First steps

ref (Graffitti et al., 2018)

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from citrine import *
from citrine.crystals import ppKTP
import numpy as np
import matplotlib.pyplot as plt

from citrine import * from citrine.crystals import ppKTP import numpy as np import matplotlib.pyplot as plt

Define central wavelengths for pump, signal, and idler

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lambda_p_central = Wavelength(775, Magnitude.nano)
lambda_s_central = Wavelength(1550, Magnitude.nano)
lambda_i_central = Wavelength(1550, Magnitude.nano)

lambda_p_central = Wavelength(775, Magnitude.nano) lambda_s_central = Wavelength(1550, Magnitude.nano) lambda_i_central = Wavelength(1550, Magnitude.nano)

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# Define a range of wavelengths for signal and idler (in nm)
spectral_width = Wavelength(50, Magnitude.nano)
steps = 128
lambda_s = spectral_window(lambda_s_central, spectral_width, steps)
lambda_i = spectral_window(lambda_i_central, spectral_width, steps)

# Define a range of wavelengths for signal and idler (in nm) spectral_width = Wavelength(50, Magnitude.nano) steps = 128 lambda_s = spectral_window(lambda_s_central, spectral_width, steps) lambda_i = spectral_window(lambda_i_central, spectral_width, steps)

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# Calculate grating period
grating_period = calculate_grating_period(
    lambda_p_central,
    lambda_s_central,
    lambda_i_central,
    ppKTP,
)

# Calculate grating period grating_period = calculate_grating_period( lambda_p_central, lambda_s_central, lambda_i_central, ppKTP, )

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# Calculate Δk matrix
delta_k = delta_k_matrix(
    lambda_p_central,
    lambda_s,
    lambda_i,
    ppKTP,
)

# Calculate Δk matrix delta_k = delta_k_matrix( lambda_p_central, lambda_s, lambda_i, ppKTP, )

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# Calculate the phase matching function
phase_matching = phase_matching_function(delta_k, grating_period, 1e-2)

# Calculate the phase matching function phase_matching = phase_matching_function(delta_k, grating_period, 1e-2)

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# Define pump bandwidth (in nm and convert)
sigma_lambda_p = Wavelength(0.5, Magnitude.nano)
sigma_p = 2 * np.pi * bandwidth_conversion(sigma_lambda_p, lambda_p_central)

# Define pump bandwidth (in nm and convert) sigma_lambda_p = Wavelength(0.5, Magnitude.nano) sigma_p = 2 * np.pi * bandwidth_conversion(sigma_lambda_p, lambda_p_central)

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# Calculate the Gaussian pump envelope
pump_envelope = pump_envelope_gaussian(
    lambda_p_central, sigma_p, lambda_s, lambda_i
)

# Calculate the Gaussian pump envelope pump_envelope = pump_envelope_gaussian( lambda_p_central, sigma_p, lambda_s, lambda_i )

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# Calculate the Joint Spectral Amplitude (JSA)
JSA = pump_envelope * phase_matching

# Calculate the Joint Spectral Amplitude (JSA) JSA = pump_envelope * phase_matching

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# Plot the results
fig, axs = plt.subplots(
    2, 2, figsize=(8, 8), sharex=True, sharey=True, squeeze=True
)

# Plot Δk
axs[0, 0].pcolormesh(
    lambda_i.value,
    lambda_s.value,
    delta_k,
    cmap='viridis',
    shading='gouraud',
)
axs[0, 0].set_title(r'$\Delta k$')
axs[0, 0].set_xlabel(r'$\lambda_s$ (nm)')
axs[0, 0].set_ylabel(r'$\lambda_i$ (nm)')

# Plot the pump envelope
axs[0, 1].pcolormesh(
    lambda_i.value,
    lambda_s.value,
    pump_envelope,
    cmap='viridis',
    shading='gouraud',
)
axs[0, 1].set_title(r'$\alpha(\lambda_s, \lambda_i)$')
axs[0, 1].set_xlabel(r'$\lambda_s$ (nm)')
axs[0, 1].set_ylabel(r'$\lambda_i$ (nm)')

