figure 3.1. An incident photon with

Figure 3.1: Illustration of the two-photon absorption process using an intermediate virtual state.

an energy of Eph < Eg is absorbed, causing an electron to be excited from the valence

band to a virtual band somewhere in the band gap region, as shown in Figure 3.1 (a) and (b). This electron is then instantaneously moved to the conduction band by the absorption of a second electron as in Figure 3.1 (c) and (d). By increasing the intensity of the incident light, hence increasing the number of incident photons per second, the probability of two- photon absorption increases. It is this nonlinear response and the ultra-fast response time of 10−14s at 1550 nm [14] that allow TPA to be used for nonlinear optical thresholding. Again it should be noted that the TPA process involves the simultaneous absorption of two photons via a virtual state, resulting in the generated photocurrent becoming proportional to the square of the incident optical power. In contrast a two-step absorption process would require a real intermediate state, with a finite lifetime, resulting in a different intensity- dependent absorption relationship [15].

3.2.1 TPA Photocurrent

Assuming the semiconductor active region has a linear or single photon absorption (SPA) coefficient α and a two-photon absorption coefficient β, the differential equation for the intensity propagation I(z) along the z axis is given by,

dI(z)

dz = − αI(z) − βI(z)

Solving for I(z) gives [16],

I(z) = I0

e−αz

1 + (βI0/α)(1 − e−αz)

(3.2) Both the SPA and TPA contributions to the total absorption for a sample with length L can be derived as, I_absα = I0  1 −e −αL C  αL αL + lnC (3.3) I_absβ = I0  1 −e −αL C  lnC αL + lnC (3.4)

where C = 1+(βI0/α)(1−e−αL). It can be shown that the photocurrent due to two-photon

absorption is given by,

J = eS hv  A1 Iabsα + 1 2A2I β abs  (3.5) where e is the electron charge, S is the illuminated area, hv is the photon energy and A1

and A2 are the probabilities of carrier generation due to one- or two-photon absorption re-

spectively.

The generated photocurrent as a function of incident optical power for a semiconductor device is shown in Figure 3.2. The device has a length L = 1 µm, an illuminated area S = 1 µm2, a TPA coefficient of β = 2 × 10−12 m/W and various values for the SPA coefficient α. The dynamic range over which TPA dominates can be clearly seen, with the TPA response characterised by having a slope of two. The TPA response is limited by SPA which becomes dominant for lower optical powers, with this linear response having a slope of one. TPA is also limited at higher powers by total absorption. It can be seen that the SPA contribution increases as the SPA coefficient is increased, resulting in a reduced dy- namic range. Therefore, decreasing the α/β ratio ensures that the dynamic range increases. Increasing the length of the device can also increase the dynamic range, however, this in- creased length reduces the operating the speed of the device. The level of photocurrent generated by the device in Figure 3.2 is also quite large, with a photocurrent of 100 µA resulting from an incident optical power of 1 W. This is due to the fact that the quantum efficiency of both the SPA and TPA responses, A1 and A2 in equation 3.5 are assumed to

be 100% and as a result of other simplification assumptions. Despite this however, the use of a TPA-based device for optical signal processing is still feasible, and combined with the advantages previously mentioned for using such a device, makes it a viable candidate for nonlinear optical thresholding.

Figure 3.2: Photocurrent as a function of incident optical power for a semiconductor with L = 1 µm, S = 1 µm2, β = 2 × 10−12 m/W, an incident wavelength of 1550 nm and various values of α.

3.3

Characterisation of a 1.3 µm FP Laser as a TPA-Based De-