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added AiryBeam1D and AiryBeam2D commands and Airy beam example
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‎Examples/AiryBeam/2DAiryBeam.py

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import numpy as np
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from LightPipes import *
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import matplotlib.pyplot as plt
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from matplotlib.offsetbox import OffsetImage, AnnotationBbox
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import matplotlib.image as mpimg
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'''
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Generation of an Airy beam.
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===========================
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LightPipes for Python, Fred van Goor, 11-1-2022
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A non-diffracting Airy beam can be generated by substituting a cubic phase distribution
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in a laser beam. After a 2D Fourier transform with a positive lens the
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Airy beam will exist.
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With the parameters below, the Airy beam exists from z = 0 cm to z= 30 cm.
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Ref:
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G.A. Siviloglou, J. Broky, A. Dogariu and D.N. Christodoulides, PRL 99,213901(2007)
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T. Latychevskaia, D. Schachtler, and H.W. Fink, Applied Optics Vol. 55, Issue 22, pp. 6095-6101 (2016)
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'''
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wavelength = 650*nm #wavelength
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N=624
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size=N*32.0*um
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dN1=N//2-40
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dN2=N//2+40
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beta=117/m #
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w0=10*mm #beam waist laser
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f=80*cm #focal length of Fourier lens
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k=2*np.pi/wavelength
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#Generate input beam
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F0=Begin(size,wavelength,N)
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F0=GaussHermite(F0,w0)
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#Cubic Phase Plate (CPP):
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X,Y = F0.mgrid_cartesian
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c = 2 * np.pi * beta
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c3 = (c**3)/3
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CPP=c3*(X**3 + Y**3) + np.pi
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F0=SubPhase(F0,CPP)
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phase=Phase(F0)
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#initiate figure 1:
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fig1, axs1 = plt.subplots(nrows=3, ncols=1,figsize=(5.0,6.0))
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figure1 = mpimg.imread('figure1.jpg')
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imagebox = OffsetImage(figure1, zoom=0.15)
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ab = AnnotationBbox(imagebox, (0.4, 0.6),frameon=False)
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s1=r'Generation of an Airy beam.'+'\n\n'
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s2=r'References:'+ '\n'\
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r'(1) G.A. Siviloglou, J. Broky, A. Dogariu and D.N. Christodoulides, Phys. Rev. Lett, 99,213901(2007)'+'\n'\
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r'(2) T. Latychevskaia, D. Schachtler, and H.W. Fink, Appl. Optics, 55, 6095-6101(2016)'+'\n\n'
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s3 = r'LightPipes for Python,' + '\n' + 'AiryBeam.py' + '\n\n'\
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r'Parameters from ref 2:' + '\n'\
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r'$\lambda = {:4.1f}$'.format(wavelength/nm) + r' $nm$' + '\n'\
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r'$size = {:4.2f}$'.format(size/mm) + r' $mm$' + '\n'\
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r'$N = {:4d}$'.format(N) + '\n'\
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r'$w_0 = {:4.2f}$'.format(w0/mm) + r' $mm$'+ '\n'\
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r'$f = {:4.2f}$'.format(f/cm) + r' $cm$'+ '\n'\
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r'$\beta = {:4.2f}$'.format(beta/m) + r' $m^{-1}$'+ '\n'\
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r'${\copyright}$ Fred van Goor, January 2022'+ '\n'
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axs1[0].text(0.,1.3,s1,fontsize=15, verticalalignment='top')
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axs1[0].text(0.,1.0,s2+s3,fontsize=5, verticalalignment='top');axs1[0].axis('off')
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axs1[1].add_artist(ab);axs1[1].axis('off')
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axs1[1].text(0.0,1.1,'figure 1 from reference 2',fontsize=5, verticalalignment='top')
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s=r'Phase distribution SLM'
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axs1[2].imshow(phase,cmap='gray'); axs1[2].axis('off'); axs1[2].set_title(s)
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#Fourier transform lens:
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F0=Lens(F0,f)
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#Propagate a distance f:
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F0=Fresnel(F0,f)
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def AiryBeam(z):
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'''
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Propagates the Airy beam a distance z from the focal point..
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returns a tuple:
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Position of the maximum intensity,
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The intensity distribution at a distance z,
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The peak intensity of the Airy beam at z.
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'''
