EE473 PHOTONIC SYSTEMS

Section A – Attempt TWO questions from this section.

Q1. (a) What are the electric field magnitude and polarisation direction of the following plane electromagnetic waves:

i) 𝐸𝑥 = √3 cos(𝜔𝑡 − 𝑘𝑧) , 𝐸𝑦 = cos(𝜔𝑡 − 𝑘𝑧) , 𝐸𝑧 = 0;

ii) 𝐸𝑥 = √3 cos(𝜔𝑡 − 𝑘𝑧) , 𝐸𝑦 = cos(𝜔𝑡 − 𝑘𝑧 + 𝜋) , 𝐸𝑧 = 0;

iii) 𝐸𝑥 = 3 cos(𝜔𝑡 − 𝑘𝑧), 𝐸𝑦 = 3 cos (𝜔𝑡 − 𝑘𝑧 − 𝜋 2 ) , 𝐸𝑧 = 0.

5 marks

(b) Linearly polarised light, of wavelength 1.45 µm, is incident on a birefringent crystal at 45° with respect to the crystal’s primary axes. The refractive indices of the ordinary and extraordinary axes are no = 1.50000 and ne = 1.50955 respectively. Calculate the minimum length of crystal required to generate right circularly polarised light (∆∅=90°)?

4 marks

(c) Briefly explain why light can only propagate in optical waveguides at certain discrete angles?

4 marks

(d) Describe what happens to the modes of a three-moded step index waveguide as the input wavelength is progressively increased.

3 marks

(e) A single-mode symmetrical step index waveguide is required for operation at both 1310 nm and 1550 nm. Using two dielectric optical materials of refractive indices n1 = 1.48 and n2 = 1.481, what is the maximum permissible waveguide thickness to achieve single-mode operation at both wavelengths?

4 marks

Q2. (a) Briefly describe the three primary photon interactions with a material containing atoms that have two allowed energy levels denoted by Ei and Ej. State what condition is required for optical amplification and provide examples of how this can be achieved for different gain media. 5 marks

(b) A gain medium and a Fabry-Pérot cavity resonator are combined to form a laser. Discuss the fundamental conditions required to achieve lasing and describe the origins of the wavelength characteristics of the laser output in terms of both the cavity and the gain medium.

5 marks

(c) The 3 level gain medium of a particular laser has 2 energy levels at 2.57 10-19 J and 1.25 10-19 J above the ground state. The output power of the laser is 2.5 W and the measured linewidth is 0.6 10-12 m.

i) What is the required pump wavelength?

ii) What is the lasing output wavelength?

iii) How many photons are emitted in a 4-second time period?

iv) What is the coherence length? 6 marks

(d) A laser has a wavelength of 1550 nm and an output line-width of 3.2 10-11 m. If the cavity is 20 cm long and contains a gain medium that is 15 cm long with a refractive index of 1.5, approximately how many modes can operate within the laser?

4 marks

Q3. (a) What is the attenuation limited link length for the system parameters shown below? Launched power = 100 mW

Fibre attenuation = - 0.4 dB/km

Fibre dispersion = 2.0 ps/km.nm

Joint loss and system margin = 8 dB

Receiver sensitivity = -30 dBm

Maximum tolerable pulse spreading = 0.25 x T where T is the period of the data transmission.

5 marks

(b) If the linewidth of the optical source in part (a) is 2 nm, what maximum bit-rate can the system have if it is to remain attenuation limited?

3 marks

(c) A InGaAs receiver has the following parameters: Bandwidth B = 10 MHz, Load resistance RL =2.1 kΩ. Calculate the thermal noise current for the receiver at an effective temperature of 300 K and 10 K. 3 marks

(d) Discuss the 3 main noise sources for photodetectors. For each noise source describe its origin and highlight the dominant noise term at room temperature (300 K). Using the example detector parameters below, calculate the mean square noise current for each noise source to help your explanation of the dominant noise term at room temperature.

Primary photocurrent, Ip, 1 µA, Dark current, Id, 5 nA, Bandwidth, B, 1 GHz, Load resistance, RL, 50 Ω.

9 marks

Section B – Attempt ONE question from this section.

Q4. (a) A telecommunications operator leases 50 nm of fibre bandwidth centred around 1550 nm to a customer at a cost of £300/GHz per annuum. What is their annual income for the lease?

