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Second Harmonic Generation N=1:21



gnuplot> set xrange [-180:180]
gnuplot> set yrange [-180:180]


splot sin(cos(x*pi/180))*sin(cos(x*pi/180))/(cos(x*pi/180)*cos(x*pi/180))*sin(cos(y*pi/180))*sin(cos(y*pi/180))/(cos(y*pi/180)*cos(y*pi/180))+sin(cos((x+1)*pi/180))*sin(cos((x+1)*pi/180))/(cos((x+1)*pi/180)*cos((x+1)*pi/180))*sin(cos((y+1)*pi/180))*sin(cos((y+1)*pi/180))/(cos((y+1)*pi/180)*cos((y+1)*pi/180))+sin(cos((x+2)*pi/180))*sin(cos((x+2)*pi/180))/(cos((x+2)*pi/180)*cos((x+2)*pi/180))*sin(cos((y+2)*pi/180))*sin(cos((y+2)*pi/180))/(cos((y+2)*pi/180)*cos((y+2)*pi/180))+sin(cos((x+3)*pi/180))*sin(cos((x+3)*pi/180))/(cos((x+3)*pi/180)*cos((x+3)*pi/180))*sin(cos((y+3)*pi/180))*sin(cos((y+3)*pi/180))/(cos((y+3)*pi/180)*cos((y+3)*pi/180))+sin(cos((x+4)*pi/180))*sin(cos((x+4)*pi/180))/(cos((x+4)*pi/180)*cos((x+4)*pi/180))*sin(cos((y+4)*pi/180))*sin(cos((y+4)*pi/180))/(cos((y+4)*pi/180)*cos((y+4)*pi/180)) +sin(cos((x+5)*pi/180))*sin(cos((x+5)*pi/180))/(cos((x+5)*pi/180)*cos((x+5)*pi/180))*sin(cos((y+5)*pi/180))*sin(cos((y+5)*pi/180))/(cos((y+5)*pi/180)*cos((y+5)*pi/180))+sin(cos((x+6)*pi/180))*sin(cos((x+6)*pi/180))/(cos((x+6)*pi/180)*cos((x+6)*pi/180))*sin(cos((y+6)*pi/180))*sin(cos((y+6)*pi/180))/(cos((y+6)*pi/180)*cos((y+6)*pi/180))+sin(cos((x+7)*pi/180))*sin(cos((x+7)*pi/180))/(cos((x+7)*pi/180)*cos((x+7)*pi/180))*sin(cos((y+7)*pi/180))*sin(cos((y+7)*pi/180))/(cos((y+7)*pi/180)*cos((y+7)*pi/180))+sin(cos((x+8)*pi/180))*sin(cos((x+8)*pi/180))/(cos((x+8)*pi/180)*cos((x+8)*pi/180))*sin(cos((y+8)*pi/180))*sin(cos((y+8)*pi/180))/(cos((y+8)*pi/180)*cos((y+8)*pi/180)) +sin(cos((x+9)*pi/180))*sin(cos((x+9)*pi/180))/(cos((x+9)*pi/180)*cos((x+9)*pi/180))*sin(cos((y+9)*pi/180))*sin(cos((y+9)*pi/180))/(cos((y+9)*pi/180)*cos((y+9)*pi/180))+sin(cos((x+10)*pi/180))*sin(cos((x+10)*pi/180))/(cos((x+10)*pi/180)*cos((x+10)*pi/180))*sin(cos((y+10)*pi/180))*sin(cos((y+10)*pi/180))/(cos((y+10)*pi/180)*cos((y+10)*pi/180))+sin(cos((x+11)*pi/180))*sin(cos((x+11)*pi/180))/(cos((x+11)*pi/180)*cos((x+11)*pi/180))*sin(cos((y+11)*pi/180))*sin(cos((y+11)*pi/180))/(cos((y+11)*pi/180)*cos((y+11)*pi/180))+sin(cos((x+12)*pi/180))*sin(cos((x+12)*pi/180))/(cos((x+12)*pi/180)*cos((x+12)*pi/180))*sin(cos((y+12)*pi/180))*sin(cos((y+12)*pi/180))/(cos((y+12)*pi/180)*cos((y+12)*pi/180))+sin(cos((x+13)*pi/180))*sin(cos((x+13)*pi/180))/(cos((x+13)*pi/180)*cos((x+13)*pi/180))*