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F=Fresnel(F0,z)
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I=Intensity(F)
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#Find the coordinates of the maximum intensity:
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result = np.where(I == np.amax(I))
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Coordinates = list(zip(result[0], result[1]))
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for Coord in Coordinates:
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Xmax=X[Coord[0],Coord[1]]; Ymax=Y[Coord[0],Coord[1]]
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print(Xmax/mm,Ymax/mm) #Xmax should be equal to Ymax
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return Xmax,Ymax,I,I[result][0]
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def xmax(z):
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'''
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Returns:
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The theoretical deflection at z,
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The peak intensity of the Airy beam at a distance z,
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according to Latychevskaia et al.
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'''
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c=z*f/(f+z)
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zdivc=(f+z)/f
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xmax=(1.0188*(beta*wavelength*f)-c**2/(4*k**2*(beta*wavelength*f)**3))*zdivc
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return xmax, (f/(f+z))**2
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zstart=0*cm
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zend=31*cm
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z=np.arange(zstart,zend,1*cm)
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n=z.shape[0]
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deflection=np.zeros(n)
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Imax=np.zeros(n)
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#initiate figure 2:
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fig2, axs2 = plt.subplots(nrows=4, ncols=2,figsize=(6.0,6.0))
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fig2.suptitle('simulation with data Latychevskaia et al.')
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fig2.subplots_adjust(hspace=0.8)
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for i in range(0,n):
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Xmax,Ymax,I,_Imax=AiryBeam(z[i])
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if z[i] == 0*cm:
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axs2[0,0].imshow(I,cmap='jet')
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s=r'$z = {:2.1f}$'.format(z[i]/cm) + r'$cm$'
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axs2[0,0].imshow(I,cmap='jet'); axs2[0,0].axis('off'); axs2[0,0].set_title(s)
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axs2[0,0].set_xlim(dN1,dN2)
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axs2[0,0].set_ylim(dN2,dN1)
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if z[i]== 10*cm:
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s=r'$z = {:2.1f}$'.format(z[i]/cm) + r'$cm$'
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axs2[1,0].imshow(I,cmap='jet'); axs2[1,0].axis('off'); axs2[1,0].set_title(s)
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axs2[1,0].set_xlim(dN1,dN2)
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axs2[1,0].set_ylim(dN2,dN1)
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if z[i]== 20*cm:
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s=r'$z = {:2.1f}$'.format(z[i]/cm) + r'$cm$'
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axs2[2,0].imshow(I,cmap='jet'); axs2[2,0].axis('off'); axs2[2,0].set_title(s)
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axs2[2,0].set_xlim(dN1,dN2)
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axs2[2,0].set_ylim(dN2,dN1)
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if z[i]== 30*cm:
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s=r'$z = {:2.1f}$'.format(z[i]/cm) + r'$cm$'
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axs2[3,0].imshow(I,cmap='jet'); axs2[3,0].axis('off'); axs2[3,0].set_title(s)
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axs2[3,0].set_xlim(dN1,dN2)
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axs2[3,0].set_ylim(dN2,dN1)
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deflection[i]=Xmax
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Imax[i]=_Imax
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gs = axs2[0,1].get_gridspec()
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for ax in axs2[0:,-1]:
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ax.remove()
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ax1=fig2.add_subplot(gs[0:2,1])
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ax1.plot(z/cm,-deflection/mm,'ro',z/cm,-xmax(z)[0]/mm)
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ax1.set_xlabel('z/cm'); ax1.set_ylabel('deflection/mm')
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ax1.legend(('simulated with LightPipes for Python', 'theory ref 2'),
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shadow=True, loc=(0.1, 0.8), handlelength=1.5, fontsize=5)
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ax2=fig2.add_subplot(gs[2:,1])
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ax2.plot(z/cm,Imax/Imax[0],'ro',z/cm,xmax(z)[1])
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ax2.set_xlabel('z/cm'); ax2.set_ylabel('Peak intensity')
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#Experimental data from ref 2, figure 2f:
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#In pixels, as good as possible....
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X_Exp=np.array([122,151,184,213,245,276,308,336,366,397,429,458,491,520,551,582])
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Y_Exp=np.array([106,139,177,216,198,207,247,266,289,327,336,354,350,360,360,366])
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Imax_Exp=1.0-1.0/(428-106)*(Y_Exp-106)
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z_Exp=30*cm/(582-122)*(X_Exp-122)
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ax2.plot(z_Exp/cm,Imax_Exp,'+')
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ax2.legend(('simulated with LightPipes for Python', 'theory ref 2', 'experiment ref 2'),
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shadow=True, loc=(0.25, 0.8), handlelength=1.5, fontsize=5)
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plt.show()