3 marks

(b) The purchaser of the above fibre bandwidth uses it to deliver fibre to the home using a Coarse Wave Division Multiplexed (CWDM) approach over a link length of 10 km. Explain why they would have chosen CWDM and estimate the number of individual wavelength channels that the fibre could support.

2 marks

(c) An optical amplifier with a gain of 20 dB and a Noise Figure of 8dB is used to amplify signals just before the receiver. The amplifier is filtered using an optical filter with a bandwidth of 0.8 nm. The receiver has a bandwidth of 40 GHz, a thermal noise σT 2 = 5 × 10−11A 2 and a Responsivity of 1. A signal wavelength of 1550 nm with an average power of -26 dBm is delivered at the input to the amplifier. Show that the beat noise between the signal and the amplified spontaneous emission 𝜎𝑆−𝐴𝑆𝐸 2 is approximately 64 times greater than the thermal noise which is 4 times greater than the beat between the amplified spontaneous emission and itself and hence 𝜎𝑆−𝐴𝑆𝐸 2 is the dominant noise source.

5 marks

(d) In the case of the system in part ‘c’, given that 𝝈𝑺−𝑨𝑺𝑬 𝟐 dominates the receiver performance, what is the minimum average signal power at the amplifier input, expressed in dBm, to achieve Bit Error Rate of less than 10-9? The amplifier before the receiver enables the system operator to tolerate a lower signal strength at the end of the link compared to the case when the receiver operates unamplified. Calculate the difference between the amplified and unamplified cases and using your knowledge of optical fibre links, estimate the additional transmission distance this would enable. Calculate also the optical power at the receiver when an amplifier is used and comment on the difference between the amplified and unamplified cases.

7 marks

(e) The Psat value for the amplifier in question ‘c’ is 13 dBm. If it requires a signal strength of -25 dBm at its input for the receiver to meet the operational specification, how many channels could it support?

3 marks

Q5. (a) An integrated optics electro-optic (EO) modulator with refractive index n = 2.21, electro-optic coefficient r = 35 × 10-12 m/V, modulator length 20 mm, electrode spacing of 30 µm and laser wavelength 1550 nm acts as a phase modulator due to refractive index changes originating from an applied electric field. The refractive index with applied field can be written as

When combining two modulators in a Mach-Zehnder interferometer configuration, shown in Figure Q5, they can act as an amplitude modulator.

i) Calculate the voltage required to create a phase shift of Δϕ of π in one modulator and subsequently the voltage required for the same phase shift in the two modulator Mach-Zehnder configuration

2 marks

ii) Explain the principle of the Electro-Optic (EO) effect, what requirements are made on the input optical light wave and what principle functionality can be achieved with an electrooptic modulator. Explain additionally the principle of the magneto-optic Faraday effect, what requirements are made on the input optical light wave and what types of components can be achieved with a Faraday rotator. Compare the two effects and highlight similarities and differences.

6 marks

(b) The fused fibre coupler shown in Figure Q5 has a coupling length Lc,1550nm = 300 µm at 1550 nm and a coupling length Lc,1650nm = 250 µm at 1650 nm. An initial total coupler interaction length is set at L = 30 mm.

i) Calculate the transmitted power Pt and coupled power Pc for both coupling lengths if a matching laser for each coupling length has a power of 1 mW.

4 marks

ii) What total coupler interaction length is needed if both input wavelengths are to have a coupling ratio of 50/50?

2 marks

(c) The frequency spacing for a dense wavelength division multiplexer (DWDM) is 200 GHz and has an operation pass band of 75 GHz. The transmission wavelength response of the DWDM depends linearly on the temperature, with a sensitivity of Δλ/ΔT = 0.1 nm °C-1 .

i) For a laser with wavelength 1550 nm centred in the passband of the DWDM, calculate the maximum allowable temperature shift of the DWDM.

2 marks

ii) The laser used in i) illuminates a fibre Bragg grating (FBG) in a fibre with core refractive index of 1.545 and an increase of the refractive index of the written grating by Δn = 4×10-4 . Calculate the grating period to have the Bragg wavelength centred at the laser wavelength.

2 marks

iii) If the FBG is exposed to the same temperature shift calculated in

i) calculate the wavelength shift in the FBG and its new centre wavelength if it is kept strain free. Assume a thermal expansion coefficient of α = 1 × 10-4 °C-1 and thermo-optic coefficient = 20 × 10-6 °C-1

2 marks