Lecture 9. PMTs and Laser Noise. Lecture 9. Photon Counting. Photomultiplier Tubes (PMTs) Laser Phase Noise. Relative Intensity

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1 s and Laser Phase Phase Density ECE 185 Lasers and Modulators Lab - Spring

2 Detectors Continuous Output Internal Photoelectron Flux Thermal Filtered External Current w(t) Sensor i(t) External System y(t) Discrete Continuous Phase Phase Density Output Thresholded External Current i(t) Continuous Recovered Discrete Distribution + Discrete ECE 185 Lasers and Modulators Lab - Spring

3 When Can You Count s? Phase Phase Conditions: Low intensity, high internal gain G, and high bandwidth so that B µ. If conditions satisfied, then individual output pulses can be resolved Each output pulse can have an amplitude greater than the average thermal noise Width narrow enough to be distinct from other pulses. Continuous output is then processing by a nonlinear thresholding circuit then each pulse above threshold is counted as single photon. Thresholding circuit transform continuous output distribution into discrete photon count distribution ŵ(t). In ideal case, ŵ(t) = w(t), where w(t) is the true internal distribution. Statistics over a time T corresponding are then Poisson. Density ECE 185 Lasers and Modulators Lab - Spring

4 Types of Photo-Multiplier D2 D3 D6 D7 Channel Plate Photo- Cathode D1 D4 D5 D8 Anode Anode Photo Electron Channel Plate Field Electrons to Anode Phase Phase Conventional Cathode Micro Channel Plate (MCP) Density ECE 185 Lasers and Modulators Lab - Spring

5 of s Iout Phase 1ns/div Standard 1ns/div Fast 1ns/div MCP- Phase Single Electron of Different s Density ECE 185 Lasers and Modulators Lab - Spring

6 Phase Phase Density current gain: FWHM width: 5 ns for typical 1 ns for micro-channel plate (MCP) Average Single Electron (SER) peak current into 50Ω load i peak = Peak current on the order of ma Orders of magnitude larger than ( 0.6 µa into 50 Ω load.) G e F W HM σ i = 4kT B N /R Peak current has a random distribution ECE 185 Lasers and Modulators Lab - Spring

7 Variable Pulse Gain Phase Phase Density mv ns a: b: Continous Light, ns Scale: Continous Light, us Scale: Random Single Electron Pulses Random SER Pulses mv us ECE 185 Lasers and Modulators Lab - Spring

8 Non-ideal characteristics Phase Phase Density Several effects that cause the estimate of the internal rate, ŵ(t), to deviate from the true internal rate w(t). Constant rate, µ d, from dark current cannot be eliminated by the thresholding process and is a form of noise. The signal from a single, sensed photon with primary charge e must generate an amplified signal larger than the average thermal noise process Requires a large number of internal gain stages. Adds excess noise, and increases the response time due to the spreading of the pulse. (Limited gain-bandwidth product GB.) Net effect is that the estimated rate, ŵ(t), after amplification and thresholding, has excess noise relative to the internal distribution, w(t), before the internal amplification process. Characterized by an excess noise factor This excess noise increases the variance of the distribution with respect to an ideal Poisson distribution. ECE 185 Lasers and Modulators Lab - Spring

9 Types of Laser Phase Phase Lasers have two types of noise: Phase - Caused by spontaneous emission detuning laser frequency Causes the laser spectrum to broaden Laser spectrum is the Fourier transform of the field autocorrelation function. - Fluctuations in the signal measured using a detector noise spectrum Fourier transform of power autocorrelation function. Best you can do is shot noise limit. Density ECE 185 Lasers and Modulators Lab - Spring

10 Phase Phase Phase Density Assume laser is operating well above threshold. Affect of spontaneous emission is to de-phase the carrier without affecting the amplitude. Study amplitude (intensity noise) later Field given by U(t) = I(t)e j(2πfct+φ(t)) where for now we only assume φ(t) is random. Valid because phase fluctuations easier to generate (less energy) than amplitude fluctuations. Form optical autocorrelation R(τ) = (U(t)U (t + τ)) = I oe j(2πfct+φ(t)) I oe j(2πfc(t+τ)+φ(t+τ)) = P oe j2πfcτ e j(φ(t) φ(t+τ)). ECE 185 Lasers and Modulators Lab - Spring

