Before answering this question, we have to understand : what is mode? what is radiating mode? In EM problem, solving separation equation, we can easily find resonant frequency (fr). This frequency is corresponding to one mode. It is found that imaginary part of Zin (i.e. X) takes the value ZERO at fr. At that frequency, if the port is matched with antenna, we will get 50 ohm value for real part of Zin (i.e. R = 50ohm). As S11 is calculated using 50 ohm matched load, we get very low value of S11. hence, good S11 occur (< -10dB ). When port impedance is not matched with 50 ohm, we get high S11 ( >-10dB ). This phenomenon is found excellent in agreement for MICROSTRIP patch where thickness is very small compared to wavelength. In case of probe fed DRA, we do not get X=0 at resonant frequency (fr). In that case, adjust the probe length/position etc, one can finally achieve X=0 but we need to optimize it. Another technique is to find the max value of R. The frequency at which R takes max value is known as resonant frequency. If the port impedance is 50ohm, R takes 50-60 ohm  (little high due to probe inductance or feed) and X becomes nearly equal to ZERO. Obviously, we will get S11< - dB. So simulate antenna using 50ohm port impedance. Plot R and X with respect to frequency (i.e. Zin plot). Find the points which are corresponding to R_max. At those point, there is one mode. The point at which R nearly equal to 50 ohm, S11 will be less than -10dB. It is not necessary to have one mode there. So Good S11 does not give mode information. It gives only matching. So within a frequency band, identify modes using Zin plot. All modes may not radiate (Radiation occurs for S11 < -10dB). Modes having S11< -10dB is radiating modes. From S11 plot, we will find the information about RADIATING MODES. This is the fundamental relation between a resonator and a radiator. Resonators have all modes where as antenna has only radiating modes. That why, 3D EM simulator provide EIGENMODE solver to identify all mode. Excitation is not considered there.

50 ohm is the characteristic impedance of input port rather than the input impedance. By taking the reference of that you are supposed to find the impedance. 

Yes you are right. 

For a perfectly matched condition, real part will be 50 ohm and imaginary part will be zero. But most of the time this is difficult to achieve without having an external matching circuit. You can use the help of smith chart to do impedance matching at the required resonant frequency to get the best results. Also some matching circuit topology have better bandwidth performance over other matching circuits. Hence if bandwidth is also a concern, choose the matching topology wisely.

Before answering this question, we have to understand : what is mode? what is radiating mode? In EM problem, solving separation equation, we can easily find resonant frequency (fr). This frequency is corresponding to one mode. It is found that imaginary part of Zin (i.e. X) takes the value ZERO at fr. At that frequency, if the port is matched with antenna, we will get 50 ohm value for real part of Zin (i.e. R = 50ohm). As S11 is calculated using 50 ohm matched load, we get very low value of S11. hence, good S11 occur (< -10dB ). When port impedance is not matched with 50 ohm, we get high S11 ( >-10dB ). This phenomenon is found excellent in agreement for MICROSTRIP patch where thickness is very small compared to wavelength. In case of probe fed DRA, we do not get X=0 at resonant frequency (fr). In that case, adjust the probe length/position etc, one can finally achieve X=0 but we need to optimize it. Another technique is to find the max value of R. The frequency at which R takes max value is known as resonant frequency. If the port impedance is 50ohm, R takes 50-60 ohm  (little high due to probe inductance or feed) and X becomes nearly equal to ZERO. Obviously, we will get S11< - dB. So simulate antenna using 50ohm port impedance. Plot R and X with respect to frequency (i.e. Zin plot). Find the points which are corresponding to R_max. At those point, there is one mode. The point at which R nearly equal to 50 ohm, S11 will be less than -10dB. It is not necessary to have one mode there. So Good S11 does not give mode information. It gives only matching. So within a frequency band, identify modes using Zin plot. All modes may not radiate (Radiation occurs for S11 < -10dB). Modes having S11< -10dB is radiating modes. From S11 plot, we will find the information about RADIATING MODES. This is the fundamental relation between a resonator and a radiator. Resonators have all modes where as antenna has only radiating modes. That why, 3D EM simulator provide EIGENMODE solver to identify all mode. Excitation is not considered there.

Yes Manoj and Sudipta.....

I agree with your points...... 

In my simulation I am getting S(1,1) as -30dB, with Z(1,1) real as 52 ohms and Z(1,1) Imagi. as 1 at 3.5GHz. Can I say it as radiating Mode or not......?

Please tell me........

Sure, it is a mode which is able to radiate. You can easily use this antenna as an efficient radiator

To Sudipta,

Can you please tell me the exact allowable values of Z(1,1) real and Z(1,1) Imagi to say it as mode.......

Dear Anvesh 

What u want is ideal condition. so it is very difficult to find perfect matching circuit, but one can optimized the value and we can prefer the impedance value at which we get maximum depth of S11

Who on earth told you that an antenna's input impedance equals 50 at resonance in general...? Have you ever taken a course on antenna theory...? What are the minimum requirements to start working towards a PhD at your university; the right social network...?

To Denis,

I am dealing Microstrip antennas with 50 ohm sources and loads.... Unfortunately, I have not mentioned this point in my question...... 

Your preposterous question and excuse make my point. This chat site is plagued with PhD want-to-bees who shouldn't be at university to start with.

 Deniss Jaisson's comment is un called for.  Another answer I saw is correct - at resonance the reaction is zero and R - 50 ohms.

To Denis sir,

If my question is clear to you, can you please help me..........?

any conducting surface can work as an antenna if they have radiating characteristics.

As we know that antenna is passive element so it required source, source may be any type of wave generator but generally available connectors having two slandered 75 ohm and 50 ohm if you have any other u go for that. but once u fix the connector u have to optimized the antenna over it. these things are not only depends upon few parameters, but we can optimized the thing over few parameters only. so keep always in your mind at resonance frequency, circuit become purely resistive (reactive part should be zero). and again if antenna impedance is not equal to the connector or external tuned circuit so the maximum power will not be transfer to the antenna.  

To Ajit kumar,

How the mode is defined with S(1,1), Z(1,1) real and Imaginary values......

Can I say number of resonant frequencies are equal to number of modes.........