def add_cavmodel(kat, T=0.001, Loss=5e-6, theta=60, L_rt = 2*12.240, R_c = 20, f1 = 11e6, gamma1 = 0, f2 = 55e6, gamma2 = 0):
    '''
    T: Transmission of mirror (ITM)
    Loss: Loss of mirror ETM
    L_rt: Round trip length of cavity
    R_c: Radius of curvature of ETM
    
    '''
    
    
    cavmodel = '''

    # Pump beam #
    l pump 1 0 0 n1        # laser with 1 W
    #lambda 2128e-9         # laser wavelength
    s s_pump1 1 n1 n2       # a space of 1 m
    mod EOM1 {f1} {gamma1} 3 pm n2 n3
    s s_pump2 1 n3 n4       # a space of 1 m
    mod EOM2 {f2} {gamma2} 3 pm n4 n5
    s s_io 1 n5 nITM_AR       # a space of 1 m
    
    # INput Mirror ITM #
    m1 ITM {T} 0 0 nITM_AR nITM_HR
    s s_ie {L} nITM_HR nETM_HR

    # Curved mirror ETM #
    m1 ETM 10e-6 {Loss} 0 nETM_HR nETM_AR
    
    # Add radius of curvature to Mc
    attr ETM Rc {Rc}

    # PDs
    pd transDC nETM_AR
    pd reflDC  nITM_AR
    pd cavDC   nETM_HR
    
    '''.format(T=T, Loss=Loss, L=L_rt/2, Rc=R_c, f1=f1, gamma1 = gamma1, f2=f2, gamma2 = gamma2)
    
    kat.parse(cavmodel)
    
    return kat


# Modify power distribution here
def TEM_power(f,m,n):
    '''
    Power in higher order modes and sidebands
    '''

    factor = 1/ (1 + m + n)**2
    return factor

def add_HGhom(kat, f1=0, f2=0, max_tem=5, ph=2):
    
    '''
    max_tem: max m+n to account for
    ph: FINESSE phase adjustment parameter for HOMs
    '''
    
    # Define cavity
    gaussparams = '''
    maxtem {}

    cav arm_cavity ITM nITM_HR ETM nETM_HR
    phase {}
    cp arm_cavity x stability
    '''.format(max_tem, ph)
    
    kat.parse(gaussparams)
    
    
    beam_hom = '''
    tem pump {m} {n} {factor} 0
    '''
    
    # Add HOMs and corresponding PDs
    hom_pd = '''
    
    ad sigHG{m}{n} {m} {n} 0 nETM_AR
    ad sig_sb1_HG{m}{n} {m} {n} {f1} nETM_AR
    ad sig_sb1_HGm{m}{n} {m} {n} -{f1} nETM_AR
    ad sig_sb2_HG{m}{n} {m} {n} {f2} nETM_AR
    ad sig_sb2_HGm{m}{n} {m} {n} -{f2} nETM_AR
    '''
    
    
    for i in range(max_tem+1):
        # cycle through i = m+n
        
        for m in range(i+1):
            n = i-m
            #print('m:'+ str(m) + ' ,n:' +str(n))
            kat.parse(beam_hom.format(m=m, n=n, factor=TEM_power(0,m,n)))
            
            # Add carrier detectors
            kat.parse(hom_pd.format(m=m, n=n, f1=f1, f2=f2))
            
    return kat

def add_x_ax(kat, r_min, r_max, n):
    xax = '''
    xaxis ETM phi lin {r_min} {r_max} {n}
    yaxis abs

    retrace off
    '''.format(r_min=r_min, r_max=r_max, n=n)
    kat.parse(xax)
    return kat