Examination Optoelectronic Communication Technology. April 11, Name: Student ID number: OCT1 1: OCT 2: OCT 3: OCT 4: Total: Grade:

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1 Examination Optoelectronic Communication Technology April, 26 Name: Student ID number: OCT : OCT 2: OCT 3: OCT 4: Total: Grade: Declaration of Consent I hereby agree to have my exam results published on the internet or by public notice in connection with my student ID number. I agree I do not agree Ulm, date, signature

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3 Examination OCT : April, 26 Problem OCT : Figure : Optical fiber coupling with laser diode (LD) through a transparent adhesive material. A multimode step-index fiber is coupled to a laser diode (LD) through an adhesive material having a refractive index of.4, as shown in Fig.. The refractive index difference between core and cladding is.5. The bit rate distance product of the fiber is 9.8 Mbit/s km. Use Figs. 2 and 3 to solve the following problems if needed. (a) Using the ray-optical model calculate the refractive indices of both core and cladding of the fiber. (b) Calculate the maximum acceptance angle. (c) What is the main effect that limits the bandwidth of a multimode step-index fiber? How could the fiber bandwidth be improved? (d) How many modes are guided in the fiber if the fiber core diameter is 8 µm and the operating wavelength is.5 µm? (e) If this fiber is to be operated in the single-mode regime, to which value does the core diameter have to be reduced? (f) A weakly guiding single-mode step-index fiber has refractive indices of core and cladding of.5 and.495, respectively. The core diameter of the fiber is 4.7 µm. The value of d 2 n/dλ 2 for the cladding is assumed as /µm 2 at the operating wavelength of.5 µm. A Gaussian pulse, having a spectral width of 27 pm, is propagated over the given fiber. Calculate the pulse broadening t D over a total distance of km. (g) The LD has an output power of mw. A total loss of dbm occurs for light coupling into the km long optical fiber. The same loss is experienced when the light from the fiber is focussed onto the detector. Additionally the optical power in the fiber is reduced through absorption by dbm and scattering by 5 dbm. Which optical power level is measured at the detector?

4 Examination OCT : April, 26 2 B V Figure 2: Normalized propagation coefficient B for various mν modes of a step-index fiber as a function of the normalized frequency parameter V V d2 (V B) dv V B d(v B) Figure 3: Normalized propagation constant B, group delay coefficient d( V B)/d V and dispersion coefficient V d 2 ( V B)/d V 2 for the fundamental mode of a step-index fiber as a function of the normalized frequency V. dv

5 Examination OCT : April, 26 3 Problem OCT 2: Figure 4: Planar film waveguide with a film thickness h f. A planar film waveguide, as shown in Fig. 4, is realized in the Al x Ga x N material system. Pure GaN is used for the film layer whereas the substrate and cladding contain 46 % of Al. The operating wavelength is λ = 45 nm. Use Figs. 5 and 6 to solve the following problems if needed. (a) Find the refractive indices of all the layers. What will happen to the refractive index of the film if 2 % of Al is incorporated? (b) Find the maximum thickness of the pure GaN film so that only the TE fundamental mode is guided at the given wavelength. (c) What will be the refractive index difference between the cladding/substrate and film in the strongest possible guiding case at the given operating wavelength? (d) Calculate the propagation angle of all existing modes in the strongest possible guiding case. Use the film thickness calculated from problem 2(b). (e) What is the physical meaning of the effective height of the waveguide? Calculate the effective height for the fundamental mode in the case of strongly guiding? (f) Which thickness of the cladding h c is necessary to attenuate the electric field of the TE fundamental mode at the interface between cladding and air by at least 4 db with respect to its maximum inside the film?

6 Examination OCT : April, Refractive Index x= Wavelength (nm) 7 8 Figure 5: Refractive index of Al x Ga x N for different Al contents..8 m = m = B a TE m = V Figure 6: B- V diagram for guided TE modes in a planar film waveguide.

7 Examination OCT : April, 26 5 Problem OCT 3: We have a laser diode with the following parameters: Mirror reflectivities 5 %, refractive index 3.5, intrinsic losses 2 cm, current injection efficiency.6, differential gain coefficient 6 cm 2, transparency carrier density 2. 8 cm 3, recombination constant A 2 = cm 3 /s. The physical dimensions of the active region are L = 2 µm, b = 5 µm and d =.2 µm. The current density at the present operating point is 3. ka/cm 2. The total emitted power from both facets is 3 mw at a wavelength of 95 nm. a) How many electrons per second are injected into the undoped active region? b) How many holes per second are removed from the valence band by spontaneous emission if bimolecular recombination prevails? c) In contrast, how many electrons per second are removed by stimulated emission from the conduction band. d) What is the total number of photons accumulated inside the resonator? How many of those photons leave the resonator each second? e) Suppose the laser current is now increased such that 5 more electrons reach the active region every second. On average, by what amount does this increase the number of emitted photons per second? Problem OCT 4: We consider the receiver of a data link operating at.4 µm wavelength. The detector is a backside (i.e., through the substrate) illuminated circular InGaAsP pin photodiode with relative dielectric constant 3 and a 3 µm thick n-doped InP substrate of refractive index 3.7. The substrate side of the photodetector is seamlessly mounted onto a plastic optical fiber where the signal propagates in all available modes. Fiber and photodiode are perfectly aligned with their longitudinal axes coinciding. The fiber core has 2 µm diameter and a refractive index of.6. The fiber numerical aperture is.6. (a) Schematically draw the setup. Indicate the doping types of the individual layers. (b) Give the divergence angle ϕ s of the beam emitted from the fiber. (c) What is the minimum photodiode diameter D PD required for full collection of the rays. (d) What is the minimum thickness of the i-ingaasp region to ensure a quantum efficiency of above 6 %? The InGaAsP absorption coefficient is 75 cm. Please account for the reflection losses at the fiber-to-semiconductor interface by assuming perpendicular incidence. (e) The actual photodiode used has a diameter of D PD = 3 µm and an absorption thickness of d = 2 µm. What receiver bandwidth is to be expected when merely considering the parasitic capacitance if the photodiode is terminated with a load resistance of R L = 5 Ω? (f) Give an estimate of the diode s quantum efficiency if the above setup is operated at λ = 85 nm wavelength.

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