sin(cos((y+13)*pi/180))*sin(cos((y+13)*pi/180))/(cos((y+13)*pi/180)*cos((y+13)*pi/180)) +sin(cos((x+14)*pi/180))*sin(cos((x+14)*pi/180))/(cos((x+14)*pi/180)*cos((x+14)*pi/180))*sin(cos((y+14)*pi/180))*sin(cos((y+14)*pi/180))/(cos((y+14)*pi/180)*cos((y+14)*pi/180))+sin(cos((x+15)*pi/180))*sin(cos((x+15)*pi/180))/(cos((x+15)*pi/180)*cos((x+15)*pi/180))*sin(cos((y+15)*pi/180))*sin(cos((y+15)*pi/180))/(cos((y+15)*pi/180)*cos((y+15)*pi/180))+sin(cos((x+16)*pi/180))*sin(cos((x+16)*pi/180))/(cos((x+16)*pi/180)*cos((x+16)*pi/180))*sin(cos((y+16)*pi/180))*sin(cos((y+16)*pi/180))/(cos((y+16)*pi/180)*cos((y+16)*pi/180))+sin(cos((x+17)*pi/180))*sin(cos((x+17)*pi/180))/(cos((x+17)*pi/180)*cos((x+17)*pi/180))*sin(cos((y+17)*pi/180))*sin(cos((y+17)*pi/180))/(cos((y+17)*pi/180)*cos((y+17)*pi/180))+sin(cos((x+18)*pi/180))*sin(cos((x+18)*pi/180))/(cos((x+18)*pi/180)*cos((x+18)*pi/180))*sin(cos((y+18)*pi/180))*sin(cos((y+18)*pi/180))/(cos((y+18)*pi/180)*cos((y+18)*pi/180))+sin(cos((x+19)*pi/180))*sin(cos((x+19)*pi/180))/(cos((x+19)*pi/180)*cos((x+19)*pi/180))*sin(cos((y+19)*pi/180))*sin(cos((y+19)*pi/180))/(cos((y+19)*pi/180)*cos((y+19)*pi/180)) title 'SHG for N=20'        
gnuplot> splot sin(cos(x*pi/180))*sin(cos(x*pi/180))/(cos(x*pi/180)*cos(x*pi/180))*sin(cos(y*pi/180))*sin(cos(y*pi/180))/(cos(y*pi/180)*cos(y*pi/180))+sin(cos((x+1)*pi/180))*sin(cos((x+1)*pi/180))/(cos((x+1)*pi/180)*cos((x+1)*pi/180))*sin(cos((y+1)*pi/180))*sin(cos((y+1)*pi/180))/(cos((y+1)*pi/180)*cos((y+1)*pi/180))+sin(cos((x+2)*pi/180))*sin(cos((x+2)*pi/180))/(cos((x+2)*pi/180)*cos((x+2)*pi/180))*sin(cos((y+2)*pi/180))*sin(cos((y+2)*pi/180))/(cos((y+2)*pi/180)*cos((y+2)*pi/180))+sin(cos((x+3)*pi/180))*sin(cos((x+3)*pi/180))/(cos((x+3)*pi/180)*cos((x+3)*pi/180))*sin(cos((y+3)*pi/180))*sin(cos((y+3)*pi/180))/(cos((y+3)*pi/180)*cos((y+3)*pi/180))+sin(cos((x+4)*pi/180))*sin(cos((x+4)*pi/180))/(cos((x+4)*pi/180)*cos((x+4)*pi/180))*sin(cos((y+4)*pi/180))*sin(cos((y+4)*pi/180))/(cos((y+4)*pi/180)*cos((y+4)*pi/180)) +sin(cos((x+5)*pi/180))*sin(cos((x+5)*pi/180))/(cos((x+5)*pi/180)*cos((x+5)*pi/180))*sin(cos((y+5)*pi/180))*sin(cos((y+5)*pi/180))/(cos((y+5)*pi/180)*cos((y+5)*pi/180))+sin(cos((x+6)*pi/180))*sin(cos((x+6)*pi/180))/(cos((x+6)*pi/180)*cos((x+6)*pi/180))*sin(cos((y+6)*pi/180))*sin(cos((y+6)*pi/180))/(cos((y+6)*pi/180)*cos((y+6)*pi/180))+sin(cos((x+7)*pi/180))*sin(cos((x+7)*pi/180))/(cos((x+7)*pi/180)*cos((x+7)*pi/180))*sin(cos((