11 Plot of the Random Walk for the Phase Phase Phase Phase Density Time ECE 185 Lasers and Modulators Lab - Spring

12 Expression for Expression for autocorrelation R(τ) = P o exp [j2πν 0 τ] exp [j (φ(t + τ) φ(t))] = P o exp [j2πν 0 τ] exp [ 2π 2 K τ ] Phase Form is double-sided exponential. Phase Density ECE 185 Lasers and Modulators Lab - Spring

13 spectrum is Fourier transform of autocorrelation function S 2 (f) = BP o/π (f f c) 2 + (B) 2 Phase Phase where B = πk is the optical half-power point. K is the rate of spontaneous emission. Functional form is a Lorentzian (note same form as gain profile for atomic media). Width of spectrum has a P 1 dependence. As the source power increases, there is more stimulated emission relative to spontaneous emission and thus less noise emitted from the laser. Density ECE 185 Lasers and Modulators Lab - Spring

14 Plot of R(τ) and S(f) Phase Phase Density Spontaneous emission rate K 1/ n where n is the mean number of photons in the resonator. The mean photon number depends on both the power and the quality of the resonator. As n increases, the ratio of stimulated emission to spontaneous emission increases. the laser becomes more coherent, and the bandwidth B decreases. Therefore, resonator structures with long photon lifetimes are desired to produce low phase noise. ECE 185 Lasers and Modulators Lab - Spring

15 Phase Phase Define normalized optical power autocorrelation function R Po (τ) = Po(t) Po(t + τ) P o 2 where P o = P o P o is the fluctuation of the optical power about the mean. At τ = 0, this correlation function becomes R Po (0) = Po(t)2 P o 2 = P 2 o P o 2 P o 2 = σ2 P P o 2 = 1 SNR Density ECE 185 Lasers and Modulators Lab - Spring

16 (RIN) Phase Phase Density Fourier transform of R Po (τ) is defined to the the relative intensity noise spectrum RIN(f) RIN(f) = 2 R Po (τ) exp[ j2πfτ]dτ Using the inverse of this transform pair and setting τ = 0, the intensity variance can be written as σp 2 o = P o 2 RIN(f)df. 0 The RIN can be directly measured using a calibrated detector with known noise characteristics and an electrical spectrum analyzer (ESA). The units of RIN are typically db/hz where db is w/respect to the average power at a specific frequency measured over a 1 Hz bandwidth. ECE 185 Lasers and Modulators Lab - Spring

17 Density Phase Phase Density Given the RIN, the electrical noise power density spectrum is N RIN (f) = R 2 P 2 RIN(f). Minimum amount of intensity noise that is sensed is generated when the laser is operating at the shot noise limit. Set N RIN (f) = N shot = 2eR P, Assuming ideal sensor with a quantum efficiency η = 1, so that R = e hf RIN shot (f) = N shot R 2 P 2 = 2e R P = 2hf P = 2e i, where i is the mean sensed signal, and R = hf e is the responsivity of an ideal sensor with η = 1. This is the minimum amount of RIN that can be generated by any laser. Additional intensity noise above this level is called excess RIN. ECE 185 Lasers and Modulators Lab - Spring

18 from Laser Phase Phase Density For many application, the RIN power density is approximately constant. Assume impulse response of the sensor and the external filter is an integrator over a time T. Then noise bandwidth B N = 1/2T. variance is σ 2 = T N RIN. 2 The density spectrum of the power fluctuations, has a P 1 dependence similar to that of the phase noise. As the source power increases, there is more stimulated emission relative to spontaneous emission and thus less noise emitted from the laser. ECE 185 Lasers and Modulators Lab - Spring