# Plot the phase matching function
axs[1, 0].pcolormesh(
    lambda_i.value,
    lambda_s.value,
    phase_matching,
    cmap='viridis',
    shading='gouraud',
)
axs[1, 0].set_title(r'$\phi(\lambda_s, \lambda_i)$')
axs[1, 0].set_xlabel(r'$\lambda_s$ (nm)')
axs[1, 0].set_ylabel(r'$\lambda_i$ (nm)')

# Plot the Joint Spectral Amplitude (JSA)
axs[1, 1].pcolormesh(
    lambda_i.value, lambda_s.value, JSA, cmap='viridis', shading='gouraud'
)
axs[1, 1].set_title(
    r'$\alpha(\lambda_s, \lambda_i) \phi(\lambda_s, \lambda_i)$'
)
axs[1, 1].set_xlabel(r'$\lambda_s$ (nm)')
axs[1, 1].set_ylabel(r'$\lambda_i$ (nm)')

# Add overall title
fig.suptitle(
    r'$\omega_p = {:.2f}\mathrm{{nm}}, \omega_s = {:.2f}\mathrm{{nm}}, \omega_i = {:.2f}\mathrm{{nm}}, \Lambda = {:.2f}\mathrm{{\mu m}}$'.format(
        lambda_p_central.value,
        lambda_s_central.value,
        lambda_i_central.value,
        grating_period * (1e6),
    )
)

# Show plot
plt.tight_layout()

# Plot the results fig, axs = plt.subplots( 2, 2, figsize=(8, 8), sharex=True, sharey=True, squeeze=True ) # Plot Δk axs[0, 0].pcolormesh( lambda_i.value, lambda_s.value, delta_k, cmap='viridis', shading='gouraud', ) axs[0, 0].set_title(r'$\Delta k$') axs[0, 0].set_xlabel(r'$\lambda_s$ (nm)') axs[0, 0].set_ylabel(r'$\lambda_i$ (nm)') # Plot the pump envelope axs[0, 1].pcolormesh( lambda_i.value, lambda_s.value, pump_envelope, cmap='viridis', shading='gouraud', ) axs[0, 1].set_title(r'$\alpha(\lambda_s, \lambda_i)$') axs[0, 1].set_xlabel(r'$\lambda_s$ (nm)') axs[0, 1].set_ylabel(r'$\lambda_i$ (nm)') # Plot the phase matching function axs[1, 0].pcolormesh( lambda_i.value, lambda_s.value, phase_matching, cmap='viridis', shading='gouraud', ) axs[1, 0].set_title(r'$\phi(\lambda_s, \lambda_i)$') axs[1, 0].set_xlabel(r'$\lambda_s$ (nm)') axs[1, 0].set_ylabel(r'$\lambda_i$ (nm)') # Plot the Joint Spectral Amplitude (JSA) axs[1, 1].pcolormesh( lambda_i.value, lambda_s.value, JSA, cmap='viridis', shading='gouraud' ) axs[1, 1].set_title( r'$\alpha(\lambda_s, \lambda_i) \phi(\lambda_s, \lambda_i)$' ) axs[1, 1].set_xlabel(r'$\lambda_s$ (nm)') axs[1, 1].set_ylabel(r'$\lambda_i$ (nm)') # Add overall title fig.suptitle( r'$\omega_p = {:.2f}\mathrm{{nm}}, \omega_s = {:.2f}\mathrm{{nm}}, \omega_i = {:.2f}\mathrm{{nm}}, \Lambda = {:.2f}\mathrm{{\mu m}}$'.format( lambda_p_central.value, lambda_s_central.value, lambda_i_central.value, grating_period * (1e6), ) ) # Show plot plt.tight_layout()

Graffitti, F., Kelly-Massicotte, J., Fedrizzi, A., & Brańczyk, A. M. (2018). Design considerations for high-purity heralded single-photon sources. Physical Review A, 98(5), 053811. https://doi.org/10.1103/PhysRevA.98.053811

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