y+7)*pi/180))*sin(cos((y+7)*pi/180))/(cos((y+7)*pi/180)*cos((y+7)*pi/180))+sin(cos((x+8)*pi/180))*sin(cos((x+8)*pi/180))/(cos((x+8)*pi/180)*cos((x+8)*pi/180))*sin(cos((y+8)*pi/180))*sin(cos((y+8)*pi/180))/(cos((y+8)*pi/180)*cos((y+8)*pi/180)) +sin(cos((x+9)*pi/180))*sin(cos((x+9)*pi/180))/(cos((x+9)*pi/180)*cos((x+9)*pi/180))*sin(cos((y+9)*pi/180))*sin(cos((y+9)*pi/180))/(cos((y+9)*pi/180)*cos((y+9)*pi/180))+sin(cos((x+10)*pi/180))*sin(cos((x+10)*pi/180))/(cos((x+10)*pi/180)*cos((x+10)*pi/180))*sin(cos((y+10)*pi/180))*sin(cos((y+10)*pi/180))/(cos((y+10)*pi/180)*cos((y+10)*pi/180))+sin(cos((x+11)*pi/180))*sin(cos((x+11)*pi/180))/(cos((x+11)*pi/180)*cos((x+11)*pi/180))*sin(cos((y+11)*pi/180))*sin(cos((y+11)*pi/180))/(cos((y+11)*pi/180)*cos((y+11)*pi/180))+sin(cos((x+12)*pi/180))*sin(cos((x+12)*pi/180))/(cos((x+12)*pi/180)*cos((x+12)*pi/180))*sin(cos((y+12)*pi/180))*sin(cos((y+12)*pi/180))/(cos((y+12)*pi/180)*cos((y+12)*pi/180))+sin(cos((x+13)*pi/180))*sin(cos((x+13)*pi/180))/(cos((x+13)*pi/180)*cos((x+13)*pi/180))*sin(cos((y+13)*pi/180))*sin(cos((y+13)*pi/180))/(cos((y+13)*pi/180)*cos((y+13)*pi/180)) +sin(cos((x+14)*pi/180))*sin(cos((x+14)*pi/180))/(cos((x+14)*pi/180)*cos((x+14)*pi/180))*sin(cos((y+14)*pi/180))*sin(cos((y+14)*pi/180))/(cos((y+14)*pi/180)*cos((y+14)*pi/180))+sin(cos((x+15)*pi/180))*sin(cos((x+15)*pi/180))/(cos((x+15)*pi/180)*cos((x+15)*pi/180))*sin(cos((y+15)*pi/180))*sin(cos((y+15)*pi/180))/(cos((y+15)*pi/180)*cos((y+15)*pi/180))+sin(cos((x+16)*pi/180))*sin(cos((x+16)*pi/180))/(cos((x+16)*pi/180)*cos((x+16)*pi/180))*sin(cos((y+16)*pi/180))*sin(cos((y+16)*pi/180))/(cos((y+16)*pi/180)*cos((y+16)*pi/180))+sin(cos((x+17)*pi/180))*sin(cos((x+17)*pi/180))/(cos((x+17)*pi/180)*cos((x+17)*pi/180))*sin(cos((y+17)*pi/180))*sin(cos((y+17)*pi/180))/(cos((y+17)*pi/180)*cos((y+17)*pi/180))+sin(cos((x+18)*pi/180))*sin(cos((x+18)*pi/180))/(cos((x+18)*pi/180)*cos((x+18)*pi/180))*sin(cos((y+18)*pi/180))*sin(cos((y+18)*pi/180))/(cos((y+18)*pi/180)*cos((y+18)*pi/180))+sin(cos((x+19)*pi/180))*sin(cos((x+19)*pi/180))/(cos((x+19)*pi/180)*cos((x+19)*pi/180))*sin(cos((y+19)*pi/180))*sin(cos((y+19)*pi/180))/(cos((y+19)*pi/180)*cos((y+19)*pi/180))+sin(cos((x+20)*pi/180))*sin(cos((x+20)*pi/180))/(cos((x+20)*pi/180)*cos((x+20)*pi/180))*sin(cos((y+20)*pi/180))*sin(cos((y+20)*pi/180))/(cos((y+20)*pi/180)*cos((y+20)*pi/180)) title 'SHG for N=21' 

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