Question

(10 points each) Consider a ruby crystal laser with two energy levels separated by an energy difference corresponding to a free-space wavelength $\lambda_0 = 0.694 \mu m$, with a Lorentzian lineshape of width $\Delta v = 330 GHz$. The spontaneous lifetime $t_{sp} = 3 ms$ is placed in a resonator. When spontaneous emission rate equals stimulation emission rate, determine: (a) The center frequency $\nu_0$, (b) The optical intensity (in mW/cm²) of this resonator. (c) Use classical Rayleigh-Jeans Formula to estimate the temperatures (T) of a thermal-equilibrium blackbody cavity emitting a spectral energy density $\rho(\nu)$, when the rate of stimulated and spontaneous emission from the atoms in the cavity walls are equal at $\lambda_0 = 0.694 \mu m$. Hint: $P_{sp} = I/A$, $I/A = 1/t_{sp}$ $W_i = I Bp(\nu_0)$, $I/B = \lambda^3/(8\pi ht_{sp})$ Rayleigh-Jeans Formula: $\rho(\nu) = [8\pi\nu^2/c^3]k_BT$

          (10 points each) Consider a ruby crystal laser with two energy levels separated by an energy difference corresponding to a free-space wavelength $\lambda_0 = 0.694 \mu m$, with a Lorentzian lineshape of width $\Delta v = 330 GHz$. The spontaneous lifetime $t_{sp} = 3 ms$ is placed in a resonator. When spontaneous emission rate equals stimulation emission rate, determine:
(a) The center frequency $\nu_0$,
(b) The optical intensity (in mW/cm²) of this resonator.
(c) Use classical Rayleigh-Jeans Formula to estimate the temperatures (T) of a thermal-equilibrium blackbody cavity emitting a spectral energy density $\rho(\nu)$, when the rate of stimulated and spontaneous emission from the atoms in the cavity walls are equal at $\lambda_0 = 0.694 \mu m$.
Hint:
$P_{sp} = I/A$,
$I/A = 1/t_{sp}$
$W_i = I Bp(\nu_0)$, $I/B = \lambda^3/(8\pi ht_{sp})$
Rayleigh-Jeans Formula: $\rho(\nu) = [8\pi\nu^2/c^3]k_BT$

(10 points each) Consider a ruby crystal laser with two energy levels separated by an energy difference corresponding to a free-space wavelength λ0 = 0.694 μ m, with a Lorentzian lineshape of width Δ v = 330 GHz. The spontaneous lifetime tsp = 3 ms is placed in a resonator. When spontaneous emission rate equals stimulation emission rate, determine:
(a) The center frequency ν0,
(b) The optical intensity (in mW/cm²) of this resonator.
(c) Use classical Rayleigh-Jeans Formula to estimate the temperatures (T) of a thermal-equilibrium blackbody cavity emitting a spectral energy density ρ(ν), when the rate of stimulated and spontaneous emission from the atoms in the cavity walls are equal at λ0 = 0.694 μ m.
Hint:
Psp = I/A,
I/A = 1/tsp
Wi = I Bp(ν0), I/B = λ^3/(8π htsp)
Rayleigh-Jeans Formula: ρ(ν) = [8πν^2/c^3]kBT

Added by Manuel G.

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