fsine=10e6;
L=10;
PS=0.2;
A=7.85e-11;
c=3e8;
dt=2e-12;
V=1;
n=1.45; %Index of refraction
eps0=8.854e-12; % [F/m] Vacuum permittivity
T=10*2*L*n/c; %Total time
Nt=round(T/dt);
t = (-T/2/dt:1:T/2/dt)*dt; %time axis
nu=(-1/2/dt:1/T:1/2/dt); %frequency axis
I1_0=PS/A;
sine = V*sin(2*pi*fsine*t); %phase modulation condition
phi=sine;
ES_0t=sqrt(I1_0/2/n/c/eps0)*exp((1i*(pi)*phi)); % Original signal in time
Power=trapz(t,2*n*c*eps0*A*abs(ES_0t).^2)/T; % Area under the curve in time domain
FFt_EL0t=fftshift(abs(fft(ES_0t/Nt))); % fourier transform of the original signal
Power_FFt=T*trapz(nu,2*n*c*eps0*A*(FFt_EL0t).^2); % Area under the curve in frequency domain
figure;
semilogy(nu/1E6,2*n*c*eps0*A*(FFt_EL0t).^2);
xlim([-1 1]*1E2)
ylabel('Amplitude');
xlabel('frequency [MHz]');
will scale to log y axis. Nothing can do about the shape of the spectrum; that's wholly dependent upon the characteristics of the time trace.