‎Examples/AiryBeam/figure1.jpg

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‎Examples/Commands/AiryBeam.py

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"""
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Test script for testing the AiryBeam command.
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"""
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from LightPipes import *
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import matplotlib.pyplot as plt
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wavelength = 1500*nm
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size = 25*mm
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N = 500
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x0=y0=1*mm
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a1=a2=0.100/mm
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F=Begin(size,wavelength,N)
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F=AiryBeam(F)
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I=Intensity(F)
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plt.imshow(I,cmap='jet')
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plt.show()

‎Examples/Commands/AiryBeam1D.py

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"""
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Test script for testing the AiryBeam1D command.
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"""
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from LightPipes import *
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import matplotlib.pyplot as plt
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import numpy as np
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wavelength = 2.3*um
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size = 30*mm
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N = 500
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N2=N//2
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x0=0.3*mm
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a=0.1/mm
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dz=1.25*cm
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NZ=200
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F0=Begin(size,wavelength,N)
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F0=AiryBeam1D(F0,x0=x0, a=a)
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Ix=np.zeros(N)
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for k in range(0,NZ):
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F=Forvard(F0,dz*k)
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I=Intensity(F)
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Ix=np.vstack([Ix,I[N2]])
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plt.figure(figsize = (12,5))
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plt.imshow(Ix,
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extent=[-size/2/mm, size/2/mm, 0, NZ*dz/cm],
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aspect=0.08,
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origin='lower',
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cmap='jet',
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)
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plt.title('1D Airy beam')
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plt.xlabel('x [mm]')
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plt.ylabel('z [cm]')
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s = r'LightPipes for Python' + '\n'+ '1D Airy beam' + '\n\n'\
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r'$\lambda = {:4.2f}$'.format(wavelength/um) + r' ${\mu}m$' + '\n'\
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r'$size = {:4.2f}$'.format(size/mm) + r' $mm$' + '\n'\
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r'$N = {:4d}$'.format(N) + '\n'\
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r'$x_0 = {:4.2f}$'.format(x0/mm) + r' $mm$' + '\n'\
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r'$a = $' + '{:4.2f}'.format(a*mm) + r' $/mm$' + '\n'\
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r'${\copyright}$ Fred van Goor, May 2022'
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plt.text(16, 50, s, bbox={'facecolor': 'white', 'pad': 5})
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plt.show()

‎Examples/Commands/AiryBeam2D.py

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"""
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Test script for testing the AiryBeam2D command.
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"""
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from LightPipes import *
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import matplotlib.pyplot as plt
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import numpy as np
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wavelength = 2.3*um
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size = 30*mm
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N = 500
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x0=y0=1*mm
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a1=a2=0.1/mm
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z=900*cm
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F0=Begin(size,wavelength,N)
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F0=AiryBeam2D(F0,x0=x0, y0=y0, a1=a1, a2=a2)
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F=Fresnel(F0,z)
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I=Intensity(F)
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plt.figure(figsize = (9,5))
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plt.imshow(I,
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extent=[-size/2/mm, size/2/mm, -size/2/mm, size/2/mm],
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origin='lower',
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cmap='jet',
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)
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plt.title('2D Airy beam')
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plt.xlabel('x [mm]')
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plt.ylabel('y [mm]')
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s = r'LightPipes for Python' + '\n'+ '2D Airy beam' + '\n\n'\
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r'$\lambda = {:4.2f}$'.format(wavelength/um) + r' ${\mu}m$' + '\n'\
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r'$size = {:4.2f}$'.format(size/mm) + r' $mm$' + '\n'\
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r'$N = {:4d}$'.format(N) + '\n'\
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r'$x_0 = y_0 = {:4.2f}$'.format(x0/mm) + r' $mm$' + '\n'\
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r'$a1 = a2 = $' + '{:4.2f}'.format(a1*mm) + r' $/mm$' + '\n'\
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r'$z = $' + '{:4.2f}'.format(z/cm) + r' $cm$' + '\n'\
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r'${\copyright}$ Fred van Goor, May 2022'
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plt.text(16, -10, s, bbox={'facecolor': 'white', 'pad': 5})
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plt.show()

‎LightPipes/__init__.py

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__all__ = [
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'ABCD',
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'AiryBeam1D',
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'AiryBeam2D',
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'Axicon',
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'BeamMix',
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'Begin',
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from .core import IntAttenuator
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from .misc import Tilt, Gain, PipFFT
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from .core import Interpol
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from .sources import PointSource, GaussBeam, PlaneWave
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from .sources import AiryBeam1D, AiryBeam2D, PointSource, GaussBeam, PlaneWave
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from .userfunc import ZonePlate, CylindricalLens, RowOfFields, FieldArray2D
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def Begin(size,labda,N,dtype=None):

‎LightPipes/_version.py

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__version__ = '2.1.2'
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__version__ = '2.1.3'

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